Thursday, December 31, 2009

Eastern APA (Part II)

On Monday night at the smoker, I finally did get a chance to get into it with Colin a bit about dialetheism, and, coming out of that discussion, a half-formed thought about Curry & contraction should be up on the blog next week.

On Tuesday, I went to see an "Author Meets Critics" session on Paul Redding's book "Analytic Philosophy and the Return of Hegelian Thought." Although I have read a good bit of Hegel in the distant past, the session mostly convinced me that I didn't remember as much about all that as I thought I did. I have flipped through the book a bit, though, and it does contain some interesting material on Hegel's attitude toward contradictions, picking up nuances rolled over both by some latter-day Hegel defenders who don't want to associate him with advocating inconsistencies on the one hand and by Graham Priest, who has made a big deal in a few places of claiming Hegel as one of his predecessors in affirming true contradictions on the other hand.

On Wednesday, I went to Brian Leiter's very interesting and entertaining talk on the foundations of religious liberty. Nussbaum argues in Liberty of Conscience that mere toleration is an insufficient moral basis on which to justify the legal tradition of singling out religion for particular constitutional protection in pretty much every western society. She thinks that we need something more, which is respect. Leiter argues against this on all the obvious grounds, given the epistemic and moral failings that religion tends to be associated with, and as far as that goes, it's hard to find fault with his argument. Where Leiter's argument went wrong in my view came in the last part of the talk where he (a) granted that even toleration is morally culpable given some utilitarian considerations, and sufficient harm caused by the thing being tolerated makes the toleration unhelpful, but (b) there's insufficient evidence that religion does more harm than good, so we don't really need to worry about (a).

Now, I am a card-carrying member of the ACLU and have been for a long time. (The EFF, too.) I'm emphatically in favor of religious freedom and other basic civil liberties. I am, however, pretty skeptical about (b). The problem, after all, about serious religious belief, is that when prophets and mystics think they're receiving direct communication about the nature and wishes of transcendent entities, the very nature of the process, insulated as it is from certain sorts of rational reflection (one doesn't second-guess the will of God), is such that it's inherently unpredictable. When you go up to the top of the mountain and fast and pray until you get a vision, by the time you come back down, you might end up telling your followers that all living things have a profound sense of connection and that we should all be peaceful and loving and compassionate, or you might end up telling them to go forth and kill all the unbelievers. Even if as a contingent fact of the matter, more of the former happens than the latter, the utilitarian calculations involved in continuing to play that particular game of societal russian roulette are deeply unclear to me.

None of which, from my perspective, means that we shouldn't tolerate religion, any more than the increased risk of street crime from respecting the 4th Amendment means that we should set up cameras on every street corner and frisk people coming onto and off of the city bus every day. It does, however, make me think that we should re-examine (a). Utilitarian considerations are probably insufficient to ground religious liberty. We need something a bit more robust and deontological.

Here endeth the sermon.

Next week, expect to see posts on Curry and on the classical re-capture.

Meanwhile, on the subject of religion, you should probably watch this video, which contains important public safety information about the dangers involved in mocking prophets.

Monday, December 28, 2009

Eastern APA (Part I)

Last night, I went to the event for New Waves In Philosophy Of Mathematics, where I got to hear Roy Cook talk about neo-logicism, Augustin Rayo talk about mathematical trivialism, Oystein Linnebo talk about the individuation of natural numbers and Otavio Bueno talk about mathematical fictionalism. I was at the original phil of math conference at the University of Miami the spring before last that the volume came out of (in fact, I had to get up early both days to go to Panera Bread to grab coffee and whatnot for the conference participants), and I indexed the book this last summer, and, yeah, Otavio is my dissertation advisor, so most of what I heard wasn't particularly new to me, but much of was interesting.

Note, in particular, that "trivialism" means something in this context totally unrelated to the sense usually used in my particular subarea--it doesn't mean that everything is true, it means that mathematical statements are just trivially true. Rayo argued (not quite convincingly to my way of thinking, but forcefully and entertainingly) that there are two kinds of mathematical Platonism: the kind that people argue for and the kind that people attack, and that the latter has very little to do with the former. They come apart because the former is non-trivial. In particular, Benaceraff-style worries about our epistemic access to mathematical objects are irrelevant to the former kind, because mathematical objects aren't an extra ingredient of reality above and beyond the more mundane sorts of objects. By way of illustrating this, he said that from the perspective of his sort of trivialist Platonism, to assert that there are no numbers is to commit oneself to a contradiction. After all, if you say that "there are no numbers," that means the same thing as "the number of numbers is zero," which means that at least one number--zero!--does exist, and you've just contradicted yourself.

Now, as an argument against someone who denies the existence of numbers, this seems transparently question-begging--why, after all, should they agree that "there are no Xs" and "the number of Xs is zero" are equivalent?--but my sense from the discussion in the Q & A was that Rayo understands this and wasn't using it in that way, but just giving an illustration of the trivialist Platonist's stance. Compare to an argument about whether Batman is Bruce Wayne or Harvey Dent. If someone thinks Dent is Batman, they will deny that Wayne is Batman, but one would be begging the question against them in a fairly silly way if one argued that to deny that Wayne is Batman is to deny that Batman is Batman and commit themselves to a logical absurdity. (After all, both sides could pull the same trick.) Like I said, Rayo's position on phil of mathematics is pretty distant from mine, but it was an interesting presentation of his view, and he concluded with some good remarks on the notions of "bloated ontology" and the like.

This morning, I went to see the "Author Meets Critics" session on Hartry Field's book "Saving Truth From Paradox." Some interesting points came out of the exchange, even if as a matter of personal taste I would have liked a bit more back-and-forth on bigger-picture philosophical issues about the book--Is Field's basic approach to the paradoxes on the right track? Is denying instances of the Law of the Excluded Middle sufficiently less counter-intuitive than accepting counter-examples to the Law of Non-Contradiction to make the considerable deficit in simplicity between dialetheism and Field's paracomplete approach worthwhile? Does his "algebraic" picture really capture the intuitive notion of truth?, etc., etc.--rather than quite so much focus on the intimate technical details. That said, some philosophical interesting points came through, particularly in the Q&A, and I finally got a chance to meet the man, who's the external reader for my dissertation committee but who I hadn't actually met in person before today.

....and, speaking of meeting people, I finally got a chance to meet Colin Caret--the guy who does the Inconsistent Thoughts blog and a regular commenter here. I guess I really should have seized the opportunity to argue about dialetheism. Instead, I ended up just exchanging a few pleasantries about the conference and whatnot then going off to (in theory) grab coffee with him and J.C. Beall and a few others, but actually just let Colin buy me a cup of coffee while I boorishly isolated myself at a corner of the table to continue a discussion with Otavio about Philip K. Dick and quantum logic.

Then came lunch with Jody Azzouni and Mark Colyvan, who I got to bore at length with exactly why I don't think Graham Priest's "classical re-capture" works. Then I ducked bag to my hotel in Koreatown to print some stuff out, put some stuff away, and blog.*

More on Wednesday.

*Just to be a complete jackass, I was sorely tempted to do a couple of Tristam Shandy-style stabs at descriptive completeness there, like "Then I wrote that sentence. Then that one...." But I just wouldn't feel right, gentle reader, wasting your time like that.

Thursday, December 24, 2009

This Is Not A Post

Not really, anyway. It's just an apology for the third consecutive week of not being great with the schedule and mostly posting things that are a bit slim on actual content when I do update, and a promise that the regular schedule will resume next week. I'll be at the Eastern APA, so I probably won't post anything too long and involved, but there should be at least somewhat substantive posts on both Monday and Wednesday.

Meanwhile, Merry Christmas, a (belated) Happy Hannukah, and, of course, a Joyous Smugmas*!

*Smugmas is the winter holiday I celebrate. It's all about sitting around the fireplace with your grad school friends, sipping a glass of good single malt and reminding each other of all the reasons why all the traditional defenses against the problem of evil fail, occasionally pausing to exchange high-fives or fist bumps.** Also, of course, occasionally gathering around the piano to sing old Smugmas favorites like "The Twelve Days Of Demonstrating The Incoherence Of Theism," "Rudolf The Red-Nosed Carnap," and "We're Smarter Than Everyone Else, Give Us Presents."

**The occasional grinch will ruin the general atmosphere of holiday cheer for everyone else by pointing out that the zombie theodicy actually holds up pretty well.

Monday, December 21, 2009

He'll Lure You In...

This is just awesome.

I mean, I disagree about analyticity, obviously, but I still love it.

The song is from The (21st Century) Mondads. Here's a bunch of their other stuff. They also provide the complete lyrics to the Quine song:

He’ll play upon
Your naturalistic intuitions
He’ll lure you in
With the promise of positions that you love
Like realism about numbers and sets
And the view that philosophy’s continuous with science.

And then you’re caught in the web
No support from the a priori
All aboard Neurath’s ship
It will all be fine
But you’re tied to the mast
It’s all a posteriori
Here on in; have a blast
With Willard Van Orman Quine.

He looks so good
Next to Carnap, Ayer and Chisholm
And there’s nothing wrong
With confirmational holism;
It’s quite nice as an account of how theories face the tribunal of
Mmm yeah.

But step away when he starts
Talking about the analytic.
Meaning’s not that strange in being tricky to define.
And it comes in small bits;
Not all holism’s terrific.
Keep your head; keep your wits
Round Willard Van Orman Quine.

Monday, December 14, 2009

Thursday, December 10, 2009

Language and Time (and Space)

Sorry about the delay. I've been pretty good about maintaining the every-Monday-and-Wednesday schedule since early October, but what with the end of the semester, grading, packing for an extended trip back to Michigan before the Eastern APA, etc., etc., etc., these things happen. Better late than never, though, so here's a post....

In Quentin Smith's book Language and Time, he argues for a moderate version of the A-Theory. Some background:

The B-Theory of Time holds that "now" is an indexical like "here," serving only to locate the speaker in time. The A-Theory is all about "the reality of temporal becoming," which basically means that there's a fact of the matter about which moment uniquely counts as "the present." The best argument for the B-Theory is that it's hard to square the admittedly compelling, common-sensical intuitions about time encoded in the A-Theory with the empirical deliverances of Einstein's Special Theory of Relativity (STR). The best argument for the A-Theory (beyond whatever immediate intuitive pull it might have) is that ordinary language sentences are tensed--that is to say, they seem to more or less constantly refer to properties of pastness, presentness and futurity--and that if we don't believe in the real objective existence of those properties, we have to either say that all tensed sentences of English and other languages are false (including, for example, the sentences physicists use to express the STR) or we have to come up with a way to paraphrase the sentences (or at least the ones we take to be true) in such a way that they no longer refer to pastness, presentness and futurity.

As it turns out, the project of coming up with such tenseless paraphrases is pretty hard. Smith is an A-Theorist, and he has a lot of fun pointing out the holes in various extant proposals to do this sort of thing. For example, the tenseless date theory says that we can translate "the meeting starts now," tokened at three o'clock as "the start of the meeting (is) at three o'clock." (The parentheses indicate that the (is) is tenseless.) So far, so good. But what, he asks, about "it is now three o'clock"? Apply the tenseless date theory, and we get "it (is) three o'clock at three o'clock." No good. For one thing, "it (is) three o'clock at three o'clock" is a tautology, and "it is now three o'clock" really really shouldn't come out that way. You need to check your cell phone* to see if "it is now three o'clock" is true, but you can be justifiably confident about "it (is) three o'clock at three o'clock" even if you just woke up in a doorless, windowless room with no memory of how you got there and your phone is out of power.

The tenseless token-reflexive theory does better with this example. It says that we should interpret "the meeting starts now" as "the start of the meeting (is) simultaneous with this utterance," which works just as well for sentences like "it is now three o'clock."

Smith, however, thinks that his counter-examples to this are just as good. For example, consider "it is true that it was true that the era devoid of linguistic utterances is present." Isn't this true? I mean, surely, there is language now, and there wasn't in the past. It isn't true now that there isn't any language, but it used to be. Right? issue is that part of what's traditionally at stake between A-Theorists and B-Theorists is that the former take propositions to change truth-values over time (this is the point of developing tense logics) whereas the latter take them to have eternal unchanging truth-values, so Smith is at the very least dancing on the edge of begging the question here.**

Another issue comes to the fore when we start think about what the "it" is that was supposed to be once true and now false. It's certainly not a linguistic utterance like a sentence, since if so it--i.e. a sentence declaring the absence of sentences from the world--would never have been true, since such a sentence could never have been true, for obvious reasons. In fact, it looks like "it" has to be a proposition, and in fact a proposition that existed despite the non-existence of sentences. That is to say, Smith's move here strongly suggests a fairly extreme version of the proposition theory of truth-bearers, whereby we believe not only in the propositions expressed by sentences, but a sort of Platonic realm of un-instantiated propositions as well.

Now, there may be a lot to be said in favor of proposition theory--see the discussion with Emil on this blog a while back--but there's surely a lot to be said against it as well (e.g. if propositions are abstract objects we can't causally interact with, how would we ever find out that they existed?), and if the price of the best philosophical account of how to make sense of the picture of reality suggested by taking our best current science seriously is that we have to abandon belief in propositions, that strikes me as a price worth paying. But someone who starts from a posture more sympathetic to propositions, presentism or both than mine might not be convinced by this. As such, I'll take a stab at pointing out the problem that originally sparked my own slow move away from the A-Theory when I was an MA student at Western Michigan (where I took several classes from Smith, and spent a lot of time thinking about these issues):

On p. 129 of "Language and Time," Smith says that it would be an "interesting task" to provide an account of indexical terms like "I" and "here" in light of his account of "now," but that "this task falls beyond the purview of the present treatise."

Even when I was an A-Theorist***, this passage always struck me as extremely unsatisfying. The more I thought about it, the more dissatisfied I was. Note, for example, that Smith's criticisms of the date theory all go through just as well for what we can call the "place theory" of spatial indexicals. Imagine the following fairly banal conversation:

P1: "I just got here?"
P2: "Where's 'here'?"
P1: "Oh, sorry, 'here' is Miami."

We might be tempted to translate "I just got here," tokened in Miami, to "I just got to Miami." That's pretty clearly not going to work for reasons that exactly parallel the problem with temporal indexicals. "Miami is here" is only true when tokened in Miami but "Miami is in Miami" is true even if tokened in Hong Kong. The best way to go here looks very much like a token-reflexive view where "Miami is here" means "Miami is co-located with the person saying this" or something roughly along those lines. I feel absolutely no inclination to beieve that claims change their truth-value from location to location. Moreover, I feel even less inclination to think that there's some sort of property of "hereness" independently objectively existing in places where no speaker is located. As such, consideration of the sentence "it is true on Mars that 'Mars is here'" gives me no reason whatsoever to believe in propositions that have a special truth-value on Mars that they don't have on Earth, or to give up on the token-reflexive view for the sake of such strange Martian propositions.

Why, exactly, should "nowness" be any different in this respect? If it feels different, is there anything motivating that feeling other than residual folk belief in the claim that there is an ontologically privileged present moment, which is, after all, precisely the bone of contention here? If so, I'm having troubling seeing what.

*Ten years ago, you would have checked whatever those things were that people used to wear on their wrists. I forget.
**I'm putting things in terms of propositions here because that's the traditional way to frame it, not because I necessarily believe in propositions.
***We all get to have a few youthful indiscretions. Hell, just between you and me, there was even a time in my life when I was a libertarian about free will. Don't judge me. I was just a kid, and everyone else was doing it.

Monday, December 7, 2009

Quote of the Day

So, re-reading one of my favorite novels, I found this surprising foray into technical philosophy buried in a discussion of Wagner and Christianity....

"Parsifal is one of those corkscrew artifacts of culture in which you get the subjective sense that you've learned something from it, something valuable or even priceless; but on closer inspection you suddenly begin to scratch your head and say, 'Wait a minute. This makes no sense.' I can see Richard Wagner standing at the gates of heaven. 'You have to let me in,' he says, 'I wrote Parsifal. It has to do with the Grail, Christ, suffering, pity and healing. Right?' And they answer, 'Well, we read it and it makes no sense.' SLAM. Wagner is right and so are they. It's another Chinese finger trap.

"Or perhaps I'm missing the point. What we have here is a Zen paradox. That which makes no sense makes the most sense. I am being caught in a sin of the highest magnitude: using Aristotelian two-value logic. 'A thing is either A or not-A.' (The Law of the Excluded Middle.) Everybody knows that Aristotelian two-value logic is fucked."

--VALIS by Philip K. Dick, pp. 132-133 which I say....


Wednesday, December 2, 2009

The problem is U trying to fit set theory into ur mathematical box.

Naive set theory says that for every property, there's a set of things that have that property. Bertrand Russell asked, "what about the property of being a set that's not a member of itself?"

This is, traditionally, seen as a bit of a problem for naive set theory.

Classical theism says that an entity exists who can perform any action. Many people have asked, "what about the action of creating a stone so heavy that he himself can't lift it?"

This sort of thing used to be a bit of a problem for classical theism.

That was before Rick Warren solved all of these problems forever.

Check it out.