St. Thomas Aquinas

De operationibus occultis naturae ad quemdam militem ultramontanum

On the Hidden Workings of Nature to a Certain KnightAcross the Mountains

tr. by J. B. McAllisterWashington D.C.: Catholic University of America Press, 1939

Rev. Bart A. Mazzetti

(c) 2013

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Sancti Thomae de AquinoDe operationibus occultis naturae

ad quendam militem ultramontanumTextum Leoninum Romae 1976 editum

ac automato translatum a Roberto Busa SJ in taenias magneticas

denuo recognovit Enrique Alarcón atque instruxit

[69886] De operationibus occultis naturae

Quoniam in quibusdam naturalibus corporibus quaedam naturales actiones apparent, quarum principia manifeste apprehendi non possunt, requisivit a me vestra dilectio, ut quid super his mihi videatur vobis transcriberem.

Videmus siquidem quod corpora elementorum in se dominantium motus sequuntur: puta quod lapis movetur ad medium secundum propria-etatem terrae dominantis in eo; metalla etiam secundum proprietatem aquae habent infrigi-dandi virtutem. Quaecumque igitur actiones et motus elementatorum corporum sunt secundum proprietatem et virtutem elementorum, ex quibus huiusmodi corpora componuntur, huius-modi actiones et motus habent manifestam originem, de qua nulla emergit dubitatio.

Sunt autem quaedam huiusmodi corporum quae a virtutibus elementorum causari non possunt: puta quod magnes attrahit ferrum, et quod quaedam medicinae quosdam determinatos humores purgant, et a determinatis corporis par-tibus. Oportet igitur huiusmodi actiones in ali-qua altiora principia reducere.

Est autem considerandum, quod aliquod agens inferius secundum superioris agentis virtutem dupliciter agit vel movetur. Uno quidem modo inquantum actio procedit ab eo secundum formam vel virtutem sibi impressam a superiori agente, sicut luna illuminat per lumen a sole receptum.

A LETTER OF THOMAS AQUINASTO A CERTAIN KNIGHT BEYOND THE

MOUNTAINSON THE OCCULT WORKINGS OF NATURE

ORCONCERNING THE CAUSALITY OF

HEAVENLY BODIEStr. by J. B. McAllister1

Washington D.C.: Catholic University of America Press, 1939

Introduction

Since in some natural bodies certain natural act-ivities appear whose principles cannot be under-stood,2 your honor has asked that I write what I think about them.

Statement of the problem

We see indeed that a body follows the move-ments of the elements governing it. A stone, for example, is moved towards the center (of the earth) according to the property of earth domin-ant in it. Metals also have the power of cooling according to the property of water. Therefore all actions and movements whatsoever of bodies composed of elements take place according to the property and power of the elements of which such bodies are made. Now such actions and movements have a clear origin, about which there arises no doubt.

But there are some workings of these bodies which cannot be caused by the powers of the elements: for example, the magnet attracts iron, and certain medicines purge particular humors in definite parts of the body. Actions of this sort, therefore, must be traced to higher prin-ciples.

We must now consider that an agent of a lower rank acts or is moved according to the power of a superior agent in two ways: one way in so far as the action proceeds from it according to a form and power imparted by a superior agent, as the moon illuminated through light received from the sun.

1 Where necessary, I have revised the translation to bring it in line with the Latin.2 Literally, “which cannot be clearly apprehended”.

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Alio vero modo inferius agens agit per solam virtutem superioris agentis, nulla forma recepta ad agendum, sed per solum motum quo a super-iori agente movetur, sicut carpentator utitur serra ad secandum: quae quidem sectio est prin-cipaliter actio artificis, secundario vero serrae inquantum ab artifice movetur: non quod talis actio sequatur aliquam formam vel virtu-tem quae in serra remaneat post motionem artificis.

Si igitur elementata corpora a superioribus agentibus aliquas actiones vel motus participant, necesse est altero dictorum modorum hoc esse: scilicet quod huiusmodi actiones consequantur aliquas formas vel virtutes impressas corporibus elementatis a superioribus agentibus, vel quod huiusmodi actiones consequantur solam motio-nem elementatorum corporum a praedictis a-gentibus.

Superiora autem agentia, quae naturam elemen-torum et elementatorum excedunt, sunt non solum caelestia corpora, sed etiam superiores substantiae separatae. Ex utrisque autem horum aliquae actiones vel motus in corporibus inferi-oribus inveniuntur, quae non procedunt ex aliqua forma inferioribus corporibus impressa, sed solum ex superiorum agentium motione. Aqua enim maris fluentis et refluentis talem motum sortitur praeter proprietatem elementi ex virtute lunae, non per aliquam formam aquae impressam, sed per ipsam lunae motionem, qua scilicet aqua movetur a luna.

Apparent etiam nigromanticarum imaginum quidam effectus, qui procedunt non ex aliquibus formis quas susceperint praedictae imagines, sed a Daemonum actione qui in praedictis ima-ginibus operantur: quod quidem etiam quan-doque contingere credimus in operatione divina, vel etiam Angelorum bonorum. Quod enim ad umbram Petri apostoli sanarentur infirmi, vel etiam quod ad tactum reliquiarum alicuius sancti aliqua aegritudo pellatur, non fit per aliquam formam his corporibus inditam, sed solum per operationem divinam quae huiusmodi corporibus utitur ad tales effectus.

Manifestum est autem non omnes operationes elementatorum corporum occultas rationes habentes esse huiusmodi. Primo quidem, quia

In another way it acts only through the power of the superior agent, without receiving a form for acting. It is moved only through the motion of the superior agent, as a carpenter uses a saw for cutting. The sawing is indeed primarily the work of the artisan but secondarily of the saw in so far as it is moved by the artisan—not because such an action follows upon some form and power which might stay in the saw after the artisan has used it.

If, then, elemented bodies3 share in the actions or movements of superior agents, it ought to be in one or the other of the above mentioned ways; either the actions result from forms and powers impressed by superior agents in the elemented bodies, or the actions merely follow upon the movement of the elemented bodies by the superior agents.

Superior agents which exceed the nature of ele-ments and elemented bodies are not only heavenly bodies, but also superior separated substances. Each of them produces in inferior bodies actions or movements which do not spring from a form impressed in the inferior bodies, but which come solely from the move-ment of the superior agents. For the sea, in its ebb and flow, has this motion over and above the property of the element (water) from the power of the moon, not indeed through an impressed form, but through the moon’s move-ment, which agitates the water.

Then again necromantic images have effects which do not issue from [any] form they may have received, but from demons who are active in the images. And we think the same thing sometimes happens through the action of God or the good angels. For the fact, that sick people were cured at the shadow of Peter the Apostle or that some illness is dispelled upon contact with a saint’s relics, is not attributable to a form implanted in these bodies, but only to the divine power which uses the bodies for these results.

It is clear that not all the workings of elemented bodies manifesting occult operations are like these. Firstly, the said workings, since they do

3 i.e. bodies composed of the elements.

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praedictae operationes quae non consequuntur aliquam formam impressam, non inveniuntur communiter in omnibus quae sunt eiusdem speciei: non enim omnis aqua fluit et refluit secundum motum lunae, nec omnia mortuorum ossa apposita sanant aegrotos.

Quaedam vero operationes occultae in quibus-dam inveniuntur corporibus, quae similiter conveniunt omnibus quae sunt eiusdem speciei, sicut omnis magnes attrahit ferrum. Unde relinquitur huiusmodi operationes consequi aliquod intrinsecum principium quod sit com-mune omnibus habentibus huiusmodi speciem.

Deinde quia operationes, de quibus supra dictum est, non semper ex huiusmodi corporibus procedunt: quod est evidens signum tales operationes non provenire ex aliqua virtute indita et permanente, sed ex solo motu alicuius superioris agentis; sicut serra non semper secat lignum sibi coniunctum, sed solum quando ad hunc effectum ab artifice movetur.

Quaedam autem actiones occultae sunt corporum inferiorum, quae quandocumque ad-hibeantur suis passivis, similes effectus pro-ducunt; sicut rheubarbarum semper purgat determinatum humorem. Unde relinquitur, huiusmodi actionem provenire ab aliqua virtute indita et permanente in corpore tali.

not arise from some impressed form, are not found commonly in every individual of the same species: for not every bone nor all the relics of the saint heal upon touch, but those of some at some times. And so neither does every image have effects of this sort, nor does all water flow and ebb according to the movement of the moon.

But certain secret workings are found in some bodies which are likewise found in all which are of the same species—for example, every magnet attracts iron. Whence it follows that these (lat-ter) activities arise from an intrinsic principle common to [all] things of the same species [as well as from a celestial body].

Secondly, [because] activities, which have been mentioned above, do not always proceed from bodies of this sort: which is an evident sign that such activities do not proceed from some perm-anently impresssed power, but rather solely from the motion of a superior agent,4—just as the saw does not always cut wood brought into contact with it, but only when it is moved for this purpose by an artisan.

Now there are certain hidden workings of in-ferior bodies which, whenever they are applied to their passive subjects, produce similar effects, as rhubarb always purges a definite humor. And from this it is concluded that the action arises from some power residing and permanent in such a body. (my revised trans.)

Restat autem considerandum, quid sit illud principium intrinsecum permanens a quo huiusmodi operationes procedunt.

Manifestum est autem hoc principium potentiam quamdam esse: hoc enim dicimus potentiam principium intrinsecum quo agens agit, vel patiens patitur; haec quidem potentia secundum quod refertur ad ultimum in quod aliquid potest, accipit nomen et rationem virtutis.

Huiusmodi autem virtus quae est talium action-num vel passionum principium, manifeste os-

Explanation

It remains now to consider what is that perma-nent intrinsic principle from which such act-ivities proceed.

Clearly this principle is some potency: for the internal principle by which an agent acts or suf-fers action we call a potency. And indeed this potency according as it is referred to the limit of anything’s possible activity receives the name and description of power.

Now the power which is the principle of such

4 I have revised the translation, which incorrectly reads, “The evident proof for this is that they do not pro-ceed from a power residing and permanent in them, but only from the motion of a superior agent,” etc. On this matter, see my separate discussion appended to my translation of the De Motu Cordis.

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tenditur ex forma rei specifica derivari: omne enim accidens quod est proprium alicuius speciei derivatur ex principiis essentialibus illius speciei, et inde est quod ad demonstrandum proprias passiones de suis subiectis, accipimus pro causa definitionem designantem essentialia principia rei. Est autem essentiae et quidditatis principium forma in determinata materia exis-tens. Oportet igitur huiusmodi virtutes pro-cedere a formis talium rerum secundum quod in propriis materiis existunt. Deinde, cum natura rei dicatur forma vel materia illius; si qua virtus alicuius rei ab his non derivetur, non erit tali rei naturalis, et per consequens nec actio vel passio a tali virtute procedens erit naturalis.

Huiusmodi autem actiones quae sunt praeter naturam, non sunt diuturnae, sicut quod aqua calefacta calefacit; actiones autem occultae, de quibus nunc loquimur, eodem modo se habent semper, vel sicut frequenter. Relinquitur ergo virtutes quae sunt harum actionum principia, esse naturales et a forma rei procedere secun-dum quod in tali materia existit.

Formarum autem substantialium principium Platonici quidem attribuebant substantiis separ-atis, quas species vel ideas vocabant, quarum imagines dicebant esse formas naturales mater-iae impressas. Sed hoc principium non potest sufficere. Primo quidem, quia oportet faciens simile esse facto. Id autem quod fit in rebus naturalibus, non est forma, sed compositum ex materia et forma. Ad hoc enim aliquid fit, ut sit. Proprie autem esse dicitur compositum subsis-tens; forma autem dicitur esse ut quo aliquid est. Non igitur forma proprie est id quod fit, sed compositum. Id igitur quod facit res naturales non est forma tantum, sed compositum.

Deinde formas absque materia existentes ne-cesse est immobiles esse, quia motus est actus existentis in potentia, quod primo materiae convenit: unde necesse est quod semper eodem modo se habeant. A causa autem eodem modo se habente procedunt formae uniformiter se habentes: quod quidem in formis inferiorum corporum non apparet propter generationem et corruptionem huiusmodi corporum. Relinquitur

actions and passions is shown to be derived especially from the specific form of a thing; for every accident which is proper to some species, is derived from the essential principles of that species. Hence it is that to explain the charac-teristic passions of their subjects we take for the cause a definition designating the essential prin-ciples of the thing. But the principle of essence and quidditas is a form existing in determinate matter. Therefore such powers ought to proceed from forms of things according as they exist in their own matters. Secondly, since the nature of a thing is said of its form and matter, if a power of a thing should not be derived from them, it will not be a power natural to the thing, and consequently no activity or passion proceeding from such a power will be natural.

Now such activities which go beyond nature are not abiding—for example, that water when heated heats; but hidden activities of which we are now speaking are always the same, or fre-quently so. Hence the conclusion that powers which are the principles of these actions are essential and proceed from a form according as it exists in such matter.

The Platonists indeed were wont to attribute the principle of substantial forms to separated sub-stances which they called species or ideas, the individual representations of which they said were natural forms impressed in matter. But this principle cannot be sufficient. First, the thing making ought to be like the thing made. Now that which comes about in natural things is not form, but a composite of matter and form; for to this purpose something is made, that it be. Properly the composite is said to be subsistent,5

whereas the form is said to be that whereby something is. Therefore, that which comes to be is not rightly form but a composite, and that which makes natural things to be is not only form but the composite.

Secondly, forms existing apart from matter ought to be unmoved, because movement is an act of something in potency, which is the case with prime matter. And so these forms ought to be unchangeable. Now from a cause that is al-ways the same proceed forms that are always the same. But this is not evident in the forms of inferior bodies, because of the coming-to-be and

5 I have corrected the text, which reads, Properly it is said to be the subsistent composite, etc.

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igitur quod principia formarum huiusmodi corruptibilium corporum sunt caelestia corpora, quae diversimode se habentes secundum accessum et recessum, ad generationem et cor-ruptionem in his inferioribus causant. Pro-cedunt tamen huiusmodi formae a substantiis separatis sicut a primis principiis, quae medi-ante virtute et motu caelestium corporum impri-munt formas apud se intellectas in materiam corporalem. Et quia actiones et virtutes naturali-um corporum ex formis specificis causari osten-dimus; consequens est quod ulterius reducantur, sicut in altiora principia, et adhuc ulterius in substantias intellectuales separatas.

passing-away of these bodies. Therefore, of these corruptible bodies the principles of their forms are heavenly bodies, which, being dif-ferent according to their approach and with-drawal, cause coming-to-be and passing-away in inferior bodies. Nevertheless, such forms are derived from separated substances as first prin-ciples, which, through the power and movement of heavenly bodies, impress upon corporeal matter forms which they can understand in themselves. And, since we have shown that act-ivities and powers of natural things are caused by their specific forms, it follows that they may be traced back further, namely to higher principles, to heavenly bodies or to the powers of heavenly bodies, and still further to separated intellectual substances.

Utrorumque autem principiorum vestigium quoddam apparet in ipsis naturalium rerum operibus. Nam quod huiusmodi naturae opera fiunt cum quadam transmutatione, et secundum certum temporis spatium, provenit ex corpore caelesti, per cuius motum temporis mensura definitur. Sed a substantiis separatis intellectu-alibus invenitur in naturae operibus quod determinatis viis ad determinatos fines ordine et modo congruissimo procedunt, sicut et ea quae fiunt ab arte: ita quod totum opus naturae videtur esse opus cuiusdam sapientis, propter quod natura dicitur sagaciter operari.

Opus autem sapientis oportet esse ordinatum: nam hoc proprie ad sapientem pertinere dici-mus, ut omnia convenienti ordine disponat. Quia igitur formae inferiorum corporum proveniunt ex sapientia substantiae separatae mediante virtute et motu caelestium corporum, necesse est in ipsis formis inferiorum corporum quemdam ordinem inveniri: ita scilicet, quod quaedam sint imperfectiores et materiae vicini-ores, quaedam autem perfectiores et propinqui-ores superioribus agentibus.

Imperfectissimae quidem formae et maxime materiae propinquae, sunt formae elementorum, ex quibus alia inferiora corpora materialiter componuntur; quae quidem tanto sunt nobiliora, quanto a contrarietate elementorum recedentia, ad quamdam aequalitatem mixtionis accedunt; per quam quodammodo assimilantur caelestibus

A trace of both of these principles is evident in the very workings of natural things; for the fact, that the activities of Nature take place with a certain change and according to a definite inter-val of time, is due to a heavenly body upon whose movement the reckoning of time is based. But due to separated intellectual sub-stances one finds in the operations of Nature that they proceed along fixed paths to deter-mined ends, with order and in a most fitting way, like those things which are made by human skill; so that the whole work of Nature seems to be the achievement of a wise agent. Thus Nature is said to act with wisdom.

Now the work of a wise man ought to be well-ordered; for we say rightly that this is charac-teristic of the sage, that he disposes of all things harmoniously. Therefore, because the forms of inferior things arise from the wisdom of separ-ated substances through the intermediary of the power and movement of heavenly bodies, some order ought to be found among these forms of inferior bodies, and in such a way, namely, that some are less perfect and closer to matter, while others, however are more perfect and closer to superior agents.

The most imperfect forms, though, and espec-ially close to matter, are the forms of elements, of which the inferior bodies are composed as regards their matter. And these (inferior bodies) are indeed the more noble (the more) that, being removed from a contrariety of elements, they approach uniformity of composition, and thus

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corporibus, quae sunt ab omni contrarietate aliena.

Medium enim quod ex contrariis componitur, neutrum contrariorum est actu, sed potentia tantum. Et ideo, quanto huiusmodi corpora ad maiorem aequalitatem mixtionis accedunt, tanto nobiliorem formam participant, adeo quod corpus humanum, quod est temperatissimae commixtionis, ut probat bonitas tactus in homine, nobilissimam formam habeat, scilicet animam rationalem.

Virtutes autem et actiones necesse est formis proportionari utpote procedentes ex eis. Et inde est quod formas elementorum quae sunt max-ime materiales, consequuntur qualitates activae et passivae, puta calidum et frigidum, humidum et siccum et aliae huiusmodi qualitates quae pertinent ad dispositionem materiae. Formae vero mixtorum corporum sed inanimatorum, puta lapidum, metallorum, propter virtutes et actiones quas ab elementis participant ex quibus componuntur, quasdam alias nobiliores virtutes et actiones habent consequentes formas eorum specificas, puta quod aurum habet virtutem laetificandi cor, sapphyrus habet virtutem sang-uinem constringendi.

Et sic semper ascendendo, quanto formae specificae sunt nobiliores, tanto virtutes et operationes ex formis specificis procedentes excellentiores existunt: intantum quod nobilis-sima forma, quae est anima rationalis, habet virtutem et operationem intellectivam, quae non solum transcendit virtutem et actionem ele-mentorum, sed etiam omnem actionem corpor-alem et virtutem.

become in some way or other like to heavenly bodies, which are free of all contrariety.

Now that which is composed of contraries is neither of the contraries in act but only in po-tency. And therefore the greater the uniformity of mixture which such bodies approach, so much the more noble a form do they receive from God. Such is the human body, which, enjoying a most uniform composition, as the excellence of touch in men indicates, has a most noble form, namely a rational soul.

Powers and activities ought to be in proportion to the forms from which they proceed. And thus it is that the forms of elements which are for the most part material give rise to active and pas-sive qualities, for example, heat and cold, moi-sture and dryness and other similar things which regard the disposition of matter. But the forms of mixtures, namely of inanimate bodies like stones, metals, minerals, in addition to the powers and activities which they share with the elements of which they are composed, have certain other more noble virtues and activities arising from specific forms—for instance, gold gladdens the heart and the sapphire stops bleeding.

Thus, always in an ascending order, the more noble the specific forms, so much the more ex-cellent are the powers and operations which come from them, till that most noble form, the rational soul, is reached, which has intellectual power and activities which not only surpass the power and activity of the elements but also every corporeal power and activity.

Ex extremis igitur formis oportet de mediis iudicium sumere. Sicut enim virtus calefaciendi et infrigidandi est in igne et in aqua consequens proprias formas eorum, et virtus et actio intellectualis in homine consequens animam rationalem ipsius, ita omnes virtutes et actiones elementorum, consequuntur proprias formas eorum et reducuntur sicut in altiora principia in virtutes caelestium corporum, et adhuc altius in substantias separatas. Ex huiusmodi enim prin-cipiis formae inferiorum corporum derivantur, excepta sola rationali anima, quae ita ab im-materiali causa procedit, scilicet Deo, quod nullo modo causatur ex virtute caelestium cor-

Now from the forms at either end of the scale we ought to pass judgment on the forms in be-tween. For as the power of heating and cooling is in fire and water as a result of their special forms, and as man’s intellectual power and activity arise from his rational soul, so all powers and activities of things in between which exceed the virtues of the elements, arise from their proper forms, and are traced back to higher principles, to the powers of heavenly bodies, and still further to separated substances. For from these principles the forms of inferior bodies are derived, the rational soul alone ex-cepted, which so proceeds from an immaterial

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porum; alioquin non posset habere virtutem et operationem intellectualem a corpore penitus absolutam.

Quia igitur huiusmodi virtutes et actiones a forma specifica derivantur, quae est communis omnibus individuis eiusdem speciei, non est possibile quod aliquod individuum alicuius speciei aliquam talem virtutem vel actionem obtineat praeter alia individua similis speciei, ex eo scilicet quod est sub determinato situ cael-estium corporum generatum.

Possibile est tamen quod in uno individuo eiusdem speciei virtus et operatio consequens speciem vel intensius vel remissius inveniatur secundum diversam dispositionem materiae et diversum situm caelestium corporum in gener-atione huius vel illius individui.

Ex hoc autem apparet ulterius quod, quia formae artificiales sunt accidentia quae non consequuntur speciem: non est possibile quod aliquod artificiatum aliquam huiusmodi vir-tutem et operationem a caelesti corpore in sua compositione sortiatur ad producendum ex vir-tute indita aliquos effectus naturales transcend-dentes elementorum virtutes. Huiusmodi enim virtutes si quae essent artificiatis, ex caelestibus corporibus nullam formam consequerentur, cum forma artificialium nihil aliud sit quam ordo, compositio et figura, ex quibus prodire non possunt tales virtutes et actiones.

Unde manifestum est quod si quas huiusmodi actiones aliqua artificiata perficiant, puta quod ad aliquam sculpturam moriantur serpentes aut immobilitentur animalia vel laedantur, non pro-cedit hoc ex aliqua virtute indita et permanenti, sed solum ex virtute agentis extrinseci quod utitur talibus sicut instrumentis ad suum effect-tum.

Nec potest dici quod huiusmodi actiones pro-veniant ex virtute caelestium corporum, quia caelestia corpora naturaliter agunt in ista infer-iora; et ex hoc quod aliquod corpus sic vel aliter figuratur, nullam idoneitatem vel maiorem vel minorem habet ad recipiendum impressionem naturalis agentis;

cause, that is, from God, that it is in no way the product of the power of heavenly bodies. Otherwise it could not have intellectual power and activity wholly free of the body. Therefore, because such powers and workings are derived from a specific form which is com-mon to all the individuals of the same species, it is impossible for an individual of a species to have some kind of power or activity beyond the other individuals of the same species, just be-cause it came into being under a definite config-uration of heavenly bodies.

Yet it is possible that in an individual of the same species the power and activity arising from the species should be found more or less intense according to a diverse [disposition] of matter and the different configuration of the heavenly bodies at the coming into being of this or that individual.

From this it is further evident that artificial forms are certain accidents which do not arise from the species. For it is impossible that an artificial product can have or share in a heaven-ly body’s operation and virtue, in order that, through some endowed power, it might effect natural results transcending the virtue of the elements. If there were any such powers in artificial things they would not arise from a form (impressed) by heavenly bodies, since the form produced by the artisan is nothing other than order, composition and shape, from which such powers and activities cannot come.

Clearly, then, if artificial things evidence some such powers—for example, should serpents die at the sight of some sculpture or animals be paralyzed in their tracks or suffer injury—it does not come from same impressed and perma-nent virtue but from the power of an external agent, which uses these things as instruments for its own results.

Nor can it be said that such activities result from the power of heavenly bodies, because they act only in a natural way on those inferior things. And that a body has such and such a shape does not make it either more or less suitable for receiving the impression of a natural agent.

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unde non est possibile quod imagines vel sculp-turae quae fiunt ad aliquos effectus singulares producendos, efficaciam habeant ex caelestibus corporibus, quamvis sub certis constellationibus fieri videantur, sed solum ab aliquibus spiritibus qui per imagines et sculp-turas tales operantur.

Sicut autem imagines ex materia naturali fiunt, sed formam sortiuntur ex arte; ita etiam verba humana materiam quidem habent naturalem, scilicet sonos ab hominis ore prolatos, sed sig-nificationem quasi formam habent ab intellectu suas conceptiones per huiusmodi sonos expri-mente. Unde pari ratione nec verba humana habent efficaciam ad aliquam immutationem corporis naturalis ex virtute alicuius causae naturalis, sed solum ex aliqua spirituali sub-stantia.

Thus it is impossible that images or sculptures which are made for producing extraordinary effects should have their efficacy from heavenly bodies, although they seem to be made under certain constellations. They have it only from superior agents which work through images and sculptures.

Just as images are made from natural matter, but get their form through human skill, so also hu-man words have indeed their matter, that is, the sounds produced by the mouth of man, but they have their meaning and as it were their form from the intellect expressing its concepts through such sounds. And so, for a like reason, human words do not have any efficacy for changing a natural body through the power of some natural cause, but only through some spir-itual substance.

Hae igitur actiones quae per huiusmodi verba fiunt, vel per quascumque imagines vel sculp-turas, vel quaecumque alia huiusmodi, non sunt naturales, utpote non procedentes a virtute in-trinseca, sed sunt empericae; et ad super-stitionem pertinentes. Actiones vero quas supra diximus consequi corporum formas, sunt naturales, utpote ex principiis intrinsecis pro-cedentes.

Et haec de operationibus et actionibus occultis ad praesens dicta sufficiant.

Conclusion

For these works which are effected through such words, or through any kind of image or sculp-ture, or any such things, are not natural, because they do not spring from an intrinsic but only from an extrinsic virtue. Rather they are to be classed as superstition. The activities, however, which we have said above arise from the forms of things are natural, because they proceed from internal principles.

And so let what has been said about occult wor-kings and activities suffice for the present.

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I. NOTES.

1. A brief overview of the work.

Cf. Encyclopedia of Science and Religion, St. Thomas Aquinas:6

In a letter to a soldier, Thomas explained how bodies could perform actions that do not follow from the nature of their constituent elements, as, for example, the attraction of a mag-net for iron. Thomas regarded such actions as occult, explaining the causes of such phenol-mena by the behavior of two kinds of superior agents: (1) celestial bodies, or (2) separate spiritual substances, which included celestial intelligences, angels, and even demons. A superior agent can either communicate the power to perform the action directly to an inferior body, as is the case with the magnet; or the superior agent can, by its own motion, cause the body in question to move, as, for example, the moon causes the ebb and flow of the tides.

2. On the power of a thing as being derived from the essential principles of the species.

Cf. Quaestiones Disputatae de Potentia Dei. On the Power of God by Thomas Aquinas, translated by the English Dominican Fathers (1952), q. III, art. 9, obj. 11:

11. You will say that these actions belong to the embryo not through the soul, but by some power of the soul known as the formative power.—On the contrary, power is rooted in substance; hence it occupies a place between substance and operation according to Dionysius (Coel. Hier. xi). Consequently if the soul’s power is there, its substance is there also. (emphasis added)

Cf. St. Thomas Aquinas, De Motu Cordis (On the Movement of the Heart), n. 6 (tr. B.A.M.):

6. Now some say that this natural motion comes not from any particular nature intrinsic to the animal, but from some “universal” nature, or even from an [angelic] intelligence. But this seems ridiculous. For in every natural thing the proper passions of any genus or species follow upon some intrinsic principle. For natural things are those of which the principle of motion is in them. Now nothing is more proper to animals than the motion of the heart, upon the ceasing of which their life ends. There must, then, be some principle of this motion in animals. (emphasis added)

Cf. Thomas Aquinas. Commentary on Aristotle’s De Sensu et Sensato. Translated by Kev-in White. In Commentaries on Aristotle’s “On Sense and What Is Sensed” and “On Mem-ory and Recollection”. Translated with introductions and notes by Kevin White and Ed-ward M. Macierowski. Washington, 2005, from Chapter 9, Commentary, Difficulties:

II

But there still might be a difficulty. For if the principle of action in the elements is not substantial, but accidental form, then, since nothing acts beyond its own nature, it does not seem that matter is changed by the natural action of the elements with respect to substantial form, but only with respect to accidental form.

6 (http://www.enotes.com/science-religion-encyclopedia/thomas-aquinas [11/29/09])

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For this reason some held that all substantial forms are from a supernatural cause, and that a natural agent merely disposes to a form by altering.*

* Gauthier, p. 55, indicates that Avicenna is meant, with reference to the following: Aquinas’s Summa contra gentiles III, 69, Summa theologiae I, Q. 115, a. 1, and Questions on the Virtues, Q. 8; Averroes’ commentary on the Metaphysics (VII 31, XI[XII] 18); and Avicenna’s own statements in Avicenna Latinus. Liber de philosophia prima V-X, ed. S. Van Riet, Louvain-Leiden: E. Peeters, 1980, tr. IX, c. 5, lines 29-48 (pp. 489-90) and lines 94-95(p. 493).

This reduces to an opinion of the Platonists, who held that separate forms are the cause of generation and that all action is from an incorporeal power. On the other hand the Stoics, as Alexander says, held that bodies act of themselves, that is, inasmuch as they are bodies. But Aristotle here holds the middle way, which is that bodies act according to their qualities. And so it must be said that each thing acts according as it is (ens) in actuality, as is clear from On Generation I.*

* Gauthier, p. 55, points out that this axiom might be constructed on the basis of On Generation and Corruption, I, 5, 320b17-19, and notes that it is common in Aquinas’s works.

But just as the being (esse) of elemental qualities is derived from their essential princi-ples, so, necessarily, power of acting also belongs to such qualities from the power of the substantial forms. But everything that acts by the power of something else produces something like that in the power of which it acts: for instance a saw makes a house by the power of the house that is in the soul; and natural heat generates animate flesh by a power of soul. And it is also in this way that matter is changed by the action of elemental qualities with respect to substantial form. (emphasis added)

Cf. St. Thomas Aquinas, Disputed Questions on Spiritual Creatures, translated by Mary C. Fitzpatrick and John J. Wellmuth (Milwaukee, 1949), art. 2, c. (excerpt), pp. 36-37:

Now it must be borne in mind that the more perfect a form is, the more does it surpass corporeal matter. This is clear from induction in regard to the various orders of forms. For the form of an element does not have any activity but the one which takes place through active and passive qualities, which are the dispositions of corporeal matter. But the form “mineral body” has an activity that goes beyond active and passive qualities, and is a consequence of its species by reason of the influence of a heavenly body; for instance, that a magnet attracts iron, and that a sapphire cures an abscess.13 And further, the vegetative soul (anima vegetabilis) has an activity to which the active and passive or-ganic qualities of course contribute; but nevertheless, over and above the power of qualities like these, the soul itself achieves an effect of its own by nurture and growth up to a definite limit, and by carrying on other functions of this sort. And the sensing soul (anima sensitiva) has a further activity to which the active and the passive qualities do not extend in any way, save insofar as they are needed for the composition of the organ through which this sort of activity is exercised; such as seeing, hearing, desiring, and the like. But the most perfect of forms, the human soul, which is the end of all natural forms, has an activity that goes entirely beyond matter, and does not take place through a corporeal organ; namely, understanding. And because the actual being of a thing is proportioned to its activity, as has been said, since each thing acts according as it is a being (ens), it must be the case that the actual being of the human soul surpasses corporeal matter, and is not totally included in it, but yet in some way is touched upon by it.

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Inasmuch, then, as it surpasses the actual being of corporeal matter, having of itself the power to subsist and to act, the human soul is a spiritual substance; but inasmuch as [36-37]

13 Cf. De Unit. Intell., c. 1, sec. 27: “just as the magnet has the power to attract iron and the sapphire to stop bleeding.”

it is touched upon by matter and shares its own actual being with matter, it is the form of the body. Now it is touched upon by corporeal matter for this reason, that the highest point of the lowest always touches the lowest point of the highest, as Dionysius makes clear in the seventh chapter [lect. 4] of De Divinis Nominibus; and consequently the human soul, which is the lowest in the order of spiritual substances, can communicate its own actual being to the human body, which is the highest in dignity, so that from the soul and the body, as from form and matter, a single being results. But if a spiritual substance were composed of matter and form, it would be impossible for it to be the body’s form: because it is essential to matter that it be not in anything else, but that it should itself be the primary subject. (emphasis added)

Cf. St. Thomas Aquinas, Against the Averroists: On There Being Only One Intellect. Tran-slated by Ralph McInerny (West Lafayette, 1993), sec. 27:

[27] It is not difficult to understand how the soul can be the form of a body yet some power of the soul not be a power of body if one takes into account other things as well. For in many things we see that a form is indeed the act of a body of mixed elements and yet has a power which is not the power of any element, but belongs to that form because of a higher principle, namely a celestial body, e.g. the magnet has the power to attract iron and jasper of coagulating blood. And presently we shall see that insofar as forms are nobler they have powers which more and more surpass matter. Hence the ultimate form, the human soul, has a power, namely intellect, which wholly surpasses corporeal matter. Thus the intellect is separate because it isn’t a power in the body but in the soul, and soul is the act of the body. (emphasis added)

Cf. St. Thomas Aquinas, De Motu Cordis (On the Movement of the Heart), n. 13 (tr. B.A.M.):

13. Now we must consider that upward motion is natural to fire as a consequence of its form: and so the generator, which gives the form, is per se its mover in place. Now just as some natural motion follows the form of the element, in the same way other natural motions follow upon other forms. For we observe that iron is naturally moved toward the magnet, which motion is nevertheless not natural to it according to its character of being heavy or light, but insofar as it has such a form. In this way, therefore, inasmuch as an animal has such a form which is the soul, nothing prohibits it from having a natural motion; and the mover which gives it its form [gives it] this motion. (emphasis added)

Cf. St. Thomas Aquinas, Summa Contra Gentiles, Book II: Creation. Translated, with an Introduction and Notes by James F. Anderson (Notre Dame, 1975), ch. 30, nn. 8-13:

[8] In created things, however, there are diverse modes of necessity arising from di-verse causes. For, since a thing cannot be without its essential principles, which are matter and form, whatever belongs to a thing by reason of its essential principles must have absolute necessity in all cases.

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[9] Now, from these principles, so far as they are principles of existing, there arises a threefold absolute necessity in things. First, through the relation of a thing’s principles to its act of being. Since matter is by its nature a being in potentiality, and since that which can be can also not be, it follows that certain things, in relation to their matter, are necessarily corruptible animals because they are composed of contraries; fire because its matter is receptive of contraries. On the other hand, form is by its nature act, and through it things exist in act; so that from it there results in some things a necessity to be. And this happens either because those things are forms not existing in matter, so that there is no potentiality to non-being in them, but rather by their forms they are always able to be, as in the case of separate substances; or because their forms equal in their perfection the total potentiality of their matter, so that there remains no potentiality to another form, nor consequently, to non-being; such is the case with the heavenly bodies. But in things whose form does not fulfill the total potentiality of the matter, there still remains in the matter potentiality to another form; and hence in such things there is no necessity to be; rather, the power to be is in them the result of the victory of form over matter, as we see in the elements and things composed of them. The form of an element does not embrace the matter in its total potentiality, for matter receives the form of one element only by being made subject to one of two con-traries; but the form of a mixed body embraces the matter according as it is disposed by a certain kind of mixture. Now, contraries, and all intermediaries resulting from the mixture of extremes, must have a common identical subject. The manifest consequence of this fact is that all things which either have contraries or are composed of contraries are corruptible, whereas things not of this sort are everlasting—unless they be corrupted accidentally, as forms which are not subsistent but which exist by being in matter.

[10] Secondly, from essential principles of things absolute necessity arises in them from the order of the parts of their matter or of their form, if it happens that in certain things these principles are not simple. For, since man’s proper matter is a mixed body, having a certain temperament and endowed with organs, it is absolutely necessary that a man have in himself each of the elements and humours and principal organs. Even so, if man is a rational mortal animal, and this is his nature or form, then it is necessary for him to be both animal and rational.

[11] Thirdly, there is absolute necessity in things from the order of their essential principles to the properties flowing from their matter or form; a saw, because it is made of iron, must be hard; and a man is necessarily capable of learning.

[12] However, the agent’s necessity has reference both to the action itself and the resulting effect. Necessity in the former case is like the necessity that an accident derives from essential principles; just as other accidents result from the necessity of essential principles, so does action from the necessity of the form by which the agent actually exists; for as the agent actually is, so does it act. But this necessitation of action by form is different in the case of action that remains in the agent itself, as understanding and willing, and in action which passes into something else, as heating. In the first case, the necessity of the action itself results from the form by which the agent is made actual, because in order for this kind of action to exist, nothing extrinsic, as a terminus for it, is required. Thus, when the sense power is actualized by the sensible species, it necessarily acts; and so, too, does the intellect when it is actualized by the intelligible species. But in the second case, the action’s necessity results from the form, so far as the power to act is concerned; if fire is hot, it necessarily has the power of heating, yet it need not heat, for something extrinsic may prevent it. Nor in this question does it make any difference whether by its form one agent alone suffices to carry out an action, or whether many agents have to be assembled in order to perform a single action-as, for example, many men to pull a boat—because all are as one agent, who is put in act by their being united together in one action.

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[13] Now, the necessity in the effect or thing moved, resulting from the efficient or moving cause, depends not only on the efficient cause, but also on the condition of the thing moved and of the recipient of the agent’s action; for the recipient is either in no way receptive of the effect of such action—as wool to be made into a saw—or else its receptivity is impeded by contrary agents or by contrary dispositions in the movable or by contrary forms, to such an extent that the agent’s power is ineffective; a feeble heat will not melt iron. In order that the effect follow, it is therefore necessary that receptivity exist in the patient, and that the patient be under the domination of the agent, so that the latter can transform it to a contrary disposition. And if the effect in the patient resulting from the agent’s victory over it is contrary to the natural disposition of the patient, then there will be necessity by way of violence, as when a stone is thrown upwards. But if the effect is not contrary to the natural disposition of its subject, there will be necessity not of violence, but of natural order; the movement of the heaven, for example, results from an extrinsic active principle, and yet it is not contrary to the natural disposition of the movable subject, and hence is not a violent but a natural movement. This is true also in the alteration of lower bodies by the heavenly bodies, for there is a natural inclination in lower bodies to receive the influence of higher bodies. Such is the case, also, in the generation of the elements; for the form to be engendered is not contrary to prime matter, which is the subject of generation, although it is contrary to the form that is to be cast aside; for matter existing under a contrary form is not the subject of generation. (emphasis added)

Cf. St. Thomas Aquinas, Summa Contra Gentiles, Book II: Creation. Translated, with an Introduction and Notes by James F. Anderson (Notre Dame, 1975), ch. 68:

Chapter 68

HOW AN INTELLECTUAL SUBSTANCE CAN BE THE FORM OF THE BODY

[1] From the preceding arguments, then, we can conclude that an intellectual substance can be united to the body as its form.

[2] For, if an intellectual substance is not united to the body merely as its mover, as Plato held that it is, nor is in contact with it merely by phantasms, as Averroes said, but as its form; and if the intellect whereby man understands is not a preparedness in human nature, as Alexander supposed it to be, nor the temperament, according to Galen, nor a harmony, as Empedocles imagined, nor a body, nor the senses or the imagination, as the early philosophers maintained, then it remains that the human soul is an intellectual substance united to the body as its form. This conclusion can be made evident as follows.

[3] For one thing to be another’s substantial form, two requirements must be met. First, the form must be the principle of the substantial being of the thing whose form it is; I speak not of the productive but of the formal principle whereby a thing exists and is called a being. The second requirement then follows from this, namely, that the form and the matter be joined together in the unity of one act of being; which is not true of the union of the efficient cause with that to which it gives being. And this single act of being is that in which the composite substance subsists: a thing one in being and made up of matter and form. Now, as we have shown, the fact that an intellectual substance is subsistent does not stand in the way of its being the formal principle of the being of the matter, as communicating its own being to the matter. For it is not unfitting that the composite and its form should subsist in the same act of being, since the composite exists only by the form, and neither of them subsists apart from the other.

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[4] Nevertheless, it may be objected that an intellectual substance cannot communicate its being to corporeal matter in such fashion that the two will be united in the same act of being, because diverse genera have diverse modes of being, and to the nobler substance belongs a loftier being.

[5] Now, this argument would be relevant if that single act of being belonged in the same way to the matter as to the intellectual substance. But it does not. For that act of being appertains to the corporeal matter as its recipient and its subject, raised to a higher level; it belongs to the intellectual substance as its principle, and in keeping with its very own nature. Nothing, therefore, prevents an intellectual substance from being the human body’s form, which is the human soul.

[6] Thus are we able to contemplate the marvelous connection of things. For it is always found that the lowest in the higher genus touches the highest of the lower species. Some of the lowest members of the animal kingdom, for instance, enjoy a form of life scarcely superior to that of plants; oysters, which are motionless, have only the sense of touch and are fixed to the earth like plants. That is why Blessed Dionysius says in his work On the Divine Names that “divine wisdom has united the ends of higher things with the beginnings of the lower.” We have, therefore, to consider the existence of something supreme in the genus of bodies, namely, the human body harmoniously tempered, which is in contact with the lowest of the higher genus, namely, the human soul, which holds the lowest rank in the genus of intellectual substances, as can be seen from its mode of understanding; so that the intellectual soul is said to be on the horizon and confines of things corporeal and incorporeal, in that it is an incorporeal substance and yet the form of a body. Nor is a thing composed of an intellectual substance and corporeal matter less one than a thing made up of the form of fire and its matter, but perhaps it is more one; because the greater the mastery of form over matter, the greater is the unity of that which is made from it and matter.

[7] But, though the form and the matter are united in the one act of being, the matter need not always be commensurate with the form. Indeed, the higher the form, the more it surpasses matter in its being. This fact is clearly apparent to one who observes the operations of forms, from the study of which we know their natures; for, as a thing is, so does it act. That is why a form whose operation transcends the condition of matter, itself also surpasses matter in the rank of its being.

[8] For we find certain lowest-grade forms whose operations are limited to the class of those proper to the qualities which are dispositions of matter; qualities such as heat, cold, moisture and dryness, rarity and density, gravity and levity, etc. And those forms are the forms of the elements: forms which therefore are altogether material and wholly embedded in matter.

[9] Above these are found the forms of mixed bodies. Although their operations are no greater in scope than those which can be effected through qualities of the aforesaid variety, nevertheless they sometimes produce those same effects by a higher power which they receive from the heavenly bodies, and which is consequent upon the latter’s species. A case in point is that of the lodestone attracting iron.

[10] One rung higher on the ladder of forms, we encounter those whose operations include some which exceed the power of the previously mentioned material qualities, although the latter assist organically in the operations of those forms. Such forms are the souls of plants, which likewise resemble not only the powers of the heavenly bodies, in surpassing the active and passive qualities, but also the movers of those bodies, the souls of plants being principles of movement in living things, which move themselves.

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[11] A step above, we find other forms resembling the higher substances, not only in moving, but even, somehow, in knowing, so that they are capable of operations to which the aforesaid qualities are of no assistance, even organically, although these operations are performed only by means of a bodily organ. Such forms are the souls of brute animals. For sensation and imagination are not brought about by heating and cooling, although these are necessary for the due disposition of the organ involved.

[12] Above all these forms, however, is a form like to the higher substances even in respect of the kind of knowledge proper to it, namely, understanding. This form, then, is capable of an operation which is accomplished without any bodily organ at all. And this form is the intellective soul; for understanding is not effected through any bodily organ. That is why this principle, the intellective soul by which man understands and which transcends the condition of corporeal matter, must not be wholly encompassed by or imbedded in matter, as material forms are. This is proved by its intellectual operation, wherein corporeal matter has no part. But since the human soul’s act of understanding needs powers-namely, imagination and sense-which function through bodily organs, this itself shows that the soul is naturally united to the body in order to complete the human species. (emphasis added)

§

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II. SUPPLEMENTAL TEXTS.

1. On the two ways in which an agent of a lower rank may be moved by the power of a superior agent.

Cf. St. Thomas Aquinas, De operationibus occultis naturae ad quemdam militem ultra-montanum, tr. by J. B. McAllister (Washington, 1939):

We must now consider that an agent of a lower rank acts or is moved according to the power of a superior agent in two ways: one way in so far as the action proceeds from it according to a form and power imparted by a superior agent, as the moon illuminated through light received from the sun. In another way it acts only through the power of the superior agent, without receiving a form for acting. It is moved only through the motion of the superior agent, as a carpenter uses a saw for cutting. The sawing is indeed primarily the work of the artisan but secondarily of the saw in so far as it is moved by the artisan—not because such an action follows upon some form and power which might stay in the saw after the artisan has used it. (emphasis added)

2. The two ways in sum:

(1) according to a form and power imparted (to the patient) by a superior agent, as with light imparted to the moon giving it the power to illuminate

(2) not according to a form and power imparted by a superior agent, but only through the power of the superior agent, as with a saw which is moved only so long as the carpenter moves it

Note that St. Thomas’ first example is but one of three cases: For the form the superior agent imparts either remains after the activity of the agent ceases or it does not, and if it does remain, it is either abiding or transient. An example of a form that is abiding is the power a magnet has to attract iron; but a form that does not remain would be, for instance, light captured by a reflective surface like a mirror, which is transmitted by it only so long as the source of the light is active; such a surface retaining no power to reflect light what-soever after the latter ceases. A transient form is the illumination of the moon, which remains for a short time after the withdrawal of its source, as with a coal that has been heated; the matter in this case having begun to admit of the form itself.

§

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2. Supplement: On the operation of principal and secondary causes in a living thing.

Cf. St. Thomas Aquinas, Commentary on Aristotle’s De Anima translated by Kenelm Foster, O.P. & Sylvester Humphries, O.P. (New Haven, 1951), Book II, lect. 8 (in part):

TEXT415b28–416a18

BOOK II, CHAPTER IV, CONTINUEDTHE VEGETATIVE PRINCIPLE CONTINUED

TWO ERRORS REFUTED

Empedocles is mistaken here, adding that growth occurs in plants by their sending a root downwards, because earth is by nature below, and also upwards because of fire. § 324

Nor did he understand aright ‘up’ and ‘down’; for these are not for all things the same as for the Universe; but roots of plants correspond to the head, in animals, if it is permissible to identify organs by their functions. For we reckon those organs to be the same which perform the same operations. §§ 325-7

Besides, what holds fire and earth together if they tend in contrary directions? They must come apart if there is nothing to prevent this. But if there is such a thing, it must be the soul; and be also the cause of growth and nourishment. § 328

Now it seems to some that the nature of fire is the sole cause of growth and nutrition; for it certainly seems to be the only one of the bodies and elements that is self-nourishing and self-increasing. Whence the notion that it is this that is operative in plants and animals. §§ 329-30It is indeed a concomitant cause, but the cause absolutely is not fire, but rather the soul. For the increase of fire is infinite so long as there is anything combustible. But there are limitations to all things that subsist naturally, and some definite principle governs their dimensions and growth. And this belongs to the soul, not to fire, and to a specific principle rather than to matter. §§ 331-2

ST. THOMAS’S COMMENTARYLECTIO EIGHT

§ 324. The Philosopher has just shown that the activities we call vegetative have their origin in the soul. He now proceeds to refute two errors on this subject, which he deals with respectively in two sections; the second of which begins at ‘Now it seems to some that the nature of fire’. In the first section he begins by stating the error, and then, at ‘Nor did he understand’ attacks it.

Regarding the error itself, we should note that just as Empedocles refused to explain other cases of purposeful arrangement in Nature by any natural finality—for example he said that animals had the sort of feet they have, not in order to help them to walk, but simply because the matter of that part of their bodies happened to be arranged in that sort of way; so also the growth of living things he ascribed merely to the motion of light and heavy bodies. Observing that living things increase their size in different directions, e.g. up and down—as is evident in plants, which thrust their roots down and their branches up—he said that the downward growth of plants was due to the earth in their composition, which is heavy and therefore necessarily tends downwards; whilst their upward growth was due to fire which, being light, must tend upwards.

<…>

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§ 329. Next, at ‘Now it seems to some’, he states another theory; which, at ‘It is indeed’ he then disproves. Unlike the theory of Empedocles, which put the causes of growth and nutrition in both earth and fire, this theory ascribes them only to fire.

§ 330. The reason given is that the cause of anything’s modifications or motion would appear to be whatever had such modifications or motions essentially—e.g. fire, being essentially hot, is the cause of heat in things that contain other elements as well; and in the same way earth is the cause of heaviness. Now of the elements fire alone seems to ‘feed’ itself and to ‘grow’ ; if we take these terms in a superficial sense. Therefore fire alone would seem to cause growth and nutrition in plants and animals. But whether fire really feeds itself and grows will be made clear later.

§ 331. Then he attacks the above opinion. But note its grain of truth. All food has to be cooked, and this is done by fire, so that fire does play a part in nutrition, and consequently in growth also; not indeed as the principal agent (which is the soul) but as a secondary, instrumental agent. To say then that fire is a sort of concurrent or instrumental cause of growth and nutrition is true. But it cannot be the principal cause or agent, as he goes on to show.

§ 332. The principal agent in any action is that which imposes the term or natural limit upon what is done; thus in artificial things like boxes or houses the limit or term is fixed, not by the instruments used in the work, but by the art itself. The instruments, as such, are quite indifferent as to whether they are used to produce a thing of this shape and quantity or of that. A saw, as such, can be used to cut wood for a door or a bench or a house, and in any quantity you please; and if it cuts wood in this or that particular shape and quantity, this is due to the man who uses it. Now in Nature each thing obviously has certain limits to its size and its increase; each thing grows to a certain fixed pattern. For as each species of thing requires its own accidental modifications, so it needs its own measure of quantity, though some margin must be left to material differences and other individual factors. Men are not all equal in size. But there is a limit both to their largeness and their littleness; and whatever determines this limit is the true principal cause of growth. But this cannot be fire, because the growth of fire has no naturally fixed limits; it would spread to infinity if an infinite amount of fuel were supplied to it. Clearly, then, fire is not the chief cause of growth and nutrition, but rather the soul. And this is reasonable enough, for the quantitative limits of material things are fixed by form—the specific principle—rather than matter. Now the soul of a living being is to the elements it contains as form is to matter; the soul, then, rather than fire, sets the term and natural limit to size and growth.7

Cf. Michael Augros, “Notes from the Berquist Seminars,” 2/2/94, n. 172 (= Duane Ber-quist on St. Thomas’s Commentary on the De Anima of Aristotle [duane.2]):

172) INSTRUMENTAL AND CHIEF CAUSES OF LIVING OPERATIONS. n 331. Aristotle would not deny that enzymes etc. cause digestion. He would merely say they are not the chief causes. They are merely instrumental causes.

7 For the related notion that a natural body is not infinitely divisible with respect to quantity (an observation also relevant to the discussion of atomism to be found below), cf. St. Thomas Aquinas, In I Physic., lect. 9, n. 9 (tr. William Wallace, O.P.):

Although a body, understood mathematically, is infinitely divisible, a natural body is not divisible to infinity. For in a mathematical body all that is considered is quantity, and in this there is nothing that is repugnant to division, whereas in a natural body there is a natural form that requires a determinate quantity, just as it requires other accidents. Wherefore quantity cannot be found under the species of flesh unless within certain determined limits.

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III. THE DOCTRINE OF THE HIDDEN WORKINGS OF NATURE: ITS ORIGIN IN TRADITIONAL PHILOSOPHY.

Cf. St. Thomas Aquinas. Treatise on Separate Substances. Translated by F. J. Lescoe (West Hartford, 1959), Chapter II, nn 10-12 (with an omission):

10. -There are, accordingly, many separate substances that are in no way united to any bodies; there are, likewise, many intellectual substances united to heavenly bodies. Aristotle attempts to find out the number of these on the basis of the number of motions of the heavenly bodies.*

* Aristotle, Metaph., XI, 8 (1073b I-1074a 14).

<…>

Between us and the heavenly bodies, Aristotle did not locate any intervening animate body. Thus, according to the position of Aristotle, between us and the highest God, there exists only a two-fold order of intellectual substances, namely, the separate substances which are the ends of the heavenly motions; and the souls of the spheres, which move through appetite and desire.

11.—Now this position of Aristotle seems to be surer because it does not depart greatly from that which is evident according to sense; yet it seems to be less adequate than the position of Plato.

In the first place, there are many things which are evident according to [the] senses, for which an explanation cannot be given on the basis of what Aristotle teaches. For we see in men who are possessed by devils and in the works of sorcerers, certain phenomena which do not seem capable of taking place except through some intellectual substance. Certain followers of Aristotle, as is evident in Porphyry’s letter to Anebontes the Egyptian,*

* All 12 mss. read variously from Anempotem (A) to Cermephontem (L); hence, the emendation according to Cap. XIX, no. 106 (p. 112) below, where St. Thomas cites St. Augustine’s De Civ. Dei, X, II (PL 41, 288-291) concerning Porphyry’s letter.

tried to reduce the causes of these phenomena to the power of the heavenly bodies, as if the works of the sorcerers attained certain unusual and marvelous results under the influence of certain constellations. Furthermore, they say that it is through the influence of the stars that persons who are possessed sometimes foretell future events, for the realization of which there is a certain disposition in nature through the heavenly bodies. But in such cases, there are manifestly certain works which cannot in any way be reduced to a corporeal cause. For example, that people in a trance should speak in a cultivated way of sciences which they do not know, since they are unlettered folk; and that those who have scarcely left the village in which they were born, speak with fluency the vernacular of a foreign people. Likewise, in the works of magicians, certain images are said to be conjured up which answer questions and move about, all of which could not be accomplished by any corporeal cause. Therefore, as the Platonists see it, who could evidently assign a cause of these effects, except to say that these are brought about through demons. (emphasis added)

§

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IV. THE CAREER OF OCCULT WORKINGS IN LATER PHILOSOPHY.

1. The alchemist’s understanding of occult qualities as the source of characteristic activ-ities: Cf. The Philosophy of Natural Magic, by Henry Cornelius Agrippa [1533], L. W. de Laurence ed. [1913], at sacred-texts.com:

CHAPTER X.

OF THE OCCULT VIRTUES OF THINGS.

THERE are also other virtues in things, which are not from any Element, as to expel poison, to drive away the noxious vapors of minerals, to attract iron p. 63 or anything else; and these virtues are a sequel of the species and form of this or that thing; whence also they being a little in quantity, are of great efficacy; which is not granted to any Elementary quality. For these virtues, having much form and little matter, can do very much; but an Elementary virtue, because it hath more materiality, requires much matter for its acting. And they are called Occult Qualities, because their causes lie hid, and man’s intellect cannot in any way reach and find them out. Wherefore philosophers have attained to the greatest part of them by long experience, rather than by the search of reason: for as in the stomach the meat is digested by heat, which we know, so it is changed by a certain hidden virtue which we know not: for truly it is not changed by heat, because then it should rather be changed by the fire-side than in the stomach. So there are in things, besides the Elementary qualities which we know, other certain imbred virtues created by Nature, which we admire and are amazed at, being such as we know not, and indeed seldom or never have seen. As we read in Ovid of the Phœnix, one only bird, which renews herself:

All Birds from others do derive their birth,But yet one Fowle there is in all the Earth,

Call’d by th’ Assyrians Phœnix, who the wainOf age repairs, and sows her self again.

And in another place—

Ægyptus came to see this wondrous sight;And this rare Bird is welcom’d with delight.

Long since Matreas brought a very great wonderment upon the Greeks and Romans con-cerning himself. He said that he nourished and bred a beast that did devour itself. Hence many to this day are solicitous what this beast of Matreas should be. Who would not wonder that fishes should be digged out of the Earth, of which Aristotle, Theophrastus, and p. 64

Polybius the historian, makes mention? And those things which Pausanius wrote concerning the Singing Stones? All these are effects of Occult Virtues. So the ostrich concocts cold and most hard iron, and digests it into nourishment for his body; whose stomach, they also report, cannot be hurt with red-hot iron. So that little fish, call echeneis, doth so curb the violence of the winds, and appease the rage of the sea, that, let the tempests be never so imperious and raging, the sails also bearing a full gale, it doth notwithstanding by its mere touch stay the ships and makes them stand still, that by no means they can be moved. So salamanders and crickets live in the fire; although they seem sometimes to burn, yet they are not hurt. The like is said of a kind of bitumen, with which the weapons of the Amazons were said to be smeared over, by which means they could be spoiled neither with sword nor fire; with which also the gates of Caspia, made of brass, are reported to be smeared over by Alexander the Great.

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We read also that Noah’s Ark was joined together with this bitumen, and that it endured some thousands of years upon the Mountains of Armenia. There are many such kind of wonderful things, scarce credible, which notwithstanding are known by experience. Amongst which Antiquity makes mention of Satyrs, which were animals, in shape half men and half brutes, yet capable of speech and reason; one whereof St. Hierome reporteth, spake once unto holy Antonius the Hermit, and condemned the error of the Gentiles in worshiping such poor creatures as they were, and desired him that he would pray unto the true God for him; also he affirms that there was one of these Satyrs shewed openly alive, and afterwards sent to Constantine the Emperor.

N.B. The reader will note how the foregoing consideration of occult qualities makes scant use of the philosophical underpinnings of the doctrine such as we find them in St. Thomas Aquinas. One is almost, though not quite, in the presence of the desiccated scholasticism that sought to explain the power, e.g., of a soporific, by its “dormative virtue”—that is, by its power to put someone to sleep—an ‘explanation’ that was rightly rejected as explaining nothing at all. As we shall see, thinkers in the subsequent tradition of ‘experimental’ philo-sophy wanted to go beyond such claims, desiring instead an empirically-arrived-at ex-planation of such a manifest effect, looking to a ‘quality’ or attribute that was quantifiable, and therefore able to be brought under a general rule or “Law of Nature”, as the following excerpts make clear.

2. The denial of occult qualities as founded on the specific forms of things.

Cf. Sir Isaac Newton, Opticks (London, 1704). Excerpt from Query 31:

All these things being consider’d, it seems probable to me, that God in the Beginning form’d Matter in solid, massy, hard, impenetrable Particles, of such Sizes and Figures, and with such other Properties, and in such Proportion to Space, as most conduced to the End for which he form’d them; and that these primitive Particles being Solids, are incomparably harder than any porous Bodies compounded of them; even so very hard, as never to wear or break in pieces; no ordinary Power being able to divide what God himself made one in the first Creation. While the Particles continue entire, they may compose Bodies of one and the same Nature and Texture in all Ages: But should they wear away, or break in pieces, the Nature of Things depending on them, would be changed. Water and Earth, composed of old worn Particles and Fragments of Particles, would not be of the same Nature and Texture now, with Water and Earth composed of entire Particles in the Beginning. And therefore, that Nature may be lasting, the Changes of corporeal Things are to be placed only in the various Separations and new Associations and Motions of these permanent Particles; compound Bodies being apt to break, not in the midst of solid Particles, but where those Particles are laid together, and only touch in a few Points.8

8 On all these matters, cf. Mortimer J. Adler, The Syntopicon, Chapter 21, “Element”:

THE WORDS “ATOM” AND “ELEMENT” express basic notions in the analysis of matter. To some extent their meanings seem to be the same. Atoms or elements are usually understood to be ultimate units, the parts out of which other things are formed by combination. But as soon as further questions are asked – about the divisibility or indivisibility of these units, or about their number and variety – we are confronted with differing conceptions of the atom, and with a theory of the elements which is opposed to the atomic analysis of matter. Even when the two notions are not opposed to one another, they are not interchangeable. “Atom” has a much narrower meaning. It usually designates a small particle of matter, whereas “element” signifies the least part into which anything at all can be divided. [cont.]

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It seems to me farther, that these Particles have not only a Vis inertiae, accompanied with such passive Laws of Motion as naturally result from the Force, but also that they are moved by certain active Principles, such as is that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies. These Principles I consider, not as occult Qualities, supposed to result from the specifick Forms of Things, but as general Laws of Nature, by which the Things themselves are form’d; their Truth appearing to us by Phaenomena, though their Causes be not yet discover’d. For these are manifest Qualities, and their Causes only are occult. And the Aristotelians gave the Name of occult Qualities, not to manifest qualities, but to such qualities only as they supposed to lie hid in Bodies, and to be the unknown Causes of manifest Effects: Such as would be the Causes of Gravity, and of magnetick and electrick Attractions, and of Fermentations, if we should suppose that these Forces or Actions arose from Qualities unknown to us, and uncapable of being discovered and made manifest. Such occult Qualities put a stop to the Improvement of natural Philosophy, and therefore of late Years have been rejected. To tell us that every Species of Things is endow’d with an occult specifick Quality by which it acts and produces manifest Effects, is to tell us nothing:9 But to derive two or three general Principles of Motion from Phaenomena, and afterwards to tell us how the Properties and Actions of all corporeal Things follow from those manifest Principles, would be a very great step in Philosophy, though the Causes of those Principles were not yet discover’d: And therefore I scruple not to propose the Principles of Motion above-mention’d, they being of very general Extent, and leave their Causes to be found out. Now by the help of these Principles, all material Things seem to have been composed of the hard and solid Particles above-mention’d, variously associated in the first Creation by the Counsel of an intelligent Agent. For it became him who created them to set them in order.

<…>

ACCORDING To the Greek atomists, matter is not infinitely divisible. Lucretius writes, If nature had not set a limit / To fragmentation, by this time all matter / Would have been so reduced by time’s attrition / That not one thing could move from a beginning / To full, completed growth. There must then be a “sure and certain limit” to the breaking of matter – a limit in physical division which ultimately reaches units of matter that are absolutely indivisible. Lucretius calls them “first beginnings” of “singleness / Solid, coherent, not compound, but strong / In its eternal singleness” – the “seeds of things,” or atoms. The Greek word from which “atom” comes literally means uncuttable.

For an application of this understanding of matter by a prominent successor of Newton, cf. John Dalton, A New System of Chemical Philosophy, (Manchester, 1808), CHAP. II. On the Constitution of Bodies:

There are three distinctions in the kinds of bodies, or three states, which have more especially claimed the attention of philosophical chemists; namely, those which are marked by the terms elastic fluids, liquids, and solids. A very famous instance is exhibited to us in water, of a body, which, in certain circumstances, is capable of assuming all the three states. In steam we recognise a perfectly elastic fluid, in water a perfect liquid, and in ice a complete solid. These observations have tacitly led to the conclusion which seems universally adopted, that all bodies of sensible magnitude, whether liquid or solid, are constituted of a vast number of extremely small particles, or atoms of matter bound together by a force of attraction, which is more or less powerful according to circumstances, and which as it endeavours to prevent their separation, is very properly called in that view, attraction of cohesion; but as it collects them from a dispersed state (as from steam into water) it is called, attraction of aggre-gation, or more simply affinity. Whatever names it may go by, they still signify one and the same power. It is not my design to call in question this conclusion, which appears completely satisfactory; but to shew that we have hitherto made no use of it, and that the consequence of the neglect, has been a very obscure view of chemical agency, which is daily growing more so in proportion to the new lights attempted to be thrown upon it.

9 The decidedness of this opinion reminds one of Milton’s similarly Olympian dismissal of the comparably traditional doctrine that angels have no bodies: “the common gloss / Of Theologians….” (PL V.435-36)

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And if he did so, it’s unphilosophical to seek for any other Origin of the World, or to pretend that it might arise out of a Chaos by the mere Laws of Nature; though being once form’d, it may continue by those Laws for many Ages. For while Comets move in very excentrick Orbs in all manner of Positions, blind Fate could never make all the Planets move one and the same way in Orbs concentrick, some inconsiderable Irregularities excepted, which may have risen from the mutual Actions of Comets and Planets upon one another, and which will be apt to increase, till this System wants a Reformation. Such a wonderful Uniformity in the Planetary System must be allowed the Effect of Choice. And so must the Uniformity in the Bodies of Animals, they having generally a right and a left side shaped alike, and on either side of their Bodies two Legs behind, and either two Arms, or two Legs, or two Wings be-fore upon their Shoulders, and between their Shoulders a Neck running down into a Back-bone, and a Head upon it; and in the Head two Ears, two Eyes, a Nose, a Mouth, and a Tongue, alike situated. Also the first Contrivance of those very artificial Parts of Animals, the Eyes, Ears, Brain, Muscles, Heart, Lungs, Midriff, Glands, Larynx, Hands, Wings, swim-ming Bladders, natural Spectacles, and other Organs of Sense and Motion; and the Instinct of Brutes and Insects, can be the effect of nothing else than the Wisdom and Skill of a powerful ever-living Agent, who being in all Places, is more able by his Will to move the Bodies within his boundless uniform Sensorium, and thereby to form and reform the Parts of our own Bodies. And yet we are not to consider the World as the Body of God, or the several Parts thereof, as the Parts of God. He is an uniform Being, void of Organs, Members or Parts, and they are his Creatures subordinate to him, and subservient to his Will; and he is no more of the Species of Things carried through the Organs of Sense into the place of its Sensation, where it perceives them by means of its immediate Presence, without the Intervention of any third thing. The Organs of Sense are not for enabling the Soul to perceive the Species of Things in its Sensorium, but only for conveying them thither; and God has no need of such Organs, he being every where present to the Things themselves. And since Space is divisible in infinitum, and Matter is not necessarily in all places, it may be also allow’d that God is able to create Particles of Matter of several Sizes and Figures, and in several Proportions to Space, and perhaps of different Densities and Forces, and thereby to vary the Laws of Nature, and make Worlds of several sort in several Parts of the Universe. At least, I see nothing of Contradiction in all this. As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths. For Hypotheses are not to be regarded in experimental Philosophy. And although the arguing from Experiments and Observations by Induction be no Demonstration of general Conclusions; yet it is the best way of arguing which the Nature of Things admits of, and may be looked upon as so much the stronger, by how much the Induction is more general. And if no Exception occur from Phaenomena, the Conclusion may be pronounced generally. But if at any time afterwards any Exception shall occur from Experiments, it may then begin to be pronounced with such Exceptions as occur. By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general. This is the Method of Analysis: And the Synthesis consists in assuming the Causes discover’d, and establish’d as Principles, and by them explaining the Phaenomena proceeding from them, and proving the Explanations. In the two first Books of these Opticks, I proceeded by this Analysis to discover and prove the original Differences of the Rays of Light in respect of Refrangibility, Reflexibility, and Colour, and their alternate Fits of easy Reflexion and easy Transmission, and the Properties of Bodies , both opake and pellucid, on which their Reflexions and Colours depend. And these Discoveries being proved, may be assumed in the Method of Composition for

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explaining the Phaenomena arising from them: An Instance of which Method I gave in the End of the first Book. In this third Book I have only begun the Analysis of what remains to be discover’d about Light and its Effects upon the Frame of Nature, hinting several things about it, and leaving the Hints to be examin’d and improv’d by the farther Experiments and Observations of such as are inquisitive. And if natural Philosophy in all its Parts, by pursuing this Method, shall at length be perfected, the Bounds of Moral Philosophy will be also enlarged. For so far as we can know by natural Philosophy what is the first Cause, what Power he has over us, and what Benefits we receive from him, so far our Duty towards him, as well as that towards one another, will appear to us by the Light of Nature. And no doubt, if the Worship of false Gods had not blinded the Heathen, their moral Philosophy would have gone farther than to the four Cardinal Virtues; and instead of teaching the Trans-migration of Souls, and to worship the Sun and Moon, and dead Heroes, they would have taught us to worship our true Author and Benefactor, as their Ancestors did under the Government of Noah and his Sons before they corrupted themselves.10

Cf. “Newton’s Philosophy”, The Stanford Encyclopedia of Philosophy, sec. 2:11

2. Newton and Cotes on occult qualities and the nature of matter

Although Samuel Clarke may be Newton’s most famous defender and spokesperson in the eighteenth century, no understanding of Newtonianism would be complete without a discussion of the role of Roger Cotes, the Plumian Professor of Astronomy at Cambridge in the early eighteenth century and the editor of the second edition of the Principia. Although Cotes was one of Newton’s ablest defenders, his role as what we might call a Newtonian spokesperson did not prevent him from challenging Newton on occasion, nor from interpreting the implications of Newton’s theory of gravity in a way that may have been at odds with Newton’s preferred interpretation. An important episode in Cotes’s relation to Newton centers on their disagreement concerning the best rebuttal to the infamous charge – popularized by Leibniz, among others – that Newton, or at least his physical theory, treats gravity as an occult quality.

2.1 Occult qualities

Regarding the first episode, one should note that although Newton was criticized for invoking an occult quality, that fact did not prevent Cotes, in his defense of Newton, from employing this as a term of criticism against other philosophers. For instance, in his extensive and illuminating preface to the second edition — which consists of a lengthy polemic against various “Cartesian” views — he writes:

Those who have undertaken the study of natural science can be divided into roughly three classes. There have been those who have endowed the individual species of things with specific occult qualities, on which – they have then alleged – the operations of individual bodies depend in some unknown way. The whole of Scholastic doctrine derived from Aristotle and the Peripatetics is based on this. Although they affirm that individual effects arise from the specific natures of bodies, they do not tell us the causes of those natures, and therefore they tell us nothing. And since they are wholly concerned with the names of things rather than with the things themselves, they must be regarded as inventors of what might be called philosophical jargon, rather than as teachers of philosophy (Newton 1999, 385).

10 Had he ever had occasion to discuss such matters with an informed Aristotelian such as William Harvey, Newton undoubtedly would have been shocked to learn the extent to which his own lucubrations were in-debted to the Peripatetics, especially with regard to his appeals to the operation of final causality in nature.11 (http://plato.stanford.edu/entries/newton-philosophy/#OccQua [1/13/10])

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This passage from Cotes is apt because it illustrates a common problem with criticisms that reference occult qualities: the criticism seems so polemical that one often lacks a clear sense of why the quality in question is said to be occult in the first place.

To try to sharpen this notion up, then, we can treat a quality as occult if it meets three con-ditions (let’s take these as sufficient, but perhaps not as necessary). First, the quality is exhaustively characterized by the effects that it generates in one or more other objects. Second, the quality itself is said to be distinct from the effects it is said to produce. Third, the quality is said to be distinct from each of – and indeed, from the conjunction of – the primary qualities that characterize the bearer of the quality. When it is employed as a term of abuse, as it typically is, two criticisms are typically leveled against a quality meeting this threefold definition: (1) that it is unintelligible, or more specifically, that one cannot have an idea of it, and therefore, according to some, that one cannot have a thought about it, but can only talk about it; and, (2) that it fails to be explanatory.

One should acknowledge that (2) requires an immediate clarification: it may not be the case that any quality that meets the three – jointly sufficient – conditions listed above will fail to explain just any natural phenomenon or sensible effect. Rather, claim (2) should really be taken to mean: the quality cannot explain the sensible effects through which it is said to be exhaustively characterized. This of course is said to hold in the ubiquitous dormative virtue case. Some canonical critics of the Scholastics present claim (2) without this caveat, which may be unfair.

In his famous and influential preface to the second edition, Cotes attempts to defend Newton from the then-ubiquitous charge that he treats gravity as occult. In writing his defense, he can barely conceal his contempt for Newton’s critics:

I can hear some people disagreeing with this conclusion and muttering something or other about occult qualities. They are always prattling on and on to the effect that gravity is something occult, and that occult causes are to be banished completely from philo-sophy. But it is easy to answer them: occult causes are not those causes whose existence is very clearly demonstrated by observations, but only those whose existence is occult, imagined, and not yet proved. Therefore gravity is not an occult cause of celestial motions, since it has been shown from phenomena that this force really exists. Rather, occult causes are the refuge of those who assign the governing of these motions to some sort of vortices of a certain matter utterly fictitious and completely imperceptible to the senses (Newton 1999, 392).

So from Cotes’s point of view, gravity itself is not occult, only its cause is; and, according to Cotes, this is compatible with contending that gravity itself is a cause of phenomena. This indicates, first of all, an ambiguity in the term occult, for the term can apparently mean one of two things. In what we can call its non-technical sense — where one needn’t meet the three-fold definition above – saying that the cause of gravity is occult means simply that the cause is hidden or unknown. But in the technical sense above, the claim means that the cause of gravity is an unintelligible power of bodies.

If Cotes has the ordinary, rather than the technical, meaning in mind, then gravity’s cause is something that we could, as far as his discussion is concerned, hope to discover, even if we do not yet know it in 1713. And it seems as clear as anything that in each edition of the Principia, Newton thinks that it is perfectly reasonable to search for a cause of gravity, which is to say, at the least, he certainly thinks that gravity does have some cause (Newton 1999, 943). If Cotes has the technical sense in mind, however, then gravity’s cause is obviously not something that we could hope to discover, not because it is hidden or

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microscopic, but because it is not intelligible and therefore not the sort of thing that could be discovered. That is to say, if the cause of gravity is occult in the technical sense, then the proper response is presumably that we ought to reject this very idea, rather than to endorse a search for something answering to it. So Cotes’s claim appears to be twofold: first, it is incorrect to contend that gravity itself is an occult quality – on the contrary, it is perfectly evident; and second, it is incorrect to contend that gravity’s cause is an occult quality, if by that we mean more than the claim that gravity’s cause is unknown.

2.2 The nature of matter

But what does it mean to claim that gravity is evident? Cotes intends specifically that we should add gravity to the usual list of primary qualities. Of course, conceptions of the primary qualities differ, but for our purposes here, we might take such qualities to charac-terize all macroscopic bodies, along with all of their microscopic parts; there is a broad consensus in this period that certain qualities do in fact characterize all material bodies (and their parts), but considerable disagreement concerning the proper list of such qualities. Cotes writes:

The extension, mobility, and impenetrability of bodies are known only through experi-ments; it is in exactly the same way that the gravity of bodies is known…Thus all bodies for which we have observations are heavy; and from this we conclude that all bodies universally are heavy, even those for which we do not have observations… Among the primary qualities of all bodies universally, either gravity will have a place, or extension, mobility, and impenetrability will not (Newton 1999, 392).

It is quite natural for Cotes to make this point, for Newton himself employs the third of his Rules for the Study of Natural Philosophy, to which Cotes here alludes, to prove that gravity acts “universally” (Newton 1999, 795-96). In every other case, Rule Three is employed to show how we can justifiably infer that some quality found within the reach of our experi-ments is, given certain background conditions, a quality of all bodies universally. And so Cotes contends that gravity, too, is a quality of all bodies universally, and thereby attempts to block two criticisms: one, that gravity is a quality of bodies, but not of all bodies universally (that is a claim about the inference we can make from our empirical evidence); and two, that gravity must be considered an occult quality if it is a universal quality, a view he rebuts in the paragraph quoted above, which in fact follows the paragraph just quoted. However, Cotes and Newton appear to differ on this crucial point. For his part, Newton denies that gravity is an occult quality not by insisting that we have sufficient evidence to consider it a “primary quality” of bodies, but by contending that it is not an “essential” quality. So Newton appears to shift the discussion from considering which properties are universal — or “primary” — to considering which are “essential” to material bodies. After reviewing the relevant empirical evidence in Book Three of the Principia, Newton concludes the discussion of Rule Three as follows: “it will have to be concluded by this third rule that all bodies gravitate toward one another” (Newton 1999, 796). If by that Newton means that gravity is a universal quality of bodies, he might be interpreted as agreeing with Cotes. But he then inserts a significant caveat: “Yet I am by no means affirming that gravity is essential to bodies. By inherent force I mean only the force of inertia. This is immutable. Gravity is diminished as bodies recede from the earth” (ibid.). This passage repeats a claim in one of Newton’s letters to Richard Bentley from many years earlier, namely the denial that gravity is “essential” to matter (cf. the section on Bentley). He presents the denial, reasonably enough, on the grounds that the gravitational interaction between any two massive bodies is a function of their distance, so if their distance is increased, the strength of their interaction is diminished. The interaction, and therefore the (supposed) property, would seem to disappear entirely in the case of a lonely body. The implication seems to be as follows: since

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gravity fails to meet what is sometimes called the “lonely corpuscle” criterion, it cannot be an essential quality of bodies. A lonely body would lack gravitational interactions.

Gravity does not meet the “lonely corpuscle” criterion, but since Newton contends that all bodies gravitate toward one another, it may seem that gravity is a type of ubiquitous relational property, one that is instantiated when two or more bodies with mass exist in the same world. Perhaps this indicates that it is actually akin to a secondary quality, rather than to a primary quality, as Cotes alleges. The fact that, from Newton’s point of view, this reading appears to fail might be illuminating here. Gravity conforms to the third law of motion, so if X and Y are two massive bodies, we should not infer that we can simply attribute to X a “power” to attract Y, or to Y a “power” to attract X. Rather, for X to be attracted to Y is precisely for Y to be attracted to X (and vice versa). To be any kind of quality of either body in the interaction, it must be a quality of both, and a quality of precisely the same type. Gravity therefore seems to lack what we might call the asymmetric character of ordinary secondary qualities, such as colors. These qualities seem to involve asymmetric interactions because they are said to dispose objects to appear a certain way to us, or to cause certain ideas in perceivers; gravity presumably cannot be fully understood on these models.

The question of whether gravity can be considered a type of quality can also be illuminated, from Newton’s point of view, by contrasting it with the case of mass. Since Newton employs force of inertia as another name for (inertial) mass — it is a potentially misleading name, but we can bracket that here — the passage from the Principia above invites us to consider Newton’s distinct treatment of mass and of gravity. Since mass cannot be diminished by a body’s spatiotemporal position (unlike gravity), and since it remains a property even of a lonely corpuscle, Newton distinguishes it from gravity, taking it to be an essential quality of all material bodies. Thus if the theory in the Principia uncovers a new essential quality of material bodies, according to Newton, mass is actually the quality, rather than gravity. This indicates that although gravity is not essential to matter, what we might call the basis for gravitational interactions, namely mass, is in fact essential to material bodies. This highlights a subtlety in Newton’s view often missed by his critics.

In contending that inertial mass is — whereas gravity is not — to be considered an essential property of matter, and in listing inertial mass alongside extension, impenetrability and other ordinary “primary” qualities, we might read Newton as aligning himself with a broader tradition identified by Margaret Wilson. She helpfully distinguishes the view that the primary qualities must be accessible to ordinary perceptual experience from the view that the qualities ought to be defined by the latest scientific theory, regardless of our perceptual access to them (Wilson 1999, 455-94). Whereas some of the “mechanists” defended the first view, Newton appears to be allied with the second tradition. The inertial mass of a given body does not appear to be directly perceptible in ordinary experience, and it does not appear to be perceptible through the perception of other primary qualities, such as extension, or of other properties, such as weight. And even if one thinks that inertial mass is perceptible in one of these ways, it is nonetheless distinct from other primary qualities at least in the sense that it is perceptually unavailable to perceivers who lack an acquaintance with the relevant theory. It would seem that one cannot perceive inertial mass independently of gaining the relevant concept from Newton’s theory: independently of the theory, one would presumably not know that in certain cases, one perceives a body’s resistance to acceleration. More generally, then, Newton seems to think that we cannot generate a comprehensive list of the primary qualities independently of our physical theory concerning the interactions of bodies. On that point, perhaps Cotes would agree, despite his disagreements with Newton.

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More generally, it should be noted that Cotes’s interpretation — according to which gravity is a universal quality of all bodies, and possibly an essential quality — gained considerable support as the eighteenth century progressed. For instance, the view that gravity ought to be understood as essential to matter, even on the basis of evidence available to Newton himself, was defended at length in Kant’s Metaphysical Foundations of Natural Science (Friedman 1990). In that regard, we might think of Cotes and Kant as falling into the same post-Newtonian interpretive tradition, one whose proponents took a step that Newton himself seemed unwilling to take.

For a perceptive account of Newton’s understanding of “hypothesis”, cf. Mortimer J. Ad-ler, The Great Ideas: A Syntopicon of Great Books of the Western World (Chicago, 1952), Vol. I, Chapter 36, “Hypothesis” (Introduction), p. 753:

IN THE Mathematical Principles of Natural Philosophy, Newton says, “I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypo-theses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.” The context of this passage, and of a similar statement at the end of the Optics, as well as the association in Newton’s mind of hypotheses with occult qualities, substantial forms, and hidden causes, seems to indicate a special meaning of “hypothesis.” Newton criticizes the vortices in the physics of Descartes on the ground that it is unne-cessary to appeal to occult or unobservable entities in order to explain natural phenomena. The Cartesian vortices, like the substantial forms of Aristotle, are, for Newton, hypotheses in a very special sense. They are hypothetical entities. They are not inferred from the phenol-mena. Although treated as if they were realities underlying the phenomena, they are, as Gilbert says of the primum mobile, a “fiction, something not comprehensible by any reason-ing and evidenced by no visible star, but purely a product of imagination and mathematical hypothesis.” There is almost a play on words in this identification of hypotheses with imaginary entities to which reality is attributed; for in their Greek and Latin roots, the words “hypothesis” and “hypostasis,” “supposition” and “substance,” are closely related. The first word in each of these pairs refers to a proposition which underlies reasoning, the second to a reality which underlies observable qualities or phenomena. To make hypotheses, in the sense in which Newton excludes them from experimental philosophy, is to hypostatize or to reify, that is, to make a thing out of, or to give reality to, a fiction or construction of the mind. It has seemed to some critics that, no less than the Cartesian vortices, the ether in Newton’s theory of light is an hypothesis in precisely this sense—an imaginary entity. For many centuries, the atoms and molecules postulated to explain chemical combinations and changes were attacked as fictions and defended as useful hypotheses. On the one hand, there is an issue concerning the theoretic usefulness of such constructions; on the other, a question concerning their counterparts in reality.

3. A rebuttal of the Newtonian position.

Cf. Voltaire, The Works of Voltaire, Vol. VI (Philosophical Dictionary Part 4) [1764] “Occult Qualities”:

Occult qualities have for a very long time been much derided; it would be more proper to deride those who do not believe in them. Let us for the hundredth time repeat that every principle, every primitive source of any of the works which come from the hand of the demiourgos, is occult, and eternally hidden from mortals.

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What is the centripetal force, the force of gravitation, which acts without contact at such immense distances? What causes our hearts to beat sixty times a minute? What other power changes this grass into milk in the udder of a cow? and this bread into the flesh, blood, and bone of that child, who grows proportionally while he eats it, until he arrives at the height determined by nature, after which there is no art which can add a line to it?

Vegetables, minerals, animals, where is your originating principle? It is the hands of Him who turns the sun on its axis, and who has clothed it with light. This lead will never become silver, nor this silver gold; this gold will never become diamond, nor this straw be transformed into lemons and bananas. What corpuscular system of physics, what atoms, determine their nature? You know nothing about it, and the cause will be eternally occult to you. All that surrounds us, all within us, is an enigma which it is not in the power of man to divine.

The furred ignoramus ought to have been aware of this truth when he said that beasts possess a vegetative and sensitive soul, and man a soul which is vegetative, sensitive, and intellect-tual. Poor man, kneaded up of pride, who has pronounced only words—have you ever seen a soul? Know you how it is made? We have spoken much of the soul in these inquiries, but have always confessed our ignorance. I now repeat this confession still more emphatically, since the more I read, the more I meditate, and the more I acquire, the more am I enabled to affirm that I know nothing.

§

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V. PRINCIPLES OF NEWTONIAN MECHANICS.

Cf. Sir Isaac Newton, The Mathematical Principles of Natural Philosophy (1729) New-ton’s Principles of Natural Philosophy, Dawsons of Pall Mall, 1968; Opening pages of the Principia up to the three laws of motion; opening pages of Book III, The System of the World, with rules for Philosophy, plus the closing comments with his view of God, etc.:

Definitions

DEFINITION I

The quantity of matter is the measure of the same, arising from its density and bulk conjointly.

THUS AIR of a double density, in a double space, is quadruple in quantity; in a triple space, sextuple in quantity. The same thing is to be understood of snow, and fine dust or powders, that are condensed by compression or liquefaction, and of all bodies that are by any causes whatever differently condensed. I have no regard in this place to a medium, if any such there is, that freely pervades the interstices between the parts of bodies. It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body, for it is proportional to the weight, as I have found by experiments on pendulums, very accurately made, which shall be shown hereafter.

DEFINITION II

The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly.

The motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple.

DEFINITION III

The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line.

This force is always proportional to the body whose force it is and differs nothing from the inactivity of the mass, but in our manner of conceiving it. A body, from the inert nature of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita may, by a most significant name, be called inertia (vis inertiae) or force of inactivity. But a body only exerts this force when another force, impressed upon it, endeavours to change its condition; and the exercise of this force may be considered as both resistance and impulse; it is resistance so far as the body for maintaining its present state, opposes the force impressed; it is impulse so far as the body, by not easily giving way to the impressed force of another endeavours to change the state of that other. Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest, which commonly are taken to be so.

DEFINITION IV

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An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line.

This force consists in the action only, and remains no longer in the body when the action is over. For a body maintains every new state it acquires by its inertia only. But impressed forces are of different origins, as from percussion, from pressure, from centripetal force.

DEFINITION V

A centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre.

Of this sort is gravity, by which bodies tend to the centre of the earth; magnetism, by which iron tends to the loadstone; and that force, whatever it is, by which the planets are continually drawn aside from the rectilinear motions, which otherwise they would pursue, and made to revolve in curvilinear orbits. A stone, whirled about in a sling, endeavours to recede from the hand that turns it; and by that endeavour, distends the sling, and that with so much the greater force, as it is revolved with the greater velocity, and as it is let go, flies away. That force which opposes itself to this endeavour, and by which the sling continually draws back the stone towards the hand, and retains it in its orbit, because it is directed to the hand as the centre of the orbit, I call the centripetal force. And the same thing is to be understood of all bodies, revolved in any orbits. They all endeavour to recede from the centres of their orbits; and were it not for the opposition of a contrary force which restrains them to, and detains them in their orbits, which I therefore call centripetal, would fly off in right lines, with an uniform motion. A projectile, if it was not for the force of gravity, would not deviate towards the earth, but would go off from it in a right line, and that with an uniform motion, if the resistance of the air was taken away. It is by its gravity, that it is drawn aside continually from its rectilinear course, and made to deviate towards the earth, more or less, according to the force of its gravity, and the velocity of its motion. The less its gravity is, or the quantity of its matter, or the greater the velocity with which it is projected, the less will it from a rectilinear course, and the farther it will go. If a leaden ball, projected from the top of a mountain by the force of gunpowder, with a given velocity, and in a direction parallel to the horizon, is carried in a curved line to the distance of two miles before it falls to the ground; the same, if the resistance of the air were taken away, with a double or decuple velocity, fly twice or ten times as far. And by increasing the velocity, we may at pleasure increase the distance to which it might be projected, and diminish the curvature of the line which it might describe, till at last it should fall at the distance of 10, 30, or 90 degrees, or even might go quite round the whole earth before it falls; or lastly, so that it might never fall to the earth, but go forwards into the celestial spaces, and proceed in its motion in infinitum. And after the same manner that a projectile, by the force of gravity, may be made to revolve in an orbit, and go round the whole earth, the moon also, either by the force of gravity, if it is endued with gravity, or by any other force, that impels it towards the earth, may be continually drawn aside towards the earth, out of the rectilinear way which by its innate force it would pursue; and would be made to revolve in the orbit which it now describes; nor could the moon without some such force be retained in its orbit. If this force was too small, it would not sufficiently turn the moon out of a rectilinear course; if it was too great, it would turn it too much, and draw down the moon from its orbit towards the earth. It is necessary that the force be of a just quantity, and it belongs to the mathematicians to find the force that may serve exactly to retain a body in a given orbit with a given velocity; and vice versa, to determine the curvilinear way into which a body projected from a given place, with a given velocity, may be made to deviate from its natural rectilinear way, by means of a given force.

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The quantity of any centripetal force may be considered as of three kinds: absolute, accelerative, and motive.

DEFINITION VI

The absolute quantity of a centripetal force is the measure of the same, proportional to the efficacy of the cause that propagates it from the centre, through the spaces round about.

Thus the magnetic force is greater in one loadstone and less in another, according to their sizes and strength of intensity.

DEFINITION VII

The accclerative quantity of a centripetal force is the measure of the same, proportional to the velocity which it generates in a given time.

Thus the force of the same loadstone is greater at a less distance, and less at a greater: also the force of gravity is greater in valleys, less on tops of exceeding high mountains; and yet less (as shall hereafter be shown), at greater distances from the body of the earth; but at equal distances, it is the same everywhere; because (taking away, or allowing for, the resistance of the air), it equally accelerates all falling bodies, whether heavy or light, great or small.

DEFINITION VIII

The motive quantity of a centripetal force is the measure of the same, proportional to the motion which it generates in a given time.

Thus the weight is greater in a greater body, less in a less body; and, in the same body, it is greater near to the earth, and less at remoter distances. This sort of quantity is the centripetency, or propension of the whole body towards the centre, or, as I may say, its weight; and it is always known by the quantity of an equal and contrary force just sufficient to hinder the descent of the body. These quantities of forces, we may, for the sake of brevity, call by the names of motive, accelerative, and absolute forces; and, for the sake of distinction, consider them with respect to the bodies that tend to the centre, to the places of those bodies, and to the centre of force towards which they tend; that is to say, I refer the motive force to the body as an endeavour and propensity of the whole towards a centre, arising from the propensities of the several parts taken together; the accelerative force to the place of the body, as a certain power diffused from the centre to all places around to move the bodies that are in them; and the absolute force to the centre, as endued with some cause, without which those motive forces would not be propagated through the spaces round about; whether that cause be some central body (such as is the magnet in the centre of the magnetic force, or the earth in the centre of the gravitating force), or anything else that does not yet appear. For I here design only to give a mathematical notion of those forces, without considering their physical causes and seats.

Wherefore the accelerative force will stand in the same relation to the motive, as celerity does to motion. For the quantity of motion arises from the celerity multiplied by the quantity of matter; and the motive force arises from the accelerative force multiplied by the same quantity of matter. For the sum of the actions of the accelerative force, upon the several particles of the body, is the motive force of the whole. Hence it is, that near the suffice of the

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earth, where the accelerative gravity, or force productive of gravity, in all bodies is the same, the motive gravity or the weight is as the body; but if we should ascend to higher regions, where the accelerative gravity is less, the weight would be equally diminished, and would always be as the product of the body, by the accelerative gravity. So in those regions, where the accelerative gravity is diminished into one-half, the weight of a body two or three times less, will be four or six times less.

I likewise call attractions and impulses, in the same sense, accelerative, and motive; and use the words attraction, impulse, or propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically: wherefore the reader is not to imagine that by those words I anywhere take upon me to define the kind, or the manner of any action, the causes or the physical reason thereof, or that I attribute forces, in a true and physical sense, to certain centres (which are only mathematical points); when at any time I happen to speak of centres as attracting, or as endued with attractive powers.

SCHOLIUM

Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed.

III. Place is a part of space which a body takes up, and is according to the space, either absolute or relative. I say, a part of space; not the situation, nor the external surface of the body. For the places of equal solids are always equal; but their suffices, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity, nor are they so much the places themselves, as the properties of places. The motion of the whole is the same with the sum of the motions of the parts; that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole is the same as the sum of the places of the parts, and for that reason, it is internal, and in the whole body.

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IV. Absolute motion is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship which the body possesses; or that part of the cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth, in immovable space, partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship, its true motion will arise, partly from the true motion of the earth, in immovable space, and partly from the relative motions as well of the ship on the earth, as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth, where the ship is, was truly moved towards the east, with a velocity of 10,010 parts; while the ship itself, with a fresh gale, and full sails, is carried towards the west, with a velocity expressed by 10 of those parts; but a sailor walks in the ship towards the east, with I part of the said velocity; then the sailor will be moved truly in immovable space towards the east, with a velocity of 10,001 parts, and relatively on the earth towards the west, with a velocity of g of those parts.

Absolute time, in astronomy, is distinguished from relative, by the equation or correction of the apparent time. For the natural days are truly unequal, though they are commonly considered as equal, and used for a measure of time; astronomers correct this inequality that they may measure the celestial motions by a more accurate time. It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. All motions may be accelerated and retarded, but the flowing of absolute time is not liable to any change. The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all: and therefore this duration ought to be distinguished from what are only sensible measures thereof; and from which we deduce it, by means of the astronomical equation. The necessity of this equation, for determining the times of a phenomenon, is evinced as well from the experiments of the pendulum clock, as by eclipses of the satellites of Jupiter.

As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be movable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions.

But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred.

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But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know, from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body, it follows that absolute rest cannot be determined from the position of bodies in our regions.

It is a property of motion, that the parts, which retain given positions to their wholes, do partake of the motions of those wholes. For all the parts of revolving bodies endeavour to recede from the axis of motion; and the impetus of bodies moving forwards arises from the joint impetus of all the parts. Therefore, if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion. Upon which account, the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise, all included bodies, besides their translation from near the surrounding ones, partake likewise of their true motions; and though that translation were not made, they would not be really at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without any removal from near the shell.

A property, near akin to the preceding, is this, that if a place is moved, whatever is placed therein moves along with it; and therefore a body, which is moved from a place in motion, partakes also of the motion of its place. Upon which account, all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place, and the motion of this place out of its place; and so on, until we come to some immovable place, as in the before-mentioned example of the sailor. Wherefore, entire and absolute motions can be no otherwise determined than by immovable places; and for that reason I did before refer those absolute motions to immovable places, but relative ones to movable places. Now no other places are immovable but those that, from infinity to infinity, do all retain the same given position one to another; and upon this account must ever remain unmoved; and do thereby constitute immovable space.

The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist. Again, true motion suffers always some change from any force impressed upon the moving body; but relative motion does not necessarily undergo any change by such forces. For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Thus, true motion by no means consists in such relations. The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; thereupon,

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by the sudden action of another force, it is whirled about the contrary way, and while the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plain, as before the vessel began to move; but after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known, and may be measured by this endeavour. At first, when the relative motion of the water in the vessel was greatest, it produced no endeavour to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved its endeavour to recede from the axis; and this endeavour showed the real circular motion of the water continually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavour does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and, like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion. And therefore in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them; the several parts of those heavens, and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truly at rest), and being carried together with their heavens, partake of their motions, and as parts of revolving wholes, endeavour to recede from the axis of their motions.

Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves. And if the meaning of words is to be determined by their use, then by the names time, space, place, and motion, their [sensible] measures are properly to be understood; and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant. On this account, those violate the accuracy of language, which ought to be kept precise, who interpret these words for the measured quantities. Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities with their relations and sensible measures. It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavour of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those

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forces ought to be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion -did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it.

AXIOMS, ORLAWS OF MOTION

LAW I

Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

PROJECTILES continue in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in freer spaces, preserve their motions both progressive and circular for a much longer time.

LAW II

The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

If any force generates n motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this- motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

LAW III

To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to

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a rope, the horse (if I may say so) will be equally drawn back towards the stone; fro the distended rope, by the saame endeavour to relax or unbend itself, will draw the horse as muchas it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. For, because the motions are equally changed, the changes of the velocities made towards contrary parts are inversely proportional to the bodies. This law takes place also in attractions, as will be proved in the next Scholium. ...

Book One, The Motion of Bodies ...

Book Two: The Motion of Bodies in Resisting Mediums ...

Book Three

SYSTEM OF THE WORLD(IN MATHEMATICAL TREATMENT)

IN THE PRECEDING BOOKS I have laid down the principles of philosophy; principles not philosophical but mathematical: such, namely, as we may 1 build our reasonings upon in philosophical inquiries. These principles are the laws and conditions of certain motions, and powers or forces, which chiefly have respect to philosophy; but, lest they should have appeared of themselves dry and barren, I have illustrated them here and there with some philosophical scholiums, giving an account of such things as are of more general nature, and which philosophy seems chiefly to be founded on; such as the density and the resistance of bodies, spaces void of all bodies, and the motion of light and sounds. It remains that, from the same principles, I now demonstrate the frame of the System of the World. Upon this subject I had, indeed, composed the third Book in a popular method, that it might be read by many; but afterwards, considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce the substance of this Book into the form of Propositions (in the mathematical way), which should be read by those only who had first made themselves masters of the principles established in the preceding Books: not that I would advise anyone to the previous study of every Proposition of those Books; for they abound with such as might cost too much time, even to readers of good mathematical learning. It is . enough if one carefully reads the Definitions, the Laws of Motion, and the first three sections of the first Book. He may then pass on to this Book, and consult such of the remaining Propositions of the first two Books, as the references in this, and his occasions, shall require.

RULES OF REASONINGIN PHILOSOPHY

RULE I

We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

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To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.

RULE II

Therefore to the same natural effects we must, as far as possible, assign the same causes.

As to respiration in a man and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the sun; the reflection of light in the earth, and in the planets.

RULE III

The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments; and such as are not liable to diminution can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which is wont to be simple, and always consonant to itself. We no other way know the extension of bodies than by our senses, nor do these reach it in all bodies; but because we perceive extension in all tht are sensible, therefore we ascribe it universally to all others also. That abundance of bodies are hard, we learn by experience; and because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided particles not only of the bodies we feel but of all others. That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and thence conclude impenetrability to be an universal property of all bodies whatsoever. That all bodies are movable, and endowed with certain powers (which we call the inertia) of persevering in their motion, or in their rest, we only infer from the like properties observed in the bodies which we have seen. The extension, hardness, impenetrability, mobility, and inertia of the whole, result from the extension, hardness, impenetrability, mobility, and inertia of the parts; and hence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and movable, and endowed with their proper inertia. And this is the foundation of all philosophy. Moreover, that the divided but contiguous particles of bodies may be separated from one another, is matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguished, and not yet divided, may, by the powers of Nature, be actually divided and separated from one another, we cannot certainly determine. Yet, had we the proof of but one experiment that any undivided particle, in breaking a hard and solid body, suffered a division, we might by virtue of this rule conclude that the undivided as well as the divided particles may be divided and actually separated to infinity.

Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth gravitate towards the earth, and that in proportion to the quantity of matter which they severally contain; that the moon likewise, according to the quantity of its matter, gravitates towards the earth; that, on the other hand, our sea gravitates towards the moon; and, all the planets one towards another; and the comets in like manner towards- the sun; we must, in consequence of this rule, universally allow that all bodies whatsoever are endowed with a principle of mutual gravitation.

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For the argument from the appearances concludes with more force for the universal gravitation of all bodies than for their impenetrability; of which, among those in the celestial regions, we have no experiments, nor any manner of observation. Not that I affirm gravity to be essential to bodies: by their vis insita I mean nothing but their inertia. This is immutable. Their gravity is diminished as they recede from the earth.

RULE IV

In experimental philosophy we are to look, upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

This rule we must follow, that the argument of induction may not be evaded by hypotheses.

Phenomena

Propositions and Theorems ...

GENERAL SCHOLIUM

The hypothesis of vortices is pressed with many difficulties. That every planet by a radius drawn to the sun may describe areas proportional to the times of description, the periodic times of the several parts of the vortices should observe the square of their distances from the sun; but that the periodic times of the planets may obtain the 3/2th power of their distances from the sun, the periodic times of the parts of the vortex ought to be as the 3/2th power of their distances. That the smaller vortices may maintain their lesser revolutions about Saturn, Jupiter, and other planets, and swim quietly and undisturbed in the greater vortex of the sun, the periodic times of the parts of the sun’s vortex should be equal; but the rotation of the sun and planets about their axes, which ought to correspond with the motions of their vortices, recede far from all these proportions. The motions of the comets are exceedingly regular, are governed by the same laws with the motions of the planets, and can by no means be accounted for by the hypothesis of vortices; for comets are carried with very eccentric motions through all parts of the heavens indifferently, with a freedom that is incompatible with the notion of a vortex.

Bodies projected in our air suffer no resistance but from the air. Withdraw the air, as is done in Mr. Boyle’s vacuum, and the resistance ceases; for in this void a bit of fine down and a piece of solid gold descend with equal velocity. And the same argument must apply to the celestial spaces above the earth’s atmosphere; in these spaces, where there is no air to resist their motions, all bodies will move with the greatest freedom; and the planets and comets will constantly pursue their revolutions in orbits given in kind and position, according to the laws above explained; but though these bodies may, indeed, continue in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws.

The six primary planets are revolved about the sun in circles concentric with the sun, and with motions directed towards the same parts, and almost in the same plane. Ten moons are revolved about the earth, Jupiter, and Saturn, in circles concentric with them, with the same direction of motion, and nearly in the planes of the orbits of those planets; but it is not to be

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conceived that mere mechanical causes could give birth to so many regular motions, since the comets range over all parts of the heavens in very eccentric orbits; for by that kind of motion they pass easily through the orbs of the planets, and with great rapidity; and in their aphelions, where they move the slowest, and are detained the longest, they recede to the greatest distances from each other, and hence suffer the least disturbance from their mutual attractions. This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems: and lest the systems of the fixed stars should, by their gravity, fall on each other, he hath placed those systems at immense distances from one another.

This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God pantokrator, or Universal Ruler; for God is a relative word, and has a respect to servants; and Deity is the dominion of God not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The Supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: these are titles which have no respect to servants. The word God’ usually signifies Lord; but every lord is not a God. It is the dominion of a spiritual being which constitutes a God: a true, supreme, or imaginary dominion makes a true, supreme, or imaginary God. And from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done. He is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever, and is everywhere present- and, by existing always and everywhere, he constitutes duration and space. Since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere. Every soul that has perception is, though in different times and in different organs of sense and motion, still the same indivisible person. There are given successive parts in duration, coexistent parts in space, but neither the one nor the other in the person of a man, or his thinking principle; and much less can they be found in the thinking substance of God. Every man, so far as he is a thing that has perception, is one and the same man during his whole life, in all and each of his organs of sense. God is the same God, always and everywhere. He is omnipresent not virtually only, but also substantially; for virtue cannot subsist without substance. In him are all things contained and moved; yet neither affects the other: God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God. It is allowed by all that the Supreme God exists necessarily; and by the same necessity he exists always and everywhere. Whence also he is all similar, all eye, all ear, all brain, all arm, all power to perceive, to understand, and to act; but in a manner not at all human, in a manner not at all corporeal, in a manner utterly unknown to us. As a blind man has no idea of colours, so have we no idea of the manner by which the all-wise God perceives and understands all things. He is utterly void of all body and bodily figure, and can therefore neither be seen, nor heard, nor touched; nor ought he to be worshiped under the representation of any corporeal thing. We have ideas of his attributes, but what the real substance of anything is we know not. In bodies, we see only their figures and colours, we hear only the sounds, we touch only their outward surfaces, we smell only the smells, and taste the savours; but their inward substances are not to be known either by our senses, or by

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any reflex act of our minds: much less, then, have we any idea of the substance of God. We know him only by his most wise and excellent contrivances of things, and final causes; we admire him for his perfections; but we reverence and adore him on account of his dominion: for we adore him as his servants; and a god without dominion, providence, and final causes, is nothing else but Fate and Nature. Blind metaphysical necessity, which is certainly the same always and everywhere, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing. But, by way of allegory, God is said to see, to speak, to laugh, to love, to hate, to desire, to give, to receive, to rejoice, to be angry, to fight, to frame, to work, to build; for all our notions of God are taken from the ways of mankind by a certain similitude, which, though not perfect, has some likeness, however. And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy.

Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances. Gravitation towards the sun is made up out of the gravitations towards the several particles of which the body of the sun is composed; and in receding from the sun decreases accurately as the inverse square of the distances as far as the orbit of Saturn, as evidently appears from the quiescence of the aphelion of the planets; nay, and even to the remotest aphelion of the comets, if those aphelions are also quiescent.

But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea. And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighbouring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles. But these are things that cannot be explained in few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates.

END OF THE PRINCIPIA

§

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VI. HYPOTHESIS AND INDUCTION.

Cf. Mortimer J. Adler, The Great Ideas: A Syntopicon of Great Books of the Western World (Chicago, 1952), Vol. I, Chapter 36, “Hypothesis” (Introduction), pp. 749-756:

A COMPARISON of their Greek and Latin roots shows that the English words “hypothesis” and “supposition” are synonymous. To hypothesize or to suppose is to place under—to make one thing the basis of another in the process of thought. The word “hypothesis” is today often popularly misapplied to mean a guess or hunch. The sleuth in a detective story speaks of having an hypothesis about who committed the crime. The popular notion of what it means to suppose something, or to entertain a supposition, more accurately reflects the meaning of hypothesis in logic, mathematics, and scientific or philosophical method. A supposition is generally understood to be something taken for granted, something assumed for the purpose of drawing implications or making inferences. What is supposed is not known to be true; it may be true or false. When we make a supposition, our first concern is to see what follows from it, and only then to consider its truth in the light of its con-sequences. We cannot reverse this order, when we employ suppositions, and ask first about their truth. The word “if” expresses the essence of supposing. The word “then” or the phrase “it follows that” introduces the consequences for the consideration of which we make the supposition. We are not interested in the “if” for its own sake, but for the sake of what it may lead to. In any statement of the “if . . . then . . .” sort, it is the if-clause which formulates the supposition or the hypothesis; the other part of the statement, the then-clause, formulates the consequences or implications. The whole complex statement, which makes an if the logical basis for a then, is not an hypothesis. Rather it is what is traditionally called in logic a hypothetical proposition.

THERE IS ONE USE of the word “hypothesis” in mathematics which seems at odds with the foregoing summary. In Euclid’s Elements, for example, an hypothesis is that which is given, not as the basis from which the conclusion is drawn or proved, but as a condition of solving the geometric problem under consideration. Let us take Proposition 6 of Book I. It reads: “If in a triangle two angles be equal to one another, then the sides which subtend the equal angles will also be equal to one another.” In the demonstration of this theorem, a triangle having two equal angles is regarded as given or granted. That figure or geometrical condition is a fact obtained by hypothesis. It is the fact stated in the hypothesis, or the if-clause, of the theorem. If the geometrical reality of that fact itself is questioned, the answer would have to be obtained by a prior proof that such a figure, conforming to the definition of an isosceles triangle, can be constructed by the use of no other instruments than a straight edge and a compass. The construction is not made, however, as part of the proof of Theorem 6, any more than is the demonstration of an antecedent theorem, which may have to be used in the proof of Theorem 6. In the proof of Theorem 6, the first line, beginning with the word “let,” declares that the constructibility of the figure is to be taken for granted as a matter of hypothesis. The whole problem of Theorem 6 is to prove that the then-clause follows from the if-clause. Euclid appears to accomplish this by introducing other propositions drawn from his axioms, definitions, postulates, or theorems previously demonstrated which establish this connection and so certify the conclusion as following from the hypothesis. Two points about this procedure should be noted. First, the conclusion does not follow from [749-750] the hypothesis directly, for if that were so, the “if-then proposition would be self-evident and would need no proof. The mind which sees immediately that the sides opposite to the equal angles in an isosceles triangle are

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necessarily equal does not need any demonstration of the connection between equal angles and equal sides. The Euclidean demonstration consists in making this connection, which is not immediately evident, mediately evident; that is, evident through the mediation of other propositions. It is not the hypothesis alone which proves the conclusion, but the hypothesis in the company of other propositions which serve to take the mind step by step from the hypothesis granted to the conclusion implied. Second, the proposition with the truth of which the reasoning seems to end is not the proposition to be proved. The Q.E.D. at the end of a Euclidean demonstration does not apply to the last proposition in the line of proof, but to the theorem itself, for that is the proposition to be proved. The last proposition in the reasoning is merely the consequent which, according to the theorem, is proposed as following from the hypothesis. When he is able to verify the proposed connection between the hypothesis and its conclusion or consequent, Euclid says Q.E.D. to the theorem as a whole—the whole if-then statement. The process of proof seems to be the same when the theorem is stated categorically rather than hypothetically. For example, Theorem 6 might have been stated, as other Euclidean theorems are, in the following manner: “The sides subtended by equal angles in a triangle are also equal to one another.” This variation in mode of statement raises a question, not about the meaning of “by hypothesis” in Euclidean proof, but about the difference between hypothetical and categorical propositions, which we will consider later.

THE EUCLIDEAN USE of a given (that is, a constructible) figure as an hypothesis does not seem to be a method of making a supposition in order to discover its implications. Nor does it seem to be a way of testing the truth of an hypothesis by reference to its consequences. Both of these aspects of hypothetical reasoning do appear, however, in Plato’s dialogues. In the Meno, for example, Socrates proposes, at a certain turn in the conversation about virtue and knowledge, that he and Meno entertain the hypothesis that virtue is knowledge. Socrates immediately inquires about the consequences. “If virtue is knowledge,” he asks, “will it be taught?” Since Meno already understands that knowledge is teachable, he answers the question affirmatively. The utility of advancing the hypothesis that virtue is knowledge gradually appears in the next phase of the dialogue, wherein it is discovered that virtue is not teachable at all, or at least not in the way in which the arts and sciences are teachable. The discovery throws some doubt on the truth of the hypothesis that virtue is knowledge; at least it does not seem to be knowledge in the same sense as science or art. This mode of reasoning exemplifies the use of an hypothesis to test its truth in terms of its consequences. The underlying logical principle is that the denial of the consequences requires a denial of the antecedent hypothesis, just as an affirmation of the antecedent would require an affirmation of the consequent. Nothing follows logically from a denial of the hypothesis, or from an affirmation of its consequences. This example from the Meno also illustrates the difference between Euclid’s and Plato’s use of hypotheses. Socrates is not here trying to prove that virtue is knowledge, then virtue is teachable. The validity of the foregoing if-then statement is already understood in terms of the fact that knowledge is teachable. With the if-then statement accepted as valid, Socrates uses it for the purpose of ascertaining whether or in what sense virtue is knowledge. It is not the hypothetical or if-then statement which is proved, but the hypothesis—the antecedent in that statement—which is tested. The same general method of employing hypotheses and testing them is found in the empirical sciences. In medical practice, the physician, according to Hippocrates, “must be able to form a judgment from having made himself acquainted with all the symptoms, and estimating their powers in comparison with one another”; he should then “cultivate prognosis,” since “he will manage the cure best who has foreseen what is to happen from the present state of matters.” [750-751] The preliminary diagnosis states an hypothesis (what the disease may be) and the prognosis foresees a set of consequences (what is likely to happen if the diagnosis is

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correct). Observation of the course of the symptoms and the patient’s changing condition will either confirm or invalidate the prognosis. Confirmation leaves the diagnosis a lucky guess, but fails to prove it. If the disease does not run the predicted course, however, the diagnosis on which the prognosis was based can be dismissed as a false hypothesis.

WHEN AN HYPOTHESIS takes the form of a prediction of what should happen if the hypothesis is true, the failure of the consequences to occur refutes the hypothesis. Though discussions of scientific method frequently speak of “prediction and verification,” it would seem as though prediction can only lead to the refutation of an hypothesis rather than to its verification. An hypothesis is overthrown when its prediction fails, but it is not verified when its prediction comes true. To think that it can be verified in this way is to commit the logical fallacy of arguing from the truth of a conclusion to the truth of its premises. How, then, do empirical scientists prove an hypothesis to be true? What do they mean by prediction and verification in relation to the use of hypothesis ? There seem to be two possible ways in which an hypothesis can be proved by empirical or experimental research. One way can be used when we know that the consequences implied follow only from the truth of the hypothesis. Should the consequences implied be impossible unless the supposed condition exists, then the confirmation of the prediction verifies the hypothesis. The other possible method of verification has come to be called “the method of multiple working hypotheses.” The validity of this method depends on our knowing that the several hypotheses being entertained exhaust all the relevant possibilities. Each hypothesis generates a prediction; and if upon investigation the observed facts negate every prediction except one, then that one remaining hypothesis is verified. If negative instances have eliminated the false hypotheses, the hypothesis remaining must be true, on the condition, of course, that it is the only possibility which is left. Both of these methods seem to be valid only if a prerequisite condition is fulfilled. To verify one of a series of multiple hypotheses through the elimination of the others, the scientist must know that the hypotheses enumerated are truly exhaustive. In the verification of a single hypothesis by the confirmation of its prediction, the scientist must know that the observed consequences can follow from no other supposition. Since such knowledge is often unavailable, probability rather than complete proof results from the testing of hypotheses by observation or experiment. In his Treatise on the Vacuum, Pascal offers a summary of the logical situation by distinguishing the true, the false, and the doubtful or probable hypothesis. “Sometimes its negation brings a conclusion of obvious absurdity, and then the hypothesis is true and invariable. Or else one deduces an obvious error from its affirmation, and then the hypo-thesis is held to be false. And when one has not been able to find any mistake either in its negation or its affirmation, then the hypothesis remains doubtful, so that, in order that the hypothesis may be demonstrable, it is not enough that all the phenomena result from it, but rather it is necessary, if there ensues something contrary to a single one of the expected phenomena, that this suffice to establish its falsity.”

BOTH THE USE of hypotheses and the method of verifying them vary from science to science, according as the character of the science happens to be purely empirical (e.g., the work of Hippocrates, Darwin, Freud), or experimental (e.g., the work of Harvey and Faraday), or a combination of experimentation with mathematical reasoning (e.g., the work of Galileo, Newton, Fourier). Not all scientific work is directed or controlled by hypotheses, but in the absence of well-formulated hypotheses, the research can hardly be better than exploration. A well-constructed experiment, especially what Bacon calls an experimentum crucis derives its demonstrative character from the hypothetical reasoning which formulates the problem to be solved. The value of such a crucial experiment appears in Bacon’s reasoning about the rise and fall of the tides. “If it be found,” he writes, “that during the ebb

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the surface of the [751-752] waters at sea is more curved and round, from the waters rising in the middle, and sinking at the sides or coast, and if, during a flood, it be more even and level, from the waters returning to their former position, then assuredly, by this decisive instance, the raising of them by a magnetic force can be admitted; if otherwise, it must be entirely rejected.” In the field of mathematical physics, and particularly in astronomy, the meaning of hypothesis is both enlarged and altered. So far we have considered hypotheses which are single propositions implying certain consequences. But in mathematical physics, a whole theory—a complex system of propositions—comes to be regarded as a single hypothesis. In his preface to the work of Copernicus, Osiander says that the task of the astronomer is “to use painstaking and skilled observation in gathering together the history of the celestial movements; and then since he cannot by any line of reasoning reach the true causes of these movements to think up or construct whatever causes or hypotheses he pleases, such that, by the assumption of these causes, those same movements can be calculated from the principles of geometry, for the past and for the future too.” The elaborate system constructed by Copernicus and the system constructed by Ptolemy which Copernicus hopes to replace are sometimes called “the Copernican hypothesis” and “the Ptolemaic hypothesis”; and some- times these two theories are referred to as “the heliocentric hypothesis” and “the geocentric hypothesis.” A whole theory, regarded as an hypothesis, must be tested in a different way from a single proposition whose implication generates a prediction, As rival hypotheses, one theory may be superior to another in internal consistency or in mathematical simplicity and elegance. Kepler is thus able to argue against Ptolemy by appealing to criteria which Ptolemy accepts, pointing out that Ptolemy himself wishes “to construct hypotheses which are as simple as possible, if that can be done. And so if anyone constructs simpler hypotheses than he—understanding simplicity geometrically—he, on the contrary, will not defend his composite hypotheses.” But even if the Copernican hypothesis is superior on the grounds of being geometrically simpler, it must meet another test. As indicated in the chapter on ASTRONOMY, mathe-matical theories about physical phenomena must be more than ideal constructions of possible universes. They must try to account for this one real world and are therefore subject to the test of their applicability to reality. However elegant it may be mathematically, an hypothesis when considered from the point of view of physics is satisfactory only if it accounts for the phenomena it was invented to explain. In the words of Simplicius, it must “save the appearances.” An hypothesis can therefore be tested for its application to reality by the way in which it fits the observed facts. “In those sciences where mathematical demonstrations are applied to natural phenomena,” Galileo writes, “the principles” which are “the foundations of the entire superstructure” must be “established by well-chosen experiments.” By such means Galileo chooses between the hypothesis that the uniform acceleration of a freely falling body is proportional to the units of space traversed and the hypothesis that it is proportional to the units of time elapsed. To borrow Plato’s expression in the Timaeus, the mathematical consistency of a theory makes it “a likely story.” The theoretical integrity of the hypothesis makes it credible. But when competing credible hypotheses exist, each saving the relevant appearances equally well, which is to be believed ? The fact that one of them, as in the case of the Copernican-Ptolemaic controversy, is mathematically superior cannot decide the question, since the question is, Which is true of reality? Sometimes a single fact, such as the phenomenon of the Foucault pendulum, may exercise a decisive influence, if one of the two competing theories finds that fact congenial and the other leaves it inexplicable. Sometimes, as appears in the discussion of the Copernican hypothesis in the chapter on ASTRONOMY, of two hypotheses which are equally satisfactory so far as purely astronomical phenomena are concerned, one may have the

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additional virtue of covering other fields of phenomena which that hypothesis was not originally designed to explain. As interpreted by Kepler and as developed in Newton’s theory of universal gravitation, [752-753] the Copernican hypothesis brings the terrestrial phenomena of the tides and of falling bodies under the same set of laws which applies to the celestial motions. The hypo-thesis then has the amazing quality of consilience, a bringing together under one formulation of phenomena not previously thought to be related. This seems to be what Huygens has in mind when he considers the degree of probability that is attainable through experimental research.” We have “scarcely less than complete proof,” he writes, when “things which have been demonstrated by the principles assumed, correspond perfectly to the phenomena which experiment has brought under observation; and further, principally, when one can imagine and foresee new phenomena which ought to follow from the hypotheses which one employs, and when one finds that therein the fact corresponds to our prevision.” Then, in common parlance, we say that it is no longer a theory, but has become a fact. Yet the question remains whether the empirical tests which eliminate the less satisfactory hypothesis can ever make the more satisfactory hypothesis more than a likely story.

IN THE Mathematical Principles of Natural Philosophy, Newton says, “I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypo-theses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.” The context of this passage, and of a similar statement at the end of the Optics, as well as the association in Newton’s mind of hypotheses with occult qualities, substantial forms, and hidden causes, seems to indicate a special meaning of “hypothesis.” Newton criticizes the vortices in the physics of Descartes on the ground that it is unne-cessary to appeal to occult or unobservable entities in order to explain natural phenomena. The Cartesian vortices, like the substantial forms of Aristotle, are, for Newton, hypotheses in a very special sense. They are hypothetical entities. They are not inferred from the phenomena. Although treated as if they were realities underlying the phenomena, they are, as Gilbert says of the primum mobile, a “fiction, something not comprehensible by any reasoning and evidenced by no visible star, but purely a product of imagination and mathematical hypothesis.” There is almost a play on words in this identification of hypotheses with imaginary entities to which reality is attributed; for in their Greek and Latin roots, the words “hypothesis” and “hypostasis,” “supposition” and “substance,” are closely related. The first word in each of these pairs refers to a proposition which underlies reasoning, the second to a reality which underlies observable qualities or phenomena. To make hypotheses, in the sense in which Newton excludes them from experimental philosophy, is to hypostatize or to reify, that is, to make a thing out of, or to give reality to, a fiction or construction of the mind. It has seemed to some critics that, no less than the Cartesian vortices, the ether in Newton’s theory of light is an hypothesis in precisely this sense—an imaginary entity. For many centuries, the atoms and molecules postulated to explain chemical combinations and changes were attacked as fictions and defended as useful hypotheses. On the one hand, there is an issue concerning the theoretic usefulness of such constructions; on the other, a question concerning their counterparts in reality. It is sometimes thought that fictions are useful for purposes of explanation even when their unreality is admitted. Rousseau, for example, explicitly denies any historical reality to the idea of man living in a state of nature prior to the formation of society by the social contract. In this matter, he says, we can lay “facts aside, as they do not affect the question.” These related notions—the state of nature and the social contract—are “rather calculated to explain the nature of things, than to ascertain their actual origin; just like the hypotheses which our physicists daily form respecting the formation of the world.”

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Similarly Lavoisier posits the existence of “caloric” for its explanatory value. “It is difficult,” he writes, “to comprehend these phenomena, without admitting them as the effects of a real and material substance, or very subtile fluid, which, insinuating itself between the particles of bodies, separates them from each [753-754] other; and, even allowing the existence of this fluid to be hypothetical, we shall see in the sequel, that it explains the phenomena of nature in a very satisfactory manner.”

ONE OTHER MEANING of hypothesis remains to be considered. It is the sense in which postulates or assumptions are distinguished from axioms in the foundations of a science. In Euclid’s geometry, as in Descartes’, both sorts of principles appear. The axioms or common notions are those propositions which are immediately seen to be true without proof. The postulates or assumptions are hypotheses in the sense that their truth is taken for granted without proof. Both sorts of propositions serve as principles or starting points for the demonstration of theorems, or the conclusions of the science. Both are principles of demonstration in that they are used to demonstrate other propositions without themselves being demonstrated. But axioms are traditionally regarded as intrinsically indemonstrable, whereas hypotheses pos-tulates or assumptions may not be indemonstrable. They are simply asserted without demonstration. The possibility of demonstrating an hypothesis gives it the character of a provisional assumption. In the Discourse on Method, Descartes refers to certain matters assumed in his Dioptrics and Meteors, and expresses his concern lest the reader should take “offence because I call them hypotheses and do not appear to care about their proof.” He goes on to say: “I have not named them hypotheses with any other object than that it may be known that while I consider myself able to deduce them from the primary truths which I explained above, yet I particularly desired not to do so, in order that certain persons may not for this reason take occasion to build up some extravagant philosophical system on what they take to be my principles.” The distinction between axioms and postulates or hypotheses raises two issues. The first concerns the genuineness of the distinction itself. Axioms, self-evident propositions, or what William James calls “necessary truths,” have been denied entirely or dismissed as tautologies. The only principles of science must then be hypotheses – assumptions voluntarily made or conventionally agreed upon. This issue is more fully discussed in the chapter on PRINCIPLE. The other issue presupposes the reality of the distinction, but is concerned with different applications of it in the analysis of science. Aristotle, for example, defines scientific knowledge in terms of three elements, one of which consists of the primary premises upon which demonstrations rest. The principles of a particular science may be axioms in the strict sense of being self-evident truths and hence absolutely indemonstrable; or they may be provisional assumptions which, though not proved m this science, can nevertheless be proved by a higher science, as in “the application of geometrical demonstrations to theorems in mechanics or optics, or of arithmetical demonstrations to those of harmonics.” The latter are not axioms because they are demonstrable; yet in a particular science they may play the role of axioms insofar as they are used, without being demonstrated, to demonstrate other propositions. Reasoning which rests either on axioms or on demonstrable principles Aristotle calls scientific, but reasoning which rests only on hypotheses he regards as dialectical. Reasoning results in scientific demonstration, according to Aristotle, “when the premises from which the reasoning starts are true and primary, or are such that our knowledge of them has originally come through premises which are primary and true.” In contrast, reasoning is dialectical “if it reasons from opinions that are generally accepted,” and, Aristotle explains, “those opinions are ‘generally accepted’ which are accepted by everyone or by the majority or by the philosophers…, by all, or by a majority, or by the most notable and illustrious of them.” In another place, he adds one important qualification. In defining a dialectical

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proposition as one that is “held by all men or by most men or by the philosophers,” he adds: “provided it be not contrary to the general opinion; for a man would assent to the view of the philosophers, only if it were not contrary to the opinions of most men.” For Aristotle, dialectical reasoning or argument moves entirely within the sphere of opinion. Even an opinion generally accepted, not only by the philosophers but also by most [754-755] men, remains an opinion. The best opinions are probabilities propositions which are not self-evident and which cannot be proved. They are not merely provisional assump-tions. Resting on assumptions which cannot ever be more than probable, the conclusions of dialectical reasoning are also never more than probable. Since they lack the certain foundation which axioms give, they cannot have the certitude of science. Plato, on the other hand, seems to think that the mathematical sciences are hypothetical in their foundation, and that only in the science of dialectic, which he considers the highest science, does the mind rise from mere hypotheses to the ultimate principles of knowledge. “The students of geometry, arithmetic, and the kindred sciences,” Socrates says in the Republic, “assume the odd and the even, and the figures and the three kinds of angle and the like in their several branches of science; these are their hypotheses, which they and everybody are supposed to know, and therefore they do not deign to give an account of them either to themselves or others.” There is a higher sort of knowledge, he goes on, “which reason herself attains by the power of dialectic, using the hypotheses not as first principles, but only as hypotheses that is to say, as steps and points of departure into a world which is above hypotheses, in order that she may soar beyond them to first principles.” The issue between Plato and Aristotle may be only verbal—a difference in the use of such words as “science” and “dialectic.” Whether it is verbal or real is considered in the chapters on DIALECTIC and METAPHYSICS. In any case, the issue throws light on the difference between an hypothesis as a merely provisional assumption, susceptible to proof by higher principles, and an hypothesis as a probability taken for granted for the purposes of argument, which is itself incapable of being proved.

FINALLY WE COME to the meaning of “hypothetical” in the analysis of propositions and syllogisms. The distinction between the categorical and the hypothetical proposition or syllogism, briefly touched on in Aristotle’s Organon, is developed in the tradition of logic which begins with that book. In his work on Interpretation he distinguishes between simple and compound propositions. The compound proposition consists of several simple propositions in some logical relation to one another. In the tradition of logical analysis, three basic types of relation have been defined as constituting three different kinds of compound proposition. One type of relation is the conjunctive; it is signified by the word “and.” Another is the disjunctive; it is signified by the words “either . . . or . . .” The third type is the hypothetical and is signified by the words “if . . . then . . .” To take an example we have already used, “virtue is knowledge” and “virtue is teachable” are simple propositions. In contrast, the statement, “if” virtue is knowledge, then virtue is teachable,” is a compound proposition, hypothetical in form. If the proposition were stated in the sentence, “either virtue is knowledge or it is not teachable,” it would be disjunctive in form; if stated in the sentence “virtue is knowledge and virtue is teachable,” it would be conjunctive in form. In each of these three cases, the compound proposition consists of the two simple propositions with which we began, though in each case they appear to be differently related. Whereas Aristotle divides propositions into simple and compound, Kant divides all judgments into the categorical, the hypothetical, and the disjunctive. In the categorical judgment, he says, “we consider two concepts”; in the hypothetical, “two judgements”; in the disjunctive, “several judgements in their relation to one another.” As an example of the hypothetical proposition, he offers the statement, “If perfect justice exists, the obstinately wicked are punished.” As an example of the disjunctive judgment, “we may say . . . [that]

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the world exists either by blind chance, or by internal necessity, or by an external cause.” Each of these three alternatives, Kant points out, “occupies a part of the sphere of all possible knowledge with regard to the existence of the world, while all together occupy the whole sphere.” The hypothetical judgment does no more than state “the relation of two propositions . . . Whether both these propositions are true remains unsettled. It is only the consequence,” Kant says, “which is laid down by this judgement.” [755-756] In the Prior Analytics, Aristotle distinguishes between the categorical and the hypothetical syllogism. The following reasoning is categorical in form: “Knowledge is teachable, virtue is knowledge; therefore, virtue is teachable.” The following reasoning is hypothetical in form: “If virtue is knowledge, it is teachable; but virtue is knowledge; therefore it is teachable”; or “If virtue is knowledge, it is teachable; but virtue is not teachable; therefore it is not knowledge.” The basic issue with respect to the distinction between categorical and hypothetical syllogisms is whether the latter are always reducible to the former. One thing seems to be clear. The rules for the hypothetical syllogism formally parallel the rules for the categorical syllogism. In hypothetical reasoning, the consequent must be affirmed if the antecedent is affirmed; the antecedent must be denied if the consequent is denied. In categorical reasoning, the affirmation of the premises requires an affirmation of the conclusion, and a denial of the conclusion requires a denial of the premises. With respect to the distinction between the categorical and hypothetical proposition, there is also an issue whether propositions stated in one form can always be converted into propositions having the other form of statement. In modern mathematical logic, for example, general propositions, such as “All men are mortal,” are sometimes expressed in hypothetical form: “If anything is a man, it is mortal.” Logicians like Bertrand Russell think that the hypothetical form is more exact because it explicitly refrains from suggesting that men exist; it merely states that if the class ‘man’ should have any existent members, they will also belong to the class ‘mortal.’ Apart from the question whether a universal proposition should or should not be interpreted as asserting the existence of anything, there seems to be a formal difference between the categorical and hypothetical proposition. This is manifest only when the hypothetical is truly a compound proposition, not when it is the statement of a simple proposition in hypothetical form, as, for example, the simple proposition “All men are mortal,” is stated in hypothetical form by “If anything is a man, it is mortal.” Because it is truly a compound proposition, and not merely the hypothetical statement of a general proposition, the proposition, “If virtue is knowledge, then virtue is teachable,” cannot be restated in the form of a simple categorical proposition. A simple proposition, whether stated categorically or hypothetically, may be the conclusion of either a categorical or a hypothetical syllogism. But the hypothetical statement which is really a compound proposition can never be the conclusion of any sort of syllogism, though it may be one of the premises in hypothetical reasoning.

Cf. ibid., Vol. I, Chapter 39, “Induction” (Introduction), pp. 805-811:

AS the list of Additional Readings indicates, the theory of induction falls within the province of logic and is part of the logician’s concern with the methods of inference or reasoning employed in the sciences. The great controversies about induction seem to be of relatively recent origin in the history of logic, beginning perhaps with the argument between William Whewell and J. S. Mill over the contributions of reason and experience to the inductive process. Later in the nineteenth century and in our own time, writers like Johnson and Keynes, Russell and Nicod, who present different formulations of inductive inference, call attention to the unsolved problems with which any theory is left. They underline the assumptions that seem to be unavoidable in any statement of the formal conditions which validate the so-called “inductive leap”—the jump from observed particulars to general

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truths, truths having a wider generality than the particular evidences from which they are drawn or on which they are based. The problem of induction, in anyone’s version of it, is the problem of generalization. This may involve psychological questions about how the mind generalizes from experience. But however they are answered, the basic logical questions remain substantially unaltered. By what criteria is valid distinguished from fallacious induction? Can induction be secured from error by rules of inference? Is induction indispensable in the development of scientific knowledge, or is there, as Whewell, for example, suggests, a sharp distinction between the inductive and the deductive sciences? What is the relation of induction to deduction? Is it the relation of a method of discovery to a method of demonstration or proof? Is it a relation between two modes of reasoning, both of which can be formulated as processes of proof? Is there both an inductive and a deductive type of syllogism, or is induction the very opposite of all forms of reasoning and proof? It is with these last questions that the discussion of induction begins in the great books, especially in Aristotle’s Organon and Bacon’s Novum Organum, but also in the writings of Descartes and Locke, and in observations on scientific method by Newton, Harvey, and Pascal. Though many of the controversies and problems which become central in the nineteenth century do not appear explicitly in the earlier tradition, they are anticipated by the fundamental distinctions and issues which can be found in the earlier writers. Bacon’s dissatisfaction with Aristotle, for example, leads him to formulate specific rules for induction. Going further in the same general direction, Mill later develops his elaborate theory of inductive inference. We move in the opposite direction if we are guided by Aristotle’s distinction between scientific and dialectical induction and by his way of setting induction off as the very opposite of reasoning. The question then arises whether Bacon and Mill are treating induction in all or in only one of several quite distinct senses.

AS THE CHAPTER ON LOGIC indicates, the names of Aristotle and Bacon are sometimes used as the symbols of opposed tendencies in logic. The one is supposed to represent an almost exclusive emphasis on deduction, the other the primacy and importance of induction. An opposition between Aristotle and Bacon is also implied in the current use of such phrases as “inductive logic” and “deductive logic.” These phrases are sometimes used to suggest that the inductive or the deductive process can be favored to the exclusion, or at least the sub-ordination, of the other. Such understanding of [805-806] the matter usually includes the popular notion that induction is always reasoning from particulars to universals and deduction always reasoning from universals to particulars. But none of these things seems to be true, or at least not without serious qualification. Neither Aristotle nor Bacon emphasizes deduction or induction to the exclusion of the other. On the contrary, both appear to insist on the absolute priority of induction, since, according to them, it provides deductive reasoning with its ultimate premises. Far from conflicting, induction and deduction complement each other. “The consilience of the results of both these processes,” Mill writes, “each corroborating and verifying the other, is requisite to give to any general proposition the kind and degree of evidence which constitutes scientific proof.” Until principles are established, the deduction of their implications or consequences cannot begin. Unless principles, once they are obtained, are then used in the proof of other truths, or are otherwise rationally employed, the purpose of inductive generalization is not fully realized. In this understanding of the relationship between induction and reasoning, Aristotle and Bacon do not seem to disagree, nor does either of them conceive induction as a process of reasoning from particulars to universals. There is no question that the direction of induction is from particulars; but in the precise sense in which induction precedes deduction—the sense in which both Bacon and Aristotle regard it as the source of axioms—they do not think it is a process of reasoning or a form of

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proof. As for deduction, it is questionable, at least for Aristotle, whether its direction can be described as from the universal to the particular. Aristotle seldom uses the word “deduction” as the name for that phase of thought which is complementary to induction. He speaks rather of demonstration. Demonstration takes place through the various forms of reasoning which he calls “syllogisms.” As the chapter on REASONING explains, these are collections of premises each of which yields a conclusion by valid inference. In the most perfect forms of reasoning, the conclusion is as universal as its premises, and though there are syllogisms in which a particular proposition can be demonstrated from a universal and a particular premise, it is seldom the case that from exclusively universal premises a particular conclusion can be validly drawn. The statement that deduction is reasoning from universals to particulars certainly does not seem to fit Aristotle’s theory of the syllogism, and even less his conception of scientific demonstration, the aim of which is to prove universal, not particular, propositions.

“WE LEARN EITHER by induction or by demonstration,” Aristotle writes in the Prior Analytics. “Demonstration develops from universals, induction from particulars.” In the Posterior Analytics he says that the ultimate premises of demonstration must be primary or basic truths. A basic truth is an immediate proposition—what is sometimes called a “first principle” or an “axiom.” Since in his view “an immediate proposition is one which has no other proposition prior to it,” the basic premises cannot be demonstrated. Whence come these primary premises which are indispensable to demonstration but which demonstration cannot establish? Aristotle’s answer is that “we know the primary premises by induction.” In another place he says, “it is by intuition that we obtain the primary premises.” The word “intuition” indicates an essential characteristic of the sort of induction which, because it is not itself a form of reasoning, can be prior to all reasoning and must be, in order to supply the premises from which reasoning proceeds. Reasoning is discursive. It is a process involving steps. One proposition is drawn from another by the mediation of a third. Intuition, in contrast, is immediate. Like an act of seeing, it apprehends its object at once and directly. When Aristotle speaks of induction as a kind of intuition, he implies, therefore, that it consists in the immediate grasp of a universal truth. The proposition thus held he calls “immediate” precisely because it can be known intuitively and in no other way. Intuitive induction, as opposed to what may be called “inductive reasoning,” consists in seeing the universal in the particular. When what is seen is expressed in the form of a proposition, the universal implicit in the known particulars is made explicit. [806-807] Induction and intuition are, however, not identical for Aristotle. In one passage in the Prior Analytics he considers syllogistic induction, which can hardly be called “intuitive.” And in the Ethics, where he discusses intuitive reason, he distinguishes between two sorts of primary truth that can be known by intuition. “Intuitive reason,” he writes, “is concerned with the ultimates in both directions; for both the first terms and the last are objects of intuitive reason and not of argument, and the intuitive reason which is presupposed by demonstrations grasps the unchangeable and first terms, while the intuitive reason involved in practical reasoning grasps the last and variable fact, i.e., the minor premise. For these variable facts are the starting-points for the appre-hension of the end, since the universals are reached from the particulars; of these therefore we must have perception, and this perception is intuitive reason “ This applies to theoretic as well as practical knowledge. By intuitive reason, it seems, we grasp both the universal principles or axioms and the particular facts of sense-perception. As perception is intuition on the part of the sensitive faculty, so induction is an intuitive use of the intellect (though Aristotle attributes both to “intuitive reason”). These two forms of intuition are functionally related. The induction of universal truths from particulars is impossible without sense-perception, “for it is sense-perception alone

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which is able to grasp the particulars.” But, according to Aristotle, a single isolated perception does not give rise to an intuitive induction. Repeated perceptions of things of a certain sort—particulars of a certain class—are formed by memory into what he calls “an experience.” Because the experience refers, not to a single individual, but to a class of similar individuals, it provides the material for the mind’s intuitive act of induction. This theory of the role of experience in induction is more fully discussed in the chapter on EXPERIENCE. For our present purposes, the main point is that the universal, lying im-plicitly in the experience, is ready, as it were, to be extracted therefrom and made explicit. “Though the act of sense-perception is of the particular, its content is universal,” Aristotle writes. With the help of memory and experience, induction makes the latent universal manifest.

BACON’S CRITICISM of the logic of Aristotle seems to rest on two counts: first, he complains of Aristotle’s over-emphasis on syllogisms, whether they are used dialectically or demonstratively; and second, he charges Aristotle with a superficial understanding of induction. One of the chief efforts of the Novum Organum is to correct the latter mistake. “There are and can exist,” says Bacon, “but two ways of investigating and discovering truth. The one hurries on rapidly from the senses and particulars to the most general axioms, and from them, as principles, and from their supposed indisputable truth, deduces the intermediate axioms. This is the way now in use. The other constructs its axioms from the senses and particulars, by ascending continually and gradually, until it finally arrives at the most general axioms, which is the true but unattempted way.” Where Aristotle proposes that only the primary truths or first principles be established by induction, while all the others (which Bacon calls “intermediate axioms”) are to be derived from them by demonstration, Bacon urges a method of induction which shall mount gradually from the least general to the most universal propositions. We should not “suffer the understanding to jump and fly from particulars to remote and most general axioms.” We should “proceed by a true scale and successive steps, without interruption or breach, from particulars to the lesser axioms, thence to the intermediate (rising one above the other), and lastly, to the most general.” According to this theory, induction can intuitively draw more general from less general truths, as well as the least general truths from the particulars of perception. It might seem at first as if there were no place for deduction in the development of science. But Bacon divides the study of nature into two phases: “the first regards the eliciting or creating of axioms from experiments, the second the deducing or deriving of new experiments from axioms.” Here too there seems to be a crucial difference between Bacon and Aristotle. This difference is indicated by Bacon’s emphasis upon experiments both as [807-808] the source of inductive generalization and also as that which is ultimately derived by deduction from axioms. The difference between experience (which Aristotle makes the source of induction) and experiment is more than verbal. “The axioms now in use,” Bacon contends, “are derived from a scanty handful, as it were, of experience, and a few particulars of frequent occurrence.” There has been too little attention given to negative instances, that is, of cases which seem to run counter to the generalization being formed. “In establishing any true axiom,” Bacon insists, “the negative instance is the most powerful.” The chapter on EXPERIENCE dwells on the difference between ordinary experience and planned experiments. Where Aristotle seems to be satisfied with the ordinary experience which arises from the perceptions of men in the course of daily life, Bacon thinks it does not suffice. Because it is haphazard, it fails to collect the variety of instances, both positive and negative, upon which genuine and solid inductions can be founded. Unusual and special experiences must be sought out, and the effort must be made to invent experiences which do not arise spontaneously. For this, experiment or the production of experiences is necessary. Bacon thinks we must, “by every kind of experiment, elicit the discovery of causes and true axioms.”

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TWO CONSEQUENCES FOLLOW from the several differences we have noted between Aristotle’s and Bacon’s theories of induction. In the first place, Aristotle does not seem to think that induction can be methodically prescribed by logical rules. It is a natural act of intelligence to draw universals from experience. Though men may differ in the readiness of their native wit, the induction of the primary truths, which are the axioms or first principles of science, does not require special genius nor can it be improved or rendered more certain by following rules. Precisely because it is intuitive rather than discursive, induction, unlike reasoning, cannot be regulated by rules of inference such as those which govern the syllogism. Without disagreeing that it is intuitive rather than argumentative, Bacon seems to think that induction requires the practice of the most detailed and precise method. Not only must the various ascending stages of induction be regulated by observance of an order of generality, but the making of experiments and the collection and arrangement of particulars, “forming tables and coordinations of instances,” must be governed by a complex set of rules. The twenty-seven tables of instances, set forth in the second book of the Novum Organum, constitute the heart of Bacon’s method of induction. This new method “of discovering the sciences,” he observes, “levels men’s wits and leaves but little of their superiority, since it achieves everything by the most certain rules.” In the second place, since genuine induction depends for Bacon upon ample experiments, it belongs primarily to the method of the experimental sciences—the physical or natural sciences in which experimentation is possible. Though the first principles or axioms of arithmetic and geometry may be learned by induction, the method of gradual ascent from experiments through intermediate generalizations does not apply to mathematics. Here we may have the beginning of the notion that only the experimental sciences are primarily inductive, whereas other sciences, like mathematics, are primarily deductive. But such a division of the sciences does not accord with Aristotle’s theory of induction. He thinks mathematics and metaphysics require induction for their foundation no less than physics and in no different way; if anything, induction is of the greatest importance for metaphysics, because all its principles are indemonstrable, whereas some of the principles needed in mathematics and physics can be demonstrated in metaphysics. Yet no science is peculiarly inductive, just as none stands in a special relation to experience. All depend equally upon experience for the induction of the primary truths on which their demonstrations rest. Descartes seems to fall somewhere between Aristotle and Bacon. He regards arithmetic and geometry as more certain than the physical sciences, because mathematics is largely developed by deduction, whereas the study of nature depends upon induction from experiments. In this lies the superiority of mathematics. “While [808-809] our inferences from experience are frequently fallacious,” Descartes writes, “deduction, or the pure illation of one thing from another . . . cannot be erroneous when performed by an understanding that is in the least degree rational.” Nevertheless, Descartes does not exclude induction as the source of the axioms of mathematics or, for that matter, of metaphysics; he only excludes the kind of induction which depends upon experiments. Such axioms as when equals are taken from equals the remainders are equal or the whole is greater than any of its parts are products of induction, as may be seen, he points out, from the fact that a child can be taught these general truths only “by showing him examples in particular cases.” Similarly, the metaphysical truth in the proposition I think, therefore I exist cannot be learned by deduction or syllogistic reasoning. The axiom that to think is to exist has to be learned by induction “from the experience of the individual that unless he exists he cannot think. For our mind is so constituted by nature that general propositions are formed out of the knowledge of particulars.” FROM THE FOREGOING we can gather that different theories of induction may be, in large part, theories about different kinds of induction. Common to induction of every sort is the motion of the mind from particulars, apprehended by sense, to general propositions or

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universal notions. But the character of the induction, or its conditions and method, may differ according to the precise character of its source: (1) whether it arises from ordinary sense-experience or from planned experiments; and (2) whether it is based upon a single experiment or upon an enumeration of instances. There remains the most radical distinction in type of induction: (3) whether it is intuitive or discursive accomplished by an act of immediate insight or by a process of reasoning from premises to a conclusion. These three divisions cross one another to some extent. Descartes, for example, seems to regard the complete enumeration of a series of connected facts as a way of drawing a general conclusion about their connection. That he has inductive reasoning rather than intuitive induction in mind, we learn from his statement that “by adequate enumeration or induction is meant that method by which we attain surer conclusions than by any other type of proof, with the exception of simple intuition.” Pascal seems to be making the same point, when he says that “in all matters whose proof is by experiment and not by demonstration, no universal assertion can be made except by the general enumeration of all the parts and all the different cases.” Bacon, on the other hand, always thinks of induction as intuitive generalization, and therefore maintains that “induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, and is exposed to danger from one contradictory instance.” The elaborate procedure which Bacon proposes for collating instances stresses, not completeness of enumeration, but an examination of their relation to one another and, in the light thereof, an interpretation of their significance. Mill’s four or five methods of induction bear a close resemblance to Bacon’s more numerous tables of instances; but Mill’s methods are attempts to formulate the rules of inference for inductive reasoning, whereas Bacon’s rules are rules, not of reasoning, but of tabulating the particulars from which intuitive generalizations can be formed. On Mill’s view of induction, it may be questioned whether induction from an exhaustive enumeration is induction at all, for it seems to result in a summary of the facts enumerated rather than a generalization from particulars. Where there is no inductive leap, there is no induction. Where the inductive leap does occur, however, it seems easier to understand it as an intuitive act—a seeing of the universal in the particular—rather than as a process of reasoning. Each of Mill’s methods requires a rule of inference which is itself a universal proposition. His critics have asked, Whence come these universal propositions about the relations of cause and effect or about the order and uniformity of nature? They point out that he cannot answer that these propositions are themselves conclusions of inductive reasoning without begging the question.

SUCH CRITICISM of inductive reasoning does not seem to apply to Aristotle’s conception of [809-810] it, for with him it is not, as with Mill, distinct in form from the syllogism. It is simply a distinct type of syllogism, which consists in reasoning from effect to cause rather than from cause to effect. Nor does the observation that an inductive inference cannot be more than probable apply to what Aristotle means by an inductive syllogism. The certainty or probability of non-syllogistic induction depends on the source of the inference—whether it derives from a single specially constructed experiment or from an enumeration of particular instances, with or without a statistical calculation based on their frequency. The conception of a perfect experiment implies that the operation of a universal law can be exhibited in a single case. It is almost as if the controlling aim of the experiment were to make the universal manifest in the particular. Newton’s experiments on reflection and refraction seem to be of this sort. From them certain laws of optics are directly induced, even as, according to Aristotle and Descartes, the axioms of mathematics or metaphysics can be directly induced from simple experiences, available to a child or familiar to all men. Yet Newton does not think that the inductive establishment of such laws is as certain as demonstration.

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The analytic method, he writes, “consists in making experiments and observations and in drawing general conclusions from them by induction. And although the arguing from experiments and observations by induction be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much stronger, by how much the induction is more general. If no exception occur from phenomena, the conclusion may be pronounced generally; but if at any time afterwards any exception shall occur from experiments, it may then begin to be pronounced with such exceptions as occur.” Because it must depend on inductive generalizations from experience which, in his view, can never be certain, Locke doubts that physics can ever become a science. “I deny not,” he writes, “that a man, accustomed to rational and regular experiments, shall be able to see further into the nature of bodies and guess neither at their yet unknown properties, than one that is a stranger to them; but yet, as I have said, this is but judgment and opinion, not knowledge and certainty. This way of getting and improving our knowledge in substances only by experience and history, which is all that the weakness of our faculties in this state of mediocrity . . . can attain to, makes me suspect,” Locke concludes, “that natural philosophy is not capable of being made a science.” Hume offers two reasons for the inconclusiveness and uncertainty which he thinks qualify all our generalizations or inductions from experience. The first calls attention to the fact that, unlike mathematical reasoning, inferences from experience in the realm of physical matters depend on the number of cases observed. “The conclusions which [reason] draws from considering one circle,” he says, “are the same it would form upon surveying all the circles in the universe. But no man, having seen only one body move, after being impelled by another, could infer that every other body will move after a like impulse.” The principle “which determines him to form such a conclusion” is, according to Hume, “Custom or Habit”; and precisely because inductive generalization is an effect of custom rather than of reasoning in the strict sense, the strength of the induction or the force of custom varies with the number of cases from which it arises. “After the constant conjunction of two objects heat and flame, for instance, weight and solidity—we are determined by custom alone to expect the one from the appearance of the other. This hypothesis,” Hume maintains, “seems . . . the only one which explains the difficulty, why we draw, from a thousand instances, an inference which we are not able to draw from one instance, that is in no respect different from them. Reason is incapable of any such variation.” Since all the relevant cases can never be exhaustively observed, the inference from a customary conjunction must always remain uncertain, no matter how high a probability it derives from the multiplication of like instances. To this first point, concerning the dependence of the probability of generalizations from experience upon the frequency of the observed instances, Hume adds a second point about the similarity of the cases under obser- [810-811] vation. Analogy, he says, “leads us to expect from any cause the same events, which we have observed to result from similar causes. Where the causes are entirely similar, the analogy is perfect, and the inference drawn from it is regarded as certain and conclusive. . . . But where the objects have not so exact a similarity, the analogy is less perfect, and the inference is less conclusive; though still it has some force, in proportion to the degree of similarity and resemblance.” The absence of perfect similarity is Hume’s second reason for the inconclusiveness or uncertainty of inductive generalizations. The contrary supposition that one case can be perfectly representative of an infinite number of similar cases may explain why Aristotle seems to think that induction is able to produce the primary truths or principles of science with a certitude which gives certainty to all the demonstrations founded on these axioms. Another explanation of Aristotle’s view may be found in his distinction between scientific and dialectical induction. He regards the former as based on the kind of common experience which, unlike even the best experiment, admits of no exceptions. In contrast, dialectical induction, or the still weaker form of induction which he calls “rhetorical,” is based on an enumeration of cases (which may not be

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complete) or upon a single example (which provides no safeguard against possible exceptions). In its dialectical form, the inductive argument proceeds from a number of particulars taken for granted. Aristotle offers this example of dialectical induction: “Supposing the skilled pilot is the most effective, and likewise the skilled charioteer, then, in general, the skilled man is the best at his particular task.” In its rhetorical form, no more than a single example may be used, as when the orator generalizes that honesty is the best policy from the story of a particular individual who was finally rewarded for his virtue. In both forms, the inductive generalization is at best probable; and it is more or less probable according to the soundness of the suppositions or the examples from which it originates to be tested only by extending the enumeration of particulars. But if an induction is merely probable in the first place, it can only be made more probable, it can never be made certain, by multiplying cases or by increasing their variety. Aristotle’s theory of dialectical induction thus seems to have a bearing on the probability of induction from limited experiments (or from a single experiment whose perfection is not assured) and of induction from the frequency or variety of observed instances. The other point to be noted is that Bacon’s basic rule of gradual ascent from particular cases through less general to more general propositions seems to be relevant to dialectical induction, but not, on Aristotle’s view, to that kind of induction which produces the axioms or principles of science.

§

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VII. THE DEFINITION OF INDUCTION.

Cf. Michael Augros, “Logic Notes”. The Logic of the Third Act (Spring 1995):

INDUCTION is a progression from statements about like singular things to the universal statement.12

Cf. Michael Augros, Notes on the Posterior Analytics, Book I:

Chapter 18

Concerning the ignorance of simple (immediate) negations (St Thomas, Lectio XXX). If any sense power is lost, so too is some part of scientific knowledge, since “we learn either by induction or by demonstration” (eiper manthanomen e epagoge e apodeixei, 81a40), and demonstration proceeds from universals, whereas induction proceeds from particulars (or individuals) into universals. Hence demonstration, having first principles, requires another way of knowing, namely of knowing the first principles, which is induction (more to be said in II.19). And the first principles are the self-evident and immediate propositions and the self-evident natures (simple truths and first concepts, manifested in axioms and definitions). These are gathered up from sense experience. But, because someone might doubt this in the case of abstract things, Aristotle mentions that even abstract things (aphairesios) can be grasped only by induction (81b3). E.g. someone might think that mathematics, which demonstrates about things not found in nature and does not resolve to sense, does not arise out of sense experience (e.g. Kant). But that is not so, since math demonstrates about things constructed in the imagination, and there is no imagination without prior sense experience. And even if the mathematician studies these things separately (e.g. squares) from material sensible things which do not exist separately from them, still he is studying something which he gathered from sense experience (quantity) and merely considering it apart from the particular natures in which it is found.

Cf. Ibid., Book II, ch. 13:

Chapter 13 <…>

2) DEFINING BY COMPARISON. P 222 there is a road to definition by the comparison of similar and dissimilar things. This is proportional to induction, in which one proceeds from individual statements to universal ones, or from less universal statements to more universal ones. Here one proceeds from individual things sensed to a universal grasp of what they are, or from less universal examples of a thing to a more universal grasp of what they all have in common. P 224 one must arrive at something common, because the definition regards the universal (cf. Heraclitus, “one must become strong in what is common to all). This method has two advantages: a) moving from the less common to the more common is natural to us and easier. One does not start by examining everything which can be called “brave” or whatever it is that is to be defined, but by examining only some such things. b) One thus avoids equivocation more easily, because one is beginning with lower universals. E.g. it is easy to think “being” is universal, but not if one begins with “dog”, “cat”, “tree”, “blue”. One sees a difference there in the very meaning of the word “thing”, that blue is a “thing” in a different sense, since it is something of a thing (of a “thing” in the first sense).

12 E.g., from such statements as, “This fire burns” and “This fire burns” we proceed to the universal, “Every fire burns.”

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Cf. Michael Augros, “Spring 1993 Scrapbook,” Logic, n. 10 (Scrapboo.1):

How should one go about finding a definition for the soul (or just “finding out what the soul is”, which is desirable because we must know this to determine whether or not the human soul is immortal)? Almost anyone would admit it is hard to tell where to begin. But in logic one learns (Posterior Analytics) that there are two ways of approaching a definition. One is proportional to induction to a universal statement, namely the approach from ex-amples in which one separates out what is common to them. The other is by division of a word into its meanings and of a genus into its species. Already logic has given us a way of proceeding. Which shall we choose? Since the soul is not known directly, but through other things, then it is not likely that the road of comparing examples will be helpful, since this road is useful precisely because it brings us from what is closer to sense to what is further. Hence, if the soul is not close to sense, it seems we must approach a definition of it by division.

Cf. Duane H. Berquist, “Notes From the Berquist Seminars,” Logic, n. 25 (Duane.1):

3/17/93 In Posterior Analytics II, we learn that there are two roads to definition. One is the division of the genus, and the other is “per similia et dissimilia”, by comparison of many examples of the “definitum”, the thing to be defined. One arrives at a definition this second way by separating out what the examples have in common. This is proportional to induction, in which we see many instances of a proposition and come to see or suspect that it is true universally. This way is more proportioned to us, since we come to know through the senses, which know the singular and not the universal. Because it is so natural, we often fall into the mistake of giving examples themselves as a definition, without separating out what they have in common, as Meno does when trying to define virtue, or as Euthyphro does when trying to define piety, or as Theaetetus does when trying to define EPISTEME.

Cf. Ibid., Logic, n. 8 (Duane.2):

TWO ROADS TO DEFINITION. n 213. There are two roads to a definition (this is found in the Posterior Analytics). One is the comparison of things like and unlike, which is proportional to induction, and so is closer to sense and easier for us, and the other is division, which is proportional to syllogism, and so is harder for us but more rigorous in itself. Now it is impossible to have inductions conclude about angels (even more so about God, since there is only one), and likewise the soul does not admit of the road of comparison. That is why Aristotle adopts the harder road.

Cf. Michael Augros, “Notes on the Posterior Analytics,” Book II, ch. 19:

Chapter 19

Aristotle sums up that demonstration has now been treated. It remains to return to a question that was proposed at the beginning of the first book, which is “how do we come to know the truth of the first principles?”. If one has science, one must know the first principles with certitude, and since they are first and immediate (one must come to a stop in demonstrating), therefore one cannot know them by demonstration. So how are they known? P 235 com-mentary: to have scientific knowledge of demonstration, one must know how the principles are known, since scientific knowledge of anything requires knowledge of its principles, causes, and elements (and the first principles are causes of demonstration, and also they can be called “elements” since they are immediate, i.e. indivisible: Aristotle even calls them “atomos”).

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There are three questions about the first principles. 1) Is there one knowledge of all first principles? 2) i.e. is there a science of all first principles or is there none, or is there science of some but not of others? 3) Does habitual knowledge of principles come to be in us, or are we born with it?

3) If the principles are not acquired, then we are not aware (early on) of the principles which are more certain than the conclusions which we draw from them later on, which conclusions cannot escape our notice. But if they are acquired, then how can we maintain that learning proceeds from pre-existent knowledge?

Hence (99b30) we did not always possess the first principles, nor did we get them from absolute ignorance without some kind of pre-existent knowledge and some pre-existent natural principle. We must have in the beginning, before we know the principles, some knowing power, which cannot be just sense, because the first principles—both simple concepts and truths—are universal.

As in the Metaphysics, Aristotle climbs the ladder from imperfect knowledge closer to sense toward perfect knowledge in reason. The lower animals have external senses only. Higher animals have memory. Man has experience (empeirias, 100a6), which is the ordered collection of like memories of singular things sensed. Experience is found only in man, since it requires an ordering and comparing of like things, and only in man is there a power capable of this (universal reason alone knows order and relation as such), which orders the singulars within the internal sense called particular reason. The experience arises in that internal sense power as in a subject, but the agent is universal reason (which is one in subject with particular reason: both belong to one individual man). Within this experience, the universal reason considers what is common to many, leaving aside what is peculiar to each.

Hence the mind arrives at the universal by attending to what is common apart from the individuals, so that (p 238) the universal is the “one outside the many” not as existing apart from the individuals, but as a common thing being considered by reason without considering the peculiarities and the changeable individuals in which it is found.

A problem arises that we have here the senses giving more than they have, i.e. the univer-sal is made known to the universal reason by the senses, which do not know the universal. One cannot teach what one does not know. But the senses do not exactly teach reason the universal, but rather bring to it the materials out of which the universal is contained confusedly, something as form is in the ability of matter, since what is common is found there, but it is there mixed with what is peculiar. Reason discerns and separates out what is common and essential.

Aristotle, in this chapter, answers a problem (by resolving outside of logic, in fact) considered in a purely logical way in I.3.Are all statements known with certitude demon-strated, or are some undemonstrated? I.3 shows that there are some undemonstrated, and II.19 explains how they are known with certitude (if not by demonstration, then by what?).

We come to know the self-evident principles of the sciences by seeing the identity of the predicate and the subject or by seeing the union of the two resulting from their definitions. E.g. “man is an animal” is seen to be true of necessity and universally because the predicate and subject name identical things; the predicate is in the definition of the subject. And “whole is greater than any of its parts” is seen to be true not because “greater than any of its parts” is in the definition of “whole”, but because if it were not so, then there could not be more than one part in the whole, and the whole, by definition, is what is composed of parts.

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(This second case, then, resolves in some way, not exactly by demonstration, to the principle about contradiction.)

But how does one come to know the terms in the statements? How does one come to know “man”? Aristotle says we separate out what is common from a gathering of many similar memories of something, which gathering is called an experience of the thing. But how can we gather similar things together in memory, from which to pick out what is common to them, unless we already see what is common to them? In fact, animals have a similar gathering capacity (they too have “experience” of things, though not in exactly the same way). Knowledge of similarity is not required on the part of the one receiving similar things; something like instinct groups them in animals. E.g. a coin slot in a machine accepts only certain things, but not because it knows the appearance of coins and their similarity, or because it sees the dissimilarity of slugs (but rather because it was designed by something which does see these things). So too with a net or a filter. Likewise particular reason in man, which works in conjunction with universal reason, gathers together things stored in memory which are of sensible similarity, without itself knowing the similarity as such (only universal reason can make comparisons and see relation as such). Of course, after a certain amount of experience, the universal reason can command the particular reason (and other interior sense powers) to gather certain things from memory according to a principle and for a purpose known only to universal reason.

Karl Popper, in the beginning of his book The Logic of Scientific Discovery, says that induction is never certain, nor is it even useful for probability. But induction (the passage from particular statements to universal ones) and the process proportional to it for universal terms (the passage from sense experience of a thing to a grasp of what it is) can arrive at certitude, although the certitude does not arrive out of the form of the induction (as in the case of a demonstration), but out of the matter about which the induction is made. E.g. induction that all snow is white or that all water boils at 100 degrees celsius at a given pressure is certain not because of the logical form of the induction, but because one sees that these things flow from the nature, and one knows that nature is determined to one.

§

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VIII. ON THE FEIGNING OF HYPOTHESES.

1. The genus of feigning.

Cf. St. Thomas Aquinas, Qu. Disp. de Malo, q. 8, art. 3, obj. 10 (tr. B.A.M.).

Feigning pertains to reason; for to feign is to represent, which belongs solely to reason, as the Philosopher says in his Poetria.

N.B. By Aristotle’s Poetria St. Thomas means the presentation of the Philosopher’s Po-etics as it is found in Averroes’ Determinatio in Aristotelis Poetria, the Latin translation of the Commentator’s work by Hermannus Alemannus, published in 1256.

2. The definition of feigning and its division.

Cf. St. Thomas Aquinas, In IV Sent., dist. 4, q. 3, art. 2b, ad 1 (tr. B.A.M.):

It must be said that there is feigning properly when someone shows something by word or deed that is not in the thing in truth. But this happens in two ways. In one way, when from this intention something is said or done so that something other than the truth the thing has is shown. In another way, when something is shown that does not have the truth of the thing in word or deed, even if it not be said or done on account of this.

3. When our feigning is no lie, but some figure of the truth.

Cf. St. Thomas Aquinas, Summa Theol., IIa-IIae, q. 111, art. 1. ad 1 (tr. English Dominican Fathers, rev. B.A.M.):

As Augustine says in his book of Questions on the Gospels, not everything we feign is a lie. But when our feigning is referred to some signification, it is no lie but some figure of the truth. Otherwise, all the things that are said figuratively by wise and saintly men, or even by the Lord Himself, are to be reputed lies, since, according to the customary understanding, the truth does not consist in such sayings. Now just as things said are feigned without lying, so also are things done in order to signify something else.

4. The feigning produced by figurative expressions.

Cf. St. Thomas Aquinas, Summa Theol., IIa-IIae, q. 111, art. 1. ad 1 (tr. B.A.M.):

And he gives the example of figurative expressions: in them a certain thing is feigned, not that it be asserted to exist in this way, but we propose it as the figure of another thing that we wish to assert.

5. The nature and use of hypothesis in natural science.

Cf. Aristotle, Metaphysics XIII. 7 (1082b 2-3) (tr. W. D. Ross):

In general, to posit units as being different in any manner is absurd and fictitious (by fictitious I mean that which is forced to agree with an hypothesis)….

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For the sort of assumption Aristotle’s claim about the unchanging nature of the heavens presupposes, cf. St. Thomas Aquinas, Summa Theol., Ia, q. 32, art. 1, obj. 1 (tr. B.A.M.):

To the second it must be said that a reason is adduced for something in two ways. In one way, in order to prove some root in a way that suffices, as in natural science a reason is adduced for satisfactorily proving that the motion of the heaven is always of a uniform velocity. In another way a reason is adduced which does not sufficiently prove a root, but which shows a root already laid down to agree with an effect following on it, as in astronomy a reason is given for eccentrics and epicycles from the fact that, when these are laid down, the sensible appearances of the heavenly motions can be preserved—not that this reason suffices as proof, since perhaps they could be preserved when something else has been laid down.

Note that the “reason adduced” in the second way (e.g. given a “root” already laid down, that which shows the root to agree with the effect following on it) is usually called an hypothesis. Compare this to Aristotle’s definition of the fictitious: what is forced to agree with an hypothesis. In the latter case, one describes nature in such a way that is not rational, i.e. that does not respect her order and manner of working.

In sum:

“In another way a reason is adduced which does not adequately prove a root, but which shows a root already laid down to agree with an effect following on it.” I.e. one argues from eccentrics and epicycles which, being laid down, are able to explain the movements of the heaven. Likewise, Newton lays down his three Laws of Motion in order to explain certain things about motion. (cf. Mike Augros’ letter to Dave Augros on Newton: “some are false…”)

the root laid down: eccentrics and epicycles what follows from it: the appearances of the celestial motions, which are thereby

“preserved”

Now just as Ptolemaic astronomy laid down as root the existence of eccentrics and epi-cycles, which shows an effect following on it to agree with it, so, too, Aristotle formed the hypothesis that if the heavenly bodies were of such and such a substance, they would appear in such and such a guise (that is, as “always running” in their courses, without un-dergoing any discernible changes down the eons, so far as our inherited records indicate); but they do so appear, etc. Therefore, etc.

Cf. Charles De Koninck, The Unity and Diversity of Natural Science, Mélanges à là Mem-oire de Charles De Koninck, pp. 5-25 (excerpt):

We must consider still another difficulty, one which is more obvious in our time, and that seems to justify the distinction between philosophy of nature and natural science. The ancients did not respect the prodigiously fruitful role of fictions—“logical fictions”, as Bertrand Russell calls them. Nor did Galileo or Newton, for the matter of that; a fact ironically brought out by Newton’s famous hypotheses non fingo. (Newton actually con-trived most fruitful fictions, though he failed to realize that they were fictions.) The contemporary mathematical physicist knows that he can probe into the world of nature only

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by means of mental constructions suggested in part by experience, in part by mathematics.13

They are fictions in the strict sense of this term, whose power we must not underrate. The atom, for instance, is largely a logical fiction. If you have any doubts, look at what has happened to atoms since Dalton’s days. (I say “largely”, for in physics the mental constructs must have some foundation in experience and experiment, else they could hardly lead to further knowledge of nature)…. Now, all this faces us no doubt with a deep enough cleavage between diverse modes of knowing the things in nature. But does this cleavage restrict natural philosophy to our initial gropings under investigation? What we are agreeing to call philosophy of nature is experi-mental too, though not quite after the manner of mathematical physics nor even of advanced biology. I pointed out long ago that in the study of nature we must distinguish between strictly scientific knowledge (in Aristotle’s sense) and that which is called dialectical, as providing no more than an opinion. Now, opinions are still enunciated in words, and are in fact true or false if it be speculative knowledge that we mean to express. Notice, however, that an opinion is not a fiction in the strict sense of this term. It is, at bottom an inquisitive proposition. The opinion that “the world is eternal” still leaves open the question whether the world really is or has to be eternal. We can unfold what we mean by “world” and by “eternal”, but can we in truth say the latter of the former? The notions of “world” and “eternal”, though vague, have a relatively stable meaning. What we are ques-tioning is not their meaning, of course, but their connection in a proposition. Is such a proposition necessary? Is the eternity of the world a fact? But in mathematical physics, when words are used to describe, not how things are in fact, but merely how a certain symbolic construction has been laid down, e.g., that of the atom, we must be aware that, unlike the terms used in a statement about nature, the symbols, the construction, and the names we choose to employ for the purpose of communication do not have a stable meaning. The only stable meaning the word “atom” ever had was that of “indivisible”. In other words, we are now entitled to question not merely the connection of the terms, but the very terms themselves. At any rate, these are utterly provisional, whereas what “world” or “eternal” stand for are not.

Note that St. Thomas calls an ‘hypothesis’ what De Koninck calls a ‘(logical) fiction’.

Cf. Duane Berquist, Commentary on the Categories:

6/17/96

…The third thing that I wanted to say was in imitation of Msgr. Dionne’s comparison of the Prior Analytics to the De Anima, that these things are considered in quadam abstractione, but not in a complete abstraction, from things. Thomas will say sometimes that logic is not about things, but it’s about syllogisms, enunciations, and so on. But other times he will say that logic is about things in some way. So there is not a complete abstraction there from things, and there can’t be if you mean by “logic” something which is ordered to knowing things. How could you abstract from things altogether, with no order to them, if what you are talking about is for knowing things? Secondly, if this is going to be a sure guide, if it is going to be knowledge, and not just fiction, it has to have a foundation in things. It doesn’t have to have a proximate foundation, but it does have to have a remote foundation in things. If something has no foundation whatsoever in things, either remote or proximate, Thomas says you’re talking about a “chimera”, a fiction. Logic would be fiction if it had no foundation in things.

6/18/96

13 This evidently is Dr. De Koninck’s definition of “fiction”.

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….A second reason is that logic is not only ordered to knowing things, but it’s a knowledge and art in the strict sense ordered to knowing things, and therefore it has to be something certain. It can’t be something that has no foundation in reality. It can’t be a chimera or a fiction. And therefore it has to have a foundation in things. So even when logic talks about naming, there has to be a remote foundation in things. Is there a remote foundation, say, in what a man is and what a horse is, that they could have a name in common, with the same speech about what they are? Is there a foundation in the things themselves? Yes. As for the man and the picture or painting of the man, there is a foundation there in the things for why they cannot have the same name “animal” in common with the same speech about what they are. So these are two birds that Aristotle kills there. At the same time, there is no problem in seeing what an equivocal or univocal name is once you’ve done what he’s done. From those very same things you could see what he would mean if he’s going to talk about univocal names, or names that are genera or species, and that these are going to be distinguished into the ten groups, when they’re said without intertwining. So Aristotle has indicated that logic is ordered to knowing things, that it has a foundation in things, but at the same time, the third bird, which you can obviously see from what he’s saying what it would mean to speak about a univocal name, or an equivocal name. A fourth thing, which I haven’t mentioned yet, is that his procedure will help you to understand when you get to the division ton onton, of beings, well, what kind of name is “being”, which is said of substance and accident? It is said equivocally. And when you come to Chapter 4, you don’t say that man is virtue, but that man is virtuous, and you don’t say that man is courage, but that man is courageous, so something is being said denominatively. Well, we’ve talked about that in the first chapter. So maybe we’ve killed five or six birds.

6/19/96

In the second division he doesn’t say that it is a division “nominum”, of names, or “onomaton”. He says “of beings”. Why does he say that? For the same reason that he began from things in Chapter 1. And that is that logic, if it’s knowledge, and not fiction, it must have a foundation in things. There are interesting texts of Thomas, especially in the Sentences, where he speaks of how something can have a proximate foundation in things, like when you speak about man or dog, it can have a remote foundation in things, like when you speak about genus or species, or it can have no foundation in things, as when you speak about (as he says) a chimera, a fiction. In order for you to have truth and knowledge in the strict sense, you must have at least a remote foundation in things. Now, in natural philosophy you have a proximate foundation in things. But in, say, geometry, you have a remote foundation in things. And in logic you have a remote foundation in things. The proximate foundation is in reason itself. Now that’s brought out here beautifully, because we’re talking about “things as they are in our knowledge or reason”. “Things” is the remote foundation, and “as they are in our knowledge or reason” is the proximate foundation. And when we go on to distinguish things by the way that something is said of something, you can see the proximate foundation is there, because it’s universal, and in reason. But there is a remote foundation in things. See how subtle that is?

Cf. St. Thomas Aquinas, In I Sent., dist. 2, q. 1, art. 3, c. (tr. B.A.M.):

I reply that is must be said that, as was said above in the body of the preceding article, wisdom and goodness and everything of the sort are in every way one thing in God, but they differ in ratio. And this ratio is due not only to the one reasoning himself, but also to a property of the thing itself. For the evidence of this matter, in order that it be diligently explained, since the whole understanding of the things which are said in the first book depend on this, one must see four things:

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First, what a ratio is insofar as we say ‘things attributed differ in ratio’. Second, in what way a ratio is said to be or not to be in a thing. <…>

Regarding what pertains to the first point, one must bear in mind that ratio, as it is taken here, is nothing other than that which the intellect apprehends from the signification of a name: and this—in those things which have a definition—is the definition itself of the thing, according to what the Philosopher says: ‘the ratio which the name signifies is the definition’. But some things are said to have a ratio in the way mentioned which are not defined, such as quantity and quality and the like, which, since they are the most general genera, are not defined. And nevertheless the ratio of quality is what is signified by the name of ‘quality’; and this is that from which quality has what quality is. For this reason, he does not refer to whether those things which are said to have a ratio either have or do not have a definition. And so it is clear that the ratio of wisdom which is said about God is what is conceived from the signification of this name, although the divine wisdom itself cannot be defined. Nor yet does this name ratio signify the conception itself because this is signified by the name of ‘wisdom’ or by another name of the thing; but it signifies the intention of this conception, just as the name ‘definition’ and other names of second imposition do. And from this the second point is clear, namely, how a ratio is said to be in a thing. For this is not said as if the intention itself which the name of ratio signifies is in the thing; nor as if the conception itself to which such an intention belongs is in the thing outside the soul, since it is in the soul as in a subject—but it is said to be in the thing inasmuch as in the thing outside the soul there is something which corresponds to the conception of the soul, as the thing signified (corresponding) to the sign. For this reason, it must be understood that the conception itself of the intellect is related to the thing outside the soul in three ways. For sometimes what the intellect conceives is the likeness of a thing existing outside the soul, just as what is conceived from the name ‘man’; and such a conception has a foundation in the thing immediately, inasmuch as the thing itself from its conformity to the intellect makes it that the intellect be true, and so the name signifying that intellect is said properly of the thing. Sometimes, however, what this name [sc. ratio] signifies is not a likeness of the thing existing outside the soul, but is something that follows from the mode of intellect the thing which is outside the soul. And of this sort are the intentions which our intellect comes upon [discovers], as the thing signified by the name of ‘genus’ is not the likeness of something existing outside the soul; but from the fact that our intellect understands animal as (being) in many species, it attributes to it the intention of a genus; and for intentions of this sort, although there is no proximate foundation in the thing, but rather in the intellect—nevertheless, there is a remote foundation in the thing itself. For this reason, the intellect which discovers these intentions is not false. And the case is similar in all other things which follow from the mode of understanding, as in the abstraction of mathematicals and the like. But sometimes what is signified by the name does not have a foundation in the thing, either proximate or remote, as the conception of a chimera: since it is neither the likeness of something outside the soul, nor does it follow from the mode of understanding some thing of nature: and so such a conception is false. For this reason, the second point is clear, namely, that a ratio is said to be in a thing insofar as the thing signified by the name, to which the ratio happens to be, is in the thing: and this happens properly when the conception of the intellect is a likeness of a thing….

6. Supplement on Newton’s method: “Hypotheses non fingo”.

Cf. Michael Augros, Letter to David P. Augros:

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Concerning Newton…. He is a brilliant mathematician, and a marvelous observer, which two qualities make him an apt mathematical physicist. But he is a terrible philosopher of nature. Awful. What does that mean? It means he is not good at the demonstrative part of natural philosophy, at discovering and enunciating general principles, and, in a word, at studying nature in the medium of words rather than symbols. Already by Newton’s time, “science” has come to mean seeing necessary conclusions about nature, which necessary conclusions must follow not as spoken conclusions from spoken premises, but as numbers from a calculation. This is not a bad thing; but it is certainly limited, and it presupposes “science” in Aristotle’s sense of demonstration in speech. But I will overlook a more detailed account of what it means to say Newton is a bad philosopher of nature…, and I will speak a bit more at length about what it means for him to be an apt mathematical physicist. It means he is good at watching nature with an experimental eye, noticing regularities, and proposing quantitative rules of behavior (which can be mathematically deduced from simple laws) that match nature’s quantitative behavior very closely indeed. This done, his simple laws have a kind of likelihood to them, i.e. “If my laws were truly operative in nature, that is, if my laws express what is truly going on out there, then the following mathematical conclusions would also follow in nature, that is, these other more complicated things would also have to be going on. But, according to our measurements, these more complicated things are going on; nature is behaving in ways that match our descriptions, which descriptions followed from certain assumed principles. Therefore, those assumed principles are very likely.” Now Newton was not too clear about the probable nature of his mathematical physics. He might not have concluded that his principles are “very likely”, but that they are “true” simply speaking. He was really at the beginning of this method in physics, so one can hardly blame him. Why is the method of mathematical physics only probable? For two reasons.

1) From formal logic alone, we can see this. The method of mathematical physics (meaning by this the mathematical study of all natural things) is to propose or invent quantitative principles which you think might be operative in nature, then to see what would follow in observable phenomena if those principles were operative, and then to see whether or not the things which follow are in fact observed. In syllogistic form, this comes to affirming the consequent of a hypothetical statement, which gives no necessity to any conclusion: “If our principles are operative in nature, then the following will be observable, but the following is observable, therefore our principles are operative in nature.” Notice that this does not differ in logical form from “If he has stomach cancer, he is seriously ill, but he is seriously ill, therefore he has stomach cancer.” The conclusion simply does not follow. Now, although it does not follow, if there are fewer and fewer causes which could be responsible for the thing observed, the conclusion becomes more and more likely. Thus, if the only two diseases which could make one seriously ill were stomach cancer and lung cancer, the conclusion that he has stomach cancer, though not necessary, becomes quite probable. Likewise in mathematical physics, if one’s principles account for what is out there, and do so with great simplicity (and nature herself is simple, as Newton says in his philosophic rules in book III of the Principia), and predict or account for things which no one could predict or account for before, then one’s principles become all the more likely, but they are not known to be true and cannot be known as true by such a method. 2) Because measurement is essential to verifying that what one has predicted is in fact observed. What one predicts is concluded mathematically from exact mathematical assumptions. Thus we have exact quantitative values as the results of our theory. Can we be sure that the phenomenon we are measuring is exactly equal to the predicted result concluded from our assumed principles in the theory? No, because for all we know our standard of measurement (the second, the gram, the meter, etc.) is incommensurable with the thing measured. But a measure is that by which a quantity is made known, specifically by an act of counting: I know how long a yard is, and I know that the house is twenty yards, and so

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I know, by knowing the length and number, how long a house is. If it is 20.5 yards, then it is 41 unit lengths each equal to a half yard, since the half length has become the unit as soon as I started using decimal points. Thus a unit of measure is only such for magnitudes with which it is commensurable—for in the case of anything incommensurable with it, no matter how many subdivisions we might make, the thing measured will always foil us with a bit left over which remains unaccounted for, and so its exact magnitude remains unknown to us. Consequently, we can never be absolutely sure that what we have predicted is in fact what we are observing, since the predictions are mathematically exact, whereas our measurement cannot be (unless our unit of measure were a point—for this alone is “commensurable” with every magnitude—but that is impossible, since it does not measure a magnitude). For these two reasons, then—the logical structure of mathematical physics, and its essential dependence on measurement—mathematical physics is essentially probable, and perhaps very probable indeed, but it can never present the truth as known. We can be sure only that we are getting closer to the truth all the time with more and more accurate and simpler and simpler mathematical principles. So much for a general account of what Newton is up to. What about Newton’s principles in particular? Well, some of them are false, others are neither true nor false, others are true. Of those that are false, some are known to be false by demonstration, others are known to be false because what follows from them is in fact not observed in nature, although something very close to it is observed in nature (Newton didn’t have the instruments to tell the difference). Those that are known to be false by demonstration, such as the first law of motion, do not necessarily interfere with the likelihood of Newton’s conclusions (remember it is not a question of truth for the two reasons [given] above), since we may eliminate their falsehood by a small adjustment without rendering them useless for his purposes. E.g. “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it” is simply false. Uniform motion is not a state, nor could something be inclined toward an infinite straight line motion (demonstrable: see book VI, end of ch. 10 in the Physics for starters, but even should it be possible for something to be so inclined, it would require a mover of infinite power), which would have to be the case if the only thing which would slow down a body in uniform motion is some other body. Of course, all locomotion requires a bodily medium (demonstrable), and every bodily medium offers resistance (even on Newton’s account), but this is quite irrelevant, since although this means the principle cannot be verified in itself, still it might be verifiable in what follows from it. Newton thinks there is such a thing as absolute space (which we will get to in a moment) and that uniform motion does not require a cause, inclining him all the more to believe this principle. Now this principle is used right away in proposition I. But since it is demonstrably impossible on other grounds, it must be altered, yet without rendering it useless. It could easily be readjusted to “every body continues in its state of rest unless compelled [from] that state of rest by external causes. And every body in uniform motion endeavors to continue in uniform motion in a right line, diminishing in speed only after immense distance, except to the extent that it is compelled to change that motion by external causes. In other words, for all practical purposes of measurement and prediction power (and therefore likelihood), this statement is equivalent to Newton’s first law, but it does not have built into it any impossibility. Even given that what we observe in nature is exactly what follows from Newton’s principles (which is not the case by the way), still, his first law would not necessarily be true, since it could just as well follow from the law I put down. I could say “things continue long enough in uniform motion, without slowing down for any reason except external ones, so that we observe what we observe”, and yet a body would begin to slow down after a great long while and even then only a very little bit because of something internal, which fact, although unobservable, is demonstrable (that is, a body is itself resistant to motion, even uniform motion).

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Now someone might complain that my provisos are a bit complex, whereas Newton’s first law is much simpler. True. But, again, Newton’s first law is demonstrably impossible (a physical body cannot tend of its own accord to move along an infinite straight line path), whereas the above more complicated formulae is not impossible. However, if such complexities are required in Newton’s system to avoid impossibilities and for it to remain consistent with nature, this indicates his principles and conclusions are not exactly in keeping with nature. And that, we know since Einstein and others, is true. E.g. Newton’s laws of gravitation seemed to explain the motions of heavenly bodies (although even that is not so: the rings about Saturn are left unaccounted for, and so too the duration of the sun—why didn’t it burn out a long time age?, and so too Mercury’s precessing elliptical orbit), but they certainly could not explain the tremendous stability of the parts of an atom. If one thinks of the atom, as a Newtonian who knows it has parts certainly must, as a small solar system of billiard balls, then it is impossible to see how atoms remains the atoms that they are for any length of time. If our solar system collided with another, we would be in big mess, according to Newton’s laws. But atoms rub each other all the time, and vibrate wildly, and remain intact nonetheless. The answer is that energy comes in discreet quanta, part of quantum theory, as opposed to Newton for whom energy and force comes in a perfect continuum. There is an abundance of other phenomena for which Newton cannot account—no need to go into it now. Another Newtonian principle which is demonstrably false is that there are such things as absolute space and time. Absolute time is not necessary since the ubiquitous identity of the “now” (that is, it is the same “now” everywhere in the universe) can be accounted for by a unity in the first bodily cause of all motion, or perhaps by a unity of order in the spatial relations of all bodily things. Absolute space is not necessary since the existence of motion that is not merely relative motion is intelligible in the light of a finite universe (whereas Newton thinks it is infinite, which is again demonstrably impossible). Absolute time and space, then, are demonstrably impossible things, and the very things for which they are posited in the first place may be explained on Aristotelian principles. As for those principles which are seen to be false because they don’t account for things that Einstein has predicted, etc., this shows that although nature operates very nearly as Newton describes, his principles are not quite true to nature. As for those which are neither true nor false, I have in mind some of his definitions, in which he is assigning quantitative meanings to certain terms. This is certainly legitimate; and at time Newton does it well, at others, badly. Let me give an example from Descartes, who says that the quantity of matter, or mass, is nothing other than the volume of a body. Now if that is what you want “mass” to mean, OK. Can’t stop you, pal. But then why not just use the word “volume”? We do have some vague grasp of what “mass” means, which we all intend by the word, and which is not irrelevant to mathematical physics. It is just this which we wish to quantify, and which Descartes overlooks. This is not so much falsehood as missing the point. There is something like falsehood in a bad definition, because a bad definition is going to lead to false statements, e.g. if I define “the place of a body” as “the surface of its volume”, I will obviously be inclined to make a false statement: “the place of a body is the surface of its volume”, which is impossible since a thing may change its place (here understood to mean the thing we all grasp vaguely) without changing shape. What Newton and Descartes do when they assign certain quantitative definitions to “mass” is something along those lines. Whereas Descartes equates it with volume, since matter for him is nothing but extension, Newton implicitly equates it with the number of ultimate particles in a volume. Perhaps I should speak about this in more detail in a later letter. As for those Newtonian principles which are true, such as the third law, and perhaps the second, well, they’re true…. The third law has equivalents in Aristotle and St. Thomas—if one body acts on another, it is acted upon in return, since bodies act on one another by physical contact.

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But how does the mathematical physics, essentially probable in its conclusions (and therefore sometimes called “dialectical” by De Koninck and others of that persuasion), compare to the physics of Aristotle and St. Thomas? Something like a part to a whole. The general way of proceeding for the physicist which Aristotle sketches out applies in all its parts to mathematical physics. E. g. the mathematical physicist must define what he studies with sensible matter, although he will define it as subject to common sensibles rather than proper sensibles since he is studying it precisely in its behavior regarding quantity and quantitative modes. E.g. he will define “charge” as “the quality in a metal that makes the needle in a meter built in such and such a fashion go so far in that direction”, or some such thing, and “temperature” will be “a quantity of heat proportional to the height of a mercury column in an instrument built in such a manner”. Although “mercury” itself, and other such terms in such definitions, must be defined with sensible matter, the point is mercury need not be there at all—we might build an instrument to measure temperature which has an alcohol column instead. Again the order of determination of his subject matter is, for the mathematical physicist as well as the philosopher of nature, from the more universal to the less universal. And he resolves to sense experience of nature perhaps even more conspicuously than does the philosopher of nature, employing experimental method, etc. Mathematical physics is the more particular account of natural things that one reaches as one proceeds further into the study of nature.—one goes further and further into matter, and consequently further and further into what is unintelligible in itself. For this reason, it becomes necessary to look to the first formal property of matter, which is quantity; how it behaves will tell us something about the matter and nature which give rise to it. There are other reasons why the further you go into matter, the further you go into mathematization—see De Koninck’s Introduction to the Study of the Soul, chapters XIV—XVIII (very dense reading). The relation, roughly speaking, of the study of nature found in Aristotle’s Physics and De Anima, to the study of nature as we see it going on today (begun with Galileo and Newton and the like), is one of whole to part, general to particular, and therefore certain but vague to distinct but probable. To sum up. Newton is not your teacher. He is the first of the great mathematical physicists (his contemporary, Leibniz, does not even compare). Consequently, since things are most clearly seen when watched from their beginnings (as Aristotle put it in the Politics), he is eminently worth studying as an example of how to carry out mathematical physics. We all wish somewhere in our secret souls that his principles and conclusions were true, since they are so easily grasped and, in some ways, quite beautiful. Unfortunately, although such a theory cannot be proved (for the reasons we gave above), it can be disproved, and Newton’s has been. This does not mean that there are no elements of truth in him—I for one am sure that there are. But I believe most of his physics is really too much like abstract mathematics, like Euclid, to match nature precisely. That is one reason why it is so appealing to us: Euclid is beautiful and simple and easy to grasp, well-proportioned to our minds. If we were to design nature ourselves, we would make it according to Euclidean geometry. Unfortunately, nature is not, like mathematics, abstracted from the natures of things. And nature is not the human art in things, but something of the divine art in things. But enough about Newton for now.

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Supplement:

Cf. Steven Horst, Ph.D., Ch. XX. “Newton and Nomic Naturalism”, Newtonian Naturalism 1. 12/6/01, pp. 6-14:14

This brings us to Newton’s most important work in physics, the Principia, in which he summarized the motions of the planets in terms of a set of mathematical laws of gravitational attraction, and in the process united terrestrial gravitation with celestial mechanics. By the time Newton wrote the Principia, he had realized that he could not cling to the mechanistic theory of a corpuscularian aether to explain gravitational attraction. However, he had no mechanism to offer in its place, and refused to offer a hypothetical explanation of it. Thus in the famous passage [6-7] with which he concludes the General Scholium in Book III of the Principia asserts:

Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power.....But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea. (Principia General Scholia, trans. Motte, revised by Cajori, pp. 546-547.)

This passage, which first appeared in the Second Edition of the Principia, was to serve as the inspiration for many self-styled followers of Newton in the eighteenth and nineteenth centuries, such as Thomas Reid, David Hume, and Ernst Mach. The assertion, “I frame no hypotheses” (hypotheses [7-8] non fingo) has attracted special attention, both because it seems to be a firm rejection of the hypothetical style of reasoning employed by Galileo and Descartes, and because almost all scholars agree that Newton in fact did make use of hypotheses, even labeling several as such in the Principia. There has been, in fact, a kind of cottage industry of Newton scholarship centered on the problem of what Sir Isaac really meant by this dark saying, with interpretations ranging from the idea that what he really meant was that he rejected baseless speculations (N.R. Hanson), to Newton’s hatred of controversy leading him to withhold ideas that might bring criticism (Cajori), to long analyses of the various things Newton meant by ‘hypothesis’ in different places (I.B. Cohen), to the suggestion that Newton was a great scientist but a mediocre philosopher and hence did not really understand what he was saying in this passage and hence we can safely ignore it (Burtt). I shall not enter into this controversy here beyond saying that the scholarly problems seem real, given that (a) there are other passages, both in works intended for publication and in correspondence, in which Newton expresses suspicion of hypotheses that go beyond what can be derived from the phenomena, (b) Newton himself applies the word to some of his own ideas, yet (c) in replies to critics often argues that his theories are not hypothetical in character. Instead, I wish to focus on two elements of what Newton seems to be doing here—one which was made central by Newtonians like Reid and Hume, and another which may have been closer to Newton’s own purposes—and draw from them a common theme upon which to build an alternative to compositive naturalism. The first side of Newton’s disavowal of

14 (http://shorst.web.wesleyan.edu/mwn/pdf%20versions/NewtonNomicNaturalism.pdf [1/18/10])

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hypotheses is based on [8-9] the distinction between hypotheses and observations. Newton says that a hypothesis “is what ever is not deduced from the phenomena” 2 and that “an hypothesis is any proposition which is not phenomenologically based; one which is neither a phenomenon nor deduced from phenomena.”3 This idea, picked up and transformed into a general principle by eighteenth-century Newtonians, leads to an emphasis upon finding good characterizations of the regularities found in phenomena (especially in the form of mathematical laws) and a rejection of introduction of theoretical ideas about things that cannot be observed. This theme has been cited with approval by such important commentators on scientific method as Hume and Mach. But it is not clear that Newton himself was much drawn to it. For there is every indication that Newton himself was disturbed at the time by the lack of a mechanism to explain gravity, and may have felt the sting of criticisms from continental critics who claimed that he was re-introducing the kinds of “occult forces” that mechanism had attempted to eliminate from physics. Nor was it Newton’s own practice to stop with mathematical regularities when further explanation was available. What seems particularly important in this case is that further explanation of gravitation was not available. It was the work of the next generation to turn this attitude into a thoroughgoing rejection of invisible causes.

2 Cf. Isaac Newton, Sir Isaac Newton’s Mathematical Principles, ed. Florian Cajori (Berkeley, 1946), General Scholium, penultimate paragraph, p. 547.3 Newton to Roger Cotes, 28 March 1713, quoted in J. Edleston (ed.), Correspondence of Sir Isaac Newton and Prof. Cotes (London, 1850), page 155.

The second idea that is at work here, and much closer to Newton’s own later thought (and perhaps his motivations at the time), is that the lack of a mechanical explanation of gravity suggested to Newton that the explanation was not to be found in any property of matter, which is passive in nature, but in some other active principle. In the second edition of the Optics in 1704, for example, Newton explicitly says that gravity is an “active principle.”

It seems to me farther, that these Particles have not only a Vis inertiae [force of inertia], accompanied with such passive Laws of Motion as naturally result from that Force, but also that they are moved by certain active Principles, such as is that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies. (400-401, quoted in Dobbs and Jacob, 1995, page 52)

By this time, twenty years after the completion of the Principia, Newton had begun to consider two new explanations of gravitation, though his caution and abhorrence of controversy kept him from ever committing them to print. Newton’s first view was that God, who is omnipresent, is Himself the direct cause of gravitational activity, and hence is constantly intervening in nature to uphold his laws. Newton additionally believed that the physical world actually required Divine intervention to keep it running in order. As Dobbs and Jacob write,

because of the mutual influence of many bodies on each other he had not supposed [the solar system] would run forever in its present order. [10-11] He had thought that when the perturbations in the solar system, for example, grew sufficiently great, the system would need a reformation, and at that time God would step in to set it in order again. (Dobbs and Jacob, 1995, 58)

This direct intervention of the Divine with affairs in the world—which was the occasion for the derisive quote from Leibniz earlier in the chapter—was in some tension with Newton’s Arian theological leanings,4 which called for a highly transcendent God, whose influence on the universe would be communicated by an intermediary. As a result, Newton began to see a

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second explanation of gravitation in the properties of electricity he saw demonstrated as President of the Royal Society. He began to examine the idea of a highly elastic but incorporeal aether that could serve as a kind of “spiritual body.” (Dobbs and Jacob, 1995, pages 53-54) This idea, needless to say, did not endure, though the idea of an aether was not definitively rejected until the Michaelson-Morley experiment at the beginning of the twentieth century.5

4 Arianism was a variety of Christianity that was very influential in the fourth century. Arians rejected the trinitarian views that were to be adopted at the Council of Nicaea (theArians were the losing side in the Nicene Council), in favor of the view that the Son wascreated, not begotten. As such, the Son or Logos becomes an intermediary through which God the Father interacts with creation. Newton’s Arian views were not known until examination of his extensive manuscripts in the twentieth century, but may well explain his request for a special dispensation from the requirement that he, as Lucasian Professor of Mathematics at Cambridge, join the Anglican clergy or give up his post. Arianism, as an historically prominent heresy, was held in less regard in England of his day than alchemy.5 It is worth noting that Michaelson and Morley performed their experiment in an attempt to show that there was an aether, but luckily chose the sort of experiment where any conclusive result, whether positive or negative, could establish one’s career. [11-12]

Now what is common to these very different interpretations of Newton—(1) that he rejected hypothetical micro-explanation in favor of laws governing observables, and (2) that he favored a theologically-motivated active principle to explain gravity—is a rejection of the idea that the standard of scientific explanation is the resolutive-compositive method. Whether gravity is simply without explanation or requires a theological explanation, in eithercase what has been rejected is the idea that it must be explained by reducing it to actions of the smallest bits of matter. And it was this idea that would take hold among Newtonians and radical empiricists like Hume, Mach and the behaviorists: namely, that science requires only the description of empirical regularities and not a compositive explanation of them in more fundamental terms, at least not when this requires appeals to unobservables.

Newton himself expressed this view in a different way as well, when he distinguishes between considering forces “physically” and “mathematically.” Thus in Definition VIII of Book I of the Principia he writes:

I...use the words attraction, impulse, or propensity of any sort towards a center, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically; wherefore the reader is not to imagine that by those words I anywhere take upon me to define the kind, or the manner of any action, the causes or the physical reason thereof, or that I attribute forces, in a true and physical sense, to certain centres (which are only [12-13] mathematical points); when at any time I happen to speak of centres as attracting, or as endued with attractive powers. (Principia, Book I, Definition VIII, pp. 5-6)

We might very well take Newton here to be saying that he is considering real properties of force, but focusing on some of their properties (their mathematical relations and the motions they cause) while abstracting away from others (namely, the “cause” or “manner” of the force).

This Newtonian paradigm of scientific explanation found its most important philosophical proponent in the British Empiricist David Hume. Hume, like many other Newtonians, read “hypotheses non fingo” in the extreme sense of rejecting hypothetical reasoning. Not only

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was Hume hostile to theoretical or retroductive explanation, he even went so far as to say that words whose reference cannot be traced back to sense experiences (what he called“impressions”) were literally meaningless! Likewise, he rejected both the notion of causation and that of substance, as they were never presented in impressions. This Newtonian paradigm re-emerged with a vengeance in psychology at the beginning of this century in the behaviorism of Watson and Skinner, which took it as a methodological axiom that sciences should restrict themselves to the investigation of regular relations betweenobservables (in the case of psychology, stimuli and behaviors) and should eschew any talk of unseen (hence hypothetical) entities such as mental states. Arguably some people in cognitive science and artificial intelligence who stress the independence of programs from their physical [13-14] realization view their subject matter in similarly Newtonian terms as well.

This Newtonian view is, again, arguably more extreme than Newton’s, in that Newton does not seem to have shared Hume’s thoroughgoing hostility to hypothetical reasoning. But this should not blind us to the fact that Newton does seem clearly to reject the idea that one musttrace all phenomena back to the relations of simple particles by way of resolutive-compositive reasoning.

Cf. Charles De Koninck, “The Unity and Diversity of Natural Science,” Mélanges à là Memoire de Charles De Koninck, pp. 5-25 (excerpt):

[given above]

Cf. Charles De Koninck, Natural Science As Philosophy:

We are often told of a distinction between philosophical psychology and experimental psychology. This is a distinction that I do not understand. Take the beginning of the De Anima, where Aristotle shows that even here we must provide natural definitions as distinguished from the logical or dialectical. His example is that of ‘anger’. It is true that anger is ‘a desire for vengeance’. But this definition is purely formal, somewhat like the definitions of mathematics, i.e. ‘per species’. Now, in mathematics, formal definitions are sufficient to the subject, since the subject is abstract; anger, however, is also something physical, as may be seen in the behavior of any person in a rage. If we are to form a natural definition of what anger is, we will have to add something to that ‘desire for vengeance’, such as ‘attended by an effervescence of the blood about the heart’. A psychology which would confine itself to formal definitions would be no more than dialectical. (Notice, however, that this natural definition of anger is itself only dialectical, but dialectical in a different sense. For propositions—and a definition is virtually a proposition—may be called dialectical for two different reasons: either because the composition or division of the known terms which it comprises is no more than probable; or because one or both of the terms themselves are insufficient, which is the case of purely formal definitions of natural things. We have to do with something less than dialectical when the terms are themselves no more than likely constructs, even though they have some basis in experience. Such was the case of Aristotle’s ‘incorruptible’ heavenly bodies, and of Dalton’s ‘atoms’.) In the definition of anger as ‘a desire for vengeance attended by an effervescence of the blood about the heart’, the former part is certain, though dialectical; the latter part, taken by itself, is natural, yet dialectical qua insufficient even as a natural definition. Natural, because it refers to something sensible; dialectical because no more than provisional.

Cf. Michael A. Augros, Scrapbook.6:

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3) The two reasons we cannot demonstrate anything with perfect certitude in mathematical physics:

a) The logical form of the method of mathematical physics is this: “IF A IS B (some unobservable law we might think operates in natural things), THEN BY MEANS OF MATHEMATICS WE SEE IT WOULD FOLLOW THAT X IS Y (some observable phenomenon). BUT X IS Y, THEREFORE A IS B.” Of course, to assert “A is B” without qualification is to commit the fallacy of affirming the consequent. E.g. “If John has stomach cancer, then he is seriously ill. But he is seriously ill, therefore he has stomach cancer”, it is obvious that there is no necessity here. He might be seriously ill because of some other cause.

Likewise, if Newton lays down certain quantitative laws he thinks operative in nature, and by mathematical proofs shows that certain consequences we should be able to find in natural things would follow, and if we look and find these consequences do in fact seem to occur in natural things, we cannot conclude with certitude that these consequences are the results of Newton’s laws operating in nature, since these effects might be the results of other laws. Hence, the principles of mathematical physics become more and more certain (though we never see them as necessary) the less likely it is that their mathematical consequences found in nature could be due to any other causes.

Hence, it is particularly convincing when the predicted consequences had never been observed or suspected before we deduced them as results of the theory, and found them in trying to in some way verify the theory.

b) WE CAN NEVER MEASURE ANYTHING WITH PERFECT EXACTNESS. The assumed laws or principles in mathematical physics, and all their mathematical consequences, are always perfectly exact. Hence, even if we knew a priori that the only possible cause for these results were the principles we have assumed, we could never be absolutely sure that the mathematical results are really what we are observing in nature. For the results of the theory are exact mathematical quantities, whereas what we find in nature (if it is something exact at all) cannot be known with exactness. Our senses, by which we measure, limit our capacity to measure beyond a certain accuracy, and so for all we know the thing measured might be incommensurable with our unit of measure.

In short, not only does “A is B” not follow from “If A is B, then X is Y, but X is Y”, but also we can never be sure that “X is Y”.

4) The “principles” of mathematical physics, the assumed laws, are “principles” not in the sense that they are self-evidently true, but in the sense that they are the things from which we reason. They are freely assumed in the beginning; they are a good guess. Rather than judging the consequences in the light of the principles, we judge the “principles” in the light of their consequences. The more accurately and simply and completely they account for phenomena, the better are our principles. This is no different from Ptolemy’s method.

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De operationibus occultis naturae ad quemdam militem ultramontanum

On the Hidden Workings of Nature to a Certain KnightAcross the Mountains

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tr. by J. B. McAllisterWashington D.C.: Catholic University of America Press, 1939

Rev. Bart A. Mazzetti

(c) 2013 Bart A. Mazzetti. All rights reserved.

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