Tuesday, November 20, 2007

New Blog

This is, as the title indicates, about dialetheism, which is the view in the philosophy of logic that there are "true contradictions," or true statements of the form (P&~P). (This should be distinguished from "paraconsistentism," which simply denies that anything follows from a contradiction. A paraconsistentist prefers to work in a logic where this is cleared up, but does not necessarily believe that there really are any "truth value gluts." All dialetheists are paraconsistentists, but not all paraconsistentists are dialetheists.) If you've never heard of dialetheism before, I'm guessing your reaction is going to be, "that's the craziest thing I've ever heard." And it is. It is, however, also surprisingly difficult to come up with a good argument against it. If you continue to read this blog, you'll hear more about this.

(For anyone looking for the skiffy-related bits of my life, see my other blog.)

OK, so why did I set up the new blog?

I am, as most people who know me from other contexts probably know, a PhD student in Philosophy at the University of Miami, down in sunny and decadent south Florida. This is my last semester of coursework. A couple of weeks ago, I got the word that all of my course requirements have been checked off as met, and a week before that I got my dissertation subject approved. The way the system works at Miami, this means that shortly after the semester is over--i.e. in a couple of weeks--I should get my reading list for my qualifying exams. This should be about 15-20 books and a similar number of articles about my chosen subject, which I will then have five months to study. At the end of that time, during the two "reading days" between the end of classes for the spring semester and the beginning of finals week, I'll have to sit down for eight hours of examination on this topic.

In order, basically, to force myself to think out loud about all this material I'll be reading, gather my half-baked thoughts about it, etc., without boring my friends in contexts where they don't want to hear about it, I've set this up as a socially acceptable venue for that. Let the reader be warned.


J said...

Attacks on the law of contradiction are not new. Empiricism--starting at least with Hobbes-- itself sort of called into question a priori-city itself did it not? And in a sense that is the real philosophical issue: if a priori-knowledge (and/or a certain sort of platonism) cannot be justified than the supposed a priori status of logic, including the LOC, and mathematics cannot be upheld, but should be viewed as any other type of empirical knowledge.

Constructivism still might lead to upholding the LOC (and I think it should--- as did Quine, at least a constructivist on occasion) but that seems to take away the "necessary" aspect of logic and mathematics, at least to some degree. So we agree to uphold the LOC, since most shit works a lot better (like say History: it's rather problematic to have some notion of "truth" where Hitler was and was not the fascist dictator of nazi germany, or Charles Manson was and was not guilty. Or to say mammals have hearts and they don't have hearts. That will not do. ).

Ben said...

Well, I'd say that there question of whether logical laws are known a prior or a posteriori is a wholly separate one from whether any particular (alleged) logical law is true. It's possible to say that logical laws can be known a priori but to say that on the basis of a priori evidence (e.g. the liar paradox), the Law of Non-Contradiction is false, and it's possible to say that logical laws are subject to empriical evidence (as e.g. Otavio Bueno does in his contribution to "The Law of Non-Contradiction: New Essays") and say that the evidence favors the truth of the Law of Non-Contradiction.

In fact, a strong empiricist who believed that all that existed was the "observable world," and who believed that we can only know about it through empirical evidence, would probably have stronger grounds that just about anyone for denying dialetheism, given that even Graham Priest argues at length that there are no true contradictions in the "observable world."

As far as your history case, I'd imagine that no dialetheist would be likely to claim that Hitler was and was not the German dictator, for the simple reason that we have evidence for the "was" part and no evidence for the "was not" part. All history would need is a rejection of trivialism, the position that *all* contradictions are true.

The Charles Manson guilt thing might be a trickier case, since criminal trials usually involve evidence for both guilt and innocence, such that we have to weigh the evidence for one against the evidence for the other to see which one is stronger. I *do* think that there's a serious epistemic problem with why, given dialetheism--i.e. the position that *some* contradictions are true--we don't take all cases of mixed evidence as cases of evidence for true contradictions.

J said...

"In fact, a strong empiricist who believed that all that existed was the "observable world," and who believed that we can only know about it through empirical evidence, would probably have stronger grounds that just about anyone for denying dialetheism, given that even Graham Priest argues at length that there are no true contradictions in the "observable world."

Not sure about that. How about "he loves her and he doesn't love her"? Not real fancy, but sort of true, at least informally. He loves some things about her, and he doesn't love others. OK, you could say that just means "he loves her" but methinks, at least at level of normal language that verbs (or is it verb phrase) are not themselves truth functional. Similarly with "he is guilty, and he is not guilty." Partial guilt is assigned, quite often. Or guilt is mitigated (premeditated murder is counted worse than 187 in "heat of passion").

There's more to the story, but induction--and probability--- may present problems for the logician. Time itself presents a problem (Carnap discusses this somewhere). It might be raining and not raining, at least in say a ten mile square chunk of sky. And what about cause???? There might be multiple causes, all rather difficult to trace. Didn't other analytical people discuss this? (if not Hume) Logic does not always work with observation. Falsifiability itself another issue (Newtonian mechanics were assumed to be "true", until modified by Einstein).

Ben said...


"He loves her and he doesn't love her" wouldn't, I think, be considered any kind of contradiction, by either a dialetheist (who thinks some contradictions or true) or a defender of the Law of Non-Contradiction, for precisely the reason you say, that what's meant is that he loves some things about her, but not others. A logical contradiction involves something being simultaenously true and false in *precisely the same sense,* not something being sort-of-one-way and sort-of-the-other.

If sloppy, informal language were enough to generate contradictions, then Graham Priest & co. certainly wouldn't be bothering with complex maneuvers about things like the semantic paradoxes. After all, informal conversational usage constantly involves pseudo-inconsistent language ("did you like the movie?" "well, I did and I didn't...") that everyone automatically understands is being used to express consistent information ("I liked the acting, and the plot was cool, but the dialogue was awful...") The logical issue, and any logical problems, arise when we nail down the precise meaning.

If we really meant that he both loved and, at the same time and in precisely the same sense, did not love her, *that* would be a contradiction. Similarly, if in the same place at the same time it was and was not raining in precisely the same sense of "raining," *that* would be a contradiction. If raining is pouring down from one part of the same ten-mile chunk of sky and not from another part, though, there's no contradiction there.

J said...

Ah now I seem to recall one dude who opposed the LNC: Heraclitus: "We step and do not step into the same rivers" . T v F??? IN some sense quite accurate--- The Rio Grande moves, and so the H20 molecules have passed on when you step in and then step in again 10 minutes later. And yet it's still the Rio Grande (the term refers to the same place/event, more or less). A bit vague (and I don't mean any mystical BS by the example), but sort of similar to the rain in a 10 mile square area of sky. Given time, and motion, and certain parameters you can make contradictory statements of some type . I agree that is not the same as saying "X is a right triangle is and it is not," but then physics is not mathematics.

I'm not the one denying the law of contradiction, of course (nor do I really care for Da Classix, Heraclitus or Aristotle). The point is that many events are not truth functional, or discrete, as in Heraclitus's river, or even the "love" example. Ricky says he loves Luci on Jan 1. But over a year's time, they fight bicker, etc. and then make up. So at year's end, did he love her or not? Does it depend on what he says? Ricky may say he loves her, but it doesn't appear that way when he backslaps Luci. Yeah sort of lame, but "love" is not discrete.

At the same time, I believe my initial comment still holds (and even some philo-hacks seem to agree): the Law of contradiction itself is a given, and cannot really be established. It sort of presupposes itself, or some weird Kantian concept like that. IN some primitive tribe or "Lord of the Flies" scenario, humans might develop a language that was contradictory (or so it seemed). They might not even have a word for "Truth" (or negated truth, etc.). I suspect that is the case for primitive oral cultures; they most likely have names for things, and then syntax, and sort of point or gesture or bark at things. The Aristotles arrive much much later.