Quick viewing(Text Mode)

Non-Aristotelian Logics

Non-Aristotelian Logics

studien\seminarTEXT published in: TheMonist,45 (1935) p. 100-117. exclaimed: "ThankGod,mathematicians ofabsolutes fr of thedisappearance craves for.Letusbesure iswhat,beyond of itsresultsforthat he stated that the charm ofpuremathematic he statedthatthecharm subtlecritic thatotherwise Lewis Carroll, insistent. Thisfaith intheeternalcerta In mathematicsandlogicth wished. the Universeknowsmoremathematics than vi realismofthetheistic in thePlatonic culture.Thelatestra of WesternEuropean in animportant exercised has butwhateverthecorrectacco satisfactory, arerarely explanations not master itintellectually.Suchpsychoanalytic came todespisena paradoxes ofmotion) continues,some theargument And so, Leibniz, todealwithawo and ofNewton calculus the technique, amathematical didnothave Greeks ofmathematics su onestudent as may be, inthecaseofPl , And in defectsofthephysicalenvironment. compensate forthe those absoluteswhich moths andrust.Itappearstobetruein inhisimag external forces:hecreated all men dowhodevelopaninferiority himself manhadtoadapt (pre-scientific) exalt thepermanent andinvariant,itmight befound thatsinceearlier apsychologicale If oneweretoseekfor Einstein's system. of ofthevelocitylightisanintegralpart (absoluteness) the constancy of theprinciple for mechanics, Newtonian hasreplaced relativity physicswhich demand Perhapsthephysicist's absolutes. space, forexample, physics, Newtonian Inscienc markchange isa ofimperfection. as the fieldofphilosophy, is worshipofthechangeless Not !"This itcanth Of suchanobjectofreverence crav One ofthedeep-seated NON-ARISTOTELIAN something permanent, for something eter something forsomething permanent, * Oliver L.Reiser[ University ofPitsburgh * ] of something!" More recently, in commenting on the fact incommenting onthe ofsomething!"Morerecently, rld characterizedbyvarious

is known,nolessaperson e demand for something abso ings of thehuman mind se inty of something permanent was voiced by wasvoiced inty ofsomethingpermanent en be exclaimed, "Oh Thou Who Changest "OhThouWhoen beexclaimed, Changest religion that the "eternal verities" embody "eternalverities"embody religion thatthe xplanation of this tendency of the mind to ofthemind tendency ofthis xplanation ew of Jeans, whose supreme Architect of of ew ofJeans,whosesupreme Architect still havethelawofcontradiction!" all mental treasure,thehuman intellect ination an ideal worl ination anideal om naturalscience, by nomeans confined nally thesame,changelessandabsolute. of conventional habits of thought, when habits ofthought, ofconventional ture philosophicallybecausetheycould atonic preference for the changeless, it forthechangeless,it preference atonic to a changing environment,hedidwhat achanging to of the Greeks (e.g. Zeno, with his his (e.g.Zeno,with oftheGreeks mification of this influence is evidenced mification of isevidenced thisinfluence complex in the face of overmastering complex inthefaceofovermastering fluence an the subsequent subsequentphilosophies the an fluence e this idea has also manifested itself. In e thisideahasalsomanifesteditself.In time, andmatter as areconceived unt may be,itistruethatthePlatonic s "lieschiefly intheabsolutecertainty ggested, thatthiswassobecausethe ever thought of, or could have thoughtof,orcouldhave Platoever for an absolute even appears in the inthe appears even anabsolute for modes andratesofchange. ems to be a desire for for beadesire to ems than Plato argued that than Platoarguedthat lute hasbeennoless amathematician d incorruptibleby to religion, for, in to religion,for, Sommer-Edition 2004 Sommer-Edition

studien\seminarTEXT excluded middle valida out thoseuniversalandinvariant conservatism. Thisconservatismwasillust thinking, hasalso,untilrecently,showna mathematics, dealingwith nothing !)havesoughttoescapefrom this tobelievenothing–noteven who profess ofhumanconservatis example fl abidingamidst universal unchanging, tosurrenderthe This unwillingness 1 the CopernicanandEinsteinianrevolutions regardedasfixe been laws oflogichave mind mustemploy if itistothinkcorrectly once!Anewerandmore evenstep universalrelativity flux intowhichonecannot couldst whichno man into of Heraclitus, inhu profound modification outcome.Ifthelaws bythe be determined The threelawsofthoughtmark thefinalba possibility nowhasoccurred.No asa thethingwhich ourancestorsneverconsidered modern thoughtthat seriously. Butsodeeplyhasthevirusof of Until moderntimes thepossibility anentirephilosophy deduce seenin alogicis an base ametaphysics varied,but has use ofthelawsthought extenttowhich terms. Ofcourse,the in illogical –acontradiction isliketalkingabout logic non-Aristotelian to talkabout AsonePersonhassaid: system. science andofintellectual and appeartosomelogicians this would su chance andifbyany upon assacrilegious, deeply rootedisthistraditi fi providinganArchimedean regarded as natureofhuman ortothe the universe ha Oftenthey alternatives. of noconceivable identity the follows:(a) And nowletusstatethesethreelawsofthought,as logic la three ofthe abandonment part of theAristoteliantraditioninlogic. these principlesisgenerallycreditedto or in allvalidthinking,whetherdeductive arethe regulatory fundamental which logicmay totraditionallogicthemost According beemployed. interpretationsin concrete then begiven "AlternativeSystems ofLogic," Monist, 1932, Vol. XLII,pp. 481-507. Oliver L. Reiser Non-Aristotelian Reiser L. Oliver . ; (b)the . AsProfessorC.I.Lewis[ law of

contradiction

on that any challenge tothe anychallenge on that the supposedly permanent and necessary forms of forms of andnecessary permanent supposedly the from the law ofidentity. from thelaw man intellectuallife willo ws of thought wouldco ws ofthought m. Veryfewthinkers( w thelastcitadelof abso (or various systems of philosophy have made made have ofphilosophy various systems ting forms of infere , andtheacceptanceofthemisa Aristotle, d and archetypal ; and as such they admit ;andassuchthey d andarchetypal a non-Aristotelian logic wasnottaken logic a non-Aristotelian so-called "laws of thought," presupposed so-called "lawsofthought,"presupposed mathematicians tomark thedownfallof ; andingeneraltheyhavebeen reason; ep twice,thenbeco ofthought."So xed pointintherealm ux, may bysome be belief in something permanent and permanent belief insomething the separate disciplines(sciences)in theseparate the case of Fichte, who attempted to whoattempted ofFichte, case the the extreme instance of the attempt to to instanceoftheattempt extreme the criticism penetratedintothebodyof ttle line, and the fate of absolutism will will line,andthefateofabsolutism ttle inductive. The specific recognition of recognition Thespecific inductive. , or even think at all. These forms may, oreventhinkatall.Theseforms are butshambattles. rated bythedemand thatlogicsearch of thought should fall, then the most thenthemost shouldfall, ofthought strong inclination towards intellectual strong inclinationtowardsintellectual habit, ornullify itsdesire.Logic,like 1 non-contradiction ch an attack should prove successful, shouldprovesuccessful, ch anattack ] states:"FromAristotledown,the ve been attributed to the structure of thestructure attributedto ve been that theybelieve It isforthisreasonthatany nstitute a non-Aristotelian nstitute anon-Aristotelian only the extreme skeptics, view islikelytobelooked ccur, compared to which ccur, comparedtowhich lutism isbeingattacked. nce which the human nce whichthehuman mes a super-Protean asuper-Protean mes ) ; (c)the ) ; That famous river regarded asan regarded Logics Logics law of law of 2

studien\seminarTEXT classified into three groups, as follows asfollows groups, three into classified cases.Theso indifferent are atwork line,andhavenot sectors alongthebattle traditi The attacksupontheAristotelian tomaintaininviolab invoked sanctions whichbolsteredup the world.For,asProf fallsth thefortress besure,before you may have hithertosetoutintellectualcompasse is appearingwhichthreatenstoabolish saLwo elt AsaLawofThought AsaLawofReality 2 A Law ofContradiction, A = Identity, Law of isthattheyarelawsof ofthought The commonviewoftheselaws Now weconsidertheinterpreta primitives deductivesystem. necessaryto andno that thesethreelawsarenomore, Unlike thedefenders of traditionallogic, 3. 2. 1. ofpropositions: in thelogic and algebra, intheBoole-Schroeder lawsaresymbolized,respectively, how these of physicalrealityandasla laws as epistemological, ontologicaland heads, shall interpretthelawsundertwo as lawsof Inhis essayin the an"Physics"coöperative volume,

two-valued logic,by two-valued thought a< : . Tobringoutthisdoublerefe 2. A thind is what it is. it iswhat Athind 2. 1. Whatever is, is. 1. A thing is not what it is is it what isnot Athing 1. : a a' = 0 aa' = : essor F. A. Lindemann[ not. : a + a' =1 a+a' :

ws of mentaloperations.Firs le thesanctityoflogic." Euclidian spaceareasnoth tions of these three"laws." tions ofthese Ł ukasiewicz and Tarski, and C. I. Lewis. andC.I.Lewis. andTarski, ukasiewicz ck anthelawofidentity. aclso lse Ca Calculus ofClasses the old landmarks, according to which we towhichwe oldlandmarks,according the urces of non-Aristotelian logic may be logicmaybe ofnon-Aristotelian urces come simultaneousl come mostmodernsymb s and gotten our spiritual bearings. But, bearings. andgottenourspiritual s on have come from several different on havecomefromseveraldifferent int of view ofthetransfinite. less, important than the other logical thanthe other logical important less, ere will be another decisive battle of ere willbeanotherdecisivebattle lued" logicfor theAristotelian 2. The meaning The ofatermmust 2. means. Awordmeans whatit 1. . Aword dousmean not what it 1. The Mind 2 rence (objective-subjective), I I rence (objective-subjective), ] says "the conventions and ] says"theconventions discourse. remain constant given in any does not mean.does not ing tothosewhichwillbe t, however,letusindicate . | | |    lculus ofPropositions .p .p .p y. Different motives olic logicians hold olic logicianshold ⊃ ⊃ ⊃ ~(~p) ~(~p) ~p ~p p things ∨ p as well Logics Logics 3 studien\seminarTEXT true must in every respect agree with itself."[ agreewith true mustineveryrespect inthe contained implicitly regarded as Itmight, however, be lawofidentity. the didnotformulate Aristotle apparently Somuchbywayofexplanation. nonsense. that bydeclaring dispose ofthisstatement logic(i Traditional square ornot-square." not-B," onemight ponderwhet applyingthelawof Toillustrate: nonsense. thatiseithertrue statement isa Ev existenceofpropositions. very of the These lawshavebeenregardedassofundam istrue otherofthese orthe One from J.S.Mill theothernece oneor but instant oftime, contradict notknowwhichoftwo We may following possibilities It willbenoticedthatthelawof excl A

Oliver L. Reiser Non-Aristotelian Reiser L. Oliver 2. The same proposition may, in the same same the propositionmay, in Thesame 2. verbalpropositionmay bebot Thesame 1. De Interpretatione Anal. Priora ∨ moment, and false (or true) at another. true)atanother. (or false and moment, senses. but indifferent B' (1) Matter is infinitely divisible. (1) (2) Matter isnotinfinitely divisible. (2) , 47a,9. , 18b,1-5. 3. A thing cannot have Anexistentthing hasa 2. it or exists either Athing 1. . Whateverexist doesnot 2. contradictory properties. not. certain property orit does does not exist. is non-existent.

gues thatthemostcertain , though which it is we cannot say. say. itiswecannot which , though her it would be correct to becorrect her itwould the L.E.M.isfoundin in thesame sense."Inanotherplace[ uded middle(L.E.M.) icate can both belong and not belong to the tothe canbothbelongandnot icate following statement: "Everythingthatis not be white. Again, if it is white, the itiswhite, the if not bewhite.Again, en has declared that a en BertrandRussellhasdeclaredthat .e., logic which accepts L .E.M.) would acceptsL.E.M.)would .e., logicwhich ssarily is.Hereisanillustrationtaken aken. Suchaprincipleisfoundinthis, aken. since itisneithertruenorfalse, itis ory is true atanygiven ory propositionsistrue ental thattheyhavebeenusedastests excluded middle, "A is either B or middle, iseitherBor "A excluded or false, and if it is neither, itis isneither, it andif false, or h trueandfalseatthesame time, 3 sense, be true (or false) atone (orfalse) sense, betrue 3. A class (or term) is either 3. either is (orterm) A class Twocontradictory propositions 2. or true iseither Aproposition 1. 2. Two negatives make an ] ButAristotledoesdefinitely not. or it is includein class, another cannot both betrue. false. affirment. affirment. of allisthat say, "virtueiseither Metaphysics does notexcludethe 4 ] he states: states: ] he (Bk. III. (Bk.III. Logics Logics 4 studien\seminarTEXT of Hegelianism may have been, Hegel's critic Hegel's havebeen, of Hegelianism may whatev But practicalimportance. momentous i Karl Marxtoseehowapparently developmen uponthe Hegeliandialectic of the influential philosophiesina bear fruit.Bosanquet's[ system factthatHegel's is It isacurious equilibrium inafield of force. inastate of apartandheldtogether has inmind ofoppositeskept theconcept tousbythemodeof Hegelthanisoffered "it wouldbedifficult tona point out that Hegel sometimes confused confused sometimes point outthatHegel In attackingthislaw,HegeltriestoshowthatAisbothandnon-A,butcritics ofabstractunderstandi maxim ofspeakingthe Instead unthinkable." principle of theworld:anditisridi (c) the antithesis thesis startfrom(a)a (andthoughtstoo) process,things Inthisdialectical differences. becomes whatitwasnot.Ath and beyonditself thingpasses Each andpassaway. which thingsgrow,change, movementin adynamic isprocess, ForHegelreality idealistic doctrineofchange. viewpoint. Ireferhereto comes ofthought ofalaw of thedenial Heraclitus says tostatewhowasthe difficult It wouldbe history oflogic. And nowletusconsiderthecriticisms of orfalse." true beeither denialsmust or that affirmations wastrue....Itmato theoppositeeffect proposition statingthatitwaswhitetrue;ifnotwhite,the 7 6 5 and Since forHegelthelogicofreality tobelievethe impossible foranyone evolutionist. Indiscussingthelawof contradictionAristotlesaysthat"itis butitispossible this of thought, that example of the historical influence of example ofthehistorical in terms of theprincipleof universalisfu notion oftheconcrete

Oliver L. Reiser Non-Aristotelian Reiser L. Oliver A Theory of Monads A Theoryof The LogicHegel of B. Bosanquet, B. Bosanquet, , and by an act of self- pa ofself-negation , andbyanact synthesis , from which the movement thenpasse themovement , fromwhich " (Metaphysics, 1006a, 7. Italics mine.) But the first clearcut case 1006a,7.Italicsmine.) Butthefirstclearcutcase " (Metaphysics, . Andsoitfollows forHegel[ Logic , 1911, Vol. I, p. 26 and Vol. I, p.26and , 1911, , translated by W. Wallace, 1892,p.223. Wallace, , translatedbyW. , p. 284. 7 ] Interpretationof Hegel's notio me amoreperfect illustration

ll history. One needs to recall here only the influence hereonlytheinfluence needstorecall One ll history. Hegel, whose denial of the L.E.M. is part of his ofhis denialoftheL.E.M.ispart whose Hegel, ng) we should rather say: "everything is opposite." opposite." is "everything shouldrathersay: ng) we ing is a synthesis of opposites, an organicunityof ofopposites,an ing isasynthesis identity-in-difference ndamental. H.Wildonndamental. Carrmaintained[ same thing tobeandnotbe, thing same nnocent philosophical ideas may assume ideasmay assume philosophical nnocent passim doubtful honorbelongstoHeraclitus,the

atonceoneofthe y therefore be argued that itisnecessary arguedthat be y therefore again in connection withanevolutionary inconnection again Hegel's logic,atleastuntilthepresent contradictories maxim of excluded middle (whichisthe middle ofexcluded maxim first thinker tochalle rn electricaltheoryofmatter."Carrhere the logic of thought are the same, the thesame, logicofthoughtare the these lawswhichhaveappearedinthe culous to say that contradiction is culous tosaythatcontradiction ss to the opposite pole of (b) the ss totheoppositepoleof(b) er the metaphysical and social effects effects social and er themetaphysical .

isms lawsof ofthe 5 t of the"dialecticalmaterialism" of ] that "contradiction is the moving isthe "contradiction ] that s intotheunionofopposites, is perhaps the outstanding theoutstanding isperhaps n of the concrete universal n oftheconcreteuniversal with of theconcreteuniversal most obscure and most most most obscureand contraries nge anyof thelaws thought failed to to thoughtfailed as somethink . Logics Logics 6 ] that ] that 5

studien\seminarTEXT The next step in the development of an The nextstepinthedevelopment mathematics. exists onlyafter ithasbeenexhibited,ist theI..E.M.Mathem subjectto question, are thatpropositions tobelieve Brouwer refuses until hehadlookedtosee!Since,inthe mean thatBrouwerwouldnot impossible. Ifsuchanintuitionisticview is sequence ofaninfinite theconsciousness proof cannotbeexhibited,since such caseswhateverassertionmaybemade construction, useofaninfinite upon the numb whether thesquarerootofacertain acerta Thustheproofthat demonstration. of evident nor capable apriori isassertedneither proposition which seque involvinganinfinite demonstrations ofdemonstra becapable truth must that apropositioncanbeaccepte as inconsciousness which canberecognized an knownas is Brouwer revolutionaryview. underlyingthis general thesis law of treat alineascomposedofaninfinite wholeisgreaterth thatthe rule (e.g., the rules of arithmetic donotholdwhenwe withfiniteclassesofobjects.Bu concerned ofthought allprocesses appliesto L.E.M. Brouwer doesnotdenythatthe Brouwer.[ the traditionallawsofthought,name thenexthereticwh And nowweconsider ofthings. itself inahistoricallychangingsystem isnota universal theconcrete say, would terms of theprinciple of identity-in-dife of arelativistic-organic-evolutionary view consider carefully thisprinciplebefore time.[ 10 9 8 has pointedout,istoshowthattheaband An interesting reinterpretation of the Hegelian dialectic in terms of is logic mathematical of terms in dialectic Hegelian the of reinterpretation interesting An See A. Dresden's paper,"Brouwer's SeeA.Dresden's Cont Cf, "Tendencies in the Logic of Mathematics," Mathematics," of Logic the in Cf, "Tendencies Oliver L. Reiser Non-Aristotelian Reiser L. Oliver Contradiction: Its Logical Status," Bogoslovsky's book, nature, and innature, doing and sopays his compliments Bogoslovsky, seekstoofthought the revise laws to take ofthe dynamic care aspect of given by J.B.Burke in his book, Amer. Math.Soc 8 ] Modern opponents of the , Korzybski Korzybski lawofidentity, opponentsofthe ] Modern tertium nondatur 9 ] ., 1924, Vol. 30,pp.31-40. The Technique ofControversy intuitionist (L.E.M.)mustbeabandone

agree, e.g.,thatitiseitherrainingornotraining, d itmust tobetrue,orits apriori beknowneither The Emergence of Life The Emergenceof J. of Philos J. of inmathematics onlythos on-Aristotelian logic,asE.R. Hedrickl[ on-Aristotelian ributiontheto Foundations ofMathematies," tion. Butinthecase number of points) so, Brouwer holds, the the holds, number ofpoints)so,Brouwer they abandonthelawof identityinfavor rence, doesnotexcludechange.AsHegel realm of thetransfin or unending mathematical induction. In induction. mathematical unending or an any of its parts breaks down when we we downwhen an anyofitspartsbreaks onment oftheL.E.M. o has questioned the logical necessity of of necessity thelogical o hasquestioned self-identical thing, ly, theDutchmathematician, L.E.J. er is rational or irrational, may depend isrationalorirrational,may depend er , forthelawof iden were applied ina wereapplied thetruthofanysuch nce ofoperations are dealingwithtransfinite aggregates hus unable to justify much of ordinary ofordinary much tojustify hus unable atical intuitionism,ho t just as we recognizethattheordinary t justaswe in number exists, or the question of thequestion exists,or in number ., 1929,Vol. 26,pp. 519-525. true.Accordingto must be justified by proof, but such byproof,butsuch justified be must Science , the truth or falsity of which are in orfalsityofwhichare , thetruth to Hegelian logic. For a criticism of criticism of a logic. For to Hegelian , see A. E. Avey's paper, "The Lawof paper, , seeA.E.Avey's , 1933,Vol. 77,pp. 335-343. . Afollower ofJohn Dewey,B. Dr. d. But first letusstatethe d. Butfirst ite, onecannotintuit, e things areaccepted e things but aform realizing ll casesthiswould et al et tity, interpretedin this view, in order inorder view, this isnotnecessarily lding thatathing of mathematical ., willneedto Logics Logics Bull. 10 6 ] studien\seminarTEXT proposition." If this view is correct, we iscorrect, thisview proposition." If certified bylogicalone)istautologicalinthesensethatitananalytic be nature. Thusanylogicalprinciple(and,infact,othertruthwhichcan of orthefacts abouttheUniverse particular nothingin requires assigned, and merelybe false:it explicates,or generalprinciplethatwhat a caseofthe arbitrarilyassigned."Thustheta definitions, AsLewissays selected rulesofoperation. themanipulaionsystem ofmeaningl is similar toHilbert's theory senseth there areno"laws"oflogic,inthe n-values-may be termed a non-Aristotelian logic.Inarecentbook,[ anon-Aristotelian betermed n-values-may logic,thenanyl two-valued it Fromthis and uncertainty. three-valued logic,withatrichotomy of logician some when This stepwastaken intuitionist ornot. oflogi part L.E.M. isnotanecessary tied upwithBrouwer's intuitionism.In 15 14 13 12 11 Lewis expoundsthenotionofmultiple Whitehead-Russell ofthe implication" the "material asagainst implication," of"strict interms oftheconception alogic has developed only can have it letuscall neither truenorfalse, ingenious argument,attributedtoAristo itiseither trueor that you areassuming who deniestheL.E.M.pres Aristotelians mayarguethattheviewis Farfrom it!Thereplymayput torout. the Inthefirstplace takeseveralforms. It must not be supposed from this that interest inconcreteobjectsas ofallpossibl adherence tothesimplest that theL.E.M.isnot"w Polishinvestigators, by two developing alogicinwhich of business Theactual tobetrueorfalse. considered that propositionsare itself from thelimitations of theAristote system ofmath even theRussell-Whitehead logics.TheBoole-Schroeder are two-valued Quoted fromF. P.Ramsey's book, Op. cit., p.211. "Philosophische Bemerkungen zumehrwe Oliver L. Reiser Non-Aristotelian Reiser L. Oliver Ł 51-77. Monist Symbolic Logic ukasiewicz, J andTarski,A., , Oct.1932. two values , byC. Lewis, I.,andLangford, C. H. –truthandfalsity. Allthe

rit intheheavens,"butra of mathematics,restsanthethesisthatdeductive upposes it; for if you say that yousay upposes it;forif ogic withmorethantwotrut this lawisexplicitlydisr opposed to abstract concepts." concepts." opposed toabstract is clear that ifwedefine is clearthat Comptes RendusSoc. de Varsovie Ł ukasiewicz[ The Foundations of Mathematics follows from, a meaning which has been meaningbeen a whichhas follows from, doubtful; buttheniftheLawofExcluded doubtful; the defenders oftheAristoteliansystemare truth-value systems. Lewisdeclares[ truth-value systems. e modes of division, and our predominant e modesofdivision,andourpredominant tle, may be repeated: "Ifaproposition is tle, mayberepeated: must agree with Lewis whenhestates[ Lewis must agreewith is true by definition cannot conceivably istruebydefinitioncannotconceivably s abandonedthethesis implications,intermsof truth,falsity, c or mathematics, whether onebean c ormathematics, whether lian system,istwo-valued,inthesense self-refuting, inthesensethatanyone not true (false?). Orthefollowing[ nottrue(false?). other words,onemayadmit thatthe ess symbolsaccordingtoarbitrarily at there are laws of physics. This view, at therearelawsofphysics.Thisview, rtigenSystemen desAussagenkalküls," by , the source of necessary truthisin ofnecessary , thesource ematical whichclaimed free logic, to algebra of logic is a two-valuedlogic; isa algebra oflogic utology ofanylawlogicismerely 11 ] and Tarski, who developed a Tarski,whodeveloped ] and Principia egarded was carried through egarded wascarriedthrough traditional systems of logic oflogic systems traditional ther "reflects ourstubborn "reflects ther an Aristotelian logic as a anAristotelianlogicasa h values–three,four,or the L.E.M. is not true, theL.E.M.isnottrue, , 1930,Vol. 23,111,pp. , p.66. that propositions thatpropositions 12 ] C. I. Lewis I.Lewis ] C. Logics Logics 13 . Here . Here ] that ] that 14 15 7 ] ] studien\seminarTEXT writer[ ofsimult impossibility This psychophysical term. andonlyone;meaningcanbeassignedtoanyspecified one, any giventime regulative principle.Thelawofidentityis identity isa Inthefirstsenselaw of remain constantinanygiven"universeofdiscourse." proposition) means whatitmeans,and(b)thatthemeanings ofourterms should however. Thelawof identityhastwomean –indifferent senses, andincapableofbeineviolated capable ofbeingviolated lawof isthatthe The viewherepresented law ofreality. criticisms of thelawof identity,interpreted state theviewsof thisauthor,wewill bytheintroductionofanewme problems "International Non-AristotelianLibrary," whichawaveisand according to this are bothundulatoryandcorpuscular, modern Thuswhen inphysics. phenomena Inthe beenmade. lawhas upon that If onewere toaskwhichofthethreela lastpossib And nowwecometothe its absence. Count Korzybski's book, CountKorzybski's its absence. inwhic ofscience system non-Aristotelian theproposalof wehave ourselves, liesnot ofphysics thefault physicists that suchdiffictwo canbeone.Asidefrom identity wouldundoubtedly an Andso nordoubtful. thatitisneithertrue,false, and doubtful, have notmerelythreepossibilitiesbutfour, that notbeeitherdou itneed Middle befalse, 17 16 of biologicalmutation (e incapable ofbeingviolated,though,tobe same time.Inthissenseitistrue thatfo underlyingthe thoughtof"non bodily process inprocess,the of"A"is thought patterns. Ifthebodilyprocessunderlying the ofreciprocalneuro-muscular innervation simultaneous ofthe impossibility whichnon-Euclidia relation totheoldlogic that intheLewissystem, wh this isnotsufficient to thi possible to makeit cortex) might Weiss[ issimilar towhatPaul not. Thisanalogue logic maybe,agivenpropos these L.E.M.in totheold an analogue "Biological Relativity," Relativity," "Biological of Systems," "TheNature Oliver L. Reiser Non-Aristotelian Reiser L. Oliver 17 ] has suggested, may rest upon some such physiological principle as the the suchphysiologicalprincipleas uponsome mayrest suggested, ] has descriptive law, and in the second sense itisa sense law,andinthesecond show the necessity for the L.E.M., it can be pointed out out bepointed necessityfortheL.E.M.,itcan show the J. of J. of Philos .g., theadditionof another

Monist be recommended ich claims toestablish a ition eitherpossessesoneof , 1929,Vol. 39,p. 283. ., 1931, Vol. 28, ., 1931, p. 714. le attack upon the laws ofthought. le attackuponthelaws nk of both "A" and "non-A" simultaneously, "non-A"simultaneously, and nk ofboth"A" Science andSanity Science consider, quiteindepe nse that no matter how many-valued your thatnomatterhowmany-valuedyour nse ws was the mostimpr the was ws Count Alfred Korzybski to develop a todevelopa Korzybski Count Alfred r "normal"personsthelawof identityis identity, as a "law" of thinking, is both a"law"ofthinking,is as identity, thod of thinking. Without attempting to ofthinking.Withoutattempting thod ulties, whichhavesuggestedtosome seems toviolatethelawofidentity, sure, one might imagine that somesort onemightimagine sure, so much asin inthestarsandelectrons h the law of identity is conspicuous by isconspicuous h thelawofidentity the aim of which is to solve all our our tosolveall aim ofwhichis the main the doubt arises from unusual unusual from doubtarises main the physics states that light and electrons thatlightandelectrons states physics btful or not doubtful, so that we shall sothatweshall btful ornotdoubtful, adescriptivelawinthesensethatat corpuscle isacorpuscle,andneverthe n geometrybearstoEuclidian,thereis first asalawof thoughtandthenasa aneous duplicity of meaning, as the as aneous duplicityofmeaning, -A" cannot alsobeinprocessatthat -A" cannot ings: (a)itassertsthataword(or for thatposition. Andyetanattack itistrue,thatfalse, thatitis 16 ] hastermed the new logic bearing the same same bearingthe new logic supragranular layertothe , is the first volume of the ofthe volume first , isthe thosevaluesoritdoes ndently, thepossible egnable, the law of of egnable, thelaw normative ad infinitum excluded n+1 law,or Logics Logics ." If ." If . 8 studien\seminarTEXT identical withitself in Again, asKorzybskihaspoin be, inthegivenenvironment never know.Wecanknowanob Astarisa star,of its ownpointofview. ownpoint fromits know itself, toviewath ) (through inthecase of ourselvesarewepermitted (scientist) isamember. Only (c) arelativityduetotheculturalstatus of the societyof whichtheobserver (b) arelativityduetothebiologicalconstitution of theperceivingorganism,and itis The worldasweknow . star) ofthe otherproperties(i.e.,appearblue,inthecase topossess may appear (i.e., properties appear topossesscertain circumstance thatathing(e.g.,star)vi difficultyThe final inapplyingthelawof identityarisesinconnectionwiththe specify what environment. Sothat onewayinen in electron) maybehave because oftheenvironmentitisin,an thata itisalsotrue respects. Moreover, (even ahydrogenatom)tobeitself. Butth states, that"natureataninstant"is It ofdefinition. niceproblem involves a "non-A" tobe "A" andbecomes "A"ceases atwhich oftransition precise point –e.g become whatitis(somethingelse possibility thatathingmay, inthecourse a thingremainsidenticalwithitself in The lawstatesthat(a) And nowforthelawofiden said whileusingsuchterms. have mustalsoreviseeverythingwe are freetoredefineourterms, butthenwe time ofviolationwhen capable is moment, thought twice.Thusthelawofidentit whether twice,itisdoubtful same state words acquirenewmeanings. If itistrueth thenervous experiences; terms. Wehavenew inthecourseoftime recognizethat must tothesecondmean According bothhimsel heis that indreams occurin mayactually function reciprocally, this simultaneous innervationofalterna contradictor two assign or instantaneously the caseofL.E.M.as facethe environments. Butthenweagain Oliver L. Reiser Non-Aristotelian Reiser L. Oliver all thepropertiesathinghas, at any given time given at any all respects, especially if "all" means an infinite number of if"all"meansaninfinitenumberof especially respects, appliedtoinfinite sets. ing from its "own" pointof ing fromits"own" a thingis"initself" wema tity asalawofreality. subject to(a)arelativity of acertain"cosmic epoch." ted out,difficulties arisewhen ing of the lawof identit of view, but astarcan ofview,but f and not himself simultaneously.) simultaneously.) f andnothimself ject, "A,"onlyintermsof whatitappearstous artifact, andthatitrequirestime forathing ., the stockingsofSi ., the , and(b) ewed fromone"frame potentially andactually,in tive (exclusive)patterns,thatordinarily y, incapableofviolationatanygiven all respects.Thisdoesnotexcludethe it is possible to change the meanings of meanings the tochange ispossible it d that "A" (e.g.,anorganism andan d that"A" does its work. Logic recognizes that we that work.Logicrecognizes doesits thing iswhatit(toalimitedextent) is neednotnegative course,butwhatitisinitself wecan appear red),andvi appear difficulty whichBrouwerrecognizesin difficulty vironment and in another insomeother andinanother vironment y meaningstothe of time,ceaseto at theorganism isneverinexactlythe dreams. me leastafriendinforms (At we can ever think exactly the same same the we caneverthinkexactly is also true, as Professor Whitehead is alsotrue,asProfessorWhitehead systemisconstantlyinflux; andso from some selected point of view of point selected from some y never know, unless we can wecan y neverknow,unless due tophysicalmotion, and view. Inasensebraincan never know what it is from itis never knowwhat y, as a law of thought, we ofthought,we y, asalaw wesaythatathingis r John Suckling). The r JohnSuckling).The same term.Perhaps same be whatitwasand ewed from another another ewed from the lawof identity. ofreference"may all possible Logics Logics 9 , studien\seminarTEXT

present paper to prejudge this issue. thisissue. present papertoprejudge logic willhavetobedecidedantheirow middle. Thecl lawofexcluded Aristotelian substitute themany-valued logicfor doesnot however, all "humanists.")This, andI,forone,donotclaim to superlogician, asupe Only be wecannotnowanticipate. mutation mayalterthis,thoughwhatthe presupposition of allreasoni identity remainsidenticalwithitself. In itself. If we reasonaboutidentity, logicweemploy cannotitselfbesubjecttocriticism logic,andthe employing by We predicament." arereasoni "logic-centric MarvinFarbercallsthe orwhat predicament," calls the"logo-centric and asanormative principle.Wearehere But asalawofthoughtthe empirical verificationbegsthequestion, nature. Aslawsof realitybothareinca samestatusastheequally occupies the itturnsoutthatthelaw From allthis

ISSN 1619-9324 1619-9324 ISSN Oliver L. Reiser Non-Aristotelian Reiser L. Oliver The was text originally edited andrendered into PDF file for the e-journal This material may be freelymaymaterial copied This andreus

a printable version may be obtained from [email protected] [email protected] from obtained be may version a printable law ofidentityistobeacc ng. Butasalreadyadmitted, Copyright 2004 vordenker.de vordenker.de 2004 Copyright pable of beingproved, ed, provided the author and sources are cited of identity as a law of physical reality reality ofphysical alaw of identityas the two-valuedlogicbasedupon famous principle of the uniformity of uniformity famousprincipleofthe superlogic of the coming superman may superman ofthecoming superlogic n merits,andnoattemptismade inthe invalidate the claim of those who would invalidate theclaim ofthosewhowould assume thatthemeaningof theword rman could duplicate the reasoning ofa couldduplicatethereasoning rman or presupposesthepointtobeproved. thissensethelawof identityisa ng about logic, and in doing so we are ng aboutlogic,andindoingsoweare face to face with what H. M. Sheffer aims for this type of non-Aristotelian typeofnon-Aristotelian aims forthis be a superman. (In this Sense we are (InthisSenseweare beasuperman. epted, bothasadescriptive some futurebiological and anyattemptat by E. von Goldammer Logics Logics .

10

Top View