21 December 2007

Brandom Lectures Update

The full audio of Brandom's fifth lecture, along with the reply and the full Q&A section, has been posted to the place the old version was at. I figure this is of interest to some, and wouldn't want it to get buried in an old comment thread.

Hopefully I'll get around to listening to the full version (and the final lecture) sometime before the sun becomes a cold, dark lump of coal the size of your forehead. But no promises!

edit: I have listened to the full version, and have started working through Priest's "An Introduction to Non-Classical Logic". Which has been my first formal introduction to modal logic (though I was of course not entirely ignorant of the stuff before now, my "Logic" course didn't go past the predicate calculus, so I'd been neglecting actually sitting down and working textbook problems for anything more than that). I get what Brandom's been saying about "the modal revolution" now; this stuff is neat.

I'm not sure how much Brandom's claims about "the intrinsic logic" of e.g. intuitionist logic being classical S5 really amount to. The claim seems to boil down to saying that for any autonomous discursive practice, even one in which "Not not A, ergo A" doesn't generally hold as a form of valid inference, you can say how to draw inferences according to classical S5 rules; any autonomous language game is VV-sufficient for laying out classical S5's inferential rules through a semantics that speaks only of commitment and entitlement. But this does not strike me as particularly impressive; there would still be inferences in the discursive practice whose form classical S5 would countenance which the discursive practitioners would not recognize as valid, so it strikes me as odd to say that the "intrinsic logic" of the discursive practice is classical S5. Whatever purpose "intrinsic" logic serves, it doesn't seem to have much of a relation to the inferences reasoners draw, and so it seems like a rather beggarly "intrinsic" feature of their practice. If logic isn't behind the validity of inferences, I don't see what it can be said to do at all.

I don't think there's anything here that Brandom would disagree with; he said in an earlier lecture that he doesn't think the question of "Which is the true logic" is a good one, since various logics can be used to express various sorts of inferential commitments. But then I'm left wondering what calling classical S5 "the intrinsic logic of most familiar logics" is supposed to mean, if it's not supposed to be calling classical S5 "more true" than other logics -- more closely related to our inferential practices, or somesuch. For instance, on page 2 of the lecture handout:

Fact: The incompatibility semantics over standard incompatibility relations with these semantic definitions of connectives validates classical propositional logic.
What is that supposed to mean, if we're not interested in the question of "Which is the true logic"? In what sense can classical propositional logic be "validated" short of being "the true logic"? Is this supposed to be an explanation for why classical logic came along so early, and has been so widely-liked, or something like that? (If so, it strikes me as a bad effort -- classical logic has simple truth-tables, and both "the law of excluded middle" and "the law of noncontradiction" have the support of Aristotle (and most of the tradition), which I think nicely accounts for why non-classical logics always smell a little fishy. But I suspect Brandom doesn't mean to be addressing this question, either. I just don't know what "intrinsic logic" is supposed to signify. Perhaps he's claiming that classical S5 can be worked out purely from talk of commitment and entitlement (and not of truth etc.)? But then I still don't see why "intrinsic logic" should be a good title for this feature of classical S5.)

This is to set to the side that, as I understand it, paraconsistent logics don't have classical S5 as their "intrinsic logic". Whatever the "validation" of classical logic is supposed to amount to, I suspect that this is a serious barrier to it.

On a more positive note: I liked the stuff about holism. Fodor comes under attack from yet another front; suits me fine. I am curious what Brandom's argument for holism entails for a Tarski-style theory of truth (along Davidsonian lines), since in a Tarski-style theory the truth-conditions of a sentence are derived from semantic properties assigned to sub-sentential units, that of satisfaction; the satisfaction relations are the axioms from which the familiar T-sentences are drawn as theorems. Tarski-style theories of truth are compositional. (I think I have this right; I should probably go back and read some of the earlier Davison essays to brush up on this.) Brandom's semantics is not compositional, though it is recursive. "It is holistic, that is, noncompositional, in that the semantic value of a compound is not computable from the semantic values of its components. But this holism within each level of constructional complexity is entirely compatible with recursiveness between levels. The semantic values of all the logically compound sentences are computable entirely from the semantic values of less complex sentences." I suspect that this is not a difference which makes a difference. The Tarskian details that lie behind Davidson's "Convention T" do not seem to play much of a role in the interpretive process; ""S" is true-in-L IFF P, where "P" is a translation of "S" into English, or simply S if L=English" does not seem to need any adjusting if one mucks around with the axiom system Tarski used; McDowell argues in one of his essays ("In Defense of Modesty"?) that intuitionists can make use of a Tarski-style theory of truth as a theory of meaning despite their disagreements about logic, contra Dummett & Wright, and I should think the same holds here: The important part of "Convention T" remains unassailable, though some of the things Davidson wrote about compositionality might need revising.


Shawn said...

I haven't gone back to look at the Locke lecture stuff for a while, but my guess is that what Brandom means by "validates" is fairly innocuous. It probably means that the rules for the classical connectives are valid in those sorts of incompatibility frames, so those frames can be a semantics for classical logic. I'm not sure what to make of the claim that intuitionistic logic is S5. There is a translating from S4 to intuitionistic logic and conversely. I'm also not sure, without looking over things again, why he is using the label "intrinsic logic". I remember being puzzled about this when I read the Locke lectures before.

Daniel Lindquist said...
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Daniel Lindquist said...
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Shawn said...

I listened to lecture 5 together with Peregrin's comments and the Q&A. I rather liked them. Peregrin's joke at the start was so cute.

I'm still not entirely clear on the idea of intrinsic logic. It seems to be something along the lines of the following. Brandom wants his semantics to be based on incompatibility frames. There is a set of standard conditions on the frames. If a frame meets those conditions, then it (or a subframe?) validates the theorems of classical S5 modal logic using his definitions. It sounded like whenever you have a standard incompatibility frame, you have a validation of the S5 theorems.

This is a little confusing since it seems like a frame that validates intuitionistic logic shouldn't validate S5. That is the point on which I'm still a little confused. Something along these lines was raised during the Q&A. Someone pointed out that Brandom had started defining things in a roughly classical way, which would rule out intuitionistic connectives at the outset. I don't remember his response, but it didn't seem particularly responsive.

His comments about S5 having some particular claim to being in some sense the real modal logic seemed out of place. I think you were right to be suspicious. It doesn't seem like the sort of thing that he should be saying. In fact, I think in MIE (it may have been in lecture...) he said that that sort of question, what is the one true logic?, was one that didn't make sense on his view of logic. Very odd.

I think the thing to worry about isn't validation, but rather this idea of intrinsic logic. I'd have to look at the technical appendix to figure out what is up with that, but it seems like step away from the view of logic in MIE. Moreover, it seems like a step in an odd direction

Daniel Lindquist said...

Brandom at least said the bit about "Which is the true logic" being a bad question in one of his audio lectures, since I know I've heard it. (I quoted it a few times in this post, even.)

(I recall it being in the Q&A part of one of the earlier Locke Lectures -- someone asked him about non-classical logics, and he said something about the various conditionals on offer codifying various sorts of inferential relations -- the material conditional says that B isn't false if A is true, the intuitionistic conditional says that if you have a proof that A, you can prove that B, the relevant conditional says that if A is true then there's some way to get to B from A, etc. (I recall it being fairly sketchy when I heard it, and it's probably tarnished while I held it in recollection.) So the question of "Which is the true account of the conditional?" wasn't one he was concerned with asking -- various conditionals have uses in making various inferential practices explicit. I could have sworn I wrote something down about this part of the lecture, but it appears I did not. And it's not in any of the lecture transcriptions. I suspect it was in the first or second lecture's Q&A, or one of Brandom's response-reponses.)

If Brandom dud say this in the Locke Lectures, then it would seem unlikely that the "intrinsic logic" stuff is supposed to be a change from Brandom's earlier position. Though it does look like the two don't go together very nicely.

I think you're right that "intrinsic logic" is the term to look at, though. For one thing, I don't think "vindication" or "the modal logic" are technical terms for Brandom, while "intrinsic logic" has to be. (If he hasn't given a technical meaning to it, I have no idea what it could mean.)

A brief glance at the technical appendix for lecture five shows that Brandom does discuss "the true logic", though. Page 54: "To these considerations [of intuitionistic logic and incompatibility-defeasors] we may add another, which may be instructive in comparative assessments of the expressive power of intuitionistic versus classical logical connectives (the issue that supersedes concern over which is the true or correct logic, on the expressive view of the demarcation of logical vocabulary pursued here)."

The question of "Which is the true logic?" has been "superseded" by a comparative assessment of the expressive power of the connectives of various logics. Brandom appears to be happy saying bad things about intuitionistic logic in this appendix -- it is "incomplete", it cannot give "reasons for denying the goodness of inferences the logic nonetheless insists are bad" (except when those inferences are also bad classically), in the sense of "giving reasons" Brandom is considering in this appendix (the example he considers is that of ~~p and p -- what is incompatible with p is just what is inconsistent with p (that is, whatever entails ~p). But this is inconsistent with ~~p as well as with p. There isn't anything which intuitionistic logic can offer which is inconsistent with ~~p which isn't also inconsistent with p, and so it looks like the inference from ~~p to p should be a good one -- it cannot "give a witness to the badness of the inference" despite the logic saying it's bad. So distinguishing the two based on their incompatibility relations won't work -- ~~p and p look the same from this view, and so the connectives work like classical-S5's.)

But Brandom closes his appendices with a compliment to intuitionistic logic: "The intuitionistic logical consequence relation is categorical for the logical form of the sentences it relates, in the sense that it suffices fully to determine their logical form [since p and ~p behave in systematically different ways intuitionisticly, whereas in classical logic you can switch out p and ~p throughout without "making a difference to the consequence relation"]. From an inferentialist semantic perspective, this feature expresses a significant expressive advantage of intuitionist over classical (not to mention relevance) logic." So intuitionistic logic is "incomplete" (and this is why it has classical-S5 for its consequence-intrinsic logic, rather than being sufficient unto itself) but it is "categorical". This is less clear to me than I would like it to be.

Frustratingly, it does not appear that Brandom actually discusses "intrinsic" logic in the appendices in any more detail than he did in the lecture. The term only appears twice, both in the appendix on intuitionistic logic, and both times it refers back to the lecture-text. Rereading the relevant portion of the lecture-text is not making the term clearer to me. Gah.

Rereading the final appendix, on relevant logics, it still seems awfully sketchy. I notice that Brandom resorts to Capital Letters at one point -- "one might be given pause by the fact that as far as the consequence relation of relevance logic is concerned, consistent and inconsistent sets are indistinguishable. That seems like a Bad Thing, suggesting that this way of recoiling from ex falso quodlibet has somehow gone too far." (He then notes that he's not yet looked at the relevant logics which do have a way of discriminating between consistent and inconsistent sets, those that include a sign for "absurdity", to see how their incompatibility relations shake out.) I get suspicious when someone is warning me away with Capital Letters. And Graham Priest & pals have done a good bit of work to suggest that, no, it might not be a "Bad Thing" at all -- sometimes inconsistency just isn't incoherent. If Brandom has some argument against this (apart from "my way of constructing incompatibility relations from consequence relations requires quodlibet"), then I would be glad to hear it.

A more susbtantive objection: If Brandom wants to say that S5 has a good claim at being "the modal logic of consequence relations", but he hasn't looked at several relevant logics (and doesn't even know how to look at some others), then the claim looks awfully hasty. Only handling irrelevant consequence relations would be an awfully strong blemish on "the modal logic of consequence relations." Or maybe I am just unduly opposed to ex falso quodlibet.

A rough thought, possibly horribly misguided: Perhaps Brandom's method for looking at consequence relations is itself privileging classical logic, since incompatible claims are just the explosive ones and there does not appear to be anything which could play the role of a non-explosive version of "neither p nor ~p", incompatibility-wise. So the incompatibility semantics are treating every inference as if it was made with a two-valued logic. Perhaps Brandom is smuggling bivalence in under another name (perhaps without intending to), and then claiming a victory for classical logic when it turns out that everything's coming up roses for a bivalent logic. I've been suspicious that there's something fishy in his claims to not yet be talking about truth when he talks about compatibility & incompatibility relations (since truth-talk is supposed to be derivative of these, not vice-versa), and finding that his incompatibility semantics is rigging the deck in favor of a certain understanding of truth would seem to be an indication that a notion of truth is already in play in handling incompatibility relations. (This paragraph is all very speculative.)

Shawn said...

I think you write more in response to comments than I usually do in substantive posts. Your reply expresses several things that I agree with and which I think are right. I can't reply to all of it right now though.

Brandom sees a problem in relevance logic not attributing a distinct inferential role to inconsistent sets of sentences. This is odd. Prima facie and in the shoes of the relevance logician, why should the fact that you believe ~p and p affect what you infer from a distinct q? The problem is that Brandom's incompatibility semantics, as formulated, depends essentially on ex falso, or generally an explosive consequence relation. That in itself creates some problems for analyzing a lot of logics out there.

It is very odd that this idea of intrinsic logic doesn't see more discussion considering it seems to be important for some of the claims from lecture 5 and it is in the title. The stuff about comparative expressive power sounds like what should be said, but it seems to me like there is something off about the discussion in lecture 5. It feels like a move away from the position in MIE, although nominally it is the same. That is more of a gut reaction than a worked out view though.