Well well well.

So I missed WFC, which sucks, but three good developments this week.

The first I mentioned last entry--Of Rum, Madness, Thunderstorms and Prayer is now "in print," the check's in the mail and Adicus Garton, the editor, even accomodated my absurdly long list of last-minute line changes...the chutzpah on this point was advised by Ben the Greater's avice during the Speculative Literature Foundation Mentorship Program last fall...it never hurts to ask.

The second is that Tropical Storm Noel passed us by, doing damage in Haiti and further up the coast but entirely sparing South Florida. Not only did Miami dodge the bullet, but the ripple effects in terms of gray skies and warm winds were just enough to provide the perfect atmospheric backdrop to the annual Halloween revelry in Coconut Grove. They close down several blocks of traffic for people to hang around in costume on the way to and from the bars and clubs, so it makes for a fairly striking scene.

The third is that I think I've actually finished everything I need to do to be in line to take my qualifying exam next semester, this being my last semester of coursework. On Friday I gave the Director of Grad Studies, Dr. Bueno, a packet of transcripts and old syllabi from Western Michigan to prove I've finished all the requirements, and yesterday I sent in my "qual paragraph."

The system at Miami is that at the beginning of November you turn in a little paragraph describing in general terms what you want to do your dissertation on, then if that's approved they prepare a reading list--dozens of books and articles on the subject--which they give you in December. You then have five months to study the reading list, at the end of which you take the dreaded quals....four hours a day for two days in a little room with no books answering two questions a day based on your reading list. If by some miracle you pass that, after a week of un-winding in Key West or whatever, it's time to start working on the official proposal for the dissertation, and if *that's* approved, it's time to start on the dissertation itself. So qual studying + qual-taking + proposal-writing+ dissertation writing + defense is something they allot a total of 2 1/2 years for.

Anyway, Dr. Bueno replied this afternoon with a couple of suggested changes to my qual paragraph, I adjusted it and he just sent back an e-mail that looks good. So, in theory, I now know what I'll be working on for the next two and a half years. At the very least, it should sound impressive at parties and what-not: "What do you do?" "Oh, I work on paraconsistent logic." (A friend in the program told me that sounded like "a combination of math and the ghostbusters.")

A quick glossary for those not wasting their lives on obscure areas of philosophical logic. The semantic paradoxes are things like "This sentence is false" (the Liar sentence) and trickier multi-sentence equivalents that you can't get around with any sort of move about self-referentiality, like an infinite series of sentences where each one attributes falsehood to all the sentences above it in the sequence. The set-theoretic paradoxes have to do with things like the set of sets that aren't members of themselves--if it is a member of itself, it isn't, and if it isn't, it is. Zermello-Frankel is the set theory that gets around it by positing an ordering system of sets where sets can only have sets of lower order be members of them. Tarski has a parallel move in the semantic cases, where there's an infinite hierarchy of artificial languages, where sentences in each language can only refer to languages below them in the hierarchy. Both seem arbitrary--setting up a rule that prevents you from expressing certain bits of information doesn't make them go away. Paraconsistent logics are logical systems where statements of the form (P & Not-P) are OK, unlike classical logic, where anything without exception can be derived from them. Dialetheism is the theory that there are true contradictions, so paraconistent logic models reality better than classical logic. I'm arguing against that, in defense of classical logic, though not on formal solution or trivialization-based grounds, since I don't think any of those solutions work.

Trivialization (or "explosion") is the logical term for a situation where you can derive anything, like you get from P & Not-P both being true. The problem with using that as an argument against dialetheism is that it assumes the very point being contested, since it's based on the following proof:

1. P & Not-P (assumption for the sake of argument)
2. P (from 1 and the &-elimination rule)
3. P or Q (from 2 and the or-addition rule)
4. Not-P (from 1 and the &-elimination rule)
5. Q (from 3, 4 and disjunctive syllogism, which is the rule that says that given an either-or statement and information that one of the two thing is false, you can derive the conclusion that the other one is true)

The problem of course is that disjunctive syllogism only works if you assume that something that's false can't also be true, which is precisely the bone of contention between classical and paraconsistent logic.

Anyway, having gotten that out of the way, here's the final version of the paragraph...

General topic: philosophy of logic, with a focus on dialetheism and
the semantic and set-theoretic paradoxes

The semantic paradoxes, like the Liar and it's multi-sentence equivalents, are the best-known cases of prima facie true contradictions. The set-theoretic paradoxes seem to constitute equally good evidence for dialetheism. An artificial, purely formal solution is much more widely accepted in the set-theoretic than in the semantic case, but this sort of move seems equally arbitrary in either case. Explosion-based arguments against dialetheism are radically question-begging for familiar reasons, and at best demonstrate the existence of too many true contradictions, as opposed to none at all. In fact, this begins to look like an innate structural imbalance in the argument, since any argument either for or against true contradictions must take place either within a logical context that tolerates contradictions or within one that rules them out. A dialetheist can argue for true contradictions without begging the question by generating them within contexts in which they are supposed to be ruled out, but it is hard to see what sort of parallel move within enemy territory would be possible for those on the anti-dialetheist side. Arch-dialetheist Graham Priest also identifies candidates for the status of true contradictions in the philosophy of law (in which citizens can have real, but contradictory, legal rights and obligations) and in the metaphysics of change. Given the scope and rigor of the Priest's case and the unsatisfactory nature of many of the existing attempts to defuse the semantic and set-theoretic paradoxes which provide the best evidence for dialetheism, there should definitely be enough material here for a dissertation-length argument against true contradictions.