Another Halting Problem

e claim made by CET is that there is a process, namely, the telescop- ing of semantic content until all ambiguity is removed, that is deemed to be a terminating one. What could go wrong with this process?

It seems as if there are two bad things that could happen: the pro- cess never halts, and so we would never reach an extensionally equiva- lent maximally speci c sentence (polysemy is ineliminable); or it does halt, but its output is neither extensionally, nor intensionally equiva- lent to the original sentence.

My claim, on behalf of the radical pragmaticist, is that there is actu- ally no other outcome. ese are theonlytwo things that can happen. And both are bad. So CET provides no solace to the semanticist. Pol- ysemy is here to stay.

In fact, I’ll conclude that the only choice for the semanticist is to stick with minimalist content (and adjust her claims and outlook on meaning, and perhaps life too, accordingly).

Let’s consider the argument for the non-terminability of the process rst. Here’s another quote, I’m afraid again from Wittgenstein:

A sentence like “this chair is brown” seems to say something enormously complicated, for if we wanted to express this sen- tence in such a way that nobody could raise objections to it on grounds of ambiguity, it would have to be in nitely long.

_{See the recent arguments to this conclusion in Recanati (2010).}

 | Chapter 

Let me stress right away that it is not just the presence of standard indexicality (the demonstrative ‘this’) that is the source of the prob- lem here.

e trouble goes further than that and affects, as we shall see, ex- pressions (such as sublunary predicates of the ‘xis brown’ kind) that are far less amenable to formal treatment than the familiar class of in- dexical expressions. In fact, the problem is fully general; it concerns the very nature of signs.

e Wittgenstenian idea is disarmingly simple: signs point in in- de nitely many directions. ey require an interpretation to specify their meaning (and note that the worry here is to do with indeter- minacy ofsense, not Quinian indeterminacy of reference). Each oc- currence of a sign generates inde nitely many meanings there for the taking. Any interpretation would be couched in a sign-like fashion, and would thus reproduce the problem at a higher level. Hence, de- terminacy cannot be secured by semantic means.

Now, suppose the point is sound. en CET has got a very basic design aw, for it states that we can rid ourselves of the essential pol- ysemy of signby adding more signs.

And the objector will complain that it is obscure that by adding ever morewords as the sentence gets expanded we would be able to close offallunderdeterminacy. Would not each additional word introduce more underdeterminacy in turn? Aer all, as Putnam would put

sort of argument is found in Reid (1764: Ch. 6 §24). anks to Katherine Hawley for indirectly drawing my attention to this proto-pragmaticist line. For more recent examples, see Searle (1978: 212), Travis (1985: 200, 207), (1997: 112-113), (2000: 91), (2006b: 28-9), (2006a: 40) and (2008: 2, 6), Wheeler (2000: 24), Recanati (2004a: 54, 58, 95) and Bezuidenhout (2002: 105, 108, 113).

_{I am saying two things here. at there is aspeci cdifficulty hiding behind the most mundane}

of predicates—it’s not clear e.g. how we could specify thesenseof ‘brown’ in a way that would provide forallcases (asZettel§440 put it, we canalwaysconstruct doubtful cases where our stipulations regarding applicability would be silent). In short, sublunary predicates are deeply undecidable. Secondly, there is ageneraldifficulty due to the nature of signs: signs,quasigns, can and do point in inde nitely many directions. Again, no stipulation can ensure univocality in a given case.

_{ere is more than a whiff of the Tortoise Regress from Carroll (1895) here. So one might think}

that I am saddling the semanticist with a view similar to the one Dummett (1973: 596) attributes to Quine (and criticises along anti-CET lines). e lesson seems to be that there must be rules of representation that cannot be part of a theory, that cannot be accessed in consciousness on pain of in nite regress. One could then protest that the semanticist is not committed to Quiniantheoretical

holism anyway. Sure. But as long as MDP is in place, a commitment to CET will also be in force.

_{See Putnam (1970: 140-42), Ziff (1972: 131), Searle (1980: 228) and Beaney (1997: 32). Posner}

(1980: 186-87) raises the issue of the resurgence of ambiguity in the clauses used to precisify the original meaning. Slightly different but related worries are forcefully argued for in Gross (2001: ch. 3). Yet another anti-expansion argument is in Dancy (2004: 196-197). Horwich (1990/1998: 100) also declares himself impressed with the anti-CET RPA. Carston (2002: ch. 1) is again a good guide here.

e Roots of Sense |  it, at any further step in the expansion process we are simply adding just moretheory, as we attempt to close off all available readings bar one.

It seems then as if the semanticist, by conceding that thereisa prob- lem at the rststage (i.e. by admitting that NL sentences are infected with polysemy) has barred herself from a solution (her claim that we can do something about polysemy by regimenting NL is weakened by the fact that she is simply helping herself to more of the same stuff: signs).

ere is a temptation to say that the problem only affects the Quinian formulation, that the problem is internal to the object lan- guage. Granted, expanding the sentence in the object language won’t secure determinacy of sense, but if we go the Clause-Indexicalist way instead and specify senses in our semantic clauses, formulated in a quasi-formal metalanguage where ambiguity is banned, then the problem cannot even arise.

Or can it? Why should we think that the metalanguage, whether formal, semi-formal or informal, should be exempt from what seems to be anessentialmark of the sign, i.e. its inability to self-authenticate its interpretation?

Any formal language, by de nition, will need setting up, and the stating of its vocabulary, signature and rules of inference will itself be a linguistic act carried out by linguistic means (that’s why Brouwer was so insistent that mathematics is a purelymentalact).

Much as I wish it’d go away, I think the problem is stubbornly gen- uine, and genuinely general (it affectsanylanguage, whether natural or formal, ordinary or extra-ordinary).

3.4.1.1. Rescuing CET

One could take two views regarding this stumbling block for seman- ticism.

We could think that it is in principle impossible to eternalise away context-dependence because ofourinability to articulate clauses that can specify the precise content of context-dependent thoughts.

Or we could say that the limitative result is deeper, that even godly powers could not pin down a thought with the required amount of precision. We could think, that is, that the indeterminacy phenom-

_{Putnam (1977: 18).}

_{A diagnosis of the rule-following issue along these lines is in Luntley (2003: 25). Although}

structurally similar, the two problems remain however distinct.

 | Chapter 

ena affect not just linguistic content, but contenttout court, and thus intentionality as a whole.

I happen to think the latter is the case and that this requires a revi- sion of mainstream views of rationality. I’ll take up these issues again in chapter  and . In the remainder of this chapter, however, I re- strict my discussion to the case of semantic content andourability to capture it theoretically.

We have seen that the RPA attack on the determinacy of meaning centres on the claim that meaning is inherently unstable. And if so, CET is false, because nosentence (no string of signs) could ever be eternal.

But what reason do we have for thinking that the expansion process would never terminate? We’ve not really been given a proof that it cannot be done, at best a sketch of a proof that we are supposed to accept as de nitive.

Or better: the radical pragmaticist has thrown up a challenge. Fix everything that your semantics allows you to x, we are told, and I’ll show you that your interpretation still admits of inde nitely many understandings(ways for the world to be such that the sentence would be judged, by competent speakers, to be true, or false).

What the semanticist assumed when she formulated the CET was that expressions could somehow be imbued with the magical powers to determine not just their referents but their senses too, thus block- ing the slide into indeterminacy.

In short, the expansion process could terminateonly on the assump- tion that the expressions in the expanded sentence could not be misun- derstood. But that’s not what wordsare, the argument goes. _Guess- work, that is, is not an incidental feature of NL, but rather it is an essential property of any sign-like (content-bearing) entity.

In contrast to this, Frege’s (: /) idea was that “the word ‘interpretation’ is objectionable, for when properly expressed, a thought leaves no room for different interpretations” (my emphasis). e idea embodied in CET, then, was that when we nally get a sen- tence expressing a complete thought we have reachedthe end stage of interpretation. oughts, on this view, cannot be interpreted, be-

_{As Searle (1980: 231) concluded.}

_{See e.g. Travis (2006b: 114) and my remarks in note 51.}

_{Wheeler (2000: 59-60) has an insightful discussion of this misguided conception of meaning.}

A rather extreme form of this view can be found in theCratylus. Kevin Van Anglen informed me that the Platonic conception of naming was taken up by the American transcendentalists.

_{For a conclusion along these lines see Carston (2002: 42).} _{Rorty (1989b: 65) is a good antidote to this Fregean idea.}

e Roots of Sense |  cause they are theoutcomeof interpretation.

And yet if semantic underdeterminacy is indeed a constitutive phe- nomenon of our system of signs, that Fregean idea seems deeply inco- herent. In Derridean terminology, signs are essentiallyiterable; that is, they allow for (and indeed demand) cross-contextual projection (curiously enough, that was in fact one key component in the Chom- skyan view of the CC), they cannot be kept con ned to univocal sig- ni canceeven within a single context.

With this in mind, the attempted ight from context embodied in the CET can then be seen as a self-defeating effort to neutralise it- erability (if you try to do that, you destroy the very essence of the sign).

And it’s not even clear that at any stage in the expansion process the sentence is anylessambiguous that at any previous stage (at best, it might be so only with respect to a speci c word, but the form of words used to reducethatambiguity will generate new branches and as the sentence grows in complexity, so does ambiguity).

For these reasons, I will assume that the sketch of the proof against the CET is along the right lines.

In any case, even if the terminating process could be completed, there are reasons to think this would provide little comfort to the se- manticist. Let’s see why.