1. Introduction

Michael Dummett has claimed that Wittgenstein's Investigations view of the linguistic sign is incompatible with a recognition-transcendent notion of truth, which in turn rules out realist metaphysics.

In regard to the linguistic sign, Dummett's argument is, in outline, that recognition-transcendent truth-conditions could attach to our statements only if such conditions could play an active role in language use. The key Wittgensteinian thought that drives the argument is the idea that if we did suppose ourselves to be able to grasp a particular meaning for our words that attached to a recognition-transcendent condition then the whole practice of language use would go on the same even if we had got it wrong. But this, the argument goes, is to posit a difference that makes no difference. Consequently, it drops out of consideration as irrelevant (Dummett 1993, pp.312-14).

The principal connection with metaphysics is via the notion of bivalence—the semantic principle that every statement is determinately true or false. If the truth of our statements depended on the obtaining of a worldy state of affairs (as the realist maintains), then our statements would have to be determinately true or false, according to whether or not that state of affairs obtained. However, given that we cannot guarantee that every statement is recognisable as true or recognisable as false, we are only entitled to this principle if our notion of truth is recognition-transcendent. By the above argument, it is not, and hence bivalence must be rejected and metaphysical anti-realism follows (Dummett 1963).

Nevertheless, holds Dummett, we ought to maintain the classical principle of tertium non datur, the principle that no proposition is neither true nor false. Prominent among the non-technical reasons for this claim is the idea that there is no need for a special convention to decide whether a statement is false, independent of the failure of that statement to be true. This being so, there is no purpose in distinguishing on the one hand between a failure that comes from being neither true nor false and on the other hand a lack of truth that comes from falsehood simpliciter (Dummett 1959).

Dummett’s anti-realist is therefore committed to two claims. He accepts tertium non datur, and he rejects bivalence. Recently, however, the co-tenability of these views has been challenged by Charles Travis, on the grounds that Dummett misunderstands Wittgenstein's view of the linguistic sign. Travis’ claim, roughly put, is that anti-realism tries to maintain an incoherent middle position between ‘external’ and ‘internal’ perspectives regarding language use (Travis 2008, p.143). From the external perspective, not only bivalence but alsotertium non datur fails to hold. From the internal perspective, on the other hand, even bivalence holds. Either way, the anti-realist loses; there is no middle ground.¹

2. Shadows and the external perspective

On the classical view of the linguistic sign, held for example by Frege and by Wittgenstein in the Tractatus, there is a way of manufacturing a representation that is utterly world-independent. Nothing about the way things are, or how people would react to that representation, affects what it represents. The world’s role is simply to make that representation true or false. On Travis’ view of Wittgenstein’s Investigations view, there are no such representations or ‘shadows’. Whatever is done to manufacture a representation of any kind, the world may always play a further role in determining what it represents, not just whether it is true or false. This is because the representative capacity of sentences (and anything else) is grounded in the dispositions of people to take them as correct in certain cases and incorrect in others. There is nothing one can do, when uttering a given sentence, that can legislate for all possibilities of its application and the responses people may make to it. Consequently, something is always left to the world and to other people even in regard to the determination of truth-conditions, not just in regard to the determination of truth.

Suppose, for example, that Max utters ‘Zoë is at home’, in the context where Zoë has, unbeknownst to all (Max included), recently expired in her living room. When confronted with the now ex-Zoë, we may try to use those same words to report what Max said, so we may say ‘Max said that Zoë is at home’. But, the thought is, that would be a false report. Max didn't mean there would be a corpse in her living room. Similarly, the thought goes, we cannot report Max correctly by saying ‘Max said Zoë is not at home’. Max did not assert that there would not be a corpse in the living room. The point, moreover, is not one about indirect disquotational reports. The example is designed to show that Max did not manufacture a semantic entity of which tertium non datur could be asserted in the face of this unexpected turn of events. His words, given how things have turned out, do not admit a coherent interpretation that can be either true or false.²

One way of retaining tertium non datur would be to claim that on this occasion Max’s words didn't express a proposition, i.e. a truth-apt entity, at all. On this line of response, they should be treated like stars, stones and Travis’ hat, things of which the question of truth does not properly arise. Travis’ response to this relies on the idea that what happened to Max could have happened to any of us. The only reason to claim that his utterance was not truth-apt would be if we could contrast it with a kind of semantic entity that was not subject to the possibility of such misfortune. But the only kind of entity that would be thus immune would be a shadow, and according to Travis we have no right nor need to assume that there could be such things. Indeed, for Travis, it is Wittgenstein’s basic insight that there cannot.

3. The internal perspective

As stated earlier, Travis contrasts the ‘internal’ perspective of language use with the ‘external’ perspective. But matters are no better for the anti-realist from the internal perspective. This is because, Travis claims, "[...] as long as we see statements from an object-level, internal perspective [...] we see them in a way that assumes, or presupposes, bivalence'' (Travis 2008, p.143). The idea is that the kind of ineptitude that attends the use of our terms in cases where Zoë has shuffled off this mortal coil are presupposed on any specific occasion not to occur. One would therefore, in any given context, be mistaken to claim something along the following lines:

Internal error: I wonder whether Zoë is at home, but concede that it need not be determinately true or false that she is.

The idea is that when we use our words, even to entertain a supposition, we assume that context will be favourable enough to give us an answer one way or the other. Using a sentence indicates a form of optimism, such that conditions will arrange themselves on this occasion so as to make its use felicitous.

The anti-realist is therefore in a dilemma. From the external perspective, we shouldn't just drop bivalence but also tertium non datur, and from the internal perspective we shouldn't even drop bivalence. At no point do we balance Dummett’s two views, the acceptance of tertium non datur and the rejection of bivalence.

4. Internal anti-realism

That, then, is Travis’ argument, on at least one plausible reconstruction of it. It is designed to apply to ‘sublunary discourse' i.e. everyday discourse about tables, chairs, and whether people are at home. The question is how the anti-realist, set in Dummett’s mould, should respond to it. I am going to argue that the consequences are rather more limited than Travis appears inclined to allow. Specifically, I'm going to argue that even if the anti-realist must reject tertium non datur from the external perspective, this doesn't stop him accepting it from the internal perspective, whilst rejecting bivalence. Moreover, I'll suggest that this rescues what is important to the anti-realist position.

To see why, let us first look not at sublunary discourse but instead at mathematical discourse. In mathematics, it might be that we have special reason not to assume that a well-formed assertion, uttered in the right circumstances, is determinately true or false. This might be due to some peculiar feature of mathematical concepts (the peculiarity of which Wittgenstein himself often recognised). It might be because, for example, they do not refer to an independent Platonic realm, but rather are our own logical constructions. Now, we need not here worry about whether this argument is sound; the point is merely that if it is, then we might suspend bivalence even given the usual presuppositions of felicity, or in Travis’ terms, even from the ‘internal' perspective. In this regard, such a statement might be treated differently to a declaration that ‘Zoë is at home’. In mathematics, all the external contingencies might conspire to make our statements felicitous (no corpses), and yet still it not be right to assume bivalence.

Once this is accepted, however, we see the potential for a distinction between Travis’ reasons for dropping tertium non datur from the external perspective and the special reasons for dropping only bivalence in regard to the internal perspective. Ipso facto, we see how one might square Dummettian anti-realism with Travis’ two perspectives and the bar on shadows. The anti-realist may negotiate his position in regard to the internal perspective alone. This may mean that, contra Dummett, he rejects tertium non datur from the external perspective, but from the internal perspective, i.e. assuming felicity, he drops bivalence but accepts tertium non datur, in the way distinctive of the anti-realist.

There is a question, of course, as to whether this rescues the initial motivations for anti-realism. Abstracted from Travis’ distinction between different perspectives, the point is as follows: Travis’ argument relies on the anti-realist being unable to draw a good distinction between the ordinary presuppositions of felicity that imperil all language use, and the special reasons that might be adduced by anti-realist arguments. It is on the assumption that no such distinction can be drawn that the reasons for rejecting bivalence that the anti-realist typically adduces might simply be agglomerated with those that might push us towards rejecting tertium non datur. Otherwise, it seems the anti-realist may simply make his thesis conditional on the satisfaction of certain conditions of felicity.

Let us now return to matters sublunary. Suppose we consider normal cases, where, for example, Max is not presented with a corpse. The anti-realist’s question, then, is whether the notion of truth attaching to the statement that ‘Zoë is at home’ can be recognition-transcendent. For it to be recognition-transcendent is for it to be possible for all the relevant criteria to be met (we may for example imagine seeing Zoë with our own eyes, reclining on her sofa reading a copy of The Uses of Sense) and yet it still be possible that the statement is false.

As outlined in the introduction, Dummett’s global anti-realist argument is that recognition-transcendent truth-conditions could attach to our statements only if such conditions could play an active role in language use. The Wittgensteinian thought that Dummett takes to rule this out is that even if we tried to attach such conditions, the whole practice of language use would go on the same if we had assigned them incorrectly. Consequently they wouldn't make the required difference.

It is not clear, from what Travis argues, as to why this argument would be any less applicable after we have factored in considerations pertaining to the felicity of our assertion regarding Zoë. We may suppose that even as the anti-realist sees her alive and well, ensconced on her sofa, he asks himself whether it might nevertheless be false that she is at home. For the reasons given above, he may convince himself that it is not. That would be for there to be a difference which made no difference, and that, he may think, is not how language works. The implication for bivalence follows as usual. Insofar as we cannot guarantee that we'll be in a position to recognise that ‘Zoë is at home’ is determinately true or false in all (even felicitous) circumstances, the principle is invalid. As it stands, therefore, the arguments offered by Travis are inconclusive. For all that has here been shown, Dummett’s anti-realist has no stake in shadows. Travis could be right about Wittgenstein’s theory of the linguistic sign and still anti-realism would be as viable as it ever was.