The Evolution of Modern Metaphysics: Making Sense of Things (85 page)

Arguably not. Arguably, Dummett does have an independent leverage, in the requirement to construct a systematic theory of sense for our language. This leaves him free to repudiate those aspects of our use of language that obstruct any such construction.
^41
,
42

I use the word ‘arguably’ not just in deference to the controversial nature of the requirement that a systematic theory of sense be constructible for our language, but also to register the fact that, even granted this requirement, there will be cases where judgment is needed to decide where exactly the fault lies when our use of language blocks the construction of such a theory. For example, if two or more of our linguistic practices are in tension with one another, then there may well be an irremediable indeterminacy about which is to be rejected. Still, Dummett might concede this point while insisting that the problem is hardly peculiar to him. It is just the familiar problem, he might say, with which anyone trying to make sense of things has to reckon, the problem of choosing between various competing desiderata of sense-making. (We saw both Quine and Lewis reckoning with this problem in the previous two chapters, §§7 and 3, respectively.) There is no reason to think that Dummett’s vulnerability to the lack of an Archimidean point in the implementation of his programme is special, still less that it is specially problematical – is there?

Well, perhaps there is. This is a cue for the second reply to Dummett’s anti-realist challenge.

(b) Second Reply

Let us once again consider arithmetic. And let us once again consider the thought that every even number greater than 2 is the sum of two primes. This is Goldbach’s conjecture. No counterexample to the conjecture has ever been discovered. But neither has the conjecture ever been proved. Moreover, we have no algorithmic procedure for settling the matter. An anti-realist about arithmetic therefore refuses to take for granted that the conjecture is either true or not true. According to such an anti-realist, only what we can know to be arithmetically the case – or, equivalently, only what we can prove to be arithmetically the case –
is
arithmetically the case. (So Goldbach’s conjecture cannot as it were just
happen
to be true, as a kind of infinite coincidence.) But now: ‘only what we
can
know’, not ‘only what we
do
know’.
⁴³
Thus consider a thought about some complex arithmetical calculation that no one has ever performed, say the thought that the result of the calculation contains fewer 6s than 7s. Such an anti-realist need have no qualms about taking for granted that
this
thought is either true or not true. The fact that no one has actually gone through the slog of ascertaining which does not
matter. What matters is that we do have, in this case, the very thing that we do not have in the case of Goldbach’s conjecture: an algorithmic procedure for deciding the issue. That is enough to safeguard the public ratifiability of anyone’s grasp of the thought.

But this now raises a further issue. With so much hanging on this use of the word ‘can’, the anti-realist needs to say some more about the sense in which it is intended.
⁴⁴
‘Can in principle’? Or ‘can in practice’? Each of these stands in need of further elucidation, of course, but the broad distinction between them is what is critical in this context. And it is clear that if the anti-realist means ‘can in practice’, then the resultant circumspection is going to be very radical indeed. In fact, we had better reconsider that complex calculation. What if it is not just complex? What if it is
horrendously
complex – so complex that performing it would take a trillion steps? Plainly, there is then no
practical
sense in which we can know its result. If the anti-realist means ‘can in practice’, then even the thought that the result of this calculation contains fewer 6s than 7s is liable to anti-realist circumspection.

This is where the second reply impinges. This reply has particular force in the case of anti-realism about arithmetic – and that is the form of anti-realism on which I shall focus throughout my discussion of it – but it applies in other cases too. The reply has two parts. The first part is that such extreme anti-realism, based on what is possible in practice, is totally unacceptable. The second part is that there is no rationale for a moderate anti-realism, based on what is possible in principle, that is not also,
mutatis mutandis
, a rationale for this extreme version.

Why is the extreme version unacceptable? Obviously, that needs to be argued. Not everyone would agree.
⁴⁵
But in
this
context no argument is required. For Dummett himself is among those who find the extreme version unacceptable. He regards it not just as overly extreme, but as positively incoherent. There is, he believes, an irremediable and unintelligible vagueness afflicting the notion of practicability on which it rests (‘Wang’s Paradox’). So the second part of the reply is enough for it to carry
ad hominem
force.

Dummett is aware of the reply (‘Wang’s Paradox’, pp. 248–249). To an extent he can meet it by reiterating the sheer nature of his programme, which, as I have been following him in emphasizing, is not to defend any single anti-realist thesis, but to investigate how well, and where, the basic anti-realist challenge can be met. But there are also some pertinent differences between what is possible in principle and what is possible in practice
on which he can fasten (see e.g.
Thought and Reality
, pp. 70–71). The problem, however, is that there is a significant further twist. The second reply is reinforced by a subsidiary reply which threatens the collapse of the entire anti-realist challenge.

That subsidiary reply is as follows. If practical possibility is
not
relevant here, then, given any arithmetical thought, we
can
determine whether it is true or not, and we are hence justified in taking for granted that it is one or the other. Thus reconsider the thought that every even number greater than 2 is the sum of two primes. We can determine whether this is true or not by checking successive even numbers greater than 2, ascertaining in each case whether or not it is the sum of two primes, and continuing until we either find a counterexample or have checked every such number. It is of no avail to protest, as the anti-realist no doubt will, that this procedure might never end. Something needs to be said to forestall the objection that if we spend half a minute checking 4, a quarter of a minute checking 6, an eighth of a minute checking 8, and so on, then the procedure will end in a minute – at most. Obviously, we cannot do this in any
practical
sense. But that is precisely beside the point.
⁴⁶

Dummett is equally aware of this subsidiary reply (
Logical Basis
, pp. 345–348, and
Thought and Reality
, p. 71, n. 1). My own view is that his counter-replies to it are question-begging, in that they deploy an anti-realist conception both of the infinite and of what is possible in principle. But I shall not now try to substantiate this view, since I am more interested in the fact that, even if it is correct, the counter-replies may, in their own way, be good ones, and the best available. This at last brings us back to the prospect to which I referred earlier, that Dummett is specially vulnerable to the lack of an Archimidean point in implementing his programme. ‘Specially’ vulnerable, I say. Problematically vulnerable? Well, yes, to whatever extent there was a problem for Wittgenstein in his analogous predicament (
Ch. 10
, §5). Who is to say what makes sense? Who knows but that arithmetical realists and arithmetical anti-realists make their own quite different, incommensurable, individually coherent sense of things; that this is why the former accede to assumptions for which the latter can see no justification; and that when they try to settle their differences, they are simply talking past each other? Here, as so often in our enquiry, self-consciousness plays
havoc with self-confidence.
⁴⁷

(c) Third Reply

The third reply likewise connects with the lack of an Archimedean point. It is as follows. Dummett’s anti-realist challenge to the assumption that every thought is either true or not true poses a real threat to that assumption only if there are thoughts whose truth or non-truth we cannot settle (in some appropriate sense of ‘cannot’). But
are
there any such thoughts? Some putative examples have been given (the thought involving Aristotle’s first birthday, the thought involving Descartes’ penchant for Marmite, Goldbach’s conjecture). But what would it take for any of these to be a genuine example? Well, on an anti-realist conception, we should have to be able to
tell
that it was a genuine example. That is, we should have to be able to tell that we could not settle its truth or non-truth. But how could we do that? We should need, in particular, to tell that we could not tell that it was true. The only way of telling
that
, however, again on an anti-realist conception, would be by telling that it was not true. (On an anti-realist conception, if we could not tell that it was true, then it could not
be
true. So if we could tell that we could not tell that it was true, then we could tell that it was not true.) We therefore arrive at a contradiction. It follows that there cannot, on an anti-realist conception, be any genuine examples of thoughts whose truth or non-truth we cannot settle. Nor, therefore, can there be any harm in assuming that every thought is either true or not true.

Dummett has a number of ways of dealing with this third reply. Most straightforward, and most heroic, would be to admit that there cannot be any harm in assuming that every thought is either true or not true, but still not to assume it. This would itself be an instance of anti-realist circumspection. It would be to admit that the assumption cannot
fail
to be true, but still not to accept that it
is
true.
⁴⁸

This raises an intriguing prospect. If anti-realists have no satisfactory answer to the question, ‘When exactly does assuming that every thought is either true or not true lead us astray?’, then it may be that they have no option, in the face of realist intransigence, but to maintain a kind of stoic silence. Whenever realists make assumptions that they are not themselves prepared to make, they must withhold assent, but they may have no satisfactory way of saying what is holding them back. This in turn would mean that, as far as anything they can say is concerned, their restraint might just as well be attributable, not to nonconformity, but to sheer reticence. Their knowledge of correct linguistic practice, if that is what it is, would be an example of a category that we have encountered more than once in this enquiry: knowledge that is, at least partially, ineffable.
⁴⁹

There is a loud echo of something else that we have encountered more than once in this enquiry, namely the Limit Argument. Suppose we construe sense-making in such a way that making sense of something involves having thoughts about it that are uniformly either true or not true. Then Dummett’s project, which is to see how far it is possible to sustain a realist understanding of things, looks as though it can be characterized as the project of drawing a limit (limitation) to what we can make sense of. If it can, then it is vulnerable to the Limit Argument, whose conclusion precisely precludes the proper drawing of any such limit. And that, in effect, is the third reply. The third reply, in effect, is that we cannot properly draw any such limit, since we cannot have thoughts about it that are true (or not true), since we cannot have thoughts about what lies on its far side that are true (or not true).

The counter-reply to the third reply proposed above is essentially to deny that the project
is
one of drawing any such limit. The project is rather to make sense of making linguistic sense. And the proposed embellishment of the counter-reply is to say that this is achieved by fostering a kind of knowledge which is practical and, at least in part, ineffable. As soon as an attempt is made to put this knowledge, or rather its ineffable part, into words, the result, here as in the early Wittgenstein (
Ch. 9
, §7), is nonsense about the drawing of a limit, and about our access to what lies beyond that limit. In the present case such nonsense has us entertaining thoughts that are neither true nor not true – an idea that anti-realists find as absurd as realists do.
⁵⁰

If these proposals are even roughly correct, then the similarity between what we find in Dummett and what we found in the early Wittgenstein is profound. In each case:

• knowledge of what it is to make linguistic sense
⁵¹
is practical and, in part, ineffable

• such knowledge includes a capacity to recognize failed attempts to make linguistic sense

• if someone has exercised such knowledge, by recognizing a particular failed attempt to make linguistic sense, and if that person then tries to express what he knows, by saying what the failure in the failed attempt
consists in, then his very effort to engage with the attempt will in all likelihood lead to his simply repeating it (‘It does not make sense to say that …,’ ‘There is no settling the truth or non-truth of the thought that …’)

•
the correct way to implement such knowledge would, to paraphrase 6.53 of the
Tractatus
, really be the following: to say nothing except what can be said, and then, whenever someone else attempted unsuccessfully to make linguistic sense (say by insisting that some statement was either true or not true), to demonstrate to him that he had failed to give a meaning to some of the words he was using (say by pointing out that he was not using the words ‘or’ and ‘not’ in accord with their standard meaning, as revealed in the agreed procedures for recognizing the truth of any statement involving them).