Monday, May 31, 2010

Another Revenge Paradox For Beall

In Spandrels of Truth, JC Beall abandons his previous belief in the existence of truth-value gaps, now declaring that "negation is exhaustive."

Intuitively, this means that there are now three possible statuses that statements can have on the new version of his account (unlike the old version, where there were four):

(1) (Just) true
(2) (Just) false
(3) Both true and false

In Spandrels..., Beall treads carefully around the "just" terminology, since he recognizes that for any such formulation you like, you can always devise a Liar sentence for it, e.g.

"This sentence is just false."

He does, however, sometimes express the distinction between (1)/(2) on the one hand and (3) on the other by talking about "treating" statements "classically." For example, in section 2.3.2, in his discussion of the status of non-paradoxical sentences that (like Liars) ineliminably refer to their own truth-or-falsehood status, like....

"This sentence is true."

....he says that he is open to "an asymmetric treatment of such sentences (e.g. treating some....as gluts, some classically." (p. 15)

In section 5.4, to express his view that true contradictions only arise as by-products of the introduction of notions like "truth" into our language, and that the portion of the language that's free of such terms is also free of true contradictions, he says "our base language....is classical." (p. 126)

And so on.

An important note about all this:

Given his rejection of gaps, it looks like "glutty" and "treated classically" are jointly exhaustive of the conceptual options. To really harp on the point, we can put this precisely as the Joint Exhaustion Principle (JEP).

JEP: Every statement is either a glut or classical.

Given Beall's account, I don't see how he could reject the JEP. He's a tpaints to explicitly reject the possibility of any sort of "paracomplete" break-downs of Excluded Middle, he goes out of his way to commit himself to a classical account of vagueness problems, etc. If someone who knows Beall's work can come up with a third option that he has room to adopt, I'd love to hear it in the comments, but right now, it sure doesn't look like he has the resources to deny the JEP.

So, given that all non-glutty statements are to be treated classically, what does that mean?

Presumably "is classical", "treated classically", etc., means at the very least that reasoning about it according to all the rules of classical logic (including those which dialetheists take to be invalid in inconsistent contexts) is appropriate when it comes to such statements.

(Note that, since Beall and I agree about the equivalence of "P is false" and "~P," I'll use them interchangeably in what follows.)

This language, however, seems to be just as prone to revenge paradoxes as the avoided language of "just false," etc. After all, what can he do with the following sentence?

# The (whole) sentence marked with the number sign is false and should be treated classically.

Like any conjunction, we have four options here:

(1) Both conjuncts are true, so the whole thing is true.
(3) The first conjunct is true, but the second conjunct is false, so the whole thing is false.
(3) The second conjunct is true, but the first conjunct is false, so the whole thing is false.
(4) Both conjuncts are false, so the whole thing is false.

(1) would entail triviality in a straightforward way. Given the assumed equivalence of "P is false" with "~P," noted above, a statement that's (a) both true and false, and (b) treated classically, is a statement from which triviality can be derived.

(2) would mean that # was not classical, which, given the JEP, would entail that # is a glut, and hence entail triviality.

(3) would entail triviality just like (1) would. If the first conjunct is false, it's also true. If the second conjunct is true, triviality is entailed by the contradiction.

(4) entails triviality in the same way. If the first conjunct is false, it's also true. If the second conjunct is false, the whole thing is (by the JEP) a glut, which makes the second conjunct true, which in turn means that we can derive triviality from the contradiction.

So....unless anyone can see a way out of the JEP on Beall's account...this looks like a pretty serious problem.

Of course, there's at least one way out:

Just as dialetheists (including Beall) standardly weaken the inferential power of their conditionals to get around Curry, Beall could weaken his even more in order to get around the Sentence # Paradox. He could claim that "P or Q", "if P, then R" and "if Q, then R" could all be true without R being true. If he made this move, however, then he would have no remaining motivation for believing in true contradictions. After all, he doesn't believe in "base language gluts," and given the sort of conditional-weakening proposal under consideration, no contradictions would follow from standard versions of any semantic paradox.

Wednesday, May 19, 2010

A Few Thoughts On Logical Fallibilism

Imagine that Aristotle had had Graham Priest's position that some (but not all) contradictions are true, and the first big treatise suggesting the impossibility of true contradictions wasn't published until 1987. Largely unquestioned academic orthodoxy held that some contradictions are true, mainstream probability theory reflected this assumption and so on. Everyone taking introductory logic classes slaved through the construction of long truth tables reflecting the three options T, F and B (for "Both"). The instructor might devote perhaps five minutes to illustrating the possibility of "Both" with a Liar sentence. Doubtless some Beginning Logic and Intro to Philosophy students would find it all a bit confusing--"how can it be *both* true and false?"--and smug TAs would sit around the bar and trade snotty jokes about the inability of undergraduates to understand basic logic.

Surely, nothing about the world described in the last paragraph is, y'know, impossible or unimaginable. (Nothing about the truth of orthodox ideas about logic makes it impossible or unimaginable for most people to be wrong about them. If you think that there are no true contradictions or truth-value gaps, etc., classical logic is the One True Logic and so on, you therefore think that in the actual world some actual people *are* mistaken about these matters. It's hard to see what possible basis there could be for arguing that it would have been impossible for things to be the mirror image of the way they are, and for the mistaken opinions to be the overwhelmingly popular ones.) Equally surely, from our perspective as residents of the actual world, we can all agree that it would be rational for denizens of the possible world in question to take that 1987 polemic against the possibility of true contradictions seriously, to (at the very least) seriously weigh the arguments and have a serious debate whether or not they should abandon dialetheist orthodoxy. After all, in the actual world, everyone with a position on the subject either thinks that (a) it's completely obvious that true contradictions are impossible, or that (b) far from being trivially obvious one way or the other, there's an interesting and important philosophical debate to be had on the matter. (No actual dialetheist that I'm aware of thinks that the existence of true contradictions is too obvious for it to be worth arguing about it.) If you have position (a), presumably you think that it would be rational for people in the possible world described above to question their belief in true contradictions. If you have position (b) in the actual world, presumably you'd advise the same position to people in the possible world where the debate was being held with a different balance of forces.

For (some) people with position (a), though, contemplation of the hypothetical might raise some sticky problems. After all, some people with position (a) brush off the very notion of taking the debate about these matters seriously by saying things like...

"You need logic to argue about logic. The very idea of arguing about it is ridiculous."

or

"What could be more basic than logical truths on the basis of which you could argue for them?"

or

"The denial of obvious logical truths is so nonsensical that I really don't care if I am begging the question."

Etc., etc., etc. I've heard variations on all of the above many times over the last couple of years of writing and thinking about dialetheism, and there are some famous and well-respected philosophers who've written sophisticated variations on the theme. For example, in a famous response to an invitation to contribute an essay to an anthology debating the Law of Non-Contradiction, David Lewis wrote:

"I’m sorry; I decline… My feeling is that since this debate instantly reaches deadlock, there’s really nothing much to say about it. To conduct a debate, one needs common ground; principles in dispute cannot of course fairly be used as common ground; and in this case, the principles not in dispute are so very much less certain than non-contradiction itself that it matters little whether or not a successful defense of non-contradiction could be based on them."

(Lewis, in other words, felt that dialetheism could be refuted with an incredulous stare.)

Now, consider the clearly possible world discussed above where dialetheism was orthodox and the camp that wanted to revise away the view that everyone else considered to be one of the most obvious and basic logical truths that there could be (that there are three possible truth-values that statements fall into, 'true', 'false' and 'both') was a tiny minority. Imagine that the David Lewis counterpart of that world (let's call him Bizarro-Lewis) responded to a similar invitation in the same way. Granted that Bizarro-Lewis' position (that the existence of the third standard truth-value was too obvious and epistemically basic to be debatable) would be *false.* That's not the issue. The question, for those who agree with the Lewissian position in the actual case, is whether Bizarro-Lewis' dogmatic refusal to even consider the opposition's arguments would be in some way irrational or unreasonable? (Rationality is, obviously, distinct from success. The history of science is littered with theories that we would now all agree are false, despite the fact that we would all agree that belief in them was, at one time, rationally justified.) If not, if the Bizarro-Lewissian position would be rational, does that mean that the philosophical community of that world would be entitled to remain in blissful ignorance of the truth of these matters, never learning better because they never seriously engaged with the debate? That seems like an....odd...position to take.

It's one that, however, it's terribly hard to see how actual-world Lewissians can avoid. If anyone can explain why we (orthodox logicians in the actual world) are justified in being dogmatically unwilling to engage in debate with dialetheists, whereas they (Bizarro-Lewissians) would *not* be justified in being similarly dogmatically unwilling to engage in debate with the dissenters of their world (who correctly deny the possibility of true contradictions), I'd like to hear it. My suspicion, however, is that any remotely satisfying answer to that question* would amount to a substantive defense of the truth of the Law of Non-Contradiction....

....or, in other words, it would amount to a contribution to the debate.



*"Any remotely satisfying answer" means, at the very least, "any answer which was such that the Bizarro-Lewissian couldn't easily offer up its exact mirror image as an answer to the mirror image question."

Monday, May 10, 2010

Back

Sorry about the long unannounced break. I had a bit of materal stored up from before my defense, and after I burned through that, I really needed a break.

....but I'm back now. In lieu of a real Monday post, a few things:

(1) Ryan has a fun depiction of Harry Frankfurt's take on the Stone Paradox here.

(2) A few people have asked if they could read my dissertation. I'm happy to shoot a copy over to whoever...*after* I've finished various proofreading and re-formatting things I have to do for the graduate school in any case. I'll post an announcement here when its ready.

(3) Here's a schedule for the next couple of weeks:

Wednesday, May 12th: A Few Thoughts On Logical Fallibilism

Monday, May 17th: Why Theistic Libertarians Should Believe In Future Facts and Backward Causation (If They Believe in Infallible Divine Foreknowledge)

Wednesday, May 19th: Graham Priest And The Principle Of Uniform Solution

Wednesday, April 7, 2010

April 7th

I hereby interrupt normally scheduled programming to note that today is my 30th birthday.

The task of processing that particular psychological depth charge with the help of friends and alcohol really precedence over blogging about philosophy right now, so I'll see you all back here on Monday.

Monday, April 5, 2010

Nolan & Co. On Moral Fictionalism (Part I)

"Torturing children for fun is wrong" seems to be a reasonable sort of thing to say, whereas "playing Wii Golf is wrong" seems to a massively unreasonable sort of thing to say.

An obvious way to gloss the distinction is to say that "torturing children for fun is wrong" is clearly true, whereas "playing video games is wrong" is clearly false. Sadly, however, the world fails to contain the sorts of metaphysical facts that would make "torturing children for sport is wrong" true. After all, the statement seems to be an attribution of a certain property (wrongness) to an action "torturing children for sport" and no such property seems to exist. At the very least, there is no evidence for the existence of such properties. Depending on one's theory of evidence, this might be enough--such properties don't constitute part of our best overall theory of the world, so it's rational to actively disbelieve that there are any such things--but even if one's epistemic stance leads one to agnosticism in cases where there is no evidence one way or the other, this doesn't help much in terms of making sense of the difference in our atittudes towards "torturing children for fun is wrong" and "playing Wii Golf is wrong."

That distinction surely has to do with our moral intuitions, and for shaved apes like us to "have moral intuitions" is surely ultimately for us to have a certain sort of neurological event, one resulting from genetics, environment or some eccentric combination of the two. If moral properties exist, and they are non-physical (as they certainly seem like they would be), no remotely plausible causal story relates them to humans having moral intuitions about them.

At this point, of course, one may go in any number of directions. For example, one can try to make sense of moral properties so they aren't non-physical. Volumes can be (and have been) written about this proposal in all of its myriad flavors--synthetic reductionisms, sentimentality theories and so on--but for the moment I'll just say that, while I've argued for this kind of approach in the recent past, at the moment I find the prospects for this sort of project fairly bleak.

On the opposite extreme, one can simply bite the bullet and say that, the world lacking the right sorts of facts, "torturing children for fun" and "playing Wii Golf is wrong" are equally false, to the same extent and for the same reason, and deny that our inclination towards the first statement and against the second tracks anything interesting. The case for this is easy enough to make, but one might think that if we can find a way to do better, we should.

The most familiar way to make sense of joining the full-fledged moral realist in endorsing some moral claims but not others, while joining the full-fledged error theorist in denying that the world contains the right sorts of facts which would make moral claims (at least moral claims interpreted literally as exactly the sorts of things they seem on their face to be, which is to say as descriptive claims attributing certain non-physical properties to human actions) true, is Gibbard/Blackburn-style "quasi-realism." Minimalism about truth, understood not in the straightforward "Truth As Disquotation" way in which truth is still taken to only apply to ordinary descriptive statements--"'snow is white' is true" means nothing above and beyond "snow is white"--but in terms of talk of "assertion condiitons," is supposed to connect these seemingly incompatible dots.

The quasi-realist, however, faces all sorts of obvious problems, from difficulties about how to make sense of the technical logical details(the Frege-Geach Problem) to the fact that it seems to entail relativism about truth to the poorly-defined and implausible nature of the very idea of "assertion conditions."

So, if one thinks these are big problems, but shares the quasi-realist's core committments--(1) some moral claims should be endorsed, others rejected, even though (2) there are no moral facts--what's to be done?

In an interesting article back in 2005 in the Australian Journal of Philosophy, Daniel Nolan, Greg Restall and Caroline West propose a version of fictionalism about morality that they take to successful avoid the vices of quasi-realism while assimilating all of its virtues. I'll have more to say about my own position on all of this, and a more detailed discussion of Nolan/Restall/West, soon, but for the moment I'll just settle for saying that the article is worth reading.

[Update: If you're reading this at a place where you can't access the published version for free, Greg Restall points out in the comment thread that an earlier, longer version is freely available here.]

Monday, March 29, 2010

Paraconsistency in XKCD

In case you missed it, this was funny.

Wednesday, March 24, 2010

Glenn Greenwald and Informal Fallacies

Anyone whose read this blog in the past when the subject matter has wandered onto political territory should be unsurprised to hear that I find Ann Coulter's frequently expressed views about Muslims and Arabs to be fairly loathsome. That said, free speech protections only applying to views that you like (or that are close enough to views that you like to be in your sphere of "the bounds of civilized discussion") isn't worth much, so I find the attempts of a Canadian university administrator to use that country's "hate speech" laws to stifle the free expression of Coulter's vile opinions to be pretty vile in its own way.

All of this, however, is mostly by way of preamble. What I find more interesting is that if you read the comment thread on the Glenn Greenwald article I just linked to, you find a really weird sort of confusion about the difference between fallacious slippery slope arguments against those laws and substantive objections to the laws based on fairly banally familiar sorts of social contract considerations.

The former go like this:

"It starts with the criminalization of hate speech. Then, before you know it, we're criminalizing all kinds of categories of speech, and sooner or later, Big Brother is monitoring and censoring every word that comes out of your mouth and telling you exactly what to think about every conceivable subject. We need to stop this progression before it's too late!"

This is a very silly kind of argument, for very familiar reasons. Contrast it with the following argument:

"'Hatred' is a tricky notion, and which political opinions count as expressions of hatred and which don't depends on where you're sitting. If you criminalize views you find offensive, then you might be acting against your own long-term self-interest by setting a precedent which could be used against you, if your political enemies ever take power and they find your views offensive. Really, it's in everyone's interests for society to be ordered in such a way that the expression of all views is equally and automatically protected."

Now, reasonable people can disagree about whether the second argument goes through, and it could be no doubt be objected to in all sorts of ways, but it certainly doesn't commit the glaringly obvious slippery slope fallacy at the heart of the first argument, right?

Well, in his article, Greenwald talks about how he will "never understand people's failure to realize that endorsing this power will, one day, very likely result in their own views being criminalized when their political enemies (rather than allies) are empowered." I think the "very likely" is over-reach, but still, what he's saying seems to be, very clearly, an instance of the second argument rather than anything even close to the first. Yet the comment thread is absolutely filled with people responding to Greenwald as if he'd made the first argument, going on about how Canada is hardly an Orwellian nightmare, and it's still a functioning democracy, and making snarky little comments about how Greenwald should be careful about getting a midnight knock on his door from the Mounties come to stifle his free speech and so on and so forth.

So, really, maybe I've just been doing philosophy for too long and I've lost touch with the way people argue out there in the real world, but....really? Is the distinction between those two sorts of arguments really too subtle for casual readers on Salon to sort out?