The prospect that mathematical science might someday utilize inconsistent mathematics leads to the question of dialetheist realism. For if one is a realist concerning the entities of science, one might then also have to be a realist concerning contradictory entities. And as I claimed in my last post, Meillassoux’ commitment to the absolute possibility of what is mathematically conceivable seems to lead to the absolute possibility of the transconsistent.
In The Law of Non-Contradiction, a collection of essays concerning dialetheism, an essay by Frederick Kroon argues that dialetheist realism is unacceptable. This seems to play into the hands of Meillassoux’ projected argument, since it is precisely realism about contradiction that he would want to avoid. However, the major problem Kroon sees is that a dialetheist realist has no way of ruling out trivialism: the view that all claims are true.
The question for realists is: mightn’t the actual world be trivial, even if we are constrained to think that the world is not? I argue that the dialetheist realist should accept that the world might indeed be so. Those who simply cannot make sense of this ‘possibility’ should therefore either not be dialetheists or not be realists. To the extent that the arguments for dialetheism prove irresistible, they present us with a powerful reason not to be realists about those parts of our discourse that generate true contradictions. (p. 245)
Ordinarily, the logical impossibility of contradiction is naturally taken to rule out the possibility of trivialism. But a dialetheist cannot make such an appeal. Interestingly, neither can Meillassoux, since he refuses to let the in-itself be circumscribed by the meaningful, the believable, or the coherent, and his book abounds in statements like the following: “Why should what is meaningless be impossible? As far as we know, no one has ever come back from a voyage into the in-itself with a guarantee that meaning is absolute” (After Finitude, p. 36).
In rejecting the Law of Non-Contradiction, they [the dialetheists] can’t appeal to the incoherence of something’s being both true and false, since they claim that some propositions, indeed a substantial number of them, are both true and false. So what makes the further claim that everything is both true and false incoherent? (I assume without further ado that it is incoherent – as flagrantly nonsensical as any claim could be.) (p. 246).
Since he can find no realist argument to answer this, he argues that one must be a fictionalist about dialetheism rather than admitting the “flagrantly nonsensical” possibility of trivialism. But notice, and this is the crux, that the logic of his argument cannot be adopted by Meillassoux, and the reason for this is quite striking. For the question he poses here is precisely the question that Meillassoux’ demonstration of the impossibility of an inconsistent being can answer, as follows: This “further claim”, i.e., trivialism, is incoherent – or more precisely impossible – because it violates the principle of factiality! Kroon considers, in a footnote, whether trivialism could be conceptually or metaphysically impossible, but finds no reason. Meillassoux can be considered to ground a third kind of impossibility, one might call it the “factially impossible”. It is precisely this kind of impossibility that allows (on my reading) contradiction but rules out trivialism. Meillassoux’ speculative materialism, then, allows us to coherently think a dialetheic realism.