The Unity of Opposites: a Dialectical Principle Author(S): V

S&S Quarterly, Inc. Guilford Press

The Unity of Opposites: A Dialectical Principle Author(s): V. J. McGill and W. T. Parry Source: Science & Society, Vol. 12, No. 4 (Fall, 1948), pp. 418-444 Published by: Guilford Press Stable URL: http://www.jstor.org/stable/40399913 . Accessed: 28/04/2014 18:44

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

S&S Quarterly, Inc. and Guilford Press are collaborating with JSTOR to digitize, preserve and extend access to Science &Society.

http://www.jstor.org

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES: A DIALECTICAL PRINCIPLE

v. j. MCGiLLand w. t. parry INTRODUCTION

the unityof opposites and otherdialectical principles have sufferedvarious "refutations," and certaininter- ALTHOUGHL prêtât ions and misapplicationshave quite properlybeen laid to rest,dialectic is verymuch alive today. The Platonic-Aris- toteliantradition continues, and both the Hegelian and the Marxian dialectichave manyfollowers. The unityof opposites,which Lenin describedas the mostimportant of the dialecticalprinciples,1 states thata thingis determinedby its internaloppositions. The principlewas firstput forwardby the Milesian philosophers of the sixthcentury B.C., and by theircotemporary, Heraclitus of Ephesus.It held its own throughcenturies of philosophicalthought, though it took differentforms which were seldom clearly distinguished. The purpose of the presentpaper is to separate various formsof the unityof oppositesprinciple, to show that theyare of unequal importanceand that theirconsequences are verydifferent. The principleis not a completemethod or philosophy.If one forgotall about the complementaryprinciple that a thingis determined by its fieldor milieu, the resultwould be a one-sideddistor- tion. It is well to emphasizeat the beginning,therefore, that no at- temptis to be made to describeall phasesof methodin one article, howeverdesirable this might be, but to coverone phase intensively. Lack of space also precludesan investigationof the historicalorigin and contextof the variousforms of the unityof opposites.Some are still importanttoday. We shall confineourselves to two brief examples. From the time of Heraclitusit has been prettywell agreed that

i V. I. Lenin, CollectedWorks, xra (New York,1927), p. 321. 418

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 419 change involvesa unityof opposites,of being and non-being.It is not trueto saythat the world is (being) or thatit is not (non-being), said Heraclitus,but thatit is becoming."You cannotstep twiceinto the same river,for new watersare ever flowingin upon you." The supposedcontradiction involved led the Eleatics to deny the reality of change,and has been employedto disparagechange, ever since. The Hegelian dialectic,on the otherhand, accepted the contradictionas a real aspectof theworld, which is continuallyovercome and continuallyrenews itself in the processof change. Anotherfamous historical example of the unityof oppositesis the One-Manyproblem. The One, Plato has Parmenidessay, must be manybecause it has parts,and the Many must be one, i.e., one Many.This paradoxbecame the foundation of thesystem of Plotinus2 and was also essentialto the Christiandoctrine of the trinity.The same problemreappears in contemporarydiscussions of the founda- tionsof mathematics. Thus BertrandRussell, in his earliertreatment of classesin The Principlesof Mathematics, finds it necessaryto distinguishthe class as one fromthe class as many."In the classas many,"he says,"the com- ponentterms, though they have somekind of unity,have less than is requiredfor a whole, theyhave in factjust so much unityas is required to make themmany, and not enough to preventthem from remainingmany."3 Later on he concludesthat it is morecorrect "to inferan ultimatedistinction between a class as manyand a class as one, to hold that the manyare only many,and are not also one."4 But thisraises the question what we are talkingabout whenwe refer to the class as many. It seems to be one in some sense. Although Russell venturesan answer,he neverthelessconfesses that thereare "puzzlesin thissubject which I do not yetknow how to solve."5This and otherdifficulties were avoided in PrincipiaMathematica (1910) by a solutionwhich involvedthe denial of the existenceof classes, and by the developmentof the theoryof logical atomism.Russell's new positionpermitted statements about classes,even the null-class, thoughclasses were interpreted as fictions.Apparently the one-many

2 Enneadvi, 9. 3 B. Russell,Principles of Mathematics(New York,1903; second edition, 1938), p. 69. 4 Ibid., p. 76. 5 Ibid., p. 77.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 420 SCIENCE AND SOCIETY problem was resolvedonly by translatingstatements about classes into statementsabout individualssimilar to a given individual.

THE MEANING OF OPPOSITES

The meaningof the unityof opposites6 will naturallydepend on our understandingof "opposites."We shall distinguishthe strictor formalsense of the termfrom the more concretemeanings which occur in dialecticalwritings and also in ordinarydiscourse. (1) In thispaper A and -A alwaysstand for strict opposites, i.e., propertieswhich cannot both be true of the same event E (except when E lies in a borderlineor transitionalrange). Thus A and -A can stand for contradictorieswhich cannot both be true,nor false of the same E, or for contrarieswhich cannot both be true of the same E, but maybe both false (providingthat E in no case lies in a borderlineor transitionalrange). Black and non-black,and infant and non-infant,are examples of contradictories;black and white, and infantand adult,are examplesof contraries.This usageconforms to ordinaryformal logic except for the parentheticalphrase: "providingthat E does not lie in a borderlineor transitionalrange." This phrase,however, is crucial,since it appears to constitutea principal differencebetween dialectic and formallogic. Let us take the con- trariesboy and man. Most boysare plainlynot men,and mostmen are plainlynot boys,though they may have some boyishfeatures, but there are also many borderlineor transitionalcases in which any decisionwould be arbitraryand untenable.We have to say "yesand no" or "neithernor." It is to thesestretches that our parenthetical phraserefers. Our definitionof "strictopposites" entails a revision of two principallaws of formallogic, viz.: the law of excluded middle and and the law of non-contradictionand all otherlaws of formallogic which involvenegation. The laws are restrictedto cases which do not fallin borderlineor transitionalstretches. In thesecases it is not true that everythingis eitherA or -A, and it is not falsethat any-

6 It should be noted that the dialectician recognizes the conflictas well as the unity of opposites, as was especially emphasized by Lenin, Selected Works,xi (New York, n.d.), p. 82.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 421 thingis bothA and -A. Yet our assertionthat these laws do not hold forthese stretches involves no contradiction,since we have defined A and -A as mutuallyexclusive except in transitionalranges.7 (2) The term"opposites" is also used withother meanings that differfrom the strictsense definedabove. What we describebelow as "identicalpolar opposites,""opposite determinations,"and "oppositelydirected forces" are not strictopposites, though they are not, on thataccount, as we shall see, any lessimportant.

FORMS OF THE PRINCIPLE

The principleof the unityof oppositeshas been interpretedin the followingways: 1. (a) The conception (or perception)of anythinginvolves the conception(or perception)of its opposite. To understandanything is to distinguishit fromits opposite. This is recognizedby non-dialectical logicians.8 To perceiveanything is to distinguishit fromits background,which is necessarilydifferent (contrary)in color or othersense-quality. 1. (b) The existenceof a thinginvolves the existenceof an opposite. The existenceof a thingdepends upon the existenceof certain otherthings, bound to it by a necessaryrelation: Thus no employer withoutemployee. This principledoes not hold universallyfor con-

7 In Hegelianand Marxistliterature the term"contradiction" is used in a verybroad sense,to includeconflicts and opposingforces (see, forexample, Henri Lefebvre, A la Lumièredu MatérialismeDialectique, i, Logique formelle,Logique dialectique (Paris,1948), p. 174and passim),but also in thesense of formalor logicalcontradic- tion, which is much narrower.In the firstsense, the state of the world or a segmentof it is alwayscontradictory, though the contradictionis also beingover- come. Contradictionthus representsa stage of truthand reality,often of a very highorder. In thesecond sense, on theother hand, contradiction is an unfortunate impasseof thoughtarising from mistake or ignorance.Anyone who falls into contradictionmust give up his position.He has not got the truthat all, though thecontradiction may help him to findit. To avoid thisdouble use of "contradiction," the presentauthors have used the termonly in the lattersense (though modifiedto take accountof the "fringe"). 8 J. N. Keynes,Studies and Exercisesin FormalLogic, 4th ed. (London,1928), p. 58. "The thinkingof anythingas A involvesits beingdistinguished from that which is not Ar

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 422 SCIENCE AND SOCIETY trariesor contradictories.Thus theexistence of falliblemen does not implythe existenceof infalliblemen, thoughthe existenceof men does (biologically)imply the existenceof non-men,e.g., plants or animals. 2. Polar oppositesare identical. 3. A concretething or processis a unityof oppositedeterminations. 4. A concretesystem or processis simultaneouslydetermined by oppositelydirected forces, movements, tendencies, i.e., directedto* wardA and -A. 5. In any concretecontinuum, whether temporal or non-temporal, thereis a middle ground betweentwo contiguousopposite propertiesA and -A, i.e., a stretchof the continuumwhere it is not true thateverything is eitherA or -A. 6. In any concretecontinuum, there is a stretchwhere something is both A and -A. Of these six senses of the unityof opposites,the firstfour do not run counterto traditionalformal logic. Forms5 and 6, on the otherhand, clearlyinvolve a revisionof formallogic. Sense 4 does not assertthat something is bothA and -A, but onlythat it contains oppositelydirected forces. Forms 2 and 3 appear to involvelogical contradiction,but theyreally do not, as we shall see below.

THE IDENTITY OF OPPOSITES

The unityof oppositesis sometimesequated with the identity or coincidenceof opposites. But there may be unity,even inter- penetration,without complete coincidence or identity.Thus One and Many may be conceived as formingan inseparable unity of some sort,which would in factspecifically exclude identity.In general,unity of opposites seems to implydiversity, and to exclude iden- tityin the strictsense. There are, however,two cases at least in which it is possible to speak of the identityof opposites,though even here "identity"can not be takenin a strictsense. The firstis the "fringe"phenomenon, to be discussedlater. The otheris the so-calledidentity of polar opposites. In any ordinarysense, polar opposites,or contraries,such as black and white,hot and cold, cannotbe identical. But whenyou

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 423 abstractsufficiently from circumstances, contraries such as "positive" and "negative"are interchangeableand indistinguishable.Of course, if you specifythat the positiveis, for example, positiveelectricity, and the negative,negative electricity, a distinctioncan be made. In arithmeticand logic thereare also systemsin whicheach of a set of symbolsmay be interchangedfor another of the set (or itself)ac- cordingto a certainrule, without affecting the truthof any proposition.0 This identityof oppositesoccurs only on levels of high abstraction,and the termsare not reallyopposites, but formsof oppo- sition,related to oppositesas propositionalforms are relatedto prop- ositions.10(The unityof polar opposites,on the otherhand, is com- monplace. For example,pure whiteand pure black are hypothetical end-termsof a continuumof intensities,and can be understoodonly in termsof it.) Hegel made a greatcontribution, in spite of his exaggerations, by exhibitingthe identityof oppositeson certainlevels of abstraction. Modern theoryof axiom-setsconfronts the same problem in a differentform. It becomesthe problemof interpretation.The ab- stractsystem may be "meaningless,"but if it can be interpretedas a meaningfulsystem, its usefulnessis demonstrated.

OPPOSITE DETERMINATIONS

A concretething or processis a unityof oppositedeterminations (Form 3). Thus everything,it is said, is both abstractand concrete, both universaland particular.A man, forexample, is alwaysa con- creteparticular which can occupyonly one space-timetrack. Yet all of his characteristicsseem to be abstract,capable of occurringin many places simultaneously.We say that a man is an electrician, a broker,that he is silent,wise or foolish. Since such adjectivesde- scribea man's nature,this nature must be regardedas abstractand universal. This contradictionis accepted,and embodied in the so- called theoryof the concreteuniversal. A judgmentsuch as "Jones

9 There is, for instance, the well-knownduality of Boolean algebra. such as "x is a io A propositional form (or propositional function) is an expression when an substi- philosopher" or "2 R 3," which becomes a proposition appropriate tution is made.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 424 SCIENCE AND SOCIETY is wise," it is said, is expressiblein abstractterms as: "The individual is theuniversal. "n But herea distinctionmust be made. "Jonesis wise" does not mean thatJones is identicalwith wisdom,but that Joneshas wisdom. The apparentcontradiction is resolvedby recog- nizing differentmeanings of "is." Actualityand potentialityare also opposite determinations,for what is actual cannot be merelypotential, nor vice versa,yet everythingis both actual and potential. But the contradictionagain is only apparent. The actual characteristicsof a man, for example, are thosewhich are manifestat a particulartime, whereas the potential characteristics,or "dispositional"traits, are thosewhich would be manifestif appropriatestimuli were presented.It is clear,therefore, that (except for the borderlinecases to be discussedlater) nothingis both actual and potentialin the same respectat the same time,and that there is accordinglyno contradiction(except that involvedin all transitions). Another importantexample of opposite determinationsis the unity of structureand functionin tissues,organs and organisms. Structure and function are demonstrablyinterdependent, and neithercould existwithout the other.They are inseparable,but also distinguishable,like the convex and concave sides of a curve. Still anotherexample, already mentioned, is the unityof one and many. Though whatis one cannotbe many,a classappears to be both. To dispel the contradiction,it is sufficientto specifywhat is one, and what is many,e.g., 12 disciples,and one class of 12 disciples. The difficultyarises only on levels of abstractionwhere logic, evidently, has resourcesto cope withit. In Aristotle'sphilosophy, form and matter,and act and potency, were fundamental,and the traditionhas continuedwith modifica- tions to the presentday. The unities of opposite determinations are formsof commonexperience, and furnisha conceptualframe- work presupposedby scientificinquiries. The precise interdepen- dence of the determinationsin concretecases sets problemsfor the special sciences. ii See Hegel, The Logic of Hegel (fromthe Encyclopaedia),tr. by Wallace, and edition (Oxford,1892) Section 166, p. 297.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 425

OPPOSITELY DIRECTED FORCES Form fourof the unityof oppositesprinciple states: A concrete systemor process is simultaneouslydetermined by oppositelydi- rectedforces, movements, tendencies. Thus a planetaryorbit is de- terminedat everypoint by oppositelydirected forces. Similarly,a society,or its development,may be determined(say) by conflictbe- tweenproductive forces and propertyrelations ("relationsof pro- duction"). In the psychobiologicalorganism the phenomenonis always in evidence. The opposite forcesacting upon the organism, however,are typicallyexpressed by means of antagonisticskeletal muscles-flexorsand extensors;or by smoothmuscles- radial and cir- cular fibers.In all such examples,forces operate in differentdirec- tions. The flexorpulls in, the extensorout. The employers'aim is reducinglabor costs,the employees'is higherwages. Gravityin case of a planetinduces movement toward the centerof the sun, whereas inertiadetermines movement in a straightline. The term"force" does not retainthe same meaningwhen applied in differentfields. The reductionof social forcesto physical,or mechanicalforces, is mechanism,whereas the reductionof physical forcesto social or psychologicalforces is teleology (vitalism),and neitherform of reductionismhas proved successful.Psychological goals and motivations,social movementsand tendencies,cannot be profitablytreated as meremovements, differing only in directionand acceleration. On the otherhand, psychologicaland social forcesor movementsdo alwaysinvolve directed and acceleratedmotion. This is thecommon denominator of "force"as employedin thesedifferent fields.In all examplesof the unityof opposites,in form4, thereis a systemacted upon by two forcesin such a way that,if one of these forcesgrew weaker the whole systemwould veer in the direction ofA, whereas,if theother force grew weaker, the whole system would veer in the contrarydirection, -A. Thus if the gravitationalpull of thesun decreasedsufficiently, the earth'smotion would approximate to a straightline; if the earthlost sufficientmomentum, it would be deflectedtoward the sun. Similarly,when employergroups become muchstronger, compared to the employeeorganizations, wages tend to fall,or pricesto rise,and a whole seriesof changescommonly re- sults; if conversely,the employee organizationsbecome compara- tivelystronger, wages tend to rise,and a whole trainof oppositelydi-

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 426 SCIENCE AND SOCIETY rectedmotions will ensue. Instead of silentsubmission, withdrawal and disunity,there is now vocal protest,demand of rightsand labor solidarity.Instead of prudentretirement from shop windows,the employeegoes on and purchasesneeded commodities.Instead of stop- ping at home,the family goes out forentertainment. On the psycho- biological level, we may also findoppositely directed motions, al- thoughof course we also finda greatdeal more. In any rhythmic activity,such as walking,both flexorsand extensorsare pulling simultaneously,in oppositedirections, though when one is contracted, the otheris only partiallycontracted. The characterof the activity is basicallydetermined by the relativestrength of the contractions of these antagonisticmuscles. If in walkingthe contractionof the extensorsis extraordinarilygreater than thatof the flexors,acceleration and directionof movementis shiftedupward. If the law of the unityof oppositesis to be applied to the subject matterof physics,sociology and psychology,in the same sense, thenthe commondenominator, so faras one can see, would have to be: Oppositelydirected forces or movementswithin a systemdetermine the movementof thatsystem. But as our discussionhas sug- gested,this interpretation of the law is somewhatartificial. It might directthe scientist, investigating the behaviorof a system,to the op- positionmovements within it, but since the movementsreferred to are mechanical,they would have to be reinterpretedif the system were psychologicalor sociological. The oppositelydirected forces could only be understoodwhen sufficientfacts about the organism or societywere known. While if the systemwere physical,the com- petentphysicist would have the relevantdata anyhow,and the law, it mightbe argued,would be of little use to him. It is obvious thatthe law of the unityof oppositesis not a law of physics,or of any otherscience, but a philosophicalgeneralization of findingsin varioussciences. Its identicalmeaning in variouskinds of systemsis: Oppositelydirected forcesor movementswithin a systemdetermine the movementof thatsystem. In its more important interpretation,however, the law is systematicallyambiguous, i.e., "forces"and "movements"are reinterpretedfor every new kind of systeminvestigated. The problemis how such a philosophicalgeneralization can be usefullyemployed. There is littledoubt thatphilosophical generali-

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 427 zations and perspectivesdo sometimesgive guidance to scientific work. Long beforethe evidencefor organic evolution had accumu- lated, there was a philosophyof evolution based upon a certain amount of scientificknowledge which is supposed to have given impetusto investigationsthat finallyestablished the importanceof evolutionin manyfields of science. And similarly,before Newtonian physicscame the Cartesianphilosophy of a world machine,which is supposed to have supplied problems,direction and inspiration. The question is how the law of the unity of opposites,in the fourthform, can give usefulguidance to scientificwork. That it ac- tuallydoes so in particularcases, would be a historicalquestion which lies beyondthe compassof thisbrief paper. The law could provide desirablecorrection wherever scientific method overemphasizes the effectof externalforces acting upon systems,and neglectstheir inter- nal dynamics.Sometimes the spontaneityof organismsis not suf- fientlyrecognized. The internalstimuli arising fromcomplicated needs acquired by adult human beings,for example, are not ade- quately considered,and effortsare even made to explain compli- cated learningby blind or randomtrial and error,or by fieldforces actingentirely from outside the organism. Early behaviorists seemed to have assumedthat given sufficientrepetitions learning one thing is as easyas another,that conditioned responses can alwaysbe estab- lished, the organismbeing completelyplastic and neutral. In sociology,similarly, the attempt has been made to explain basic human behaviorby climate,terrain, technology or institutionsof one kind or another,with little attention given to the needs and reactionpat- ternsof the individual. Societiesare oftencompared with respect to moreor less externaltraits, such as population,geographical extent, or durationin time,without much acknowledgmentof the crucial differencesof internalstructures. In anthropologyan example that comes to mind is the extremetheory that civilizationsand cultures developmainly by a processof "diffusion."All such tendencies,and manymore, illustrate the dangerof neglectingthose contrary forces internalto systems.The principle of the unity of oppositesmay thereforebe said to expressmethodological experience, and revised judgments,in severalfields of science. The complementaryprinciple, meanwhile, is not forgottenin dialecticalliterature. If the motionof a systemis determinedby the

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 428 SCIENCE AND SOCIETY

contraryforces or movementsinternal to it, it is also determinedby the motionsof othersystems external to it, and by the systemof sys- temsto which it belongs. But the latterprinciple falls outside the scope of thepresent article.

THE FRINGE

The fifthform of the unityof oppositesis: In any concretecontinuum,whether temporal or non-temporal,there is a middleground betweenany two contiguous,opposite qualities A and -A, i.e., a certain stretchS of the continuumwhere it is not true thateverything is eitherA or -A. Thus the law of excluded middle, which states thatS is alwayseither A or -A is restricted.12This fifthform of the unityof oppositesapplies to all contradictoryproperties, e.g., child and non-child,but also to contiguouscontrary qualities, such as infantand child. Althoughmost cases are eitherinfants or children, thereis an intermediatefringe in which this cannot be said. Non- contiguouscontrary qualities, however, such as infantand old man, would have a middleground in any case. The dichotomybetween child and adult is crude and unsatisfac- tory.There is a long stretchof the continuumS whichis neitherA nor -A. By applyingthe law of excluded middle as a kind of ideal or normof thoughtwe can reduce the size of S. We can distinguish betweenthe neonate (two days or less) and the infant (more than two days and less than two years)and the child (at least two years but not more thansixteen), etc. By introducingintermediate terms, by use of the microscope,telescope and otheranalytic methods, it is possibleto diminishS but not to eliminateit. The dichotomieses- tablishedin accordancewith the law of excluded middle prove pe- riodicallyunsatisfactory, and are replacedby new dichotomies.The law of excluded middle,as Dewey says,specifies a conditionto be satisfied,13which however, in certainstretches of a continuum,never is satisfied.

12 This restrictionof the law of excludedmiddle may not appear to be a case of the unityof oppositesbecause thereis separationof oppositeshere ratherthan unity. However,as we shall see, the denialof thislaw is normallyequivalent to thedenial of the law of non-contradiction,and hence to form6 of the principle. 13 JohnDewey, Logic, The Theoryof Inquiry (New York,1938), p. 346.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 429

The sixthform of the principleis: In any concretecontinuum thereis a stretchwhere something is both A and -A. When the as- sumptionscommon to almostall logicalsystems are made, the law of non-contradictionis equivalent to the law of excluded middle.14But then the denial that the law of excluded middle holds universally is equivalentto the denial that the law of non-contradictionholds universally.And this is equivalent to the assertionthat there is somethingfor which the law fails. We maytherefore infer from form 5 above that in any concretecontinuum there is a stretchS where somethingis both A and -A. (The continuum,of course,may be temporal,as in growthor developmentalprocesses, or static,as in the color spectrum.) The same conclusionmay be reached with the aid of Dr. M. Black's analysis,15by a directapproach. Suppose we have a seriesof colors and that we divide them into ten segmentswhich are then numberedsuccessively from 1 to 10. Now suppose thatthe colorsin segments1 to 4 are red,whereas those in segments5 to 6 are doubtful,and thosein segments7 to 10 are not-red.Red thereforeis excluded only fromthe range 7 to 10, while not-redis excluded only fromthe range 1 to 4. There is a sense, therefore,in which the rangesof applicationof red and non-redoverlap, and the law of non-contradictiondoes not hold.16

14 There is, to be sure,the systemof intuitionistlogic of A. Heyting (see his "Die formalenRegeln der intuitionis tischen Logik," Sitzungsberichteder Preussischen Akademieder Wissenschaften,Physikalisch-Mathematische Klasse, 1930,p. 47-58), whichasserts the law of non-contradictionwhile omittingthe law of excluded middle;but thisresult is obtainedby eliminatingthe law of double negation:(not notA is equivalentto A), and thusaltering the usual meaningof negation.Such a systeminvolves a revisionof traditionallogic, different from that which we propose, and maybe disregardedfor the present. 15 Max Black,"Vagueness," Philosophy of Science,iv, no. 4 (Oct., 1937),p. 435 f. 16 The argument,in Dr. Black's generalizedform, is as follows:If Lx meansL is trueof x and - Lx means L is falseof x, we may say thatLx is only definitely false for the range 7 to 10, whereas-^-Lx is only definitelyfalse for the range 1 to 4. The "inabilityto finda logical interpretationof doubtfuland perhapsin termsof the two truthvalues, truth and falsehood,forces us to admit that the rangesof applicationof Lx, 1 to 6, and of - Lx, 5 to 10, overlapin the fringe, 5, 6" (p. 436). "Whetherthe numberof termsin the fieldof referenceis finiteor infinite,"Dr. Blackgoes on to argue,"denial of theexistence of a unique boundary betweenthe domainsof Lx and - Lx leads to contradiction"(p. 437).

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 430 SCIENCE AND SOCIETY

THE UNITY OF OPPOSITES AND FORMAL LOGIC

The programof denyingthe unrestrictedvalidity of formallogic is difficult,since our thinkinghas been molded by formallogic and it is embeddedin our language. We shall go on thinkingin termsof it anyhow,but the dialectician will always be mindfulthat the dichotomieshe sets up are only approximateand can be improved. That is, thestretch S can be made smallerand moredefinite. Anotherreason why denial of the unrestrictedapplication of the law of non-contradictionand the law of excluded middle is difficult, is that these laws are confirmedby experiencein innumerablein- stances. Usually,when one says,this is a chair,a goat, or a human being,the contradictoriesare manifestlyimpossible. We see at once thatwhat we have beforeus could not be a non-chair,a non-goator a non-humanbeing. Either-oris also obviouslyvalid throughoutvast rangesof humanexperience. It is onlyin borderlinecases thatthere is doubt. It is onlyin thesecases thatthere could be anyjustification in sayingthat a certainthing is neithera chair nor a non-chair,or thatit is both. There is no question that theselaws have strongin- ductivesupport though the exceptionsare also richlyconfirmed. The main traditionof logic in the past,overlooking the excep- tions,held thatlogical laws are universaland necessarytruths, and hence impossibleto establishby induction. The view takenwas that theyare intuitivecertainties or, withKant, a prioriprinciples of the Understanding.A certaindifficulty always attached to such interpretations,however. A greatdeal of experienceof the oppositions in the world seemed necessaryto the intuition,or to the operation of the Understanding.Neither was reallya priori or de novo. In- stantaneouslogical convictions, like otherconvictions, now appear to have a history.Since the formationof logical conceptshas been studiedin childrenand variationsof logical habitshave been noted in differentsocieties, it has become evidentthat the learningof logical laws is a protracted,cumulative process, which had its beginning perhapsin those firstdiscriminations where figureis distinguished fromits opposingground, and in the firstdenials and frustrations- the "you can't have that" experience. Indeed, striving,success and frustrationwould seem necessaryto any comprehensionof negation. The main streamof modernlogic has veered away fromintui-

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 431 tionism,and fewlogicians today would talk about intuitive or trans- cendentalnecessities. The primitivepropositions, or axioms,from whichcontemporary logic deduces its theoremsare not affirmedto be self-evident,but are describedas assumptions.When this course is taken,however, the usefulness of logicwhen applied to the con- creteworld remains mysterious. Why one setof assumptions should yielda systemhaving important interpretations, another not, re- ceivesno answer. This difficulty,which is oftencited, can be avoidedby an inductiveapproach. Since in the obviousranges of experience,the for- mulaeof formal logic are always confirmed, we may say that they have a probabilityof 1 or certaintyin theseranges. Thus thereare count- lessareas (which, however, need have no sharpboundaries) where the formula"not both A and -A" alwaysholds. But in thetransitional ranges,as wehave seen, the general formula breaks down. In passing alongthe continuum from blue to green,the probability that colors will notbe bothblue and not-blue,runs from 1 to 0. In thissense we maysay thatthe probabilityof a logicalformula (i.e., where the quantifieris omitted)is determinedby the ratioof favorable to thetotal number of cases. Favorablecases abound in thelearning process.We are alwaysdiscovering that different discriminations, interpretations,needs and objectives,which we had supposedto be jointlypossible, are reallyincompatible. We have to learnin in- numerablecases thatends withoutcertain means are impossible, and thatcertain means, which seemed to conduceto an objective, arereally inconsistent with it. Either A or -A, butnot both, is richly confirmedin experience,and learningis a processof discovering whatconcrete properties exemplify A and -A. Each suchdiscovery is a favorablecase. The unfavorablecases are also encountered in everyfield, though notnearly as frequentlyas the favorable. Unfavorable cases are those in whichthere is, in fact,no wayof comingto a definitedecision as to the applicationof a certaindichotomy. Subjects confronted withthe continuum of colorsin thespectrum will be able to dis- tinguishtwo contiguous colors, such as blue and green,within the obviousranges, but thereis an intermediaterange in whichdis- criminationis impossible.Not onlywill subjectsdisagree among themselvesas to whichcolor it is, but anysubject at differenttimes

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 432 SCIENCE AND SOCIETY will disagreewith himself and, in certaincases, will be unable to de« cide whetherthe color is blue or non-blue,or blue or green.11 The same is trueof Engels*example of livingand dying:18Dying is a processthat takes place in time,and thereis thereforea stretch of the continuum in which neither "dead" nor "living" are ap- plicable. You may tryto get around the factsby sayingthat when properlyanalyzed, "dead" and "living" do not apply to the whole organism,but to the individualcells, some of whichare dead, others living,at any particulartime during the dyingof the organism.But this merelyshifts the difficultyfrom the organismto the cell. The cell also takestimes to die, and fora certainstretch neither "living" nor "dead" can be applied. Moreover,the death of the organism cannot be properlyreduced to a mere sum of dyingcells because the cells are interdependentin dyingas in living. On the empirical approachwe are taking,the failureof formallogic to apply in such caseshas an objectivebasis.

IS VAGUENESS SUBJECTIVE?

BertrandRussell, on the one occasionon whichhe discussedthis matterin print,employed the same example. "Death," he wrote,"is also a process;even when it is what is called instantaneous,death mustoccupy a finitetime. If you continueto apply the name to the corpse,there must graduallycome a stage of decompositionwhen thename ceasesto be attributable,but no one can say preciselywhen thisstage has been reached."10"Man" is also an indefiniteterm since thereare doubtfulprehistoric cases. There is no lack of examples, but Russell attributesthem, in everycase, to the vaguenessof language. "The law of the excluded middle is true," he says,"when precisesymbols are employedbut it is not truewhen thesymbols are

17 The formallogician may say that the color is, afterall, eitherblue or non-blue, whetheror not the subjectcan say which.But this presupposesthat the word "blue" has an absolutelydefinite meaning, regardless of the way it is used. Where thereis inescapableindecision as to the applicationof the term"blue" to an object,we mightas well saythat it is neitherblue nornon-blue, as thatit is either. 18 F. Engels,Herr Eugen Dührings Revolution in Science (New York,1959), p. 132 f. 19 "Vagueness,"Australasian Journal of Philosophy,i (1923),p. 88.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPÖSITES 433 vague,as in fact,symbols always are/' Althoughthe articlesets out to provethat the failureof the law of excluded middle resultsfrom the vaguenessof languageonly, no real argumentis offeredfor this subjectiveexplanation. "There is a tendency,"he says,"in those who have realizedthat words are vague to inferthat thingsalso are vague This seemsto be preciselya case of thefallacy of verbalism -the fallacythat consists in mistakingthe propertiesof wordsfor the propertyof things."20And yet nowheredoes he even state criteria of objectivityand subjectivity. This defectof Russell's articlewas remediedby a discussionby Max Black whichis, in effect,an answerto Russell'ssubjective reso- lutionof theproblem. Vaguenesscannot be explainedas theabsence of scientificprecision, Black points out, since "the indeterminacy which is characteristicof vaguenessis presentalso in all scientific measurement."21Vagueness is not a defectof language. It is not to be identifiedwith ambiguity, since even the mostprecise and unam- biguous termsare vague, the differencebeing that the ambiguous term will have more than one "fringe,"or indeterminatearea. "A symbol'svagueness," he holds,consists "in theexistence of objects concerningwhich it is intrinsicallyimpossible to say eitherthat the symbolin question does, or does not, apply. The set of all objects about whicha decisionas to the symbol'sapplication is intrinsically impossibleis definedas the "fringe"of the symbol'sfield of application."22 Black'sargument for the objectivity of vaguenessis interesting:If the vaguenessof a symbolis subjective,he suggests,its use implies somethingabout the speaker (psychologicalfacts), whereas if it is objectiveits use impliessomething about the environment(physical facts). Thus an ambiguous symbol,which is clearly a subjective phenomenon,implies psychological, but not physicalfacts. We can appeal to less equivocal symbolsand the ambiguitydisappears. In thecase ofvague symbolsthis is not true. Even when discrimination and linguisticprecision are at the maximum,the fringe,though perhaps reduced in extent,is still demonstrable.Confronted by the

so Ibid., p. 84. 21 "Vagueness," Philosophy of Science (1937)» P- 4*9< 82 Ibid., p. 430.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 434 SCIENCE AND SOCIETY continuousgradations of colorsin thespectrum, even the mostsensi- tive observers,employing the utmostrefinements of language,are unable to eliminatethe fringe. It is thereforereasonable to con- clude that the fringeis an objectivefeature of the seriesobserved. The same testis usuallyapplied to determinethe objectivityof the "reports"of scientificinstruments, such as the telescope,which are analagous to human discriminators,or reporters. If a telescope "reports"a certain phenomenon,its objectivityis determinedby employingother telescopes, located at higheraltitudes, or tiltedat a differentangle, for example,to allow for the rotationalvelocity of the earth. If the phenomenondisappears when the conditionsof observationare altered,it is not regardedas an objectivefeature of the starsobserved.28 The non-verbalcharacter of the phenomenon,it mightbe added, is also shown by discriminationexperiments, using dogs and other animals as subjects. Pavlov, for example, associatedfood with an illuminatedcircle, but no food with an ellipse of the same area. When the ellipse was of the proportion2 to 1, the dogs readilydis- tinguishedthe two figures,salivating to the circlebut not to the ellipse. When the ellipse was graduallymade thicker,the dogs were still able to discriminate.When the ratio of 9 to 8 was reached, however,and the ellipse was almosta circle,discrimination became impossible,and in threeweeks of effortno progresswas made. Evi- dentlythe limit of canine discriminationhad been reached. If hu-

23 One point is not sufficientlystressed by Professor Black. The subjectivityof the "report" of a given telescope is not decided merelyby its conflictwith the "reports" of other instruments,for the firsttelescope may be a superior one in the sense that it gives more objective reports. Many facts and theories are employed to establish the superiorityof scientificinstruments; for example, theoriesand factsabout lenses, and the distorting effectsof the earth's atmosphere. In the case of scales, the superiorityof some scales has been correlated with the type of mechanism and materials used so that the accuracy can be predicted in advance. But even the most sensitive scale which records the most minute differencesof load, will demonstrate the fringe,giving slightlydifferent recordings for the same load at differenttimes. The fact that the fringeis not eliminated under any conditions would indicate that the phenomenon is not merely verbal, nor merely subjective, but also objective. Dr. Black's furtheranalysis of the phenomenon distinguishesthree factors:symbol, subjects (or observers), and objects. We agree with him in stressing the funda- mentally objective character of the situation.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 435 man adultswere substituted for dogs, the fringewould be narrowed, and stillmore, if scientific instruments were used, but it would not be eliminated. The existenceof the fringedoes not seem, therefore, to be a whollycanine, human or instrumentalfact, but also a physical one. Even the bestinstrument would fail to discriminatea math- ematicalline dividingA from-A, since mathematicallines cannot be discriminated,and by all accounts,do not exist in nature. Though the fringeis evidentlynot a merepsychological fact, the size of the fringedoes varywith different observers, or groupsof observers.Thus the size of the fringe,or the degree of vaguenessof the symbol,is alwaysrespective to a class of observers.The size or degreeis alwaysfor a givenclass of subjects,though the class maybe a largeone. The size of the fringeis a difficultconception, however, sincethe fringehas no distinctboundaries. No one can saywith cer- taintyexactly where it begins and where it ends. ProfessorBlack has devisedan ingenioustechnique for dealing with the difficulty,24 and ProfessorHempel25 has contributedsome improvements.Pro- fessorBlack explains the vaguenessof a symbolin termsof varia- tionsin itsuse by a givengroup of users,applying it to a givenseries of objects. He defines"the consistencyof applicationof a term"to the membersof a series. Suppose the seriesto be a seriesof chairs, runningfrom the most obvious examples,such as a Chippendale chair,to evermore doubtful cases, and endingwith a shapelesspiece ofwood. Almostall observerswill call the firstmembers of the series "chairs,"and the last membersof the series,"non-chairs." In other words,the consistencyof applicationof the terms"chair" and "non- chair" will be highestat the beginningand end of the series respectively.Toward the middle of the seriesthe cases become more doubtful,however, and consistencydecreases. The term"fringe" is henceforthused by Dr. Black with a new meaning,viz.: the range of objectswhich are called "non-chairs"about as frequentlyas they

24 Moreexactly, Dr. Black'stechnique enables him to eliminatethe idea of the fringe as a definiteset of objects.This he regardsas a crude untenablenotion, since it leads to logical contradictionby the kind of argumentpresented above in the sectionon the fringe. 168. 25 C. G. Hempel,"Vagueness and Logic,"Philosophy of Science,April, 1939, p.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 436 SCIENCE AND SOCIETY are called "chairs." The vaguenessof a symbolis to be measured by the curveon whichthis varying consistency is plotted.26 Two minorobjections may be expressed. Vaguenessshould be definednot only by the conflictingdiscriminations of differentob- servers,or of thesame observerat differenttimes, but also by the in- ability, or failure,of discrimination.Such failure,hesitation or blocked responseis frequentlymet with in psychologicalstudies of sensorydiscrimination. Secondly, discriminations of differentob- servers,as of differentscientific instruments, are not of equal accuracy. Such deficienciesin the formula,however, could probablybe remedied. We must add that we believe (contraryto Professor Black) thatthe term"fringe" can be used in the originalsense consistently,provided the laws of logic are statedwith appropriatere- strictions;and this is the practicewe shall follow. POSSIBLE LOGICS FOR DIALECTIC The discussionso far poses the question: What alterationsof formallogic are entailed by the principleof the unityof opposites in forms5 and 6? It has been pointedout thatthe restrictionof the law of excluded middle would mean a radical revisionof logic; yet this has oftenbeen contemplated,even by Aristotleapparently. It seems still more drasticto restrictthe law of non-contradiction;in fact,it has generallybeen consideredunthinkable. The dialectician is as intentas anyoneelse to avoid self-contradiction,and continues to thinkof formallogic as prescribingan ideal for exact thought. There are severalpossibilities to be considered. (a) One alternativeavailable to the dialecticianis to retain the

26 If we referto a member of the series of objects as x, let L and -L stand for a term and its contradictory(e.g., "chair" and "non-chair"), let m be the number of discriminations of x as L, and n the number of discriminationsof x as -L, then Professor Black defines "the consistencyof application of L to x as the limit to which the ratio m/n tends when the number of [discriminationsof x] and the number of observers increase indefinitely" (loc. cit., p. 442). The "consistency profile" is the curve on which the consistencyof application of L to x is plotted for everyx in the series,from those most frequentlycalled L to the least frequently. This curve is steep in the middle range if L is a precise symbol, and flat if it is a vague symbol. ProfessorBlack proposes to measure vagueness by the flatnessof this curve. Professor Hempel has raised a technical objection to this method of measurement (based on the non-metriccharacter of the series), and proposed an alternative formula which avoids this difficulty(lac cit., p. 166).

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 437 principlesof formallogic, but to assertthem universally (if theyin- volve negation)only forcases whichare not in the fringe.It is not assumedhere thatthe fringehas sharpboundaries, nor that it is so well definedthat we can alwaystell whetheran object fallsin it or not. But it is assumedthat for certainthings we can decide defin- itelythat they are not in the fringebetween a certainproperty and its opposite.If we write"Fringe -A" for the fringebetween A and -A, the law of excluded middle would be expressedin thisfashion: For all x not in Fringe-A, eitherx is A or x is -A. This scheme,if it can be workedout consistently,has severalad- vantages.It retains traditionallogic for the obvious cases while acknowledgingexistence of doubtfulcases in the fringe.It also has the meritof fittingin wijththe inductiveapproach to logic,and appears to be the systempresupposed by the conceptionsof opposites and the fringeadopted in thispaper.27 (b) An alternativeprocedure is to adopt the quantitativetech- nique of ProfessorBlack. Roughly,what he saysis as follows:If we replaceL and -L by consistencycurves, representing the consistency of observersin applyingthese terms to a seriesof items,then the law of excludedmiddle, L or -L, maybe restatedin a formthat is valid.28

27 In addition to the statementsof logical principles restricted,as above, to the non- fringe,we would also have unrestrictedstatements, in which, however,it would be asserted that the logical formula applies with a certain probability- a probability determined roughly by the ratio of favorable cases to the total cases in human experience. But for furtherrefinement it must be rememberedthat not all observa- tions are of equal accuracy and weight. 28 He replaces the propositional functionLx by L(x,C), which means: "the symbol L applies to x with consistencyC." When the consistencyof application of L to x is C, then, by Black's definition,the consistencyof application of -L to x is the reciprocal,_u_Instead of the law of excluded middle in the form: "Every x is either "c" L or -L," he has an operation which permits the transformationof L(x,C) into -L (xj) (loc. cit.,p. 451 f.).

With appropriate changes, the law could also be stated for contiguous, contrary qualities which together exhaust a series. If a series begins with squarish rectangles ("plates") and gradually descends to very narrow rectangles ("sticks"), and "plates" and "sticks" are the only terms to be applied, the consistencycurve may be expected to be similar to that where the termsare "plate" and "non-plate." See LivingstonWelch's "A PreliminaryStudy of the Interactionof ConflictingConcepts of Children Between the Ages of 3 and 5 Years," The Psychological Record, 11,so (1938).

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 438 SCIENCE AND SOCIETY

This procedurediffers from that of alternative(a) in denying the existenceof the fringeas originallydefined, i.e., as a class of objects qualitativelydistinguished from the non-fringe.Any object thatis L maybe, so to speak,a littlebit -L, if some people judge it so. The term"fringe" may still be used, but redefined(as explained above); and it is not requiredfor the definitionof "vagueness."This alternativeis similarto the first,however, in involvingan inductive approach. (c) For the dialecticianwho wantslogic to recognizethe fringe, or borderlinecases, there is a thirdalternative. He may adopt pro- visionallya three-valuelogic. Instead of thetwo values, true and false, the Lukasiewicz-Tarskilogic (or ratherone of these logics) intro- duces threetruth values: 1, 1/%and 0, or "certainlytrue," "doubtful," and "certainlyfalse," as Lewis and Langfordinterpret them.29 The middle term between true and false in this systemis i/2or doubtful,and its application to the problemof the fringeis clear. There is a middlerange of blue on the color spectrumwhich nearly all observerswould call blue, and thereis a middle range of green which almostno observerswould call blue, and finallythere is be- tweenblue and greena fringewhich many observers would call blue, and many,non-blue. These latterjudgments could be interpreted as 1/2or doubtful,whereas the formerattributions would be true and false,or 1 and 0, respectively.This logic thereforeseems to be consistentwith both the fifthand sixth formsof the principleof the unityof opposites. It is significantthat neitherthe law of excluded middlenor the law of non-contradictionappears in thislogic. (d) The Heytinglogic, to which we have alreadyreferred, also seems to allow for a fringebetween A and -A, because it fails to assertthe law of excluded middle and the law of double negation, - -A = A. On theother hand thelaw ofnon-contradiction is asserted, whichwould exclude the sixthform of the principleof the unityof opposites. It is not our purposehere to pass on the meritsof thesenew logical developments,but only to point out thatthe dialecticianwho in- sistsupon the importanceof the fringehas a choice among several possiblesystems of logic.

29 C. I. Lewis and C. H. Langford,Symbolic Logic (New York, 1932) p. 214.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 439

DOES LOGIC APPLY TO THE WORLD?

Dialectic differsfrom formal logic in at least one importantre- spect.It reformulateslogical principlesso as to allow for the exist- ence of the fringe. Its empirical confirmationis thereforemuch strongerthan thatof formallogic. The latteris confirmedthrough- out the rangeof obvious cases,but failsfor the fringe,whereas dialectic holds for both. The probabilityof dialectical principlesis determined,in a manneralready explained, by theratio of favorable to the total numberof cases. Is such empiricalevidence the only typeavailable? There has been a persistentconviction that logical principlesare self-evidentand intuitivelynecessary. We do not deny the occurrenceof intuitivecertainties, but only insistthat theybe testedagainst the facts, and theirorigin traced in thelearning process. Too manyself-evident truths have turnedout false to warrantany othercourse. The view that logical laws are self-evidentand immutableis to be rejected.So also the currentconventionalism. The latterstates thatformal logic does not describegeneral features of the objective world,but prescribesverbal conventions.It is simplya set of rules for regulatingscientific communication, those rules being prefer- able whichbest accomplishcertain human ideals, such as precision and inclusiveness.Professor Nagel, who defendsthis view, inter- pretsthe principle of non-contradictionas requiring"that in a given contexta termmust not be applied to a giventhing and also denied to it; and the principleof excluded middle is formulatedin a cor- respondingway."30 But he acknowledgesthat everydaylanguage, and even the specializedlanguages of the sciences,do not entirely conformto theserequirements. There is no objectionto formulatingthe laws of logic as rules for using language. But the factthat the laws can be interpretedethi-

30 ErnestNagel, "Logic withoutOntology/' Naturalism and the Human Spirit,edited by Y. H. Krikorian(New York, 1944),p. 225. Of course,if the principlewere formulatedin the same way,it would say that in a givencontext a termmust eitherbe applied to a giventhing or denied to it; whichwould oblige us to be omniscient.If weakenedto a commandto apply the compoundterm "either A or non-A"to any giventhing, it would have the unfortunateconsequence of making silence impossible.Perhaps the principleis to be formulatedas a prohibition againstdenying both the termsA and non-Ato a giventhing.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 440 SCIENCE AND SOCIETY cally,as linguisticprescriptions, does not implythat theyhave no referenceto the objectiveworld. The materialistwill want to know whysome rules are more successfulthan othersin regulatingcom- munication,organizing our knowledge-in achievinghuman ideals. He cannot escape the convictionthat the successof an instrument dependsupon propertiesof the object to whichit is applied, as well as of theinstrument itself and its user.He will also be curiousabout the ideals themselves.Do theyvary fromone societyto another? Under what conditionsare theylearned? Such questions are rele- vant to theobjective import of logic,and cannotbe dismissedmerely because our knowledgeis still insufficientto furnishdefinitive an- swers. ProfessorNagel admitsthat the ideal of precision is not arbitrary,because communication and inquiryare directedto the achievementof certainobjectives The assertionthat this is so requires supportby empiricalevidence- evidence which it is possibleto produce. But the availableevidence is drawnfrom the studyof the behaviorof menengaged in inquiry;it does notcome from a considerationof struc- turalinvariants found in otherdomains.31

It will be observedthat on thisview logical laws are instruments for the attainmentof certainhuman objectives,and empiricalevidence is admittedlyrequired to show thatthey do in factserve these purposes. It is regrettablethat Dr. Nagel does not producesome of thisevidence. Had he done so, we could perhapsdiscover whether it is his intentionto admit as evidenceonly the behaviorof men con- ductingan inquiry,or whetherhe would also include the factsof the world with which theirinquiry deals. Dr. Nagel's positionimplies, in any case, thatsince logical laws are relativeto human ideals and objectives,they may change with a change in theseobjectives; and secondly,that since particularlogical laws are justifiedby empirical evidence,the weightof evidence mightconceivably shift with cir- cumstancesin favorof otherlaws. ProfessorNagel, nevertheless,will not allow that logical principles can ever be establishedby empirical induction. His main argumentis that logical principlescannot be refutedby negative

$i Ibid., p. 126.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 441 instances.If thereappears to be a negativeinstance, in any particular case,we alwaysre-examine the empiricaldata to bringthem into harmonywith the logical principle. We neverreject the principles themselves;for if we did not regard them as necessarilytrue, we would run counterto the establishedusage of the expressionsthey involve,such as "and" and "if . . . then."32He concludesthat there is no clear sense in which logic can be experimentallyverified. Logicalprinciples [he contends]are compatiblewith any order which the fluxof eventsmay exhibit; they could not be in disagreementwith anythingwhich inquiry may disclose,and if theyshould ever require revision,the grounds for such alterations must lie elsewherethan in the subjectmatter of the naturalsciences.38 But thispassage is contradictedby a laterone, in whichhe calls attentionto a recentsuggestion thatin orderto developthe theory of subatomicphenomena in a manner conformingboth to experimentalevidence and to certainideals of economyand elegance,a "logic"different from those normally employed mayhave to be instituted.The suggestion. . . calls attentionto thefact in a strikingway that under the pressureof factualobservation and normsof conveniencefamiliar language habits may come to be revised; and it indicatesthat the acceptanceof logical principlesas canonical need be neitheron arbitrarygrounds nor on groundsof theirallegedly inherentauthority, but on theground that they effectively achieve cer- tainpostulated ends.84

It appears,then, that Dr. Nagel's denial of the relevanceof empiricalevidence to logic,which he makesa greatdeal of in his paper, is difficultto carryout consistently. It is truethat when a logical principleappears to be violated,we usuallyre-examine and revisethe otherdata. The same thingis true of the principlesof physics.In everyfield we attemptto save the generalprinciples-whenever, that is, theyare betterestablished than the data to which theyare applied. But sometimesit is the principle whichis revised. Such revisionshave occurredmore thanonce in the historyof logic. For example,Kant correctedAristotle's for-

«2 Ibid., p. 2io. 33 Ibid., p. 220. 34 Ibid.,p. 232; italicsours. The referenceis to a paperby Birkhoff and von Neumann.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 442 SCIENCE AND SOCIETY

mulationof thelaw of contradiction,omitting the referenceto time, and the superfluousexpression of certainty.85 Many otherexamples could be given to show that logical principles, like other scientificprinciples, are not sacrosanctprescrip- tions,but modifiableto suit the purposesof logic,mathematics and other sciences. Thus Brouwer and other mathematicallogicians have revised logical formulationsto fit the needs of mathematics. It is true thatlogical principlesseem to be intuitivelytrue and even self-evident.This is because (apart fromthe fringe)there appear to be no exceptionsin our experience,and in theoverwhelming majorityof cases one is unable to imagineany. But fringephenomena, as we have seen, have to be accepted. They oblige us to admit rangesof exceptionsto formallogic, in everycontinuum. These ex- ceptions,which dialecticincorporates into the statementsof logical principles,are objectiveand important.As Dr. Black says,". . . de- viationsfrom logical or mathematicalstandards of precisionare all pervasivein symbolism;... to label themas subjectiveaberrations sets an impassable gulf between formallaws and experienceand leaves the usefulnessof the formalsciences an insoluble mystery/'36

In general,the main objection to the view thatlogic has no objective import,but is merelya systemof rules for organizingour knowledge,is that it fails to explain the enormousutility of this science. The conventionalismwe have discussedadmits the utility but makesa mysteryof it.

CONCLUSION

We have not attemptedin thispaper to give new and interesting examples of the unity of opposites,but rather to distinguishsix differentforms this principlehas taken in dialecticalliterature. It was foundthat some of theseforms are subjective,having to do with conceptionand abstraction,others concrete and objective; that the

35 Cf. P. Popov,"The Logic of Aristotleand FormalLogic," Philosophy and Phenom- enologicalResearch, vin, p. 8 f. In the same way, modernlogicians have been obligedto denythe existentialimport of universalpropositions. 36 Max Black in Philosophyof Science,loc. cit.,p. 429.

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions THE UNITY OF OPPOSITES 443 lasttwo forms required a revisionof customarylogic while theothers did not. Naturally,an illustrationof one formof the principleneed not be an illustrationof the others. The same stateof affairs,however, might illustrate various forms of the principlein differentways. A developingstrike situation, for example,is determinedby oppositelydirected movements or tendencies (form4). There is a tendencyto strikebut also an impulse to cautiouswithdrawal, and the outcomeis determinedby the composi- tion of thesetendencies and by the preponderanceof one of them. Fringephenomena (5, 6) could also have some significance.In the peripherythere are employeeswho are neitherclearly in (with) the union, nor outside (against)it. The outcome may depend, in part,upon the extentof this indeterminateor hybridfringe. An- otherfactor plays a part in such a situation. The language of the strikeorganizers may be too abstract,consisting of general slogans and appeals whichtake little account of the concreterealities, ignor- ing the circumstancesand hazardsof the employeesor the specific dispositionsof the employer. The organizershave failed, in the specificsituation, to achieve an effectiveintegration of abstractand concrete,potential and actual (3). It is well to emphasizethat dialectical principles never by them- selvesprovide any solution to concreteproblems, afford no predic- tions. They describeonly the mostgeneral determinations of proc- esses or systemsand cannot,of course,specify the outcome of any particularcase. What the principleof the unityof opposites (forms 3, 4, 5 and 6) statesis that in any systemthere is a unityof oppo- sitesof some kind appropriateto it, and thatthe specificinteraction of the oppositesdetermines the momentarycharacter of the system, but also futurestates. The testof theprinciples, in thisgeneral form, would be: Does a changein the interrelationof the oppositesbring about a change in the system?To revertto a previous example: Would the introductionof more specificand factualmaterial into the union organizers'language, in place of purelyabstract appeals and slogans,be apt to changethe developingstrike situation? Would a preponderanceof one of the opposing forceschange the system? Or finally,would the narrowingof the fringeof doubtfulemployees who are neitherclearly in, nor out of the union, or neitherclearly withnor againstit, have any appreciableeffect on the system?The

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions 444 SCIENCE AND SOCIETY

principleof the unityof oppositeswould enable you to predictthat somechange would result,but not whatchange. The principleis thereforea standinginvitation to acquire suffi- cient concreteknowledge to apply it successfully,to replace the variablesof thegeneral formula with concrete values. Hegel's whole philosophyis an insistenceon thispoint, but it was Engelswho gave the deeper materialistemphasis. It is clear thatdialectic should not be comparedto science,for it is not intendedas a substitutefor it, but as a frameworkfor scientific inquiry. Its possibleadvantages are to be seen,rather, in comparisonwith the frameworkfor inquiry provided by otherphilosophical traditions. What does the usual tradi- tion of formallogic say?We have seen that it makes no provision forthe fringe, and is obligedto overlook,for example, the mesoforms or intermediateforms which occur in the continuityof evolutionary development.And thistradition has also overemphasizedthe importanceof propositionsof the formall A is B and at least one A is B, usuallyignoring the intermediate range of quantifiers which are prac- ticallymost important. There has also been a strongtendency to re- strictbelief to certaintyand outrightrejection, as if the intermediate degreesof beliefwere not obviouslythe moresignificant. Along with thishas gone the adulation of the syllogism,and a correspond- ing depreciationof thevalue of inductionand concretestudies. The sterilityof thislogical traditionhas been greatlyremedied, but there is still much room forimprovement. Other philosophicaltraditions have also laid down general principlesof method. One emphasizes intuition;another, perception as the only testof truth;while still anotherinsists that practice, without any commitmentas to the nature of the world outside the laboratory,is a sufficientguide to inquiry. It is the obligationof the dialecticianto demonstratethat his inductivelygrounded principles provide a betterframework for in- quirythan those of otherschools. To do so, he would need to go far beyondthe boundariesof thisbrief exploratory article, and in various directions.In particular,it would be necessaryto exhibit the interrelationof the unityof oppositeswith other dialectical prin- ciplessuch as thetransition from quantity to qualityand thenegation of negation. Hunter College; Universityof Buffalo

This content downloaded from 128.95.104.66 on Mon, 28 Apr 2014 18:44:38 PM All use subject to JSTOR Terms and Conditions