Meillassoux and Dialetheism Part II: Contradiction and Realism

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).

Kroon continues:

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.

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4 Responses to Meillassoux and Dialetheism Part II: Contradiction and Realism

  1. Jeffrey Bell says:

    Nice couple of posts. I think you’re exactly right that Graham Priests’s dialetheism poses a challenge to arguments that rely on the law of non-contradiction as extensively as Meillassoux’s does. I also find interesting connections between transconsistency and other aspects of mathematics such as problematics, and hence some connections with Deleuze’s metaphysics. I’m intrigued by your effort to save Meillassoux from dialetheism by considering a third kind of impossibillity, the “factially impossible.” I see why it is needed so as to rule out trivialism, but it’s not clear what being “facitially impossible” would mean, or how it could have meaning for Meillassoux if it did not rely upon the absolutization of contingency as Meillassoux understands it, and hence rely in turn both on the law of non-contradiction and the not-All of Cantorian set theory that supports his Humean rejection of necessity. Again, a good post and some interesting conjectures put forth here.

  2. inregard says:

    Hi Jeffrey,

    Tracing the connections between transconsistency and Deleuzian metaphysics sounds interesting indeed. I think interaction between continental or post-continental philosophy and paraconsistent logics holds great promise. Priest has looked at Hegel and even some Derrida, I think, but there is definitely a lot of untapped potential still…

    As for Meillassoux and dialetheism, I think of the dialectic as something like this:
    1) Meillassoux seems forced to accept dialetheism.
    I do not see how he can avoid this, since when it comes to restricting what is possible, he has set the bar so high. In other words, I think that Meillassoux will have to accept dialetheism. Of course, if there is one thing Meillassoux is really good at, it’s developing arguments where one had previously thought no argument was possible, so it’s obviously too early to tell….
    2) Priest (and other dialetheist realists) seem forced to accept that trivialism is a real possibility.
    This, on the other hand, can be avoided if dialetheist realists adopt Meillassoux’ argumentation.
    So the wager of these posts is that while Meillassoux considers his philosophy as opposed to dialetheism by ruling out the possibility of real contradiction, he is wrong, and his philosophy is in fact an ally of dialetheism, since it provides the dialetheist with the resources needed to rule out the possibility of trivialism. Dialethism is factially possible, but trivialism is factially impossible, where “factially impossible” means “incompatible with the absolutization of contingency”.

    One could ask whether Meillassoux’ argument for the absolutization of contingency still goes through without the principle of non-contradiction. But it really should, since Meillassoux uses it to prove the principle of non-contradiction in the first place, and this proof would be circular if the principle it draws on presupposes the principle of non-contradiction in the first place…

  3. Jeffrey Bell says:

    Yes, I see where you’re going now. I’m not persuaded by Meillassoux’ argument for the principle of non-contradiction so I still see it as an axiom in his system rather than a demonstrated principle. This may be addressed more adequately in his much longer forthcoming book.

  4. Pingback: Meillassoux interview | Transcissions

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