Thanks to everyone for comments on the last post on voluntarism. There were lots of threads suggested there that I’ve been trying to follow up. Some of these led me to a recent (2002: 3) issue of the _Monist_ that had lots of relevant papers. A lot of what follows is suggested (obliquely) by John Cottingham’s paper on Descartes. I’ve also been reading (or rereading) some great papers by by “Richard Holton”:http://web.mit.edu/holton/www/pubs.html work on weakness of will and self-control. (See “this”:http://web.mit.edu/holton/www/pubs/Weakness.pdf famous paper on weakness of will, and “this”:http://web.mit.edu/holton/www/pubs/Provocation.pdf unpublished paper with Stephen Shute on provocation.)
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I’d drafted a long post on doxastic voluntarism and stuff, only to find “this paper”:http://web.stcloudstate.edu/msteup/Doxastic%20Freedom.pdf by Matthias Steup that makes some of the same points. I think I disagree with him over a few points, especially concerning the response to Feldman, but I agree with a lot of what he says. Much much more on this tomorrow.

In the meantime, here’s a comic strip about “pig philosophy”:http://www.partiallyclips.com/index.php?id=1455 that’s pretty funny. If you click through the link you’ll find a whole bunch of funny comic strips, which is convenient if you’re looking for new ways to put off jobs that really need to be finished over the weekend. (Hat tip: Geoff Pullum.)

I’ve been idly interested in Gettier cases in unusual locations for a while, at least in part to convince myself that they’re actually important, rather than just marginal philosophical cases.  Recently, I realized that there may be some that play important roles in literature.  However, the only one that came to mind is something I only very hazily recollect.  When I was young, I read several mystery novels by Agatha Christie.  In one, I seem to remember that the murderer had killed the victim in a very clever way and concealed the evidence extremely well, but used one more extra twist to protect herself.  (I believe it was a female murderer.)  She placed a lot of misleading evidence, that pointed to her having killed the person, but in a way different from how the victim actually died.  By framing herself, she hoped that the police would at first end up in a Gettier situation, with a justified, true belief that she killed the victim, but that once they saw through the flimsy framing evidence, that would throw them off the trail, so that she could get off without getting caught.  (Of course, in the end it didn’t work out for her.)

If anyone recognizes this story, it would be useful to have some more specific details, so that it can be used as an example.  And if anyone knows of any other cases that appear in literature, that would also be nice.  This one is nice also for illustrating why knowledge is much better than being Gettierized – as Timothy Williamson points out several times in Knowledge and its Limits, someone with knowledge is much less likely to get led astray than someone who merely has true belief, or for whom misleading evidence is available.  But I also think it may put some pressure on his conception of misleading evidence being only evidence for a false proposition, rather than Gettierizing evidence for a true one.

For a bit of fun, I wrote a note on the philosophy of flirting a while ago, which will shortly be appearing in The Philosophers’ Magazine. I’ve now posted a probably-final version. The main thesis I want to defend is that one cannot flirt without (in quite a weak sense) intending to do so. I therefore want to distinguish mere flirtatious behaviour from flirting proper. The inadvertantly flirtatious can, I think, fairly defend against accusations of flirting by denying having the intention. (But note that this does not absolve the inadvertantly flirtatious from all potential blame: mere flirtatious behaviour could be just as blameworthy as flirting in the wrong context!)

There are several questions about the relationship between belief and voluntariness that I’m planning to write about over the upcoming months. Several of these topics will be pretty familiar, but some might not be. (I’m interested in the role that doxastic voluntarism, or something like it, plays in Meditation Four, for instance, which is not as far as I can tell one of the big topics on the radar screen in contemporary philosophy.)

But those are for more serious posts. Today I just want to make a little observation. Philosophers often write as if it is obvious that we can’t decide to form beliefs. You might think that if this is obvious, then authors would never have characters, let alone narrators, decide to form beliefs. “But”:http://books.google.com/books?vid=ISBN0765341247&id=MyL99bXf_YkC&pg=PA157&lpg=PA157&dq=%22I+decided+to+believe%22&sig=837wA6oEE1hp6Gc_l_goZ5AN5Os “if”:http://books.google.com/books?vid=ISBN0595222900&id=ir778m3HJDgC&pg=PA56&lpg=PA56&dq=%22I+decided+to+believe%22&sig=fNWS97CZ5fpqypPaszpJXwvrdTc “you”:http://books.google.com/books?vid=ISBN0595345980&id=2NDKf8fdJXcC&pg=RA2-PA39&lpg=RA2-PA39&dq=%22I+decided+to+believe%22&sig=4XbQDx_d_X4-dG13w7Bdi72fNFc “did”:http://books.google.com/books?vid=ISBN0595391982&id=geGno9f9EC8C&pg=PA181&lpg=PA181&dq=%22I+decided+to+believe%22&sig=N_LPgJZu2C049TrWQci9b2Q4HNI “you’d”:http://books.google.com/books?vid=ISBN1595262997&id=jl9-gKr25UoC&pg=PA23&lpg=PA23&dq=%22I+decided+to+believe%22&sig=uczuxgGZZ20aKeWEg7jks82hXJE “be”:http://books.google.com/books?vid=ISBN0312323859&id=cYDSNpR3BK4C&pg=PA64&lpg=PA64&dq=%22I+decided+to+believe%22&sig=qwcscAfvCuXyqWXBoXVNd6cQsLA “very”:http://books.google.com/books?vid=ISBN0312286619&id=1696_VWQsnwC&pg=PA100&lpg=PA100&dq=%22I+decided+to+believe%22&sig=4CHgGaxDf-HMmyohKyPk0k9sUCg “badly”:http://books.google.com/books?vid=ISBN0060529741&id=T2q_1C_QttMC&pg=PA27&lpg=PA27&dq=%22I+decided+to+believe%22&sig=1U0PUEpAf4ZP3_oS94BJP8iYnTw “mistaken”:http://books.google.com/books?vid=ISBN0312964234&id=P6lDXF4m9u8C&pg=PA140&lpg=PA140&dq=%22I+decided+to+believe%22&sig=xmLLoI0mCyRgfUl4sT618p_Uqz0.

For what it’s worth, I suspect the psychological assumptions these authors are making are quite plausible. When someone tells us something that is plausible, but not such that we should obviously trust them, we have to decide whether we will, on this occasion, trust them. If we have no other reason to believe what they say, but trusting them will involve (perhaps inter alia) believing what they say, then we are deciding to believe.

“Terence Tao”:http://www.math.ucla.edu/~tao/, an Australian now working at UCLA, has won a “Fields medal”:http://www.theage.com.au/news/national/maths-man-is-number-one/2006/08/22/1156012542775.html?page=fullpage. I’m naturally very pleased to see an Australian Fields medallist. I also knew Prof Tao a little back when I was a high school maths student and he was a remarkable prodigy, having just become the youngest person to win a Maths Olympiad gold medal. I’ve always had this image, I think more from movies than anything else, that prodigies like that tend to burn out. Clearly he didn’t.

To give you a sense of how broad Tao’s work is, the work on prime numbers that was highlighted in the Fields citation is the seventh category heading on his preprints page. And he’s either editor or an editorial board member on four journals. Some days I think I need to work harder. In the meantime, congratulations to Professor Tao for some really remarkable accomplishments.

As many of you will know, Philosophical Review is moving to Duke University Press. What you might not know, what indeed I didn’t know until a few minutes ago, is that Duke has quite a nice “webpage”:http://philreview.dukejournals.org/ for the Review. If your institution subscribes to the Review, you should even be able to access recent issues (through April 2006) that are online. For many people that will mean that there are a lot of new Philosophical Review papers available for them to read!

UPDATE: Dave Chalmers pointed out to me that Duke is actually running a free trial of the Review website until September 27. So between now and then you can get any of the articles that you like. (And there are 20 or so articles that are posted that won’t have arrived by paper yet.) We might start some discussion threads on some of the papers here over that time.

At the recent Bellingham conference, Ted Sider (in discussion of a paper by Kadri Vihvelin) made what I thought was a very good point about dispositions and conditionals. What follows are largely reflections on how Ted’s point affects debates about free will. I don’t think many of my conclusions here are original – what I say ends up being pretty close to what Neil Levy says in “Frankfurt Finked”:http://au.geocities.com/neil_levy/Documents/articles/Frankfurt-finked.pdf (PDF), but perhaps the way I get there will be interestingly different. (And it is an excuse to display my Austinian tendencies in some detail.)

Consider the familiar example of the glass liked by a powerful sorcerer. The glass is a duplicate of my glass that will break if struck. But this glass won’t break if it is struck. The sorcerer will anticipate the strike and at that moment change the intrinsic structure of the glass so that it can handle being struck. Intuitively, the glass is still fragile, but it won’t break if it is struck. So the following identity is false.

* Being fragile = would break if struck

Now here is Ted’s point. From the example we know that not both of the following identities can be true.

* Being fragile = being disposed to break if struck
* Being disposed to break if struck = would break if struck

But the example alone *doesn’t* tell us which of the identities is false, just that one or the other is. Most of the recent literature on dispositions has focussed on the second identity as what is wrong. But once Ted raised it, it seemed to me that we should think again about the first identity.
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Over at “Crooked Timber”:http://crookedtimber.org/2006/08/11/ellery-eells-is-dead/, Harry Brighouse reports the sad news that his colleague “Ellery Eells”:http://philosophy.wisc.edu/eells/ has died. As Harry says, Eells’ combination of technical ability and philosophical insight was rare and valuable. I never met him, but both Harry and “Larry Shapiro”:http://leiterreports.typepad.com/blog/2006/08/in_memoriam_ell.html report he was also a wonderful person and colleague as well.

*UPDATE*: In comments Branden Fitelson, who was a student of Eells, has some memories of what Eells was like as a teacher and supervisor.

First of all, I’d like to thank Brian for inviting me to post here (like Gillian and Carrie, and some others that haven’t decided to say anything yet).

The topic I’m interested in is a parallel between the sorites arguments typical in discussions of vagueness and certain arguments for the adoption of strong new axioms in set theory. (I discussed some of those arguments in this post on my other blog.)

Basically, the idea is based on Gödel’s second incompleteness theorem. For every nice enough theory T (basically, T needs to be strong enough to represent basic arithmetic, and orderly enough that you can tell whether or not a given statement is an axiom), there is an arithmetical statement called Con(T) that says that T is consistent. However, for any such T, the statement Con(T) is neither provable nor disprovable from T itself. But if T has only true statements as axioms, then it must clearly be consistent, so T is incomplete. In particular, there is a true theory T’ that proves all the consequences of T, but also proves Con(T), and we should adopt T’ instead of T.

Because this argument then applies to T’ as well, we seem to either have to withhold judgement on our initial theory, or adopt a theory far stronger than what we started out with. (A recent post of mine discusses a parallel argument by Roger Penrose that claims to show that our mathematical knowledge is given instead by a non-computable theory.) Set theorists often use this argument to show that mathematicians who accept the axioms of ZFC (the standard framework most mathematicians tacitly accept as the foundations of what they do) must therefore accept much stronger principles as well, despite the fact that they can’t be proven.

I’d like to agree with the set theorists, but this argument reminds me of some fallacious reasoning in cases of vagueness. The idea is that for each theory T, if T is true, then T+Con(T) must be as well. This is similar to the claim that for every n, if n grains of sand don’t make a heap, then n+1 don’t either. The argument that shows mathematicians must accept every large cardinal claim that set theorists come up with is parallel to the argument that there are no heaps of sand. It seems plausible to me that whatever account of vagueness one has to block the heap argument could be adopted to block the set-theoretic argument. On the other hand, if a solution to the problem of vagueness doesn’t apply to the mathematical case (perhaps because it seems implausible to assign intermediate truth-values to mathematical claims or something), then one might see this solution as somehow lacking.

Some people might also run the sorites argument as a modus tollens instead of a modus ponens, saying that any number of grains of sand form a heap, and similarly that ZFC is not true (because adopting it as true forces them towards further claims about large sets that they have trouble believing).

A position like this is adopted by finitists, who accept claims about various finitary mathematical objects (like natural numbers, rational numbers, and the like) but only accept “potential infinities” (like a list that one can keep adding to) rather than “completed infinities” (like the actual precise value of some irrational number, or some non-computable set of natural numbers). However, most finitists accept Peano Arithmetic as a set of axioms, and a similar argument works starting with PA to drive one seemingly inexorably towards ZFC, and thus to the higher infinite.

The even more drastic solution accepted by some is known as ultrafinitism, on which one doubts even some “finite” numbers. In practice, these doubts arise about extremely large numbers, like a googolplex, which are believed to be larger than the number of subatomic particles in the entire universe. However, a similar sorites argument is going to cause trouble for the ultrafinitist – if the ultrafinitist accepts that the natural number n makes sense mathematically, then it would also seem that she should accept that the natural number n+1 does as well. (After all, one can just take the set of n things that one already has, and add this set itself as an element to create a new set!) If this is right, then once one accepts that even a single natural number makes sense, this successor principle pushes one inexorably towards at least full finitism, if not towards the infinite. The ultrafinitist has to reject the claim that every natural number has a successor, but it seems that she shouldn’t point to any number as “the last one”.

I’d like to use these arguments to show that once one adopts any amount of mathematics, one basically has to go “all the way to the top” in terms of the scales of infinity. However, these arguments seem to share troubling features with sorites arguments that we do want to block, so I’m interested in seeing what accounts of vagueness might do to them.

(The idea for this post originated in a class I co-taught last week with Mike Shulman to mathematically talented high school students at the Canada/USA Mathcamp.)