Metaphysics is metaphorics: Philosophical and ecological reflections from Wittgenstein and Lakoff on the pros and cons of linguistic creativity.

By Rupert Read

The philosopher strives to find the liberating word…the word that finally permits us to grasp what up to now has intangiblyweighed down upon our consciousness.

Wittgenstein, The big typescript, Ch. 9 : ‘‘Philosophy’’, p.165.

The word in living conversation is directly, blatantly, oriented toward a future answer-word... Forming itself in an atmosphere of the already spoken, the word is at the same timedetermined by that which has not yet been said but which is needed and in fact anticipated by the answering word. Such is the situation of any livingdialogue.

Bakhtin, 1981, p.280, my emphasis.

[Wittgenstein] “We aren’t talking of anything you would call big, and therefore not of anything infinite.”--But as long as you try to point out that we are not treating of anything infinite, this means nothing, because why not say that this is infinite? What is important is that it is nothing big.

When one is a child, “infinite” is explained as something huge. The difficulty is that the picture of being huge adheresto it. But if you say that a child has learned to multiply, sothat there is an infinite number of multiplications he can do--then you no longer have the image of something huge.

If one were to justify a finitist position in mathematics, oneshould say just that in mathematics “infinite” does not mean

anything huge. To say “There’s nothing infinite” is in a sense nonsensical and ridiculous. But it does make sense to saywe are not talking of anything huge here.

[A Student] Even when one says that a child has mastered an infinite technique, there is even there an element of hugenessand one has the idea of something huge.

[Wittgenstein] Yes, but the idea of hugeness in that case comes only from the word “infinite” and not from what it’s used for. By watching his work, we shouldn’t get the idea of anything huge. The teacher does not say to himself, “Ah, fancythese boys of ten and eleven having such vast knowledge!”

(Wittgenstein, LFM pp.255-6).

An introduction by way of a summary

In the main bulk of this paper, I offer a Wittgensteinian takeon infinity and deduce from this some Wittgensteinian criticisms of Chomsky on ‘creativity’, treating this as one among many examples of how metaphors, following the understanding of Lakoff and Johnson, following Wittgenstein, can delude one into metaphysics. As per my title: ‘metaphysics’ turns out to be, really, nothing other than metaphorics in disguise. Our aim in philosophy, then, is to turn latent metaphors into patent metaphors. When we do this, the charm of metaphysics evaporates.

I then briefly sketch some outlines of a positive picture of Wittgenstein on creativity, inspired by Cavell, and Kuhn (heregoing beyond the work I did in this regard in my recent book Wittgenstein among the sciences), and the important work on context of Hertzberg and Travis, which in my view suggests a far more ‘open-ended’ picture of creativity in language than is presentin Chomsky, while (as I sketch) not being committed to fantasies of actual-infinity.1 For what Hertzberg and Travis,

1 As noted by A.W. Moore at p.108 of his “Wittgenstein and infinity” (in TheOxford handbook of Wittgenstein, edited by Oskari Kuusela and Marie McGinn (Oxford: OUP, 2011)), Wittgenstein’s thinking on ‘the infinite’ runs in

following Wittgenstein, demonstrate, is that context, and human responsiveness thereto (including, I would add, through creativity in tone of voice, gesture, etc etc.), allows an indefinitely wide and dense capacity to mean, linguistically. In the course of this, I dispatch the red herring of Wittgenstein’s alleged linguistic ‘conservatism’.

I close by offering some thoughts that I think follow, on the pros and cons of our creative capacities in terms of (our capacities for) persuasion, propaganda, etc. . That is to say:I close by discussing political 'reframing', in thoughts inspired by Lakoff, and that loop back to Chomsky on political language. For, in relation to politics, as opposed to in relation to philosophical linguistics, Chomsky, like Wittgenstein, Kuhn and Lakoff, can I believe can help us to bring words back “from their metaphysical to their everyday use”.

Neither languages nor linguistic competences are usefully saidto be ‘infinitary’

It has often been said that a central problem/question oftheoretical linguistics and of the philosophy of language is something like the following: (Qu.): How can finite beings master infinite systems, such as natural languages? 2 But it parallel, at least initially, to Aristotle’s.

2 Contrast Ian Niles’s “Wittgenstein and infinite linguistic competence”, pp.193-213 of Midwest Studies in Philosophy Vol.XVII: The Wittgenstein Legacy (ed.s French, Uehling and Wettstein, Notre Dame, Indiana: U.Notre Dame Press, 1992). In discussing Wittgensteinian strategems directed against claims made by philosophers and linguists as tothe foundation of / conditions for infinite linguistic competence, he omits to consider that, without any substantive prior committment to finitism, Wittgenstein (or indeed any philosopher) might come to see, to say, that the postulated infinitary competence itself is illusory (though cf. his note 37). I take one of the key aspects of the present paper to be the following: that I am developing a Wittgensteinian critique of ‘the [philosophico-linguistic] infinite’, a project I take to be, perhaps contrary to appearances and expectations, as yet very largely unattempted (though see n.9, below). This

is often radically unclear what is meant by the terms ‘finite’and ‘infinite’ in this context; it is unclear how they are supposed to play a role either in stating or in resolving a problem. It is in fact my view that the question raised above contains a deep and probably irresolvable unclarity, and thus contains at least one important mistake.

I will argue, in this first substantive section of the present paper, for the following: insofar as we can assign / give any clarity to the concepts ‘natural language’ and ‘infinite’, it is at best unclear how and whether we can intelligibly speak of natural languages as infinitary systems.

Idealising slightly, by “a language” I understand a notation 3 which can (at least in principle) be employed for communicative purposes, and so allows the composition of meaningful units (i.e. sentences). Thus correlated with a language (e.g. ‘English’) is the set of sentences which it facilitates - some prefer to say that a language is constituted by this set. By ‘infinite’ I understand something qualitatively different from mere very great or extraordinary size or duration - an infinite system or quantity must be unbounded, without a point which could possibly be the termination of the system/quantity.4 Insofar as there is one, the most natural paradigm case of infinitude is simply the project, should it be successful, will knock at least one large whole into contemporary scientistic linguistics.

3 Cf. Goodman’s Languages of Art (Indianapolis: Bobbs-Merrill, 1968), Part IV. Notations require their characters and composite forms to be disjoint and differentiable, rather than dense (as are, for instance, the irrational numbers, and, perhaps, the ‘syntax of the visual arts’). (By understanding a language or notation thus, I am idealising -- from the lived reality of sentences in contexts of use, and in relation to the language in which they have their home. For detail, see my “What “There cannot be any such thing as meaning anything by any word” could possibly mean”, in The New Wittgenstein, eds. Read and Crary (London: Routledge, 2000). See also subsequent sections, below.)

4 Viz. PR para.s123-4, 144.; PR p.311; LFM p.32, pp.255-6. (Of course, if my argument below is correct, it may have to be recognised that these expressions with which “infinite” is explained are no surer and no less metaphorical than the word itself.)

expansion of the natural numbers: viz. 1,2,3,4,5... . (Though the dots at the end ought not to be read as the dots of abbreviation. The sense in which we understand the infinitude of the natural numbers, in prose rather than in the course of (e.g.) some technical-mathematical manipulation of some transfinites, is only the sense in which we understand that there is no provision for - no ‘room’ for - a last term in the series of natural numbers. Or again, the sense in which any series of natural numbers which we choose to develop will havea highest term only ‘arbitrarily’, not as a matter of absolutenumerical principle.5 )

But each and every sentence of a language must be composed out of a finite number of (finite) compositional units (viz. words of the language, punctuation marks, etc.). And each and every sentence must be finitely long - we cannot evenin principle make sense of the concept of an ‘infinitely long sentence’, because it would never be clear that it was a sentence,let alone what sentence it was (This follows from the remark about the infinite, above; we shall return to it later).6

Now, it has of course been ‘observed’ that no human ever literally exhibits or performs an infinite linguistic competence. But the above paragraphs entail that we can say (further and more strongly than this) that - no matter how you permute or count the sentences which are correlated with / constitute a

5 See pp.163-4f. of S.G.Shanker’s Wittgenstein and the turning point in the philosophy of mathematics. (It is worth noting that the way I have set things up in this paragraph resists the unhealthy tendency to speak of ‘theinfinitely large’ and ‘the infinitely small’ as ‘paradigms’ of infinity. Infinity is a concept which, if it is a concept at all, is not commensurable with concepts of size. There is a ‘categorial’ difference, ifyou like, between the vastly large or the ‘absolutely as large as possible’on the one hand and the infinite on the other. Cf. on this my epigraph, above, from LFM.)

6 On this point, compare para. 45 of Part II of Wittgenstein’s Remarks on the Foundations of Mathematics (Cambridge, MA: MIT, 1978 (revised edition), posthumously edited and published by von Wright, Rhees and Anscombe, transl. Anscombe), and PR para.127.

language - if they are finitely long and built up from a finite number of elements then they are themselves finite in number.7 Sowe have as yet no infinite linguistic system which one should need to have mastery/competence in.8

This appears to be a valid argument against the rightness, the intelligibility, of the ‘central question’ (‘(Qu.)’), mentioned above.

I can see two objections to this argument. One is the obvious one, classically cited by linguists and logicians, and, to some degree, surely correct - that we can repeat (‘iterate’) words in a sequence, and thus that there is a potential infinity of finite (and grammatical) sequences. I will respond critically to this in a moment. First though, I want momentarily to bracket this objection, and deal with the only other telling objection-schema I can imagine to the argument I have given, should this ‘repeatability of words’ objection prove to some degree ill-founded.

The other seemingly-telling objection would run as follows:

“But is this not a legitimate English sentence: “10000001!is a very large number indeed”? Surely it is, and an infinite number of such supra-mathematical sentences may be formulated,by means of inserting in turn all the numbers of a denumerable

7 Incidentally, this is true of ungrammatical sentences too, so long as one lays down that one cannot, absurdly, include just anything (e.g. purelyabstract objects) as characters of which sentences may be composed.

8 One might add - though this is neither entailed by nor required by myargument up to this point - that it seems highly likely that any actual human linguistic competence (I use that word deliberately, as it, and not the word “performance” fits most naturally the context…) will fall well short of the limits of the finite competence just described. For instance, is it not obvious that one may in some sense conceive of formulable, finitesentences that would take longer than the longest possible human attention-span to read or to parse? This is actually an important point, relevant andhelpful to some of the points I make in the text, below.

set. So the assumption that there is a finite number of elements from which sentences may be constructed must be false. Does this not show, then, that languages/linguistic systems must be infinite, by non-controversially pointing to the nesting of the sentences of mathematics within those of (e.g.) English?” (One could also ‘run’ this objection simply by treating mathematical ‘sentences’ directly as sentences of English.)

A full treatment of this objection would take us deep into (particularly) the philosophy of mathematics. I will restrict myself to making two points about it, which are I believe sufficient for present purposes.

To begin with, the objection has only limited scope in application, in that if language is infinite only in virtue of its including series which are designed/defined such that they are infinite, then one would have at least to agree that, absent the creation/discovery of such series, language and linguistic ability would be (and at one point surely were) reassuringly non-infinitary. (It might be objected here that, because of the numbers always being there to be discovered - or because of the ability always being at least latently there, waiting on its historical destiny - linguistic ability can always be said to have been infinitary. But this is a hyperbolical Platonism. Such latent ‘there-ness’ is simply a very imaginative abstract retrospective construct. We might aswell say that the concept of ‘xylophone’ is innate; or that wehave the (latent) ability to reproduce asexually and spontaneously.9 ) Note that one cannot simply appeal to the role of terms such as ‘infinity’ or ‘aleph0’ in our language - such terms have a fairly well-defined and fairly ordinary role(comparable to that of words such as ‘God’ or ‘the Universe’ or, come to that, ‘differance’), and do not in and of themselves

9 For amplification, compare H.A.Nielsen’s superb piece, “How language exists: a question to Chomsky’s theory”, Philosophical Investigations Volume 5 ,   Issue 1 ,   pages 57–71, January 1982 , whose general argument is highly consonant with mine here.

make any progress toward generating an infinitary linguistic system.10 One must suppose that it is the possibility of generating endless specific sentences about specific numbers thatentails that our language be infinite.

Relatedly, and more tellingly, this above-canvassed objection of course arrives at the infinitary nature of language only by building this in through having a language be builtout of an infinity of elements (i.e. 1, 10, 101, etc. And surely we do not wish to put all the weight of language’s supposed infinitude upon the mere possibility of endlessly adding (e.g.) “0” or “1” to whatever number one comes up with?). Traditionally, the conundrum with which this section opened has been posed as a puzzle about ‘finite beings’ manipulating a finite array of symbols and yet generating and having an ability ranging over an infinitary symbolic system. So my initial argument would, if valid but not sound, at leastnecessitate a location of the puzzle at a different level thanhas been usually supposed - the puzzle would become one of howit is possible to generate an infinite array of possible linguistic elements, of symbols. But again, that question we already know the (rather trivial) ‘answer’ to, insofar as there one: simply develop a recursively denoted and endlessly inscriptible series - viz. the natural numbers.

Once again, then, we find that it could only be in virtue of having developed notations which specifically - definitionally - allow for counting to infinity (as opposed, for instance, to a system of numerals amounting to ‘1,2,3,4,5,Many’) that our linguistic ability could justly be conceived of as infinitary. And it is vital here to bear in mind Wittgenstein’s grammatical point that even an ability conceived thus as infinitary - through an infinitude of possible linguistic elements - would not thereby realize an infinite series, nor exhibit an infinitary competence, but only satisfy a norm of representation:

10 The importance of this point is hard to over-estimate. See PR para.s 124, 144-6, and (especially) 138; PR pp.306-7 and 312-3;

“If 1 is divided by 3 there is no such thing as an infinite series of 3s. There is a law that 1 divided by 3 is 0.3 recurring. We confuse the infinite possibility of writing 3s with 3s written down. Similarly, there is an infinite possibility of constructing points on a line, but a line is not therefore made up of points.” 11

So, having dealt with the objection from mathematical language, let us consider the more familiar objection – the objection usually considered decisive - based on ‘recursion’. Based, that is, on sentences like “Jean was not not a good person” and “It was sunny and it was the 4th of July and things had never been better and yet everyone was unhappy”. Through structures such as these - the iteration of logical connectives etc, either with or without the addition of further clauses/sentences - it is held that, though sentences must be finite, and built up from a finite pool of linguistic elements, some members of that pool can be repeated indefinitely many times, without end, and that such potentially-boundless repetition entails the conclusion that natural languages, and our linguistic capacity, are infinitary.12 This objection

11 P.108 of Wittgenstein’s Lectures, Cambridge 1930-2, from the notes ofJohn King and Desmond Lee (ed. Lee, Oxford: Blackwell, 1980; see also LFM p.32). I cannot here go into how precisely a line such as this lays the groundwork for the rebuttal of the suggestion that we need to grasp an infinitary ‘grammar of mathematics’ in order to understand mathematics (and be mathematically ‘creative’, in the Chomskyan sense of that word). Itshould be clear enough from the remarks above how I would take that suggestion to involve a conceptual mistake (though perhaps not one of quitethe gravity of the mistake involved in claims of purely linguistic infinitude). See also n.5, above. (Perhaps it is best not to think there’s such a thing as understanding the infinite aside from manipulating it in maths. Even mathematicians, then, don’t understand it in any further sense.See on this discussion, below. (Cf. Wittgenstein’s vital remark: PR para.138 (p.159).))

12 There are other ways one could generate an apparently-endless supply of possible-strings, such as by iterating certain verbs (e.g. ‘had’), or bynesting quotations. These will be open to the same counter-objections I am about to make, but furthermore are more intrinsically dubious. For instance, the available number of nestable quotations cannot be greater

potentially invalidates the initial argument I gave, for it has the consequence that a finite number of linguistic elements need not entail that the total number of generatible sentences is itself finite. I did, it seems, omit to deal withthe - relevant - possibility of the same word or phrase being rightly iterable.

But the postulation of (the need for) infinitary linguistic competence (which, as already mentioned, ‘cannot’ be matched by performance; thus the radical competence vs. performance dichotomy of the Chomskian paradigm) may rest uponconfusions related to those excavated above. I wish to challengethe competence vs. performance distinction itself, by means of challenging the tenability of the apparently-flawless method of constructing or generating infinitely many indefinitely long sentences which is the linguist’s main means of generating it. I wish to do this by means of invoking some considerations adduced by Peter Winch in discussing the iterability of negation.13

Winch’s argument comes down to this: One of the key insights prompting Wittgenstein’s change of philosophical heart beginning in the late 20s was that the logical connectives are not machines running on ‘rails to infinity’ - in short, that they do not contain within them an eternally iterable meaning. It does not follow from the meaning of ‘‘not’’that two ‘‘nots’’ cancel each other out in what we are pleased

than the available number of ‘first-order’ sentences. As for iterating verb-forms (see also below): contra some logicians, is it even clear that “Jean had had had a good day” is a grammatical sequence? The third ‘had’, it appears to me, can only be an idling wheel. I am fighting (in the text) on the opposition’s strongest ground - that of the (iterable) power of ‘logical connectives’ in natural language. (A fuller treatment of this issue would directly address the question of INDEFINITE VS. INFINITE, as mathematical and extra-mathematical concepts; but this fuller treatment is not necessary to my argument here. I briefly outline a treatment of this question toward the end of the present section.)

13 “Persuasion”, on pp.123-137 of French et al. (op.cit.) . Henceforth PER. (Cf. also pp.102-5 of RFM.)

to call ‘double-negation’ (cf. ‘‘PER’’, p.126).14

Thus one has to ask how relevant to natural language is the idealisation made when one imagines that “not” can be understood, in relation to questions of combinatoriality and generativity, as having as its essential properties those which we imagine are possessed by the logical symbol for negation. In particular, if confronted (outside linguistics textbooks) with a long sentence involving a whole series of ‘“not”s’ counterposed to one another, perhaps thirty or more, should we presume that this sentence must rightly be understood in one way or another dependent solely upon whetheror not the number of ‘“not”s’ in a row is odd or even? Would it not be to lay down a new rule, if one were to state that a sentence such as “The return of Blair as Prime Minister is notnot not not not not not not not not not not not not not not not not not not not not not not not not not not not not to be tolerated!” must be understood (if uttered sincerely) as insisting that we ought to tolerate Blair’s becoming PM of Britain(‘again’)? 15 (Note that I have deliberately chosen a

14 Compare the famous story of Sydney Morgenbesser’s refutation of Austin’s claim that a ‘double positive’ necessarily meant a positive and not a negative: http://en.wikiquote.org/wiki/Sidney_Morgenbesser

15 The point I am making here may be claimed to require a certain problematization of the dualism of syntax vs. semantics too, a problematization which some will find unacceptable, and for which I cannot argue in detail at present. But briefly: of what possible philosophico-linguistical interest could an infinite ‘purely’ syntactic capacity be to us? No more than that of a random-noise-generating machine that we might conceive of which would go on and on and which we could not show would ever(have to) stop producing its noises, barring some concrete physical intervention. A putative sentence which we have no grounds for claiming could mean something in a language-game which we can actually imagine is not usefully described as ‘syntactically correct’. “Green ideas sleep furiously” is no more a sentence than “Blob bling, slob, job, - sling”. Both may have effects experientially, we may associate certain ideas with them - but that’s all, and it’s not meaning. Grammatico-phenomenological effects can have nothing to do with language, conceived of as a means of action andcommunication (cf. the argument of James Guetti’s Wittgenstein and the grammar of literary experience (Georgia: Georgia U. Press, 1993), and his “Meaningful Consequences” (jt. with myself, Philosophical Forum (Winter 1999) XXX: 4, 289-316). Cf. also the argument I make at the opening of the ‘Interview’ that concludes my Wittgenstein among the sciences). The same

sentence the most natural reading of which, if there is one atall, it seems to me is, actually, as meaning something like “Please please please we mustn’t let Blair become PM again!!”.16 Not, as one would get from checking the oddness or evenness of the number of “nots”, the opposite meaning.) I think that, if not for this sentence then at least for one somewhat longer (!), it would be to lay down a new and contestable rule,17 even if the utterer of the sentence in question were aware of (and certain of) the exact number of ‘“not”s’ contained in her utterance. One is reminded here of an argument that Kripke (in criticizing Benacerraf on what thenumbers are) has made concerning the presentation of the natural numbers. Crudely summarized the argument has the following phenomenological and rhetorical form:18 If we were to be presented with what are purportedly the natural numbers in a form so peculiar (e.g. in some very large and arcane base) that no human being were able to recognise the series as the numbers, would there remain any grounds for saying that the series still might be / is the numbers? The analogy would (Guettian) considerations will apply to the terms “infinite” and “finite”, if it is determined that (at least outside of specific technical contexts),they are in actuality merely devices for the production of philosophical confusion... That is, the employment of “infinite” and related concepts in ethics, in linguistics, and so forth, will be legible for its grammatical effects, not for its meaningful consequences. Thus semantics cannot be irrelevant; a purely syntactic version of language is not language at all, and so,semantically deeply-bizarre or incomprehensible items need not be conceded to be items of language.16 Three “pleases” I think makes sense here; but would thirty?17 In a fuller presentation, one would have here to address the issue of the vague borderline between ‘old’ and ‘new’ vis-a-vis rules etc.; this is part of the Wittgenstein’s ‘rule-following considerations’ in general. (Indeed, ideally in the present context one would also mention and discuss the way in which hyperbole, metaphor etc. arguably cannot be excluded from the ‘heartland’ of language, which would complicate matters considerably. Imake some gestures in the direction of doing this in the central portions of the present paper.)18 The argument does not exist in print -- I take it directly from Kripke’sPrinceton lectures on the philosophy of maths of 1992-3. (There is no spacehere to defend a point on which I agree with Kripke, and which is pretty crucial for granting his argument salience: the move he makes from ‘phenomenology’ to LOGIC.)

then go as follows: If one is presented with an unrecognisable sentence - that is, a purported-sentence whose syntax and thuswhose semantics is unsurveyable - does one have any reasonable/plausible grounds for thinking that nevertheless this could be a sentence of English? (There will be borderlinecases here, but they arguably mark off, in ways with which we are fairly familiar, the (vague) frontiers of what we may be pleased to call a finite system, so long as we do not have in mind a substantive contrast with a conception of an illusory -infinite – system. I will return to this point, below.)

Analogous points will surely hold for the other iterativeand recursive devices of natural languages; that is, for the other logical connectives (besides “not”) too, including even the innocuous “and”. I.e. Without endorsing or even entertaining any weird and impossible rule-scepticism, I thinkone can plainly endorse the suggestion that the meaning (indeed, the very grammaticality) of many very long strings may be largely or completely unsettled prior to their actual consideration by human beings who use or encounter them. If you string enough phrases and sentences together using “and”, the result may be unrecognisable by any master of natural language as a sentence. And without endorsing some stupid verificationism, I think that it is plain that one can back the view that if no master of a language can recognise some string as in and of that language, then that string is simply not (at least, as yet) part of that language. Language, to be language, is and must be both usable and to a considerable degree ‘surveyable’.

This results in a substantive counter-argument to the notion that one could in principle formulate endlessly many grammatical strings from a finite number of linguistic units. It re-establishes, I believe, the validity of the argument with which this section of the present paper commenced.

There is an interesting contrast between the argument just given and the extraordinary assumption of Charles

Sayward, in a piece whose perspective is otherwise fairly conducive to mine, that “[a] string of 43 trillion occurences of ‘it is not the case that’ followed by ‘is raining’...is an understandable string. It means that it is raining.” This is astipulation (and a bizarre one), in my view. It cannot be deducedfrom the mere phenomenon of recursion. Moreover, Sayward ignores that the computation/parsing of any such string would require new proof procedures, which we should not necessarily be bound to accept (for in any real situation there would be the question of whether there were actually exactly 43 trillion); but even if we accept his far-fetched stipulation, the key point is that the semantics of radically unfamiliar or weird strings is in most cases up for grabs; unless perhaps they are clearly metaphorical, which hardly helps (because compare Davidson, Guetti etc. on new metaphors). This imagined string has but little prior claim to be part of the language. Allowing that it is hampers Sayward’s argument toward the conclusion that “English is indeed finite”, and leads him to commit some rather desperate and arbitrary finitistic manoeuvring.

The important thing to notice about my Winchian argument is, again, that it does not depend upon finitistic premises, inthe manner in which the considerations cited in some of the footnotes to this essay might be argued to do so. It is a logical argument, in the sense of that word that we find in the later Wittgenstein: it is not physiological or psychological in nature, and is only phenomenological as a meansto addressing logical issues. To make the Winchian move here is to deny that the grammar of natural languages is endlessly iterable in the way in which most linguists and philosophers have in recent times supposed that it is.

And so now we can start to draw together the threads thusfar. I will do so by suggesting an analogy which I think is pretty devastating to the Chomkian picture.19 Imagine someone 19 These paragraphs are strongly influenced by correspondence with Wes Sharrock – many thanks to him for making these thoughts available to me.

asking how much music you can get out of the 88 keys of a piano. By analogy with the Chomskian picture of language (sticking for now to the basic idea of the units out of which sentences are composed being ennumeratable), one might seek tocreate a ‘boggle’ by suggesting that it is extraordinary that one can allegedly get an infinite number (sic.) of tunes out of a finite number of keys… Doesn’t this show something of theinsignificance and misleadingness of the Chomskian argument aswell as providing a reminder that its not just a matter of thecombination of the keys but also of understanding (about) the music (or otherwise) they’re used to make. In other words, real creativity. In other words, as I have stressed above: We need to be clear that the judgement that something is a tune / is a sentence depends upon its being, ultimately, recognisable as the tune /the sentence that it is. Alleged tunes or sentences that lack such perspicuity/surveyability need not be allowed to be tunes/sentences at all. This is connected with Wittgenstein’s lovely remark at 527 of Philosophical Investigations: “Understanding asentence is much more akin to understanding a theme in music than one may think. What I mean is that understanding a sentence lies nearer than one thinks to what is ordinarily called understanding a musical theme.” Understanding a language is like having to at least some basic degree a musical ear.

This piano analogy for arguments about ‘linguistic creativity’ might help one then to resist Chomsky’s key move, which is to psychologise the issue, a trick to make his linguistics into ‘psycholinguistics’ but which – as in most other supposed bases for Chomsky’s scheme – involves giving spin to what are actually utterly uncontroversial points, in this case, that, as is clear from any familiarity with language, there are a lot of words and the potential for combining them together in all sorts of ways so that the number of combinations that are available ensures that, if youcould find a way of determining how many of those combinationswould count as sentences, it would surely be a very big

number. But unless you have a way of denumerating just those combinations, then there is no such number – “indeterminate’’ is not “infinite”. When the keys on a piano are tapped in various combinations, still somebody has to do the deciding asto when one of them had delivered a tune; and you can clearly then see the indeterminacy of the answer to how many tunes, exactly, could they generate, while seeing clearly also that the answer is not: “Infinitely many”.

So: “Indeterminate”, not “infinite”, is really the word one is looking for, hereabouts: that there is no prescribed orproscribed length of sentence doesn’t mean there is no limit to sentence size. There obviously are limits to sentence-length: this is what the machine analogy damagingly screens from us. But there is no fixed limit to sentence length, whichis just another way of saying that the number of sentences a language can generate is not determinable.

In conclusion to this section: simple mathematical infinity - the infinitude of the natural numbers - provides us(at best) with the only clear notion of infinitude that we have, and, (excluding in a certain attenuated sense mathematics itself), languages simply are not infinitary systems.20 In the(limited) sense in which it is possible to envisage an

20 One might add (though this thought is close to Kripke’s thought, offered above) to the counter-objections I have thus far emphasized that there must be some upper limit to the enormity and complexity of the strings that can be composed and yet still be decidably in the notation. What grounds do we have for saying, say, that “x is a very large number indeed” is an English sentence, if x turns out to be an unparsably large number, and the sentence is thus itself unparsable? If this question is unanswerable, then the objection to my argument from mathematics would fail, because one cannot conclude from the fact that we can legitimately speak in the abstract of a series being infinitary that we could construct an infinite number of actual sentences about it - even were we to live forever! I entertain the latter absurd notion for a moment just to make clear that even if one grants provisionally one form of infinitariness, others do not necessarily follow (The same would apply to unparsably long sentences formed by many many concatenations of shorter sentences). The substantive point here is closely analogous to that made by Wittgenstein in para. 38 ofPart II of the Remarks on the Foundations of Mathematics (op.cit.):

infinite series of natural numbers (or of “3”s or “2”s), the sense in which there need be no last term, there is no corresponding series of sentences in any natural language... for such sentences, sentences that (could) make a grammatical difference, must be finitely long and finite (though incalculably large) in number. Humans - ‘finite’ beings 21 - need not be hypothesized as even in theory having a linguisticcapacity of infinite scope - only, perhaps, of ‘very large’ scope (though large compared to what, we still ought to ask. Can one language be larger than another? Does the linguistic

“An interesting question is: what is the connection of aleph0 with the cardinal numbers whose number it is supposed to be? Aleph0 would obviously be the predicate “infinite series” in its application to the series of cardinal numbers and to similar mathematical formations. Here it is important to grasp the relationship between a series in the non-mathematical sense and one in the mathematical sense. ...A ‘series’ in the mathematical sense is amethod of construction for series of linguistic expressions.

“Thus we have a grammatical class “infinite sequence”, and equivalent with this expression a word whose grammar has (a certain) similarity with that of a numeral: “infinity”...

“From the fact, however, that we have an employment for a kind of numeral which, as it were, gives the number of the members of an infinite series, it does not follow that it also makes some kind of sense to speak of the number of the concept ‘infinite series’; that we have here some kindof employment for something like a numeral. For there is no grammatical technique suggesting employment of such an expression.”

We perhaps have no good grounds, then, for supposing that there is not an upper bound on the enormity (and on the number) of sentences that can decidably be said to be in the language. (However, it is important once more (as in note 8) to observe that the argument of this note does not necessitate or necessarily eventuate from the main lines of argument in this paper.) 21 The reader may be now be starting to worry whether the expression ‘finite being’ is well-formed. If languages are not infinitary, still it sounds odd to call them finitary. Perhaps these mathematical terms are justnot unmisleadingly applicable to many human phenomena? What makes us want to call human beings ‘finite’? I am not suggesting that humans are infinite-- I have no idea what that means -- but I am laying some suggestive groundwork for the section below in which I will question the commonly-held metaphorical-metaphysical assumption that humans are finite. Contra, Chomsky, McGinn, Derrida, even Cavell, and in fact almost the whole philosophical tradition,it is not clear to me that it makes sense to describe humans as finite, so far as it is our minds rather than our bodies that we have in mind.

ability of a human outshine in magnitude that of a chimp? Saying“only very large” risks buying into the comparison of the finite and ‘the infinite’ that Wittgenstein so strongly warnedus against). The ‘central problem’ with which this paper began is simply not a problem at all.

Given this, let us now ask what the implications are for linguistics and philosophy? I would expect them to be confinedto the theoretical level; but there they might be substantial.For instance, here is one thought-experiment which, ironicallyenough, perhaps becomes possible conditional upon my argument being unrefuted: Imagine a human being whose memory were exceptionally large and whose life were exceedingly long; she might actually know all the decidably grammatical strings of alanguage. (I entertain this ‘thought experiment’ on purely ad hominem grounds; as, speaking for myself, it trades on a deeply confused picture of how and what language might be. That is, it reifies language, while, as Nielsen, Guetti, and the later Davidson among others have pointed out, ‘language’ isin its action, in its meaningful use. To postulate it even hypothetically as wholly ‘memorized’ is simply absurd; for what would be memorized would be at best idling ‘senses’, not meanings or uses at all. The tired old picture of a ‘box’ of some kind explaining one’s linguistic abilities as they are actualized (and we should not be trapped into staticizing and reifying ‘ability’ either, as I have been trying to show) mustbe discarded). What then would become of the supposed ‘creative’ aspect of language-use so beloved of generative grammarians?

A critique of Chomsky on creativity 22

Consider now Chomsky’s peculiar use of the word “creative”: “[I]n the context in which I have been speaking about 22 This section is based on thoughts first mooted in my 2000 piece, How I learned to love (and hate) Noam Chomsky. Philosophical Writings, 15/16. pp. 23-48(https://www.uea.ac.uk/~j339/ReadonChomsky.htm).

creativity, it’s a normal human act. // I’m speaking of the kind of creativity that any child demonstrates when he’s able to come to grips with a new situation: to describe it properly, react to it properly, tell one something about it, think about it in a new fashion for him, and so on. I think it’s appropriate to call those acts creative.” 23 The fundamental question here is: Why? (And by what right? For we do not normally regard many such acts as properly “creative”.24

We will need to on our guard against Chomsky’s ‘creative’ use of the term misleading us, as a result...) Is this use of theterm “creativity” its serving as a genuine scientific technical term? Well, but in that case why not just coin an entirely new term? The point appears to be persuasive: to get oneto think in a different way about a human phenomenon with which we are all familiar and which we have perfectly good ways already of dealing with in discussion etc.; and again to get one to think that something not only new and dramatic but also scientifically demonstrable is being said here (by Chomsky). But if something dramatic is in fact being said, it will surely not have the quality of a true new scientific theory, but at most of what Wittgenstein refers to as “a fertile new point of view”.25 If Chomsky is managing to do anything at all, successfully, in 23 Chomsky from Elders (ed.), op.cit. , p.151. (For a critical (though ultimately rather sympathetic) account of Chomsky on creativity, see Geoffrey Sampson’s The form of language (London: Weidenfield and Nicholson,1984), espec. pp.53-57.)24 And indeed there is a way of seeing what Chomsky offers us in his linguistics which undermines this remark of his from the discussion with Elders. See Sampson (ibid.), p.54: “In a common sense of ‘creative’...a creative activity is one whose future products will typically fail to fall under a definition constructed to account for past instances [e.g. as in art]. By treating human languages as well-defined sets of strings, Chomsky implies...that the use of language is not in this sense a creative activity.”

My thought in the present piece is this: We need to be attuned to the possibility of linguistic creativity inherently present in the language-using animal; but something will have gone wrong if virtually every single utterance made turns out to be ‘creative’.25 Culture and Value (posthumous -- ed. von Wright, transl. Winch (Oxford: Blackwell, 1980)), p.18.

the passage quoted, it is surely the kind of thing that someone like Freud did: not giving us a new demonstrable scientific result (nor even a scientific claim), but giving us a fragment of what can perhaps, if used judiciously and self-consciously, be a handy and thought-provoking new way of talking. So, for instance, Richard Rorty has said that Freud -- among other things -- democratized Nietzsche by turning us all into great ‘creators’ through the fantastic drama he found in our daily lives, in our linguistic slips, and our dreams, etc. etc. .26 Might one similarly claim that Chomsky is similarly democratizing linguistic creativity by suggesting that it is not the exclusive preserve of the poet, let alone of the scientific inventor?

This is, I think, the best that can be claimed for Chomsky’s claim here, and would turn Chomsky into a bit of a fertile strong poet or fashioner of a new vocabulary (in Rorty’s sense of these phrases). Unfortunately, this thought is mostly vitiated by:

(1) its misleading scientistic presentation in Chomsky ;

(2) its lack of originality -- for if we are to understand theterm “creative” as Chomsky suggests we ought, then not only poets and linguists but also most ordinary people have clearlylong been aware of and taken huge pleasure in the possibility of being continually ‘creative’ with and by means of language;27

and

(3) its contradiction with Chomsky’s general claim elsewhere that‘really this stuff is just recollection; it’s all innate’ -- thus Chomsky finds himself in the awkward position of wanting to assert literally both “Everyone is continually creative all the

26 In this, Rorty follows Philip Rieff, in his Freud: The mind of the moralist (New York: Harper and Row, 1966; especially p.36).27 Admittedly, it has been at times suggested that both points (1) and (2) also apply to Freud!

time” 28 and “Creativity does not exist”!29 Such an incoherent want is a useful signal that we are here dealing with a (desire for) metaphysics, with a mythology (but one not presented as such). With a metaphorical extension of a term that in this case is not wise.

And in any case, I think we can confidently predict that Chomsky would be even less willing than Freud was to begin to acknowledge that what he has created is at best a new mythology... Even were one to try to suggest to Chomsky that a‘mythology’ in this sense is not all bad, that ‘fertile’ mythologies in fact can be very fine things...

28 Cf. this bizarre remark of Chomsky’s: “This creative use of language is quite incompatible with the idea that language is a habit-structure. Whatever a habit-structure is, it’s clear that you can’t innovate by habit,and the characteristic use of language, both by a speaker and a hearer, is innovative.” (Quoted on p.18 of Transformational Grammar, by A. Radford (Cambridge: C.U.P., 1986) So if I habitually go for a walk at tea-time, I must take the exact same route -- and indeed make the exact same bodily movements -- every single time??! (See also Sampson (op.cit., pp.55-56), who usefully points out that while in one sense Chomsky allows too much creativity to language, in another sense he allows too little: “[T]here is no limit on the ways we can analogize between phenomena. ...If a sequence of words acquires a use only by virtue of a ‘creative’ act, as Wittgensteinsuggests [in his discussions of family-resemblance and of finding/inventingcontexts in which apparently nonsensical strings can make sense], then the notion of a grammar with predictive consequences seems to be a mirage; and if no grammars, then no Chomskyan theory of language.” Rorty and Davidson argued similarly on metaphor, in the latter portions of their lives.)29 Chomsky might be defended here on the grounds that the contradiction between these two moments is merely apparent: He is speaking of creativity existing within a framework. All well and good, but this is not enough to resolve the contradiction: For insofar as we regard the human being as a ‘language-machine’, it cannot properly be said to be creative at all. No morethan can, for example, a simple digital computer that has been programmed to ‘translate’ sentences from one human language to another. (Chomsky doesn’t appear to understand that at this very point he is doing philosophyunawarely. If he were aware, and tuned into Wittgensteinian philosophical ‘methods’, he could then legitimately suggest that the apparently-contradictory remarks just given are in fact ‘grammatical remarks’, utteredon particular occasions as part of a therapeutic project. This claim would be interesting to assess; however, we do not need to assess it, because Chomsky’s lack of reflexive / philosophic understanding makes the claim unavailable to him.)

Chomsky’s defenders claim that the underlying reason for their passionate defence of Chomsky’s claim to greatness and importance as a philosopher and not only as a linguist is thathe makes possible an understanding and defence of human freedom and dignity, put at risk by behaviorist etc. doctrines. Chomsky is supposed to give us a sense of the power, depth, fertility and set-apartness of the human mind. Chomsky himself has made a number of similar remarks, often atthe points where he sketches a connection between his political thinking (to which, I give all praise and credit -- see the introduction of Chapter 3 of my Wittgensteinian way with paradoxes) and his philosophical-scientific linguistics.

This claim is based above all on the ‘creativity’ point that we have just been exploring. But, when we pursue seriously why Chomsky-style ‘creativity’ is supposed to be thebasis of human distinctiveness, we encounter a problem, that brings us to the nub of the issue, already telegraphed in the previous section. For that ‘creativity’ is the kind of creativity involved in recursive rules, nothing more. It is the kind of ‘creativity’ involved in the alleged innate constructibility of ‘sentences’ such as “John had had had had had had had had had a bad morning”, or (similar to that discussed earlier), “Blair is not not not not not not not not not not not not not not not not not not not not not not not not not not not not not not not a war criminal”, or “The 1st and the 2nd and the 3rd and the 4th and the 5th and the 6th and the 7th and the 8th and the 9th and the 10th and the 11th and the 13th and the 14th and the 15th and the 16th and the 17th and the 18th and the 19th and the 20th and the 21st and the 22nd and the 23rd and the 24th and the 25th and the 26th and the 27th and the 28th are all days of the month”. All of these are probably new ‘sentences’ (the scare quotes seem necessary to me because the first two are, in my view, semantically ill-formed; they would evoke no more than bizarreness reactions, in sane hearers, uncorrupted by the metaphors run wild which form linguistic metaphysics). I have

exercised my ‘creative’ powers – in something already slightlystronger than the sense of that word usually preferred by Chomsky -- in constructing them. But it is patent that -- except (ironically) just possibly when considered specificallyunder the very particular context of a search to find ‘sentences’ that make Chomskyian theorizing look bad -- these ‘sentences’ are at very best tedious to the nth degree. They have been constructed by rote. By an application of nothing more than crude rules of iteration/recursion. They show no creativity whatsoever, in the ordinary sense of that word. They do not make the human mind valuable or special. They do not manifest my/our freedom or dignity. What does, is (among other things) real creativity. Such as the ability to create awork with coherence and structure. Or the ability to construct a joke, or a passage with some literary quality, or a musical theme. But these matters, generative linguistics is, ex hypothesi, unable to cast any light whatsoever upon. What can be generated via Chomskian ‘creativity’ is simply strings of words mechanically formed by means of the application and re-application of rules, without any discrimination. Discrimination -- the ability to pick out, latch onto, and elaborate upon strings which are of real interest, and not merely ‘well-formed’ -- is another matter altogether. It is what arguably makes human freedom possible and important. And Chomskian theory has no bearing on it whatsoever.

I think that the Chomskian play with the word “creative” is anexample of what Wittgenstein called language going on holiday.The word has been taken from its ordinary context, and projected into a new context where it may do good, but will more likely do harm.30 (There is nothing to stop anyone making

30 It’s important to note that there is of course nothing necessarily wrong with taking a word from one context and projecting it into another. On the contrary, this is of the essence of human linguistic – metaphorical, etc – creativity, which happens very frequently: See on this Cavell’s The claim of reason, especially “Wittgenstein’s vision of language”. (It is necessary to say this at all only because, unfortunately, Wittgenstein has become

such a projection. But I am trying to suggest why doing so should be seen as unnecessary, and unattractive.)

Lakoff and Johnson give impressive detailed accounts of this kind of phenomenon in their works, including notably in Philosophy in the flesh, also in Metaphors we live by.31 These works include, not coincidentally, trenchant and impressive critiques of Chomsky.

If we are to understand something worth calling linguistic creativity, we need to think beyond recursion. We need to think beyond the merely syntactic. We need to get to grips with what Lakoff in particular has talked about: the power of human beings to create linguistic novelty, by use of metaphor.

A positive vision of Wittgenstein on creativity in language use

I am not going to set out here in any detail whatsoever a positive picture of Wittgenstein on creativity. This is because, first, such a picture is already implicit in Stanley Cavell’s account of the projection of words, in The Claim of Reason. And in the ‘case-studies’ offered by Kuhn, in his account of the creative work done by Copernicus, in relation to terms such as “Earth”, and by Einstein, in relation to terms such as “space”, “time”, “curved”, etc. (Moreover,

identified in the ‘popular’ imagination with a desire to keep language as it is, to police it and freeze it. I discuss this in “Against linguistic conservatism”, below.)31 I have endeavoured to learn from them, in for instance my critique of themetaphysics of time, as nothing more than an unaware metaphorics: see in particular Chapter 2, on ‘time-travel’, of my A Wittgensteinian way with paradoxes.‘Time-travel’ is a particularly stark (but tellingly seductive) way in which metaphysics springs directly from attractive (but ultimately empty) metaphors.

others in the present volume do this job better than I may be capable of.)

Furthermore, we also already have the important work on context of Hertzberg (in his “The sense is where you find it”)and Travis (throughout his work, especially in recent years). These in my view suggest a far more ‘open-ended’ picture of creativity in language than is present in Chomsky, while not being committed to the fantasies of actual-infinity that I criticise elsewhere in the present paper. For what Hertzberg and Travis, following Wittgenstein, demonstrate, is that context, and human responsiveness thereto (including, I would add,though they omit this, sometimes through creativity in tone ofvoice, gesture, etc etc.), allows an indefinitely wide and dense capacity to mean, linguistically.

This brings us back to the point that there is an open-ended density 32 to aspects of language other than those to which Chomsky devotes theoretical priority. Intonation for example, unlike alphabetical notation, is ‘dense’. And so is context. These are where we ought to be looking, for perhaps the most truly and awesomely indeterminate endlessness of language! Not at the manipulation of symbols fitting neatly with computational metaphors.

One important obstacle to such a vision of Wittgenstein’s visionof language as Travis and Hertzberg and Kuhn and Cavell (and Nelson Goodman) make available to us is the prejudice that Wittgenstein was an advocate of ‘linguistic conservatism’. I will therefore spend a moment addressing this.

Against linguistic conservatism

32 Cf. n.3, above.

I have often argued in print against the equation of Wittgenstein with an opposition to (taking seriously phenomenaof) linguistic creativity. My two papers co-authored with James Guetti were where I did this first, taking Hacker to task for his failure to observe in practice the utterly dynamical and dialogical nature of language.

Another case in point is my “Towards a perspicuous presentation of ‘perspicuous presentation’”, co-authored with Phil Hutchinson. This latter paper sets out the later-Bakeriancase against Hackerian linguistic conservatism, Hacker’s failure (on Wittgenstein’s behalf) to appreciate the fluidity of language, a failure coincident with his excessive desire (shared with other allegedly ‘elucidatory’ readers of Wittgenstein) to map language. Once one thinks one can intelligibly desire to map language in the way Hacker suggests, it is a short distance to thinking that one can and should police its use so as to remain within the map.

To these papers, I will add here only some remarks that set out the connection between Wittgenstein’s fundamentally dynamical vision of language (once we understand Wittgenstein after Guetti, later Baker, Cavell et al, rather than after Hacker and various other linguistic-conservative misreadings of Wittgenstein) and common-sense anti-elitism in the everydayphilosophy of language.

What do I mean by the latter? I mean opposition to classist efforts to retain the ‘purity’ of a given language, and ‘fix’ it at a particular point in time…

In language, a ‘mistake’ oft-enough repeated is no longer a mistake. Something semantic may be lost in this process, but only maybe. 'Disinterested' is a good case: something DOES risk being lost, if that comes simply to mean 'uninterested’. But there are many other cases where nothing semantic is lost (e.g. most apostrophes are irrelevant to sense),33 and many 33 There are very few circumstances where apostrophes make the difference between being correctly understood or not. Lynne Truss made one such

cases where something is gained. That the latter is true is profoundly obvious as soon as one reflects that, much linguistic innovation over long time periods involves what are initially mistakes. And necessarily so.

The point is not of course that all grammar could be simultaneously and in toto suspended but that any particular bit of grammar can be at any moment (and certainly over time) recast. (I take it that this is actually a key insight of Hertzberg, Cavell and Travis, following Wittgenstein).

In putting forth this Wittgensteinian perspective there is no revisionist intention at all. The intention is simply, once more, to resist the tacitly revisionist Trussian/Hackerian etcposition that elevates grammatical conservatism into a doctrinal article of faith, at the cost of already-actual use.

Of course, it is also true that much linguistic creativity is a bad thing, when it debases our culture. Take for instance the rise of ‘managerialist’ discourse.34

This urges upon us the question: once we abandon the extremismof linguistic conservatism and the anarchy of an ‘anything goes’ mentality that denies banal truths (such as how bad the rise of managerialist discourse is), how do we judge whether and when a given instance of linguistic creativity is a good thing or not?

The answer is: this is an art, not a science. It is an ethical and a political business. All we can do is seek to grow the ‘phronesis’ that will enable us to tell the difference. To judge.

circumstance famous: That's all.34 See e.g. Loughlin M. 2002. "Ethics, Management and Mythology: Rational Decision-making for Health Professionals". Radcliffe Medical Press.& Loughlin M. 2004. "Orwellian Quality - the bosses' revolution" in: M Learmonth and N Harding (eds) Unmasking Health Management - a critical text. Nova Science, Hauppauge. pp.25-39.

Beyond finite vs. infinite

As discussed earlier, our powers to parse sentences are limited. This led me to suggest that our linguistic competence (not ‘merely’ our linguistic performance) is, in syntactic terms, finite. And that it means nothing to think of language as exceeding that competence.

But: Our powers of judgement involve an open-ended creativity. They are a feature of us that raise a question about the general, widespread assumption that human beings are finite.

The standard philosophical view of human beings is that we arefinite. Our bodies are finite, our minds are finite, etc.

But: what does this actually mean? What can it possibly mean? Finite as opposed to what?

As opposed to God, presumably. As opposed, that is, to a fantasised infinite totality / actuality. But is this a coherent way of thinking about the finite vs. infinite opposition? As we have already seen: Wittgenstein (in RFM, LFMetc) suggests not. ‘Infinite’ is only the possibility of going on endlessly. ‘The actual infinite’, in virtue of being actual, is not different enough from the finite.35 (God, conceived of as an actual infinite, is not different enough from the denizens and contents of the universe. Not truly God-like...)

If we have no clear notion of what it is for something actual to be infinite, then we have no clear notion of what it is forsomething actual to be finite. It is unclear then what it can possibly mean to call human beings finite.

35 In future work with Christian Greiffenhagen, I hope to pursue the thoughtthat a leitmotif of Wittgenstein’s thought, not just in relation to maths, is this notion of philosophy not making different enough. Wittgenstein aimed, by contrast to most philosophical thought, to teach one differences.A superb example, which undermines the apparently radical difference between mind and body in Cartesianism, is to be found at PI 339.

One might respond that it is reasonable to call human bodies, at least, finite. Because they are measurable. There isn’t thepossibility of them going on indefinitely; there isn’t the possibility of another being added to them. This is surely roughly right.

But it is much less clear that this response is reasonable with regard to the human mind / soul / person. In what sense is mind or soul measurable, numberable? Does it make any senseto speak of a limit to thought, or to feeling?

Wittgenstein, from the Tractatus onwards, thought and argued otherwise.

Thus, even most Wittgensteinians, notably Stanley Cavell, havefailed to be radical enough hereabouts. There is no good reason to think of human beings as being well-thought-of as finite beings.

Does this mean that human beings/persons/souls/minds are infinite? Of course not. That would be a philosophically visionless and pathetically self-aggrandizing move to make at this point. It is the move seemingly made by Levinas. He failsto see that there is an alternative to us being either finite or infinite. He assumes that, because we are not finite, we must be infinite. Wrong.

The alternative is to become clear that we do not fit on the spectrum of finite vs infinite. That this way of speaking of human thought / language / being is congenitally inadequate, and must be set aside.

This involves leaving behind our sense of being comparable to and utterly inferior to God. (It is misleading to describe Godas infinite, and misleading to describe us as finite; there isno useful way of comparing us and God.) That sense persists in most Post-Modernists and in Cavell and in the dominant scientific worldview, when they present us as finite.

We have instead to think human beings, to think persons, sui generis. To really think what they / we are like. Beyond ‘humble’ illusions of finitude, or silly illusions of infinitude.

The idea that human beings are finite is no more sensical thanthe idea that thought is limited or limiting.

This is why I believe that a fantasy of theism lies behind much western metaphysics, including Kant. This is what I attempt to illustrate, and to show Wittgenstein getting beyond, in Part 3 of my APPLYING WITTGENSTEIN (on time). This is why I want to challenge the fantasy of an actual infinity of mind (‘absolute mind’) that this requires, the fantasy of a realized God. Once this fantasy is eliminated, then we need no longer think of human minds as ‘limited’, ‘non-absolute’ minds.

Thus I want to suggest that the terms ‘infinite’ and ‘finite’ are unhelpful, in relation to thinking about us. Specifically,in relation to thinking about our linguistic creativity. Chomskian allegedly infinite grammatical capacities are merely a distraction. This is the ultimate reason why Chomsky’s remarks oncreativity cannot help us.

For Chomskianism inclines one to think of language as infinitary (via recursion), which is wrong (for language is notmeaningfully describable as infinitary in syntactic-recursive terms; it is more likely to be describable as finite, in thoseterms!) while it inclines us to think of humans themselves as finite beings with, in particular, finite minds, which is also wrong (And indeed it is in our open-ended multi-levelled and –aspected contextual linguistic sophistication that we are least well- or helpfully-described, in relation to language, as finite beings). The whole finite vs infinite axis is utterly unhelpful, in the project of thinking unclouded by misleading metaphors about language and about our minds.

Chomskianism misdescribes something perhaps finite (language, insofar as it concerns rules) as infinitary, and ‘something’ not finite (ourselves, including our actual responsive, creative, projective, metaphorical, contextual linguistic capacities) as finitary.

Any prose about infinity (as opposed to pure maths) is either about extreme largeness (which is ill-assimilated to the infinitary); or about not having an end (viz. a rule, etc.); or is nonsense. The nonsense is all the gas using the word “infinity” and its cognates and derivatives which is self-aware enough to realize it is not merely concerned with great dimension, but does not succeed in coherently concerning boundlessness, endlessness, whether in a technical or a prosaic sense.

Wittgenstein writes, crucially, “Where the nonsense starts is with our habit of thinking of a large number as closer to infinity than a small one. // As I’ve said, the infinite doesn’t rival the finite. The infinite is that whose essence is to exclude nothing finite. // The word ‘nothing’ occurs in this proposition and, once more, this should not be interpreted as the expression of an infinite disjunction, on the contrary, ‘essentially’ and ‘nothing’ belong together. It’s no wonder that time and again I can only explain infinityin terms of itself, i.e., cannot explain it.” (PR pp.157-8) I take that last sentence to be absolutely seminal. If one understandshow the word is used, there’s no problem. But any explanation partly falsifies it, and itself (as it veers toward pure nonsense). The same is surely not so of most of language. Might we not with profit cease to use the word “infinity” at all, given this desperate propensity it has, and ‘substitute’ the less misleading “unlimited” (see PR p.159) or “indeterminate” or the like? And simply manipulate the transfinites, if we are higher mathematicians. And if and whenwe are inclined, with those who have been directly or

indirectly criticised in this paper, to ask “How can ‘finite’ beings master ‘infinite’ systems?”, might we not better simplyabandon the question as less unanswerable than unstatable, unaskable, deeply-mistaken (both in its invocation of our alleged finitude, and in its invocation of the alleged infinitude of our linguistic competence considered syntactically) and stick instead to clarifying our concepts, or (alternatively) refining our experimental methods, and/or getting to work on uncovering the empirical preconditions for the acquisition of language?

When we model the infinite on the finite, and this is what talk of ‘actual infinity’ is, we are illicitly taking making the kind of metaphorical move criticised by Wittgenstein and by Lakoff and Johnson. We need to really take in the ‘categorial’ difference between finite and infinite.

If we are not continually to get drowned in metaphysics, we need to reach a new level of autonomy in relation to our metaphors. We need to do this together, and we need to ensure that doing it does not tempt us into delusive patterns of seeking to police language use, for reasons described earlier.

Attaining autonomy from metaphorical capture: in politics, too

Here is one reason why such attainment of autonomy is important far beyond the ivory tower: without it, we are prey to political propagandists. Our creative capacities vis a vis language need to be thought in terms of (our human capacities for) persuasion, propaganda, etc. . When one is alive to the metaphors that are mobilised in (for instance) the concept of

a ‘death tax’, one is alive to what Steven Poole calls ‘unspeak’.36

Nor is it merely a matter of not being a victim of rhetoric. Such rhetoric also needs sometimes to be constructed. It should not be dishonest; but it is dishonest to pretend that we are not through and through emotional social creatures who need inspiring language, need metaphorical mobilisation of the right kind. I am talking here of Drew Westen’s The political brain; I am talking of George Marcus’s The sentimental citizen; I am talking, above all, of the important work that George Lakoff has done in the last decade. In other words, I am now talking about political 'reframing': and this suggests, finally, a loop back to Chomsky on political language. For, in relation to politics, as opposed to in relation to philosophical linguistics, Chomsky I believe can help us to bring words back “from their metaphysical to their everyday use”.37

Chomsky and Lakoff and Wittgenstein alike can be of real value, when we put them to work, to immunize ourselves againstrhetoric that lies, and to seek to construct rhetoric that leads us, collectively, in the direction of political sanity.

Let me then seek to round out this paper by indicating in slightly greater detail how this can be done.

Lakoff, Wittgenstein, Kuhn and political metaphor

The great American linguist George Lakoff has in recent years produced a body of work (most notably, his ‘Moral politics’, (Chicago 1996, 2002)) that seeks to understand how the framingof issues works cognitively. How, for instance, one frame

36 For some detail, including a criticism that I have in this connection of Poole, see http://viewfromthehutch.blogspot.co.uk/2013/09/guest-view-towards-better-kind-of.html37 I indicate how in Chapter 6 of my Philosophy for life, “How I learned to love Noam Chomsky”.

rather than another (e.g. ‘economic refugee’, as opposed to ‘economic migrant’) can instantly elicit sympathy and transform anger.

I follow Lakoff in this respect. However, some of my research (notably, my “How and how not to write on a ‘legendary’ philosopher” (Philosophy of Social Sciences, 2005)) has sought to explore some of ways in which Wittgensteinian ‘family-resemblances’ and ‘grammatical effects’ modify and offer a latent critique of Roschian etc. cog. sci. ‘prototypes’ and ‘psychological associations’ and thus provide a sounder basis for thinking about the language-effects of words.

The philosophy of Kuhn and Wittgenstein properly understood (see for instance my ‘The New Wittgenstein’ (Routledge, 2000)), would provide a substantive resource for the framing of issues central to our contemporary world; a potentially-deep supplement to what Lakoff has already given us.

Take for instance the need for reframing, and not just for radical critique, that is central to Wittgenstein’s philosophy. A picture often holds us captive. One displaces a picture with another picture. That second picture may be a genuinely more attractive alternative. Becoming aware of seeing-as—of reframing—,the central topic of Part II of Wittgenstein’s Philosophical Investigations, often introduces new possibilities for seeing-as; by means of pointing up or creating internal relations. In situations of ‘seeing-as’, there is no ‘just seeing the facts’; one sees-as one thing, or as another.

Think also of bewitchment by language; of ‘the liberating word’; of the fly and the fly-bottle… Propaganda is often a ‘metaphysical’ constraint to freedom of thought.

As I have sought to show in my books Kuhn and Wittgenstein among the sciences, Kuhn’s vision of paradigm-change is an application of

these Wittgensteinian insights to the history and nature of science. Kuhn seeks to understand the rationality of science as involving centrally the following of a – paradigmatic – research tradition, and as occasionally involving the revolutionary overturning of that tradition. The paradigm exemplar is Copernicus’s re-centring of the solar system upon the Sun, rather than the Earth and its denizens. Copernicus suggested, basically, that the Universe did not revolve aroundus, but rather around what made us, our lives, possible.

Ecological economics 38 is the attempt to re-centre economics upon the Earth, rather than upon the things and individuals subsisting on the surface of that Earth. It involves nothing less than a Copernican – Kuhnian – scientific revolution: one that says, again, that the economic system does not revolve around us, but around our ecological conditions of possibility.Finding a way to make this cognitive switch, at the historicalmoment when the scale of our economic activities threatens to outstrip the ecological conditions of its possibility, is an urgent task. Human life will not be sustainable without so doing.

Lakoff’s groundbreaking ‘applied research’ into the framing ofissues, with suitable support from a right understanding of Wittgenstein and Kuhn, could be of immense value to a moral politics of sustainability for today and for the future.39 My 38 Which I trace to the innovative thinking of Herman Daly. For he promulgates what might be termed green ecological economics (as opposed to ‘environmental economics’, which is largely a branch of neoclassical economics, and to ‘[non-green] ecological economics’, such as the economicsof Costanza, which concurs with ‘environmental economics’ in literally pricing the atmosphere, turning commons into property, and (absurdly) pricing the biosphere itself, etc.). (For more detail, see my “How philosophy can help the green movement: in terms of economics”, forthcomingwith the Green Economics Institute.)39 Here is a very small example of the kind of thing I mean -- of some reframes -- right down to the nuts and bolts of it; a list of possible

main applied research project at present is to find rhetoricalforms that make it natural and obvious to think of ourselves as of the planet rather than overlords to it, as inhabiting and co-constituting a finite ecosystem rather than growing indefinitely, and so forth. Thinking of the Earth and its atmosphere not as a resource to mine or a rubbish tip but as our life-support system. As I like to say: “It’s the ecology, stupid”. And so forth…

As I pointed out in an earlier section of the present paper, in connection with his alleged linguistic conservatism, Wittgenstein is generally taken to be some kind of politicallyconservative figure with no relevance to societal transformation by means of reframing etc.—flying in the face of crucial remarks such as this: "I am by no means sure that Ishould prefer a continuation of my work by others to a change in the way people live which would make all these questions superfluous. (For this reason I could never found a school.)" [‘Culture and Value’, (Blackwell, 1980) p.61]—or else as a ‘cultural relativist’ thinker. Following the latter image of Wittgenstein, Kuhn is almost always taken to be a ‘cultural relativist’. He is taken to believe then that shifting from one paradigm to another for one’s thinking is relatively easy.

Rather than either of these, I have sought here to start to bring out some ways in which a Wittgensteinian take on linguistic creativity will be neither dogmatically conservative nor relativistic or post-modernistic. Rather,

‘headlines’ that could work in relation to, e.g., aviation:

‘No-fliers: The new conscientious objectors' ’Cheap' flights cost us all dear'  / 'The true cost of 'cheap' flights' 'Fair play on fuel: if drivers are taxed, why not air companies?'  'Slow travel - the smart choice'  'Seeing the world - one fine mile at a time'  'Beautiful Britain: Going green, by staying here'.

linguistic creativity is an art; it requires judgement, and the development of wisdom, to be at all deeply realised.

Nearly concluding remarksReframing, an idea born, I would suggest, in Wittgenstein, elaborated by Kuhn, and developed in great detail by Lakoff, involves simply circumventing the dominant frame through whicha policy problem is tending to be viewed by substituting a newone. Then, once one has reframed, one can add additional considerations and counter objections. But making the initial ‘paradigm-shift’ is critically important. Fail to do so, and you are simply batting on your opponent’s wicket, playing awayrather than at home. You might get quite a good score, but your chances of actually winning are minimal.

We need the ideas of green (or what might be termed eco-) economics to be naturalised, rather than seeming outlandish. Thisis part of what it will take to escape a world that is caught up in metaphorically-over-determined fantasies of ‘progress’, as Wittgenstein very clearly saw: “Our civilization is characterized by the word `progress'. Progress is its form rather than making progress one of its features. Typically it constructs. It is occupied with building an ever more complicated structure.”40

The active attempt to refigure our collective conceptual-linguistic common-sense away from such absurd ‘progress-ive’ assumptions is completely different from ‘spin’.41 Because the

40 The quote continues: “And even clarity is only sought as a means to this end, not as an end in itself.” For me on the contrary clarity, perspicuity are valuable in themselves. I am not interested in constructing a building,so much as in having a perspicuous view of the foundations of typical buildings.”, p.8. The quote ends thus (using now a different translation): “So I am aiming at something different than are the scientists and my thoughts move differently than do theirs.”41 For some great Lakoff detail as to why, see http://www.buzzflash.com/contributors/06/06/con06234.html

reframing I have in mind is honest and open. Because it is values-based; it is about getting people to see their values (e.g. survival, justice, love) reflected in the language that they use. And because the reframing that is envisaged here is difficult. This is what Wittgenstein and Kuhn taught: cognitive reframing is really hard. That it is hard is rational: otherwise, one is constantly floundering around in the condition of sociology or other subjects that see themselves as lacking an over-arching paradigm, and that flit from one would-be paradigm to another like fashionistas. To effect a scientific revolution is rightly rare; otherwise there would be no science.

Conventional economics, which dominates our world today, is in crisis;42 a real-world crisis of its own making. The reframing that is called for and that is underway must occur relatively quickly now. And it must occur across society, not just in academic debating chambers. The paradigm-shift to seeing green can be accomplished in part through the project proposed. The knowledge present in the the revolutionary thinkers I have leant on in this piece - Wittgenstein, Kuhn, Daly and (with some correction away from his ‘cog.sci.’ self-image) Lakoff - is knowledge that right now badly needs to be more widely known, and followed up on. And it is compatible with Chomsky’s radical political project.

We need to present perspicuously beyond the academic worldthe means whereby to eco-economically to reframe the world – the Earth – to its participants. To awaken them to their – our, your -- life-support system.

Conclusion

42 I am referring to the ongoing financial crisis – but also to the underlying and ultimately more intractable and serious ecological crisis.

We have gone on quite a journey in this piece. From thinking about ‘abstruse’ matters of the discourse of finite and infinite to thinking about ‘concrete’ matters of political rhetoric, ending in a thoughtful call to ecological arms.

But the distance is not as great as it might appear.

For all such thinking is thinking about how to not be caught up unawarely in metaphors that have run out of control.It is all about how to become masters, artists, of our remarkable, wonderful and dangerous capacity for linguistic creativity. For noble ends, and using virtuous means.

Metaphysics is merely metaphorics. We need to engage together in unmasking metaphors that are holding us captive, and in creating metaphors that can free us. In philosophy, in politics; in our lives, for our common future.43

43 Thanks to Wes Sharrock, Tobyn De Marco, Jeff Buechner, Anne J. Jacobson, Nick Huggett, Joel Backstrom, and the late James Guetti.