Birch, The Dialectic of Discovery (Abduction)

7/29/2019 Birch, The Dialectic of Discovery (Abduction)

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The Dialectic of Discoveryby Andrea C. Birch

I. Introduction

P EIROE OALLS the form of reasoning blY which hypotheses are formulated and selected " abduction."[Abducrtion] is the first srtep of scientific reasoning, as induction isthe concluding step. Nothing has so much contrihuted ,to presentchaotic or erroneous ideas of the logic of science as failure to distinguish the essentially different charaoters of different elements ofscientific reasoning; and one of the worst of these confusions, as weIlas one of the commonest, consists in regarding ahduction and induction taken together (often mixed wirth deduction) as a simple argument (7.218).1

Oertainly ablduction is merely preparatory. I t provides aweak largument leading to conjectureand cannot perform theverifying function of induction. Ab,duction s.uggests that sornething ma.y be) but it is. the only form of reasoning that supp,lies new ideas: "All the ideas of science come to it by theway of Abduction" (5.145). Peirce explains.:Abduction is the process of forming an explanatory hypothesis. Itis the only logical operation which introduces any new idea; forinduction does nothing but determine value, and deducrtion merelyevolves the necessary consequences of a pure hypothesis. . . . if weare ever to learn anything or to understand phenomena at all, itroust be by abduction that this is to be brought about (5.171).

1. Most of Peirce's writingsare in the Oolleoted Papers 0/ Oharles SandersPeirce, volumes one t hrough s ix edited by Charles Hartshorne and PaulWeiss (Cambridge: Harvard University Press, 1931-1935), volumes sevenand eight edited by Arthur Burke (Gambridge: Harvard University Press,1958). The convention in citing references. is to place the volume numberto the left of the decimal point and th e section number to the right.References to this work will be cited internally.

295


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296 Andrea O. BirchFr Peirce, abduetion both deseribes the discovery p,roces.s inscience and has a logie. The process of formulating new ideasis not merely amenahle to psychologieal or historical description, hut to logieal ,analysis. In fact, Peiree comp'ares abduction to the type of theoretieal argument Aristotle calls reduction. Peirce writes:... abduction (which Ithe present writer believes to have been whatAristotle's twenty-fifth chapter of the second Prior Analytics imperfectly 'described under the name apagoge, until Appellicon substituteda single wrong word and this disturbed the sense of the whole),furnishes the reasoner with the problematic theory which inductionverifies (2.776).This p,aper will llot examine Peirce's clainl that abduction

is a logie of d i s e o ~ e r y . However, his reference to reduction introduees the issue that concerns us, hare: In what way doesAristot,elian reduction con'Stitute a logic of diseovery?In heginning to ans,wer this question, we will uncover Aris

totle's elue that links reduetion to the method of analysis andsynthesi8. Since reduction is expressed in syllogistic form, thediscussion must foeus hriefly on the meaning of the syllogism.Sinee the syllogism, and most obviously the red'uctive syllogism,has its roots in dialeetic, the investigation must also seek themeaning of dialectie. In s.um, to explore the p,roces,g, of discovery in an Aristotelian context this p,aper will discu'Ss threeessential terms: reduction, syllogism, and dialectic.

11. ReductionPeirce tries to elevate abduction to the status of inductionand deduetion. He is aware that ,according to Aristortle allmodels of argument can be reduced to the logical form oi the18yllogism. Aristotle's interest in the syllogism had led him toreview the various modes of argument and to mention one important hut often neglected form of argument, namely, reduc-


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Dialectic of Discov'ery 297tion. As Peirce reeognizes, the neglect of reduetion result.s ina gap in th,e understanding of scientific method in the A r i s ~totelian sense. Reduction can he a way of arr iving at explanations needed to form the premises of demon'Strat,ive or scientifics.yllogisms.

As Peirce mentions, Aristotle discusses reduotion in PriorAnalytic 11, 25. Aristotle's example ia:Knowledge can be taught, B-AVirtue is knowledge, C-BVirtue can be taught, C-AThe characteristic element of a reduction is that the mlnorpremise CB (i.e., the relation of the middle term B to the lastterm C), although uncertain, is. equally as prohable as the oonclusion or more probahle than the conclusion CA. If the minorpremise is equally as prohable as or more probable than theconclusion, we have a reduetion: "for we are nearer to knowledge, since we have taken a new term [B, thereby ohtainingthe p,remise BA and the p,remise CB], heing so far withoutknowledge that A belongs to C." 2From Aristotle's deserip1tion of the syllogism which springs

out of reduction, it becomes increasingly clear that the deliheration involved in r:eduction can be compared to the analyticmethod in mathematics. 3 Basically, theanalytic method inmathematics entails starting with the figura to be constructedor theorem to be proved .and working back to something alreadyknown. That would mean working hack to Ja known figurewhich the mathematician can constructand from which he canthen draw the required figure; or working hack to a more easilyproved theorem from which he can deveJop' the p,roof he is seeking. The mathematician works hack until he comes to a figure

2 Aristotle, Analytica Priora, 69a28-29, trans. A. J. Jenkinson, in TheBasio Works 0/ Aristotle, ed. Richard McKeon (New York: RandomRouse, 1941).

3 W. D. Ross, Aristotle (London: Methueu, 1949) p.41.


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298 Andrea O. Birchora theorem whieh his existing knowledge enables hirn to conatruet or prove.

In Prior Analytics 11, 25 Aristotle does not compare reduction to the method of analysis. However, in the Nicoma,cheanEth.ics he indieates that the steps of any deliheration are similar to those in mathematieal investigation. Aristotle first deserihels the method used in deliberation:We deliberate not about ends but about means. For a doctor doesnot deliberate whether he shall heal, nor an orator whether he shallpersuade, nor astatesman whether he shall produce law and order,nor does :any one else deliberate about his end. They assume the endand consider ho\V' and by what means it is to be attained; and if itseems to be produced by several means they consider by which it ismost easily and best produced while if it is achieved by one onlythey consider how it will be a.chieved by this and by what means thiswill be achieved, till they come to the first cause, which in the orderof discovery is rthe last.4

The desire for A begins. the deliberation proces.s; aehievingA is the x of the problem. Persona must eon-sider by wh:at meansthey ean aehieve or ac.eomplish A. Sometimes it will takeseveral steps to aecomplish the goal. They migh.t reeall that Bis the means to A; B becomes the unknown y. If they eannotaeeomplish B, they may remembHr that C is the means to B;C beeomes, the new unknown z, hut in this ease, it is somethingthey ean do at the moment. They must then translate theirchoice of C into \aetions. The eompletion of their aetions is theaetual achievement of A.

Aristotle then eompares. the method used in deliberation tothe method of analys.is us.ed in mathematics.:For the person who deliberates seems to investigate and analyze inthe way described as rthough he were analysing a geometrical eonstruction (not all investigation appears to be deliberation-for

4: Aristotle, Nioomaohean Ethios, 1112b12-20, trans. W. D. Ross, inMcKeon.


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Dialectic 0/ Discovery 299instance mathematical investigations-but all deliberation is investigation), and whart is last in the order of analysis seems to be thefirst in the order o'f becoming.5

The method used in deliberation does seem to compare to themathematieal method of analysis. PoJya provides an algebraicexample from whieh wer will be ahle to draw out the comparison. 6 The object of the problem is to find x satisfying the equation: 8(4X + 4-X ) - 54(2X + 2-X ) + 101 = o. Someone mightrecognize that, sinee 4X = (2X )2 and 4-X = (2X )-2, it would beus.eful to introduce: y = 2X The equation with y ia simplerthan the original: 8(y2 + 1/y2) - 54(y + l /y) + 101 = o.The task is not over, because it ~ e q u i r e s another substitution:Z = Y+ l/y. The equation becomes: 8z2 - 54z + 85 = o.The steps so far have involved analysis. Analysis ends with thelast ,equation and :a known on the part of the problem-solver:how to solve quadratic equations. Synthesis i8 the second partof the method and always, aecompanies analysis. Synthesis involves carrying through the step8 of analysis in reverse order.The pTohlem-solver first find8 Z (z= 5/2, 17/4), then y (y =2, 1/2, 4, 1 ~ ) , and ends by finding x, the original thing sought(x = 1, -1 ,2 , -2 ) .Based on Aristotle's eX iample of deliheration and Polya's

ma,thematical ease it is possible to make six points concerningthe method of analysis.Firs,t, in both ease8 analysis starts with an unknown x which

the deliberator or p,rohlem--solver assumes actually exists andmeets certain conditions.. The assumption of x is provisional;it is made in order to begin the analysis. 7 The deliherator, forexample, ean imagine achieving A before he has actually doneso.

5 Ibid., 1112b2Q-24.6 George Polya, How to Salve It (Princeton: Princeton University Press,

1945) pp. 144-45.7 lbid., p. 146.


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300 Andrea O. BirchSeeond, in deliheration and in mathematical problem-solving

the person works. hackwards until he arrives at something thatean he done here and now or at something already known, oruntil he discovers. that the p,roblem has no solution. Aristotleadds, for example: "And if we eome to an inlpossibility, wegive up the seareh, e.g., if we need money and this eannot begot: b,ut if a thing ap'pears possible we try to do it." 8Third, meaningful analysis is really a dual method hecause

it must always be followed by synthesis.Fourth, the last step of analysis is the first step of synthesis.

The last step in the deliberation is the first step that must actually be taken. The last step of the mathematical analysisprovides that whieh must be solved first in the synthesis.Fifth, as hinted at in the fourth point, the order of synthesis

is opposite to the order of analysis. The order of calculation(oraetion, or earrying Ollt a plan) is opposite to the order ofdiseovery (or invention, or devising a plan).Finally, analysis, is a powerful method of discovery. Pap-

P'US, the third century geometer who expounded on the method,e o n s i d e ~ s analysis and synthesis, a powerful tool for diseoveringsolutions to geometrieal p,rhlems. 9 Aristotle elearly eonsidersanalysis a way of diseovering the means tn achieve desired ends.Polya believes that analysis is a way to discover solutions tonot only geometrieal problems but also algehraie problems andeven non.-mathematieal p:rohlems.We ean now conelude that 'Sinee reduction ig a type of de

liberation it too ean b1e eomp,ared to the method of analysis in8 Nicomachean Ethics, 1112b24-66.9 See Thomas Heath, A History 0 / Greek Mathematics., vol. 2 (Oxford:

Clarendon Press, 1921); Jaako Hintikka and Unto Remes, The Methoa0/ Analysis (Boston: D. Reidel, 1974); Norman Gulley, "Greek Geometrical Analysis," Phronesis 3 (1958) 1-14; Noretta Koertge, "Anal-ysis as a Method of Discovery During the Scientific Revolution," in Sci-en tific Discovery, Logio, a na Rationality, ed. Thomas NickIes (Boston:D. Reidel, 1980).


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Dialectic of Discovery 301mathematics. Moreover, since the method of analysis, 18 amethod of di!scovery, the steps of a delibera1tion, or specificallyof a reduction, comprise a prrocess of diseovery.One problem emerges in this scenario. Aristotle's diseussionof reductlion in the Prior Analytics 11, 25 focuses on a reductive Isyllogism rwhich seems to express only the synthetic branchof the dual methode If one desi:ves to he ahle to make th.e stalte-ment "Virtue can be taught" (x), he may introduee the statement "Virtue is knowledge" (y). That is uncertain, but ismore p.robable than x and easier to consider. Thinking hack,he knows that "Knowledge can be taught" (z). Given thisknown, he can express the syllogis.m: Knowledge can 1e taught(z); Virtue is knowledge (y) ; therefore, Virtue ean be taught(x). In isoJation from the diseovery process, the syllogismembodies only the synthesis.

By considering reduction a type of deliberation and comparing it to the method of mathemaltical analysis, we were ableto hint at a broader meaning for reduction. Now we must tryto approach reduction from a different angle in order to clarifyits links to analysis. Sinee reduction is a type of argumentwhich Aristotle says ean be expressed in syllogi8tic form, weturn to an exploration of Ari8totle's. understanding oei the syllogism as a way to shed light on the meaning of reduction. Wewill find that the syllogi8ill itself iso not as restricted to thesynthe,tic proces8 as it first ap!pears. ThiSi will have implications for reduction.

111. SyllogismAristotle's gener.al definition of the syllogism is weIl known:

" A syllogism is an argument in which, certain. things havingbeen assumed, something other than these folIows of necessityfrom their being 80."10 ThH task estahlished by this definition

1.0 Aristotle, Topica, 100a25-26, trans. E,. S. Forster (Cambridge: Har-yard University Press, 1960); Analytica Priora, 24b18. See Ernst Kapp,


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302 Andrea C. Birchof the syllogism may be int.erp,reted in two ways.. One eitherbegins with a given set of premise:s and searches for possible inferences from them, or one heings with a given " conclusion "or "thing sought" (sueh as x in the syllogism above) andsearches for the possible p,remises. Kapp ,argues that Aristotleunderstands the task in the second way.l1 To p,araphrase Kap,p,of course Aristotle's, syllogism involves possible combinationsof premises leading to a given conclusion, hut this does notmean it deals with inferences from given prenlises to a previously unknown conclusion.

Before focusing on the reductive syllogism, it is useful topoint out that evena demonstrative syllogisllt p,roductive ofseientific knowledge does not move from known premises to aconclusion previously "Lmknown. In Posterior An,al'ytiC'sJ 11, 13,Aristotle gives an example of demons,tration propter quidJdemonstration of the rHasoned fact, which alone can be considered demonstration proper hecause it gives the reason whyan attribute inheres in a 8ubject :'12What is near does not twinkle.Planets are near.Planets do not twinkle.This is a genuine seientific syllogism sinee the lniddle term expresses the cause, the explanation 01 the faot. I t is, becauseplanets are near that they do not twinkle. What is clear isthat the characteristic feature of the demonstrative syllogismis that it hasa scientific explanation in the premiseB. It doesnot contain so'mething new in the conclusion. The conclusionis already known. The movement in a demostrative syllogismis not, therefore, from known p,remises to a, conclusion pTevi-Greek Foundations 0/ Traditional Logic, (New York: Columbia UniversityPress, 1942) p. 11.

1.1 Kapp, ~ e e k Foundations, p. 71.12 Aristotle, Posterior Analytics, trans . Hugh Tredennick (Cambridge:

Harvard University Press, 1960).


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Dialeclic of Discovery 303ously unknown. The conclusion that the planets do not twinkleis an observed fact previously known by experience. The ob-served fact does follow from the two premises, "What is neardoes not twinkle" and "Planets are naar," as a. conclusion.However, it iB not a new fact inferred from the given premises.What is "new" is not the fact contained in the conclusion,but the explanation provided in the minor premise. The scien-tific explanation, discovered by other mHans Buch as induction,comprises the p,remise from which the obsHrved fact can bederived a sa conclusion. Aristotle's demonstrative syllogismsystematizes the facts of the explanatory premise and the con-clusion.

In a similar way, Aristotle's reductive s ~ l l o g i s m systematizesthe knowns of the major p1remise, the probable explanation ofthe minor premise, and the opinion which is exprHssed in theconclusion. Although the demonstrative syllogism iso de1fined bythe middle term expressing the cause and a ~ e d u c t i v e syllogismis characterized by the middle term exp,ressing merely a p,rob-able cause, their syllogistic forms, are similar. In both cases thedesired end or conclusion already exists'. The concluSlion of thedemonstrative ,gyllogism does not contain anything new. Theconclusion of the reductive syllogism contains a given opinion,but no new information. What is "new" in the demonstra-tive syllogism is the scientific explanation provided by theminor premise. What is "new" in the reductive syllogism isthe attempt to express a p,robable explanation in the minorpremise.

I t appears that Aristotle's, definition of the syllogism withinhis develop,ed formal logic is. an artificial argument frompremises to the conclusion. The conclusion does. follow fromthe premises.. Horwever, Aristotle continues to recognize that asyllogistic argument musta.ctually fir8t involve a. search forpremises that lead to the given conclusion before the syllogism


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304 Andrea C. Birchitself is expressed. As we have seen, the conclusion of a syllogism is not a new fact derived from the prenlises. Accordingto Aristotle'B understanding of the syllogiBm, then, the order ofthe premises and the conclusion in the syllogism itself is opposite to the order of thinking leading to the syllogism. If thesyllogiBm itself is p,receded by a movement from conclusion topi:r.emises that lead to the conclusion, it follows that when theconclusion appears in the syllogism it will not be somethingnew.

The examples of the demonstrative and reductive syllogismsshow that Aristotle himl8elf interprets the definition of thesyllogism as a search for premises, not as a movement frompremises to new, and previou'Sly unknown, inferencers in theconclusion. The reason for this is easy to explain if we explore the roots of the syllogism in dialectic.

IV. DialecticAristotle was. influenced by the actual syllogistic practices

he reviews in the Topics.'13 The Top!ics deals with syllogisms asthey emerge in dialectic practice.Aquinas explains the meaning of dialectic hy situating it

within the context of his discussion of reason and logic inhis Oom,menlary on the Posterior Ana.lytics.14 Aceording toAquinas, logic is the art of p,roviding directive guidance for theacts of reason. I t is a rational science not only because it is inaccordance with reason, for any art can be described as rationalin that sense. Rather, logic is called a rational science p,rincipally heeause it is concerned with the activity of reason as itsp,roper suhject matter. Since the subject matter of logic is theactivity of reaSOfi, Aqllinas writes that one should "view the

1.3 Kapp, Greek Foundations, pp. 73, 13. See Paul Durbin, Logic andScientijic Inquiry (Milwaukee: Bruce Publishing, 1968) p. 32.

14 Thomas Aquinas, Oommentary on the "Posterior Analytics" 0 / Aris-totle, trans. F. R. Larcher (Albany: Magi, 1970) pp" 1-2.


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Dia.lectic of Discovery 305parts oi logic according to the diversity among the acts oireason." 1.5

The primary act of reason is concerned with that which isproper to reason; it is the discourse from one thing to anotherin s.uch a way that through the known one comes to a knowl-edge of the unknown. Within this act of reason, Aquinas makesa threefold division. We will deal with the first tw'O divisions.

One process of reason induces necessity in such a way thatit is impossible to fal l short of the truth, and so can result inthe certainty 01 science. The part of logic concerned with thefirst proeess of rHason is c.alled Pa,rs Iu,dicaliva hecause it re-sults in judgments possessing the certitude of science. ThePoS'terior Analytics oi Aristotle, concerned as it is with thedemonstrative syllogism ordered to material resolution, exem-plifies that first part of logic.

In the second process of reason something true is concluded,hut without the accompanying necessity. Pars I nventiva is thep,art oi logic that deals, with the second process of reason. In-v'entio or discovery does: not necessarily res.ult in certitude.Aquinas differentiates three levels of certitude hased on thenearnes.s to scientific certitude. The first level concerng. us here.Although science is. not ob,tained in this first level, belief oropinion may be achieved hased on the: prob'ahility of the initialpropositions. In such eases reason leans. completely to oue sideoi a contradiction. The Topics or dialectics deals. with the firstlevel of inV'entio hecause the dialectical syllogism, which is thesubject of th,e Topics} proceeds from premises which are prob-able.

Within the first level oi Pars Inventiva} therefore, argumen-tation is diale:ctical because, although it comes closest to sci-entific certitude, it res.ults in opinion hased on the prohabilityof the p,remises. The key points for this diseussion are that

15 Ibid., p. 1.


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306 Andrea C. Birchdialectic, which deals with dialectieal argumentation, must beconsidered a branch of logic and that dialectic ean be sub..sumed under that part of logic which deals rwith inventio ordiseovery.

In the T o p i c s ~ Aristotle explains that the study of dialecticis useful for mental training, fr conversations., and for ap-plication to the sciences. Through the Topics at least fourfeatures of dialectical reasoning emerge.

First, a dialectical argument requires a questioner and arespondent. The questioner knows from the heginning what hewants to convin0e the respondent of or get the respondent toagree to. I t is. us.ually referred to as. the conelusion. However,from the perspective of the questioner, what is to be acceptedby the respondent is present from the beginn.ing.16 If we lookat the respondent we ean see that he must know the conclusionfrom the beginning becau'be, by the type of ans.wers he gives,hel tries. to avoid it.

Second, the questioner, knowing the conclu.sion he wants therespondent to ,agree to, must find appropriate questions to askthe respondent. The questioner's. task in a dialectical disputa-tion is to discover arguments that sup'port the point of view ex-pres:sed in thel conclusion. More speci:fically, his problem is to:find p,remises the r:esponde,nt will aceept and from which therespondent must acknowledge the conclusion that folIows..

Third, as Ari'stotle states. in the first chapter of the T o p i . c s ~the premises of a dialectical argument are generally acceptedopinions that "command themselves to all or the majority orto the wise." The assumptions of a dialectieal argument ,are,therefore, opinions to whieh the questioner must get the re-'spondent to agree.

Fourth, both Kap!p and Randall deseribe the thinking that16 Kapp, Greek Foundations, p. 14. :See John Herman RandalI, Aristotle

(New York: Columbia University Press, 1960) p. 39.


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Dialeclic of Discovery 307leads the questioner to finding the dialeetical syllogism as"thinking hackward."17 If a dialectieal s.yllogism is d e fined as an argument in which the conclusion is derived frompremises exp,ressing opinions admitted by the respondent, thenitappears. that the order of reasoning leading to the s.yllogismis opposite to the order of the p,remises and conclusion of thesyllogism. The questioner reasons from the conclusion (which,as we have noted, is there from the beginning) to the p,remises,although the order of the syllogis.m is from premises. to conclusion.

Kap,p argues that the demonstrative syllogigm is easily connected with Aristotle'g understanding oi the syllogism thattakes into 'account the features. of dialectieal practices, p'articularly, the givennes8 of the conclusion and the need to search forpremises. I t seems ev;en more oovious that the reductive 8yllogism should be linked to dialectic. Reduction is characterizednot only by the pre-existence of the desi:ved end or conclusionand the seareh for premises, hut also by the fact that its premises, although uncertain, are agreed upon beeause they are moreprobable than the conclusion. This as:peet of the premis.es. of areductive syllogism .al1ows for a natural c o ~ p , a r i s o n to theagreed upon opinions. that form the p,remises. of a dialecticalargument. To repeat the point, if dialeetie ean he connected todemonstration, it seems even more elear that the aetual pTacticeoi dialectic influeneed Aristotle's formulation of reduetion.

v. Cons.equences for a Logie oi DiscoveryWehave seen that Aristotle,through his discussion of d

liberation, provides the initial evidence for comparing reduc-17 Kapp, Greek Foundations, pp. 14-15; and RandalI, Aristotle, p. 39.

However, Kapp says that it is not ,as simple as a comedian indicated inanswer to a question about how he managed to have such funny ideas:"Oh, that is quite easy, first I sit down and laugh and then-I thinkbackwards."


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308 Andrea O. Birc'htion to mathematical analysis. N ow after the hrief discussionof the syllogism and dialectic we are able to determine morespecifically how r:eduction answer:s. to analysis and w:here it fitsinto the whole process of analysis and synthesis.

The p-roces8 of arriving at the premises through workingbackwards. from the thing sought can be described as reductionproper. I t is what Aristotle discusses as the process used indeliheration and what he compares to the method of mathemati-cal analysis.. Moreover, it leads. to finding the reductive syl-logism. The process of moving from a comhination of premis.esto the thing soughtas the conclusioll is the synthesis. that ex-presses the reductive syllogism. The direction that leads tofinding the reductive syllogism is opposite to the order of thepremis.es and the conclusion (which expresses the thing sought)in the reductive syllogism itself. The discussion of dialectichelp:s us to see that while the reductive syllogism certainly fol-lows the order of synthesis it is also linked to analysis. A trueunderstanding of the reductive syllogism takes account of thefact that syllogistic argunlent (in this case the reductive 8yl-logism) must firs.t involve an actual reduction or search forpremises using the method of analysis.

The search for the source of reduction and the reductivesyllogism in the definition of the syllogism artd in dialectic hasactually illuminated the meaning of analysis and synthesis intwo ways. This. becomes important for the history and philos-op,hy of scienee hecause during the scientific revolution. N ewton's dual method of analysis. and synthesis went heyond mathe-matics to become a powerful tool for discovery and proof in thep,hysical sciences.

First, just a,s the reductive syllogism recognizes the link be-tween arriving at the syllogism and the reverse order of thesyllogism itself, the ,dual method of analysis,and synthesisacknowledges the inexorable connection between the order ofanalysis and the order of synthesis. The reductive syllogism


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Dia.lectic 0/ Discovery 309cannot he understood in isolation from its dialectic roots whichexpress the p'r'ocess of discovering premises. In the same way,the deduction of synthesis. cannot be understood in isolationfrom the analytic or reductive pTocess of working hackwards todiscQiver p'remises.

Now it should be clear why mathematicians. and 8cientistsfrom Pappus to Newton have insis.ted that analysis be follow'edby synthesis. I t s.hould also he ap'parent why explaining thescientific pTocedure as following hypothetico-deductive methodology is limited. The hypothetico--deductive method focuses, inNewtonian terms, on synthesis hut ignores analysis:. I t beginswith :an hypothesis which acts as the starting point of deduction. This would he comp'arable to looking only at the deduction of synthesis. The hypot,hetico-deductive method ignoresany theory concerning how the scientist arrives at the hypothesis in the first pIace. In other words, it ignores the dialecticof analysis and reduction and thus neglects apart of the discovery process of science. A consequence of the analysis/synthesis model of discovery is that it offers the logic of analysis(with its rich sources in mathematical analysis, reduction, anddialectie) as a road to hypothesis formation. In so doing, itprovides the philosopher of science with a way to move beyondthe simplistic laheling of hypothesis. formation as a mysteriouS',irrational pTOCes.s that is not amenahle to philosophie investigation.

Secondly, if the link between reductionand the reductivesyllogism and the link between analysis, and synthesis cannotbe severed, the discovery process must he expanded to includenot only reduction and analysis, but the reductive syllogismand synthesis. In other words, the process, of discovery mustinclude both reduction and its. accompanying reductive syllogism or analysis and its accompianying :synthesis. The diseussion ofdialectic should have made itap,parent why the methodof analysis and synthesis is considered a discovery p'rocess. In


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310 Andrea G. Birchbrief, sinee dialeetic is a logic of diseovery,. and sinee the re-duetive syl10gism doe8 not forget its roots in dialec.tic, arriv-ing at p'remises through reduction and expressing them in a re-ductive syllogism ean both be eonsidered p,arts of a dialecticproeess of discovery. Sinee an,alysis eompares to reduetion,analysis appeaT8 ,as an original dialeetieal p'roeess. And sincesynthesis, whieh ean he stated as a reduetive syllogism, eannotbe understood in isolation from analysis, the dual method ofanalysis and synthesis emerges as a dialeetieal procedure anda pirocess of discovery.In eaeh ease we ean see that the analysis';synthesis model ofdiseovery (or the reduetion/reduetive syllogism model of dis-covery, whieh is the same thing) elarifies issues. in the logic ofdiseovery dehates. The analysis';synthesis model ean hegin tosolve the probilem of what " diseQivery " refers to. In diseussingthe word " discovery," fr iends of diseovery often wrestle withtwo questions. First they ask " what is being d i s e o v e r e d ~ " Theanalysis/synthesis model of discovery provides the grounds forsaying that the analytic arm in eonjunction with stages of syn-thesis involves the discoiVery of hypotheses or "ball park solu-tions" while the synthetic arm in its iinal form ean lead to thediseovery of larws or theories. In other words, the analysis/synthesis model ean easily expand the meaning of discovery toinelude the p,roeeS8 leading to either the tentative hypothesis, orthe verified theory as the aehievement.The seeond question often asked is " what is the relationship

between discovery and justification ~ One major a.dvantageof the analysis/synthesis model of diseovery is that it allows thephilosopher to diseuss d i s e o ~ 7 e r y and "justifieation" withoutgetting emhroiled in the elassieal, but misleading, diseovery/justiiication distinetion. Speeifieally, one ean diseus'S. the sup-port for a claim in terms of synthesis rather than in terms ofjustifieation aa such. Synthesis eonstituting a dialectieal p,roofresults in plausible solutions that ,are worthy of further pursuit.


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Dialectic 0/ Discovery 311This type of synthesis corresponds to preliminary justifica-tion. 18 Synthesis constituting :strict scientific or demonstrativeproof leads to universal laws. or theories. This type of syn-thesis c:an be compared to final justification.19 The point is thatthe analysis/s:ynthesis model can draw a natural connection he-tween discovery and proof or justi:fication. Analysis and dia-lectical synthesis are ,a closely intertwined discovery processand clearly illustrate the link hetween discovery and proof (aspreliminary or dialectical). In addition, analysis and dialecti-cal synthesis. can prepare the way for demonstrative synthesis.This s.how's ,a strong relationship hetween discovery (as analysisand dialectical synthesis) and justi:fication in the more tradi-tional sense of demonstration.

Further work must be done on various. issues surroundingthe logic of discovery. In those endeavors, the vocabulary as-sociated with allalysis and s:ynthesis. should not be ignored.Taking into account the distinctions and relationships betweenanalysis: and synthesis and their historical links. to reduction,syllogism, and dialectic can lead to a more p,recise way of deal-ing with the is:sues. The analysis/synthesis model of discoverycan complement some of the work already heing done. Fr ex-ample, the classical method of analysis and synthesis, whichcan trace its. roots. through Newton and Pappus to Aristotle,c:an lend support to contemporary attempts that separate dis-covery into a generation phase, a piursuit phase (including pre-liminary evaluation), and an acceptance phase (including finaljusti:fication) .2 0

To conclude, recall our original question : In what way does,Aristotelian reduction constitute a logic of d i s c o ~ e r y ~ We now

1.8 Thomas NickIes, "Introductory Essay: Scientific Discovery and theFuture of Philosophy of Science," in Soientijio Disoovery, Logio, ana. Ra-tionality, p. 20.

1.9 Ibid,.20 Ibid., pp. 10, 20.


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312 Andrea C. Birchhave at least n.ve ways. to answer that question.. First, it wouldap'pear correct to say that reduction as. a process of delibera-tion that works. hackwards toward p,remises leading to a tenta-tive solution constitutes a logic of disco:very. Second, since re-duction is a proces:s that must be expressed in the reductivesyllogism to complete the search for the thing sought, reductionand its reductive syllogism together make up a logic of dis-covery. Third, reduction aB analysis is a logic of discovery.Fourth, reduction and the reductive syllogism. as a method ofanalysis and synthesis comprise a logic of discovery. Fifth,the reason that reduction or analysis constitute a logic of dis-eovery is because, ultimately, they are dialectical procedures.The ground for all of these statements is that the syllogism,and, in particular, the reductive syllogism, has its roots indialectic, a branch of logic that deals with discovery. Ratherthan using the phrase "logic of discovery" or even "methodoi discovery," it would perhaps he most accu.rate to speak ofthe "dialeetic of discovery."

St. Mary's Oollege,Winona, Minnesota.

Documents

Birch, The Dialectic of Discovery (Abduction)