wittgenstein rules.pdf &

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Can Wittgensteinhelp free the mind from rules?The philosophical oundationsof connectionism

&C.n D. Johnson(pp. 217-226).Oxford University Press.1997

For more details:http://www.ecs.soton.ac.uk/-id/or e-mail: [email protected]

ltiel E. Dror & Marcelo Dascal

(Eds.), The Future of the Cognitive Revolution,


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Itiel E. Dror & Marcelo Dascal

Can Wittgenstein Help Freethe Mind from Rules?The PhilosophicalFoundationsof Connectionism

The question whether or not the construct "rule" is essential for cognition is one ofthe main divisions between connectionist and rival approaches in cognitive science.In this chapter, we consider the philosophical significance of this division, and itsimplications for cognitive research, in the light of several possible interpretationsof Wittgenstein's paradox of following a rule. The conclusion is that the rejection ofrules by connectionism makes it philosophically incompatible with the symbolicrule-governed approach; nevertheless, the rejection of rules does not necessarilylead, on its own, to a single way of conceptualizing the mind and its place in nature.Wittgenstein's notions of "form of life" and "language games" are used as an aid forunderstanding the philosophical foundations of connectionism.

This was our paradox: no course of action could be detennined by a role, becauseeverycourse of action can be made out to accord with the rule. The answer was: if everythingcan be made out to accord with the role, then it can also be made out to conftict withit. And so there would be neither accord nor conftict here. (Wittgenstein, 1953)

1. The "New Science of the Mind" now has two entrenched and well-developedparadigms fighting for supremacy. As candidates for pure and applied scientific the-ories, both paradigms seek to gather support from their ability to provide coherentformalized models of mental activities and from their successful implementations.Furthermore, both are believed to provide a set of principles capable of explainingall cognitive phenomena, that is, a unified theory of cognition and eventually of themind. (See Anderson, 1983; Newell, 1990, for the symbolic approach; Grossberg,1982; Rumelhart & McClelland, 1986, for connectionism.)

Although philosophical issues are often mentioned in the debate, they are usu-ally overshadowed by the quest for "empirical support." (See Dror & Young, 1994,for a discussion of how this quest for empirical support can affect the developmentof cognitive science.) However, the interpretation of such support depends on diver-

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218 Connecn'onismgent philosophical assumptions.Consequently, rogress n the debatecan only beachieved f, in conjunctionwith the empirical and practicaldevelopment f eachpar-adigm, heir philosophicalassumptions nd orientationsare carefully exalnined. nthis chapter,we examineone cluster of such assumptions, amely, hosepertainingto the role of "rules" in cognition. More specifically,we inquire what are the philo-sophical mplications of the connectionistattempts o provide a "rule-free" accountof cognition.

2. The so-called cognitive revolution" in psychologybrought abouta rehabil-itation of mentalism, n the wake of the alleged nability of behaviorism o accountfor higher cognitive processes.Once einstated. he mentalistic outlook legitimizedthe use of several concepts hat had been ruled out by behavioristic strictures.Among them was the idea that cognition is the exerciseof a set of competences,which are best described as the mastery and application of rules. Thus, Newell,Shaw,and Simon(1963) nvestigated he rules peopleuse or reasoningand problemsolving; Chomsky (1965, 1980, 1986)conceived he grammarof a languageas heset of rules hat every competentspeaker nternalizes;Atkinson and Shiffrin (1968)consideredmemory as a content-addressed,ule-basedsystem; visual recognitionwas explored hrough paradigmsof template-matching,eature analysis,and struc-tural descriptions palmer, 1975;Wmston, 1975).The development f the moderncomputerprovided both a useful ~etaphor andsupport or the view that rules ie at the centerof cognitive processes. he software-hardwaredistinction, nterpretedas parallel to the mind-brain distinction, pennittedthe symbolic approach o emphasize he non-reductionistic character of the newapproach e.g.,Putnam's 1967)notion of "functionalism"). The mind was conceivedas equivalent o a set of software, rather than to its neuronal underpinnings.Likecomputerprograms, t was said to operateby following symbolic rules. n so-called"traditional AI," computerswere used o model such processes s well as o makeuse of such model~.Newell and Simon (1972) mplemented he means-ends rob-lem-solving rule in their GeneralProblemSolver; Wmograd (1972) applied Chom-sky's heory of grammar o simulate anguage nderstandingn SHRDLU; structuraldescriptionshave been used n computer earning and in computer vision (Ballard& Brown, 1982), o namea few examples.

The underlying deology of this approach s that a physical symbol systemhasthe necessary nd sufficient means or general ntelligence Newell & Simon, 1976).The physical symbol systemcontainselements hat are put together through sym-bolic structures o form expressions.Rules which are themselves xpressionscreate, modify, reproduce, or destroy other expressionsbased on their symbolicstructure and he elements hey contain.

3. The rise of connectionismwas promptedby dissatisfactionwith the meagerpractical achievements f the symbolic approach,f comparedwith its pretensions,as well as by advancesn exploring the neural networks of the brain. (For a discus-sion on the relationship between he biology of the brain and cognitive computa-tions, seeDror and Gallogly, 1996.)The insistenceon using rules oomed arge as apossiblecause or the failures of the symbolic approach.Rules were relatively easy


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ThePhilosophicalFoundations f COMectionism 219to formulate; but they rendered systems too rigid to be able to capture the specificproperties of cognitive processes. The use of rules resulted in failure to exhibit anumber of processes,such as pattern recognition, pattern completion, automatic gen-eralization, and graceful degradation, that are important for models of cognitiveprocesses. See Rumelhart & McClelland, 1986.)With the development of an alternative way of simulating and accounting forthe computational processesunderlying cognitive abilities, connectionists also devel-oped an alternative conceptual framework for those cognitive processes hat previ-ously seemed o be naturally conceptualized in terms of rules. (See Dror & Young,1994.) Based on the idea of flow of activations between massively interconnectedsimple-units, a framework was established where rules-as explanatory con-structs-became altogether unnecessary.The idea of parallel distributed processingwould now unmask rules as fictitious theoretical constructs. In this respect, Wittgen-stein's denunciation of the paradox underlying the use of the notion of "following arule," and its possible interpretation as rejecting the explanatory value of rules alto-gether. could be a powerful philosophical ally to this framework.

4. Wittgenstein shows hat explanations n terms of rule following must becompletelymistaken.For example,how can one ascertain hat a rule has been ol-lowed, say, n constructing a given sequence f numbers?Suppose ou are given asequence f numbers,; What is the rule for generating t and ts continuation?None-Wittgenstein would say-because an infinite numberof rules could gener-ate he given sequence e.g.: multiply the preceding number by 2; add 2 to the pre-cedingnumber;etc.). One might suggest hat the next numberwill determinewhichrule hasbeenused: f 6, then the rule is add two; if 8, then t is multiply by 2. Yet, nomatterhow many exemplarsof the sequence re given, as ong as he list is finite-as t necessarily s-there will be indefinitely many rules that are able o generatethe sequence. hus, t is impossible o detenninewhich is the rule that is being fol-lowed; and, n fact, one can raise he questionwhether a rule is being ollowed at all.Supposewe enlarge he sequence f numbers rom to . s its rule nowmultiply the preceding number by 2, or add the two preceding numbersand add tothe sum heposition of the number n the sequenceminus2, sinceboth yield the samesequence?The appeal o rule following, therefore,seems o have ost its explanatoryvalue,since ndefinitely many rules can be made o conform to any courseof events.Thus,we can never deteimine which rules underlie a phenomenon;and this leads us toquestion heir existencealtogether.This conceptual argument should bolster con-nectionism's esolve to provide an accountof cognition that doesnot rely at all onthe problematicconstruct "rule."

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5. Regarding he role of rules, the contrast-both practical and conceptual-between he connectionist and the symbolic approaches an be best llustrated byconsideringan example.THEO and TheoNet are two models that have beenpro-posed o account or processes f reasoning used by experts who forecast solarflares. This kind of reasoning nvolves he use of infonnal reasoningwithin a frameof constraints, and the use of partial and inaccurate information. Both models

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220 Connectionismreceive nformation on recentactivity of the sun (numberof flares, size,distribution,and so on). THEO is a role-basedexpert system Shaw, 1989),whereasTheoNet sa three-layerconnectionistnetwork (Bradshawet at. 1989).THEO processeshe data hrough the knowledgeencoded n it, in the form ofsymbolicrules.For example,a rule in the knowledgebaseof the expert systemmaystate: "If more than one ZUrichclass lare has occurred n the past 24 hours and tssizewas arger han 5, then there s a .85 probability that an M-class lare will occurin the next 24 hours." In other words, the system elies on a symbolic meaningfulconnectionbetweenentities such as ZUrich class Baret ts size, and the probabilityof an M-class lare; and all this is encoded n the system n the form of rules. Thus,the rules of the system are the underlying entities that capture ts knowledge andaction. In contrast, TheoNet doesnot have such rules. TheoNet processeshe datathrough a set of connections hat go through a hidden ayer of units before the finaloutput vector s produced.Each connection n the network has a weight associatedwith it (which the network learns hrough training). The input data triggers a sim-ple flow of activation between he units. The system has no underlying symbolicrules.Accounting or processes f reasoningusedby experts hat forecast solar larescan rely either on the connectionistor on the symbolic rule-governedapproaches.THEa and TheoNet perform equally well, and both' perform as well as skilledhuman orecasters.Alternative accounts, uchas hese,basedon the two competingapproaches, avebeenproposed or a variety of cognitive processese.g.,models orword identification; for a review seeRueckl & Dror, 1994).Such"matches,"how-ever, have not been conclusive, and have not proven the empirical supremacyofeither approach.

6. But what is the deepersignificance, f any, of this contrastbetween he twoapproaches?s it a symptom of their radical incompatibility or can they be recon-ciled in somehigher theoretical synthesis?Are they guidedby and oriented owurdradically different visions of mind and cognition; or are they mere "notational vari-ants" of the samephilosophicalattitude oward the mind?Replies o thesequestionsvary broadly. Some eject the incompatibility thesison the grounds hat one of the approachesconnectionism) s not in fact an alterna-tive explanation for cognitive processesat the psychological level (Fodor &Pylyshyn, 1988).Others acceptboth approaches?iewing them as complementary,insofar as hey account or different cognitive processesEstes, 1988;Schneider&Detweiler, 1987).Still others see he two approaches s different levels of descrip-tion of the sameprocess,and considerconnectionism o be either the proper mple-mentation of the symbolic approach Broadbent, 1985), or an intemlediate levelbetween he symbolic and he neural evels (Smolensky,1988).One might argue,however, hat the two approaches re not so easily reconcil-able because 1) they are indeedconceptually ncompatible, and (2) they representcompletelydifferent conceptions f cognition and mind. On this view, he divergenceconcerning he role of rules s crucial becauset uncovers he deeperdifferences nphilosophicaloutlook. The issue s not ust whether rules are implicitly representedin connectionist systems hrough some form of hidden representations Hinton,


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ThePhilosophicalFoundanons f Connectionism 2211986), or whether the connectionist approach merely introduces a sub-symboliclevel (Smolensky, 1988). Such interpretations of connectionism may be remnants ofthe "old" paradigm forced on the "new" one-a very common phenomenon whenrevolutionary ideas are introduced (Dror & Young, 1994; see J. Dror, 1994, 1995,for how the acceptance of new ideas is constrained by previous beliefs). It is notuncommon to find concepts derived from the symbolic approach embedded n con-nectionist systems (e.g., Miikkulainen,1993). Another example is Pollack's (1988)attempt to employ a commonly used computer structure-a stack-in a connec-tionist network. Other examples are provided by the new generation of "hybrid"models that combine modules of symbolic rules with modules of connectionist net-works within a single operating system. Such systems may prove to be technologi-cally efficient, as they seek to,exploit the best in each approach. .

But the occasional success of such eclectic implementations is not, by itself,proof of explanatory compatibility and conceptual harmony between the twoapproaches, for it may be due to the plasticity in the practice of the programmers.From a theoretical and philosophical point of view, one should focus rather on a-presumably ideal-notion of "pure connectionism" and examine where it may leadus. In particular, what is the significance of its claim to be, n sharp contrast to "puresymbolism:' entirely "rule-free"?

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7. The implications of suchan entirely "'rule-free" connectionist nterpretationcould be far-reaching; a different conceptionof cognition s likely to emerge.Withthe rejection of the need or "rule" modesof explanation, he last bastionof dualismis conquered;not only is the mental no longer a separate ntological domain,but itis no longer a distinct epistemologicaldomain,with its specialmodeof explanation,either. The mind is thereby completely and finally naturalized,as t never had beenbefore. In this way, a remarkable Ockhamian ontological economy is achieved,along with a no less valuable epistemologicaleconomyobtained hrough the sim-plification of the explanatorymachineryof science.,:

8. Wittgenstein'sparadox-one could argue-would lend further support othis conceptualization.The trouble is that, construedas above,Wittgenstein'sargu-mentundermines ot only the appeal o rules but also he appeal o any other onD ofdata-based eneralization.For it shows hat an indefinite numberof hypotheses reequally possible candidates o capture the regularity underlying any given set ofcases-the well-known fact that dataunderdetermineheory.To be sure, his wouldprovide a unifonn accountof regularities acrossall domains,but only at the cost ofmaking such an accountequally problematic hroughout. t is doubtful that connec-tionism would be willing to give up the reliability of generalizations f all sorts.The games interpreting Wittgenstein"and "interpreting Wittgenstein's ule fol-lowing argument" are among he toughest n town. Despite he danger, t may beworthwhile, for the purposes f understandinghe philosophical oundationsof con-nectionism, o makea move.Wittgenstein's rgumentagainst ulescan be nterpretedas showing he theoretical uselessnessf this concept,since ts allegedwork can beperformedby resorting o more economical oncepts uchas "activity" or "training."This is particularly clear n his remarkson language.Wtttgenstein ejects he notion


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222 Connectionismthat language s taught ostensively-that is, "[T]he teaching of language s notexplanation, but training." Language s not a set of rules-that is, "(L)anguage spart of an activity, or of a form of life"; "Explanation is never completed. . . andnever shall!" Wittgenstein s interpretedas rejecting "rules" as he underlying con-cept of cognitive processes nd mental operations,whereby roles operateon mentalsymbols. That is, Wittgenstein is attacking the very conception of the symbolicapproachas pointless. Bingo !" would exclaim the connectionist; Our enemy's oeis our friend; thank you Mr. Wittgenstein!"

9. But the connectionistshould beware of his newly acquired riend. For onething, Wittgenstein s not necessarily uling out the notion of rules altogether;he isnot substituting he "rule" approachwith a "rule-free" approach.Wittgenstein athersuggestsconceptualizing regularities as "social practices." After all, one mightattempt o account or suchpractices n terms of the acquisition of rules, which arethen put to use.Furthermore,Wittgenstein stresses hat suchpracticesdo not nec-essarily share a common denominator o which they all can be reduced seeGert,1995).Human activity, and presumably he mind, are to be conceivedas an irre-ducible plurality of (language)gamesgrounded n a variety of "forms of life.""Bingo again!" the connectionisteuphorically might exclaim. "After all, aren'twe also talking about a plurality of processorsworking in parallel, with no single'executive' that controls all the moves n the game or even all the games hat areplayed n the mind? The 'practices' you talk about, the 'language-games,' re the'form of life' of the connectionist network playing 'games' of recurrent patterns,interactive flow of activations, and modifications of weights. Wittgenstein'ssocialnetwork of interactions s really a wonderful model for the inner structure andworkings of the connectionist framework and of the mind. Thanks again, Mr.Wittgenstein!"

10. But now, n view of thesenotions of Wittgenstein,can connectionism r0-vide nsight into the workings of cognition? f we no longer are seeking o reveal an"inner essence" f symbolic ules that allegedly govern cognition, what is it that weare seeking?Connectionism'seply is that cognition arises hrough nformation pro-cessing hat occursby parallel distributedprocessing f simple activations Wittgen-stein's practicesof languagegamesand forms of life). Connectionismcan aid inunderstanding he mechanismsand operations of this processing n a variety ofways. Connectionism an examinecomputationallyhow complex cognitive abilitiesdecomposento different subsystems, r what the principles and characteristics reby which information is processedfor a discussionon the ways connectionism anbe used or studyinghigh-level cognition,see . Dror, 1994).For example,f we wantto explore which subsystems re nvolved n a cognitive ability, we can use he "splitnetworks" techniqueor modular architectureas meansof decomposing cognitiveability into its subsystems. hese echniques etenninewhich processes re compu-tationally distinct and are thus likely to be carried out by different subsystems.Jacobset al. (1991)usedmodular architecture o explore the ways n which visualimages are decoded.Their investigation showed hat visual processing s dividedinto distinct subsystemshat process what" and "where" information.


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ThePhilosophicalFoundations f Connectionism 223Another example for using connectionism to explore cognition is by lesioning

connectionist models and examining how they break down. The changes n perfor-mance due to artificial damage to specific connectionist models are then comparedto changes in performance in people with brain damage. This technique has beenused to explore the operations involved in reading and their breakdown in dyslexia.(For a summary of these models, see Rueckl & Dror, 1994.)

11. The aboveexamples how how connectionism an account or mentalphe-nomena hat previously had been accounted or by the symbolic rule-governedapproach.However,Wittgenstein'snotions also can opennew horizons n exploringcognition. Given hat the mind is not governedby symbolic ules, we can nvestigatephenomenahat we observebut have no understanding, o far, of how they work.One way for conducting such studies s to examine he performanceof a con-nectionist network while the representationof information s systematicallymanip-ulated.This technique f manipulating epresentations xamines he effectiveness fdifferent processingschemes o achieve a given cognitive ability. Given that weknow what nfonnation s initially available,we can examine he flow of informationprocessing~ackwards- from the cognitive performanceback o the nitial informa-tion. We begin by constructinga connectionistmodel hat is trained o perform a cer-tain cognitive ask. nsteadof giving the network the nitial input, we take his initialinput and experimenton it; we process t in a variety of ways, each of which pro-ducesa different representation f the initial input. We hen eed each epresentationto the network, and examinewhich one(s)enable(s) he network to perform the cog-nitive task n question.This way we are able to ascertain he information process-ing necessaryor a given task. The systematicmanipulationof representations r0-vides many mportant nsights nto the information processingnvolved n cognitiveabilities.Dror, Zagaeski, ndMoss (1995)used his technique o examine he nformationprocessing nvolved in three-dimensionalobject recognition independent f orien-tation, basedon sonar.They trained a three-layer eed-forwardnetwork that had 248units to recognize hree-dimensional hapes. hen hey examined he network'sabil-ity to generalizeand recognize he shapeswhen hey were presentedn orientationsthat were not used n the training. The manipulation of the representationncludedtwo formats: One was a time domain representation hat was createdby digitizingthe echo waveform (it had he maximum temporal esolution and no frequency es-olution); the other was a frequency domain representation hat was createdby thepower spectrum it had the maximum frequency esolution and no temporal esolu-tion). The network that used he pure time domain representation ailed to performthe task, whereas he network that used he pure frequency domain representationwas able o generalize nd correctly recognize he shapes venwhen they were pre-sented n novel orientations.Thus, the performanceof the connectionist networkssuggests hat one needs o process requency domain nformation for object recog-nition by sonar. n addition, a cross-correlation etween he emittedsonarsignalandthe returning echoeswascreatedas nput to the network. The network was unable operform the task using cross-correlational epresentations.Given the success f thenetwork using only information contained n the actualecho, he connectionistnet-


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224 Connectionismwork demonstrated hat one does not need o examine the echoes elative to theemittedsound,but rather that the echoby itself encodeshe shapenformation of theobject.

12. At this point, we have a better dea of what is at stake n trying to under-stand he philosophicalorientation of connectionism's iew of mind, in the light ofWittgenstein's iew of rules. To be against he symbolic approach er sedoesnot yetdetermine whether one's naturalization of the mind should go inwards (to thedomainof activities within the brain) or outwards to the domainof activities withinthe socialperspective), r perhapsboth ways. Freud aid the foundationof psychol-ogy with the assumption hat the inner powers can explain behavior. However,Freud'smeans o achieveaccess o the inner powers were rejected as unscientific.Methodological behaviorism, claiming the scientific impenetrability of the innerpowers, esorted o the outer powers.The cognitive revolution, in turn, proposed ogo into the inner powers hrough the notion of executive-drivensymbolic manipu-lation according to rules. Wittgenstein renounces his latter notion and thereforerejects t asa meansof explaining he inner powers.Similar to behaviorists,Wittgen-stein urns to the outer powers.Connectionismprovides a means o account or theinner powerswithout resorting to the false and illusory construct of rules. Seen nthis ight, the relationshipbetweenWittgensteinand connectionisms not ust one of"complementarity" Mills, 1994; or a critique seeDascal, 1995); he former provid-ing a phenomenologicaldescription of the phenomena hat the latter attempts oexplain. Rather,Wittgensteinshouldbe seenas someonewho clears he ground ornew modesof explanationof cognitive phenomenahrough he rejection of a famil-iar, commonsense,nd yet unreliable heoretical construct.

AcknowledgmentsWe thank Wllliam K. Estes,Daniel L. Schacter, ay G. Rueckl, James ntriligator,and Ofra Rechter or their commentson an earlier version of this chapter.Pleasesendall correspondence oncerning his chapter o: ltiel Drar, PsychologyDepart-ment,BentonHall, Miami University, Oxford, OH 45056. USA

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