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.
When I write "P --> <>KP" I mean "If P, then it is possible to know that P." This is just Verificationism. When I write "~(~<>TP --> ~P) " I mean that it is not the case that (the impossibility of P's being thought entails that P is false) [this is the premise Meillassoux needs to block the argument from correlationism to Berkeleyan Idealism]. And the fact that the unthinkability of P entails the unknowability of P is expressed by "~<>TP --> ~<>KP." Also note that in the following "#" means that a contradiction has been arrived at. So here's the proof. [It's getting late; tomorrow I'll update this including a paragraph of natural language that talks through the proof.]
1. P --> <>KP Verificationism (if P, then it is possible to know that P)
2. ~(~<>TP --> ~P) Meillassoux's Needed Blocking Maneuver
3. ~<>TP --> ~<>KP Obvious fact
4. | ~<>TP assumption for --> introduction
5. | ~<>KP 3,4 --> elimination
6. | | P assumption for ~ introduction
7. | | <>KP 1, 6 --> elimination
8. | | # 5,7 ~ elimination
9. | ~P 6-8 ~ introduction
10. ~<>TP --> ~P 4-9 --> introduction
11. # 2,10 # introduction
This shows decisively that if one thinks that the Blocking Maneuver is correct (that the non-thinkability of some proposition does not entail its falsity), then one must either reject Verificationism, or the Obvious Fact that if something is not thinkable then it is not knowable.
But Meillassoux is committed to Verificationism, and in fact uses it in his argument against Finitude, and the Obvious Fact is just too clear.
IV. Strange Convergence
I'm tempted to invoke the old saw about the Chinese character for crisis being the same as that for opportunity. But I don't know if that's even true.
Anyhow, I won't prove this today, but I'm almost certain that if we look at the literature involving Fitch's Paradox, then two fascinating things happen (1) Meillassoux completely gets out of the problem, and (2) the difference between Harman and Meillassoux can be further explicated in terms of a logic difference between me and my advisor, Neil Tennant.
I can't work all this out tonight. But just let me note that Fitch's Paradox is a valid argument from Verificationism (all truths are knowable) to a certain kind of Berkeleyan Idealism (all truths are known). Tennant blocks this by restricting the Verificationism to only apply to propositions that are such that it is not inconsistent that they be known. This blocks Fitch's proof. I'm pretty sure (will certainly work on this more) that it also is strong enough for Meillassoux's absolutizing argument that I talked about yesterday. So if Meillassoux avails himself of Tennant's version of the first plank of correlationism, then as far as I can tell everything he wants to do can be done. The inference from correlationism to Idealism is blocked, and the absolutizing argument can be made.
V. Here's a promissory note. Even though I've defended Tennant in print on this very issue (a fun article in Australasian) I've recently published a completely different way to block Fitch's Proof that involves my novel analysis of Moore's Paradox. [J. Cogburn, “Moore’s Paradox as an Argument Against Anti-Realism,” in The Realism-Antirealism Debate in the Age of Alternative Logics (Logic, Epistemology, and the Unity of Science), ed. Shahid Rahman, Giuseppe Primiero, and Mathieu Marion, Springer (2011). Email me a joncogburn at yahoo dot com if you want a copy.] And this different way has huge resonances with certain aspects of Harman's version of Speculative Realism.
In addition to blocking Fitch’s proof, my analysis of how Verificationism is performatively valid (but just that!) both captures what is right about the Berkeleyan position, and is not strong enough for Meillassoux’s argument. Strangely, or perhaps not so strangely, my restriction strategy has strong resonances with Harman’s argument against unrestricted Verificationism. I won't elaborate this here. But it is featuring stongly in the Speculative Realism book on which I'm working now, and maybe I'll elaborate it here in the next few days.
But first I'm going to revise this post a bit in the light of day, minimally explaining the above proof to people who are not conversant in modal logic, and hopefully also doing some of the necessary exegetical work vis a vis Meillassoux's excellent book, and Harman's excellent discussion.
iv. FITCH STYLE PROOF OF FITCH’S PARADOX
(1) | K(P Ù ØKP) assumption for Ø intro.
(2) | KP Ù K(ØKP) 1 K Ù dist.
(3) | KP 2 Ù elim.
(4) | K(ØKP) 2 Ù elim.
(5) | ØKP 4 K elim.
(6) | ^ 3,5 Ø elim.
(7) ØK(P Ù ØKP) 1-6 Ø intro.
(8) []ØK(P Ù ØKP) 7 [] intro.
(9) ØàK(P Ù ØKP) 10 []Ø dist.
(10) | P Ù ØKP assumption for Ø intro.
(11) | àK(P Ù ØKP) 11 V.
(12) | ^ 10,12 Ø elim.
(13) Ø (P Ù ØKP) 11-13 Ø intro.
(14) P ® KP 14 (strictly classical)[1] equivalence
[1] Intuitionists might reject the transition from line (13) to (14), as P ® KP only really follows from Ø(P Ù ØKP) with the help of a classical negation rule such as the law of excluded middle or double negation elimination. In Williamson (1987), the author suggests that this might be thought of as providing evidence for intuitionism, albeit not very much. The denial that any claim can be both true and unknown, as stated schematically in line (13), is problematic enough.
