Jon Cogburn's Blog

(modal logical) Meditations on the Meillassoux versus Harman

Yesterday I provided a preliminary formulation of a key lemma in Meillassoux's argument that correlationism absolutizes. I'd wanted to do this in a full natural deduction form today, but my thinking got both ahead and behind the argument. Let me get behind the argument first.

I. Correlationism, and the contrast between Meillassoux and Harman

From the position of an analytic philosopher (and I pray that this is not too distorting), Meillassoux's correlationism is best presented in terms of the following three positions.

(1) Verificationism- We cannot coherently think of reality as unthought (from the British empiricists originally, though Berkeley actually argued for it). Note that this arguably entails that if P is true, then it is possible for someone to know that P is true, but that in itself it places no restriction upon who is doing the knowing, it could be "knowable by an infinite mind." Only arguments concerning finitude force the verificationism to be knowable by something human-like.

(2) Embodiment/Embeddedness-We cannot coherently think of humans without thinking of them as embedded in a reality ( Schopenhauer and then later Heidegger developing Kant's claim that concepts without intuitions are empty, Schopenhauer with respect to the body and Heidegger with respect to a reality experienced as in some sense pre-existing, modal (involving possibilities), and valuative).

(3) Finitude- We cannot coherently think of self-subsistent totalities/absolutes (from Kant’s dialectic, but Graham Priest has discovered the true nature of this argument).

Before I go any further I must make absolutely clear the contrast between Harman and Meillassoux. Harman rejects (1) the Verificationism and maintains (3) the Finitude (if I could write an aria I'd write one in praise of this insight!) by radically externalizing the manner in which Finitude is expressed by Heidegger. Meillassoux rejects (3) the Finitude while keeping the (1) Verificationism. This is in some sense the titanic strugle at the heart of Speculative Realism.

II. Meilllassoux Needs (some form of) Verificationism

As I briefly (much more is needed exegetically) argued yesterday, the way Meillassoux gets to his rejection of Finitude actually uses Verificationism as a premise.

III. Meillassoux Rejects Verificationism

Here is a big problem. As far as I can make out, Meillassoux's argument that correlationism need not entail Berkeleyan Idealism is inconsistent with the very Verificationism he uses. Meillassoux's worry is that correlationism renders the thing in itself unthinkable/unconceivable, but then we might think that it is impossible, which is the position of Berkeleyan idealism.

So Meillassoux argues, persuasively to me (and this actually has powerful resonances with Lovecraft that are in common to all of the first generation Speculative Realists, and many of the second generation ones such as myself), that unthinkability does not entail impossibility.

But I'm not sure he can argue this. First, notice that Meillassoux is arguing against a strawman. To stop Berkeleyan Idealism, he must argue against the proposition that unthinkability does not entail falsity. For the Berkeleyan Idealist need only be committed to the claim that it is false that things in themselves exist, not that it is impossible that they do so. But the proposition that unthinkability does not entail falsity is much harder to argue against than the proposition that unthinkability does not entail impossibility. In fact, it is not a proposition that I think Meillassoux can argue against (though Harman and myself, following him, can).

No Verificationist of the sort we've been considering can argue against the calim that unthinkability entails falsity! For surely unthinkability entails unknowability. But this claim, plus Verificationism, is provably inconsistent with the claim that unthinkability does not entail falsity! Let me explain the formalism before giving the proof.

One of Meillassoux's key arguments is formulizable in modal logic (and valid)

[Note: (1) Meillassoux's argument to contingency is further developed in modal logic HERE, with some dialetheist worries thrown in. (2) A clearer explanation of the difference between Meillassoux and Harman is HERE, including a distinct worry.]

Reading page 26 of Graham Harman's Quentin Meillassoux: Philosophy in the Making, and just put the key argument (of which Harman writes, "This apparently hair splitting point point is actually the key to Meillassoux's entire system, and is worthy of closer attention") in modal logic. If I have not fudged too much by putting things in terms of a knowledge predicate, it definitely works. And in a very weak modal logic to boot, I think classical K but in the next few days I will put it in natural deduction to check. 

Basically there is a simple proof from P --> <>KP (if P, then it is possible to know that P, to which the correlationist is arguably committed) to Meillassoux's conclusion ~<>K~<>R --> <>R (if it is not possible to know that R is impossible, then R is possible). Contraposing the correlationist claim gives you ~<>KP --> ~P. But then substitute in ~Q for P and you get ~<>K~Q --> ~~Q, which via classical logic entails ~<>K~Q --> Q (if it's not possible to know that something is false, then it is true). Now substitute in <>R for Q, and you get ~<>K~<>R --> <>R (if it is not possible to know that R is impossible, then R is possible).

That's it. I'll do a proper natural deduction proof (without the substitutions) in the next few days, in part because I want to find out if I had to use classical negation rules above (if I was a better logician I would know this without having to formalize it; but full formalization sometimes yields unexpected interesting things so I don't mind).

The reason this is so mind-blowing is that so much does follow from the incredibly simple point, once you think about it in a way informed by knowledge of German Idealism, as Harman and Meillassoux do. More on that soon. I have to get clearer on how this fits with Meillassoux's other key argument in this context that unthinkability does not entail impossibility. This is how Meillassoux rejects Berkeleyan Idealism while still being a Verificationist (correlationist). But then the Verificationism entails ~<>K~<>R --> <>R, and then some other commitments entail that there are a lot of Rs for which the scheme applies.

It's the fact that for the correlationist the antecedent is maintained for lots of philosophically Rs that entails much of the weird and fascinating aspects of Meillassoux's philosophy (let R equal "humans will survive their death" or "things in themselves exist"), which is why I'm going to get clearer on that next. As far as I'm getting it now, the reason we can't know so many things is from Kantian Dialectic type Finitude arguments (the Verificationism follows from Berkeleyan type arguments).

Interestingly, Meillassoux, like Graham Priest, ends up exploding the Finitude arguments while staying with the Verificationism, and Harman (to some extent like a certain period John McDowell) keeps the Finitude but jettisons the Verificationism. I should note that by saying this I'm not reducing any thinker to any other thinker or just understanding the continental philosophers as shadows of the analytic ones (a horrible, horrible tendency of a lot of analytic "pluralists"). I'm learning all sorts of new things from Meillassoux and Harman, and there are essential respects in which the two differ from the analytic analogues (among other things, Harman is not hobbled by McDowell's quiteism, and this makes a humongous difference).

It's really cool stuff. Any logician readers will have intuited interesting issues involving Fitch's Paradox as well. I have a couple of lines on that (one from Tennant, one from reflection on Moore's Paradox) that I want to try out on Meillassoux this semester.

brief thoughts about the genesis of belief

I have this strange intuition that a lot of confusion in the philosophies of mind and language arises from the fact that representations are used to explain, first, two quite different activities: (1) planning, and (2) correction, and second, two quite different kinds of things: (3) individuals, and (4) groups.

Individual planning that leads to representational explanations occur when, for example, the crow goes offline and then suddenly performs some novel activity, for example bending the paperclip in a way that allows her to unlock the cage. The best explanation is that the crow was running out counterfactuals in her mind, counterfactuals that bear a systematic relation to causal facts in the world (see THIS POST and THIS POST for a link to a relevant discussions). Mark Okrent explains intentionality in this manner, and work on counterfactual and off-line reasoning by others can help fill in the details (my student Joel Okrent and I have just started a paper on this).

Group correction is more complicated. Of course, as Feyerabend said, when conversation breaks down, then we must resort to violence. But the enlightenment ideal that we can adjudicate differences without violence rests on what Crispin Wright calls "cognitive command," the view that when two people are disagreeing, there must be some deficiency in one of them or their environment. In Truth and Objectivity, Wright has a brilliant discussion of how this gives rise to representational pictures.

affection type problems concerning modality?

It's weird to me how easily the Jacobi and Schultze's noumenal affection problem can generalize.

With Jacobi and Schultze it only concerned applying the category of causality to the thing in itself. Transcendental idealism both prohibits doing this and seems to necessitate it.

But you get a similar problem with causality and the understanding. Kant over and over again uses "imposition talk" (see Bennett's Kant's Analytic, section 38 for a plethora of examples) concerning how the understanding imposes categories on phenomena. But this is really weird, and yields another affection type argument. By transcendental idealism causality is just a relation between phenomena. But if the mind is imposing causality then something like a causal relation must exist between the mind and the phenomena. Since the mind is part of the noumena, we could call this the noumenal imposition argument, exactly analog to the noumenal affection argument (I'm sure Kant actually has more to say about this because it is so close to the way he wants to reconcile free will and determinism; which on some readings do involve a non-temporal kind of causality that determines whole deterministic causal sequences from outside of time).

Likewise, there is an analogous (and to me more interesting) problem about possibility itself. Can  we really make sense of critical philosophy as the transcendental inquiry into conditions of possibility when at the end of the day possibility is nothing more than something imposed by the understanding on phenomena? I think for Kant you get the same kind of issue as the affection and imposition arguments here. [There's also an analogous Priest type argument that John Divers talks about in his fantastic book Possible Worlds.]

Note that all three problems illustrate the Russell Paradox type inconsistent mix of what Graham Priest calls Transcencence and Enclosure. 

With possibility the problem arises for Heidegger too. Next semester I'm going to reread the stuff about possibility (if I remember right, he calls it "founded possibility" or something like that) in Being in Time and explore the extent to which that model of possibility is consistent with his own characterization of what he's doing as a transcendental project.

I'm really interested to study the history of the noumenal affection problem and see the extent to which the original players glommed onto an imposition problem and an analogous problem about modality. I don't think it's an accident that Schopenhauer was Schultze's student and that he has such a rich theory of modality. One of my projects the next four years is to read Schopenhauer the way Harman reads Heidegger, and then apply that to analytic debates about modality. Unfortunately this is going to take a few years of just getting up to speed on background. The stuff with Kant and the affection problem is just laying the groundwork for my next richer engagement with Schopenhauer. I'm starting teaching our early modern this spring, then in spring 2012 I'll teach our Kant and then spring 2013 our 19th Century class on Schopenhauer.

I know that the big project may sound flaky, but it's already in large part yielded a cowritten paper on vagueness that Frankie Worrell and I are presenting at the next Easter APA. I mean, Frankie and I got the idea from working through some Schopenhauer. So I have some evidence that the big project will yield all sorts of cool stuff along the way.