***************************************************************** * * Titel: The career of "internal relations" in Wittgenstein's work Autor: Rupert *Read* (Unversity of Norwich) Dateiname: 22-2-97.TXT Dateilänge: 18 KB Erschienen in: Wittgenstein Studies 2/97, Datei: 22-2-97.TXT; hrsg. von K.-O. Apel, N. Garver, B. McGuinness, P. Hacker, R. Haller, W. Lütterfelds, G. Meggle, C. Nyíri, K. Puhl, R. Raatzsch, T. Rentsch, J.G.F. Rothhaupt, J. Schulte, U. Steinvorth, P. Stekeler-Weithofer, W. 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Those articles and excerpts from * * articles which the subscriber wishes to use for his own * * private academic purposes are excluded from this * * restrictions. * * * ***************************************************************** My purpose in this note is as follows: to show that, even if Wittgenstein in his later work could be said to have achieved some "resolution" of the much-vexed question of "the harmony between language and reality", this has little or nothing to do with the way that a RULE and ist APPLICATION are in accord.*1* Why is this important? Because Wittgenstein's rule-following considerations remain at the nexus of disputes (around questions of "Realism" and representation) absolutely central to contemporary philosophy. Establishing more clearly Wittgenstein's 'view' on these matters ought to be of no little importance in such disputes. Gordon Baker and Peter Hacker, in virtue of their exhaustive exegetical studies, in effect claim to be the foremost authorities on Wittgenstein in this field. But their claim -- in particular, their claim that rule and application are related as language and reality, INTERNALLY related -- is not convincingly derived from the post-Tractarian texts they cite as authorities. In what follows I will seek to prove this, while restricting myself for reasons of space to those moments in Wittgenstein which seemingly provide them with their strongest ammunition. In 'Rules, Grammar and Necessity' (Oxford: Blackwell, 1985, henceforth: RGN), p.16, Baker and Hacker cite the following passage: "The relation of expectation and fulfillment is precisely that of calculation and result. 2x2, result 4. An action is the last step in a calculation. The calculation enables us to say which result is right and which wrong, but says nothing about what we will in fact write down... Thought anticipates its fulfillment in the same sense that calculation anticipates its fulfillment. Maths can be learned beforehand, and so can language. So philosophy gives rules once and for all." *2* It is notable that Baker and Hacker fail to explain Wittgenstein's interest in the 'ACTION'of the "last step" here (which is subsequent to all that is said to "anticipate" it); and they neglect to consider that nothing is said here about the application of rules, nor about "internal relations". More importantly, one must note that, with the possible exception of this (possibly garbled) remark from a lecture, it is only rules of the general form "10+2=12", rather than "the rule of addition" or even "the rule, "Add 2"", which Wittgenstein EVER actively discusses in connection with "internal relations".*3* Most other uses of the term, "internal relations", in connection with mathematics, deal with the internal relation between proof and proposition proved, a rather different matter from (or at best a most atypical case of *4*) the rule/application connection. That is, Wittgenstein NEVER utters, in all his now-published works, words to the effect that "Rule and application are internally related", or "68 and 57 are internally related to 125"; and one can be sure that Baker and Hacker would have unearthed any such utterances in unpublished manuscripts, were there any to be unearthed. Nor does Wittgenstein speak ANYWHERE of the result of applying the rule "Add 2" at a certain point as being "INTERNALLY RELATED" to the rule itself. He speaks on a FEW occasions of the idea of internal relations -- between parts of the ('A PRIORI') structure of the numbers.*5* In sum, Wittgenstein DOES indeed sometimes use the term "internal relation" in connection with mathematical cases. But FIRST it is not clear that the internal relation in question is ever that OF RULE AND APPLICATION; and SECOND, even if it is, it is not clear that it will generalise to all forms of mathematical rules, let alone to non-mathematical cases. Perhaps we should take note more seriously than we often do Wittgenstein's PARTICULAR fascination for the Philosophy of Logic and of Mathematics, and not assume that what there is to be said about the rules that 'hover' in these fields generalises beyond them. A case in which Baker and Hacker seem to get wrong even a MATHEMATICAL example important to their general case is to be found in the following passage, from RGN 91: "Like the relation between a true proposition and the fact that verifies it, the relation between a rule and an act in accord with it is internal (WWK157; cf. MS123,74). This rule would not be the rule that it is, nor would this act be the act that it is, if this act were not in accord with this rule. Because the relation is internal, no intermediary can be interposed between its two terms to effect a connection. Nothing can be inserted between a rule and its application as mortar is inserted between two bricks(WWK 154ff.). It is a grammatical platitude that a rule determines what acts are in accord with it, just as a desire determines what satisfies it...". That Baker and Hacker's main source for this critical part of their interpretation is 'Wittgenstein and the Vienna Circle', a rather early text, and once more not penned in Wittgenstein's hand, is, in itself, and once more, problematic. But in any case, the text itself reads as follows: "A RULE IS NOT LIKE THE MORTAR BETWEEN TWO BRICKS ... There is no rule that interposes itself between the expression X and its application to numbers, like X(sqare) the mortar between bricks... '1 + 1=2' is ... a picture of the rule about the transformation of equations. BASICALLY THE RULE IS THE INTERNAL RELATION which obtains between the equations: 2+2=4 1+1=2 and the equation (1+1)+(1+1)=4. As an internal relation it cannot be expressed by means of a configuration of the game." *6* Thus while Wittgenstein talks of a specific kind of logico-mathematical rule -- that involved in the substitution of equivalent expressions -- Baker and Hacker generalise to "rule and application", PER SE. And while Wittgenstein says clearly that a RULE does not act as mortar, binding linguistic expressions to applications (and, furthermore, that '1+1=2', in isolation, is a PICTURE of a rule, not even yet a rule itself), Baker and Hacker 'deduce' from this that nothing acts - nor need act - to bind rule and application, because presumably they are already 'bound'. This implies that rule and application are as one IN the standing grammar, and it misses that (the) rules do not of themselves determinately help us if and when we actually encounter hard cases. Normally, we simply "cannot lay down a rule for the application of another rule" (WWK 155). A little further on the same page from the above quotation, having just discussed the relation of a proposition to its 'truth-maker', Baker and Hacker exacerbate these problems: "SO TOO in the case of a rule (such as the rule for writing down the sequence of even integers) and the acts that accord with it. ALREADY in 1931 W. observed that 'There is no rule that interposes itself between the expression"X/X(sqare)" and its application to numbers, like the mortar between bricks; I have already to read a certain kind of application into the expression.' (WWK 155) SIMILARLY, to understand the rule 'Add 2'Is to know that the number to write down after '1000' is '1002'" (my italics). But to say that "I HAVE already to read a certain kind of application into the expression" is not to say "I have already done so", nor is it to say "I have already the reading." Even in isolation, this assertion might be more an insistence upon the URGENCY of application - given the exhaustion of logic - than upon its logical NECESSITY. In view of the active nature of rule-applications that I have emphasized, the former seems MUCH more likely. It is also worth noting that, by declaring that Wittgenstein had "ALREADY" by 1931 extended his concept of internal relations to the rule/application nexus, Baker and Hacker imply that this was part of his regular progress to the full-blown insights into rule following (as purportedly involving internal relations) of PI. A compelling contrary view is implicit in the recent work of Peter Winch, among others.*7* Moreover, the simple fact is that the invocation of internal relations in 'middle period' texts such as WITTGENSTEIN AND THE VIENNA CIRCLE, even if it is what Baker and Hacker say it is (I have argued to the contrary), is NOT echoed in later work. There are NO instances of Wittgenstein invoking the concept of 'internal relation' in the context of RULES after about 1939. In outline the 'career' of "internal relations" in Wittgenstein's thought is as follows: (1) 'Tractatus' period: Internal relations are important, and ineffable. (2) 'Middle period': Internal relations are extended in RANGE somewhat, but after what might be judged to be initial vacillation, Wittgenstein again becomes increasingly inclined against their expression.*8* (3) c.1933-1939: Internal relations largely drop out. (4) Mature philosophy. Internal relations vanish ALMOST TOTALLY (e.g. the term is simply NOT USED in Part I of PI, in ON CERTAINTY, or in the REMARKS ON THE PHILOSOPHY OF PSYCHOLOGY). On the HANDFUL of occasions where the term occurs, it is NOT used in connection with rules. This historical trajectory of "internal relations" seems strong counter-evidence to Baker and Hacker's injunction "...not to ignore these matters, but [to take for granted] as part of the background to the discussion of following a rule in the 'Investigations' [that rule and application are internally related]..." (RGN p.85). Wittgenstein's texts from period (2) MIGHT be legible as supporting Baker and Hacker's reading, but it is Wittgenstein's mature works - and his apparently increasing reluctance to believe that "internal relations" SETTLE anything, at LEAST so far as actions from words, from rules, are concerned - that one should pay the most mind to. This periodisation, (and) the general shape of my reading of Wittgenstein on 'internal relations' in relation to rules, receives strong support from the latest in-depth archival (NACHLASS-based) research in this area: David Stern's, in his important 'Wittgenstein on Mind and Language'.*9* "Internal relations" drop out of Wittgenstein's philosophy, because one of the main marks of the passing of Wittgenstein's 'middle' or 'transitional' period (the nature of which Stern delineates quite precisely) is a dawning and increasingly consistent recognition that an "internal relation" is at best properly a presumptive relation. It is only the grammar, which must be PRESUMED in order for acts of decision and application to advance any linguistic or other rule-involving sequence, in which static "internal relations" can be said to inhere. In conclusion, we can pretty safely say that any attempt to make the concept of "internal relations" central to the interpretation of Wittgenstein's mature thought on rule-following is simply out of touch with the letter of his texts, at LEAST of his texts from the time of the composition of PI on. *1* And thus to make quite clear that no positive proposal, such as that there are "internal relations" binding rules to their applications, is available to counter 'rule-scepticism'. (In my opinion, as may become evident, no such binding is REQUIRED). This implies that the topic of the application of rules (in relation to linguistic meaning etc. etc.) does not resolve any questions one may be inclined to ask concerning the connection of language to the world. I set out a positive model of how rule and application MAY justly be said to be in accord in "Acting from rules: 'Internal relations' vs. 'logical existentialism'" (jointly written with J.Guetti (to whom many thanks for advice and encouragement), in INTERNATIONAL STUDIES IN PHILOSOPHY XXVIII:2 (1996), 43-62 -- to which this note is thus in certain respects a companion piece. *2*WITTGENSTEIN'S LECTURES; CAMBRIDGE 1930-32 (LWL), ed. Lee (Oxford: Blackwell, 1980), p.62. One ought to bear in mind that this portion of Lee's notes is unverified by any other seminar-participant, and is preceded by the disclaimer that: "...my notes for this term are far less systematic than those for previous terms." A slender thread on which to hang an exegetical claim that Baker and Hacker say is "pivotal" (RGN 172, 180) to their whole reading of the rule-following considerations. *3* E.g. in WITTGENSTEIN AND THE VIENNA CIRCLE (ed. McGuiness; Oxford: Blackwell, 1967; henceforth WWK) pp.156-7, PHILOSOPHICAL REMARKS (ed. Rhees; Oxford: Blackwell, 1975; henceforth PR) p.217; PHILOSOPHICAL GRAMMAR (ed. Rhees; Oxford: Blackwell, 1974; henceforth PG) p.445, LWL p.57, REMARKS ON THE FOUNDATIONS OF MATHEMATICS (revised ed - eds. von Wright, Rhees, Anscombe; Oxford: Blackwell, 1978; henceforth RFM) p.69. *4* CONTRA Meredith Williams's sometime claim on p.195 of her "The significance of learning in Wittgenstein's later philosopy" (CANADIAN JOURNAL OF PHILOSOPHY 24:2 (June '94), 173-204). Her own claim, which might be used to support the Baker and Hacker reading, is itself undermined by her own somewhat more careful remarks, on the relation of TECHNIQUES to proofs, on p.197f. *5* Though compare the deflationary closure (para. 107) of one such discussion in RFM. *6* WWK, pp.155-7, Wittgenstein's/Waismann's italics. *7* See (e.g.) "Persuasion" in French et al (MIDWEST STUDIES IN PHILOSOPHY, XVII (1992)), p.126 et passim. *8* I would venture that this change is particularly reflected in the transition from the 'Big Typescript' to the PHILOSOPHICAL GRAMMAR; for, while there remain a good many invocations of internal relations in the latter, they are much scarcer in those sections that Wittgenstein substantially revised (i.e. mostly early in the text of PG as Rhees published it). *9* Oxford: O.U.P., 1995 (see also my "Review" of same, in the JOURNAL OF THE HISTORY OF PHILOSOPHY, 1996). See especially pp.112-124, wherein Stern's researches (though unfortunately not all of his JUDGEMENTS about them -- see e.g. p.117 and p.122) make it clearer than ever that in his 'middle period', while Wittgenstein experimented with (e.g. calculus) models of rules that were to be discarded or problematised in his 'mature' writings, the ambit of "internal relations" --which he was not so careful to classify as strictly ineffable as he had earlier -- was temporarily extended somewhat, but never beyond the STATICITY of rules such as '7 + 5 = 12', a rule which itself stands in need of an application (Might we venture, indeed, that an internal relation stands in need of an ('external') criterion... in this case, an application?!). Never in Wittgenstein's thought, that is, do internal relations come even close to accounting for / extending to the dynamic picture of techniques in action which dominates PI and later works (and thus not even to rules such as "Add 2").