Jevons, William Stanley. April 1866. on a Logical Abacus. Proceedings of Literary and Philosophical Society of Man Chester 5(14),161-165

8/8/2019 Jevons, William Stanley. April 1866. on a Logical Abacus. Proceedings of Literary and Philosophical Society of Man C

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Ordinary Meeting, April 3rd, 1866., R. ANGUS SMITH, Ph.D., F.R.S., &c., President, in the Chair.

Messrs. Wm. Brockbank and G. C. Lowe were appointedAuditors of the Treasurer's accounts.

Mr. BINNEY,F.R. S., said that he hadobser\'ed the hummingbird hawkmoth (Macroglossa Stellatarum) during the past

. summer in far greater abundance than he ever rememberedhaving seen it befOl"e. In the month of August, he sawupwards of a hundred of thel)} in a garden near Grimsby,were they appeared to prefer the commOn lavender flower forfood to any other in the place. Again in the nnt week ofOctober, he observed upwards of twenty in a garden atDouglas, in the Isle of Man. Here' they preferred to feed

. 011 heliotrope before other lIowers. I t was very interestingto watch these moths hovering over the flowers, and whilston the wing extracting their food. They appeared verywary and shy after any attempt being made to capture them,but if you merely observed without making any attempt tomolest them they would continue their feeding in confidence,and you could watch them at your leisure. So' a great dealof the shyness and c a u t i ~ n ~ o r which the little creature hasgot the credit of, is proba.bly more due to: the perseveringefforts of it s enetnies to capture it than any natural feal" ofman.

A paper was read "O n a Logical Abacus," by W. S.JXVGNS, Esq., M.A.. .

The author believed that this ~ a s t h ~ first attempt, or atall events, the fir$t successful attempt, to reduce the processes of logical inference to a m e c h a n i c ~ l form. The p l ; l l p . O S ~ of this contrivance is to sho\v tbe simple trut.h, and the perfectPaooUl>mGS-LIT# & l'mL. SocmU.-VOL. V.-No. 14-8_SIO. 1866-6.


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162generality of a new system of pUl:e Qualitative J.Jogic closelyanalagous to, and suggested by, the mathematical system oflogic of the late Professor Boole, but strongly distinguishedfrom the latter by the rejection of all considerations ofquantity.This logical abacus leads naturally to the constructionof a simple machine which shall be capable of givingwith absolute certainty all possible logical conclusions fromany sets of propositions or prelnises read off upon the keysof the instrument. The possibility of such a contrivance ispractically ascertained; when completed it will furnish amore signal proof of the truth of the system of logic embodiedin it . Still the more rudimentary contrivance called theabacus will remain the most convenient for explaining the 'nature and wOTking offormal inference, and may be usefullyemploye4 in the lecture room, for exhibiting tl1e completeanalysis of arguments and logical conditions, and the expo-sure of fallacies.

The abacus consists o f-1. An inclined black board, furnished with four ledges,

8ft. long, placed 9in. apart.! . Series of fiat slips of wood, the smallest set fOUl" i 11

number, and other sets, 8, 16, and 32 in number, markedwith combinations of letters, as follows :-

AB

FIRST SET.A ab - B

SEOOND SET.b

1 B I ~ ~ o C .0 C ee l . - . . c. T ~ e third and. fourth set6 exhibit, the corresponding com-

blDa.:ti.o ~ o f : t ~ . letters ,A,'Be , D, a %. 0 'd and ABC,. . '.. , " , 0, , , '_ , , ,D, E, :Q, /J, C,fJ, l J ~ < ' .. '


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163The slips are furnished with little pins, so that when

placed upon the ledges of the board, those marked by anygiven letter may be readily picked out by means of astraight-edged ruler, and removed to another ledge.

The use of the abacus will be best shown by an example.Take, thesyllogiem in Ba,.hara:-Man is mortal.Socrates is man.Therefore Socrates is mortal.

LetA == Socrates.B = Man.e = Mortal.The corresponding small italic letters then indicate the

negatives.a = not-Socrates,b -= not-Man,c = not.-Mortal,

and the premises may be stated asA is B,B is C.N ow take the second set of slips containing all the possible

combinations of A., B, C, a, iJ, c, and ascertain w h i ~ b ofthe combinations are possible under the conditions of thepremises.

Select all the slips marked- A, and as all these ought to beB's, select again those which are not B, or h, and reject them.Unite the Temainder, and selecting the B's, reject those whichare not C or c. There will now remain only four slips or combinations:

ABCaBC

abC [[

If we rf:quire the description' of Socrates, or A, \ve takethe only combination containing A, and observe that it is


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164joined with C, hence the Aristotelian conclusioll Socrates 'ismortal. We may also get any othel' possible conclusion.For instance the class of things not-Mall or b is seen fromthe two last combinations to be always a or not-Socrates,but either mOTtal or not-mortal as the case may be.Precisely the same obvious system of analysis is applicableto arguments ho,vever complicated. As an example take thepremises treated in Boole's Laws of. Thought, p. 1 ~ 5 ..

( 1 ) Similar figures consist of all whose correspondingangles are equal, and whose corresponding sides are proportional.

(2.) Triangles whose corresponding angles are equal havetheir corresponding sides proportional, and 'Vice versa.Let

A= similar.B -= triangle.C ::-: having corresponding angles equal.D = having corresponding sides proportional.

The premises ma.y then be expressed in QualitativeLogic, as follows :-

A = CD.Be = BD.Take the set of 16 slips; out of the A's reject those which

are not CD; out of the CD's reject those which are notA;out of the B ( ~ ' s reject those which are not BD; and outof the BD's reject t40se which ate not Be. There willremain only six slips, as follows :-

ABC1>

AboDaBcd,

t lcd

abcDabcd

From t h e s ~ we may at once read off all the conclusionslaboriously d ~ d u c ~ d by Boole in his obscure p ~ o c e s s e s . .We

.. 8ee -Pure .Logic, -or the Quality of Logic, a.pa.rt from Quantity, byw. S ~ 1 J e T o ~ 1 H.A:., Loudon (St&nford), ISM.


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165at once see, for instance, that the class a, or "dissimilarfigures, consist of all triangles (B) which have not theircorresponding angles equal (0) and sides proportional (el),and of all figures not bemg triangles (b) which have eithertheir angles equal (C) and sides not proportional (d), or theircorresponding sides proportional (D) and angles not equal,or neither their corresponding angles equaluor correspondingsides proportional/' (Boole, p. 126.)

'rhe selections as made upon the abacu8 are of coursesubject to mistake, but only one easy step is rpquired to alogical machine, in which the selections shall be mademechanically and faultlessly by the mere reading down ofthe prernises upon a set of keys, or handles, representing theseveral positive and negative terms, the copula, conjunctions,and stops of a proposition.

Mr. Jevons stated his opinion distinctly that these contri-vatlces possessed a theoretical rather than a practicalimportance. Like the analogous Calculating Machine ofBabbage or Schentz, the logical machine would hardly findpractical employment for the present at least. But its valueconsistecl in showing the true nature of logic as a system ofanalysis of tpe possible combinations of things, in short asthe highes.t and simplest form of the doctrine of combinations.Not only would the .deductive, and especially the inductiveprocesses of logic be thus presented in a new and clearer l i g h t ~ but the relation of logic, the qualita.tive doctrine of combina-tions, to mathem.atics the quantitative doctrine of combinations,.\yould be defined, and the abstract sciences thus brought intoharmony and due subordination.

In the description of his balance given in the last No. ofthe Proceedings, Dr. JOULE omitted to mention a fixedsupport against which the scale rests when the counterbalanceis ~ r e m o v e d . .By this means .the wires are kept constantly inthe ~ a m ~ $ t a ~ .of tension, and are thus preserved. from thederangement w h i c h ; ~ g h t otherwise e n 8 u e ~

Documents

Jevons, William Stanley. April 1866. on a Logical Abacus. Proceedings of Literary and Philosophical Society of Man Chester 5(14),161-165