Justin Snedegar

I'm taking a Probability and Epistemology class with Kenny Easwaran and Jim Van Cleve this semester. We've been looking at various representation theorems, and examining the axioms. One seemingly plausible axiom is from (Joyce's presentation of) Savage's theory, called "Independence". Joyce (from Foundations of Causal Decision Theory, pp. 85-85) tells us that this axiom tells us that "a rational agent's preference between [actions] A and A* should not depend on what happens in circumstances where the two yield identical outcomes." Joyce gives brief intuitive motivation for this axiom: "Given that A and A* produce equally good results when E is false it is plausible to think that any reason for preferring one to the other would have to be based on an assessment of their relative merits when E is true."

The idea is that any rational agent's preferences will satisfy the axioms. So, a counterexample to an axiom would be an agent who is rational, but whose preferences do not satisfy the axiom. As a possible counterexample to Independence, Kenny presented the Allais Paradox. It goes like this:
Imagine you have a (well-shuffled) deck of 100 cards, numbered 1-100. In the first scenario, you choose between A1 and B1:

A1:
If card number 1 is drawn, you win $0 (1% chance)
If any of cards 2-10 are drawn, you win $5 million (9% chance)
If any of cards 11-100 are drawn, you win $0 (90% chance)

B1:
If card 1 is drawn, you win $1 million
If any of cards 2-10 are drawn, you win $1 million
If any of cards 11-100 are drawn, you win $0

Next, you are asked to choose between A2 and B2:

A2:
If 1 is drawn, you win $0
If 2-10 are drawn, you win $5 million
If 11-100 are drawn, you win $1 million

B2:
If 1 is drawn, you win $1 million
If 2-10 are drawn, you win $1 million
If 11-100 are drawn, you win $1 million

Apparently, most people will choose A1 in the first game, and B2 in the second. This isn't supposed to seem irrational. But, since each of the pairs A1 & B1, and A2 & B2, are identical with respect to what happens when cards 11-100 are drawn, all that should matter, according to Independence, when it comes time to choose is what happens when 1-10 are drawn. But, in the first game, people want to pick the first option, while in the second game, people want to pick the second option, even though, once cards 11-100 are taken out of consideration, the pairs become identical. Satisfying Independence would require choosing either both A's or both B's. So, if Independence is a good axiom, rationality should require the same. But, it doesn't seem to. So, we have a counterexample to Independence.

I'm not sure what to think about this. There are reasons to think that the choice of first A1, and then B2, may be irrational, or at least motivated by non-rational motives. One of these may be risk-aversion. In the second game, choosing B2 guarantees you $1 million, while choosing A2 gives you a (small) chance of walking away with nothing. In the first game, you have a good chance of walking away with nothing with either option. So, if card 1 gets drawn and you chose A1, you may not feel so bad. But, if you could have had a guaranteed million dollars in the second game, and end up with nothing, you may feel worse. Also, I bet that the results would differ if we were dealing with smaller amounts of money, say $0, $1, and $5, or even $0, $100, $500. Is this irrational? I don't know, but it may cast a little doubt on the Paradox's status as a true counterexample.

Justin Snedegar

This might be fun:

What are some philosophical views that you really want to be true, but are pretty sure they aren't? Maybe the view would solve a lot of problems, or would really streamline your overall picture, or is just really, really cool; but, unfortunately, it seems to have one (or two) fatal flaws of its own.

This post has 2 points: (i) it will be fun to see what views people pick, and (ii) maybe someone will put up a view with a supposedly fatal problem, but someone else will know of a solution to the problem.

I'd like it if Chisholm's agent causation view were correct. It would help out a lot in the free will and moral responsibility debates (and be so empowering!). But, I feel like it's not true, unfortunately.

Josh May, UCSB

FYI, the video of Saul Kripke's talk on the first person that he gave at CUNY awhile back is available on Google Video now.



This is what was shown at UCSB's philosophy of language conference not too long ago when Kripke couldn't make it.

Note: The video is also up on CUNY's website and even available for download there. Here's the link:

http://web.gc.cuny.edu/Philosophy/events/kripke_conference.html

Justin Snedegar

I remember talking about this at some point when I was an undergrad. What is the best way to understand "If I were you..." sentences? Taken literally, they seem to be counterfactuals with impossible antecedents (given some plausible views about identity). I don't think that's a good analysis of what we mean. One way of understanding

(1) If I were you, I would x.

seems to be

(2) If I were in your situation, I would x.

Will this work? I think it misses something. Imagine that you are trying to decide whether to x. As it turns out, though, you have good reasons not to x. I, however, do not have reasons not to x. It seems that in this situation, I could say (2), but may not want to say (1). This isn't a strong intuition, and I suspect that's because there's a closely related way of understanding (1):

(3) If I were in your situation, with your reasons, beliefs, desires, etc., I would x.

(This may be just a more detailed version of (2) if we want to include things like beliefs, desires, reasons, etc. in what we call one's situation.) Does (3) work? Imagine you're trying to decide whether to x. It seems that I can still say (1), even if I know that you have beliefs that, if true, would give you reason not to x. If I know that some of your beliefs that give you such reasons are false, it seems that I can still say (1). But, I may not want to say (3). I suppose the main reason I don't want to say (3) is that it seems to downplay the advice-element of (1).

So, is this a better way to understand (1)?

(4) You ought to x.

This definitely captures the advice element, and seems to take reasons into account. But, imagine I'm a weak-willed sort of person. Doing x requires some personal sacrifice, but is clearly what you ought to do. In this case, I would say (4), but not (1). Here's a situation. You have the opportunity to give half of your money to charity. You don't really need the money, but it's always nice to have extra. It seems that you really ought to give your money to charity. But, it seems I can truly say something like "Man, it's definitely what you ought to do, but if I were you, I wouldn't."

Thoughts?

Josh May, UCSB

Mark Schroeder (USC) talks about his recent book Slaves of the Passions (OUP, 2007):



http://bloggingheads.tv/diavlogs/15404

Justin Snedegar

I remember seeing this argument in my undergraduate metaphysics class. I don't remember where it came from originally, or specifically what conception of universals it was against. So, this post has two points (i) to present the problem, and hopefully encourage discussion, and (ii) to ask where to find this (or the cleaned-up version of this) argument.

We postulate universals to make our claims like "The blue car and the blue pen have something in common" true. What the car and the pen have in common is the universal blueness.

So, the argument takes the form of a dilemma:

Either blueness instantiates itself (is blue), or it does not.

If blueness instantiates itself, then we can make a true claim like "The blue car and blueness have something in common". What does blueness have in common with the blue car? It seems weird to say that it is blueness itself. So, it must be super-blueness. But then, we can ask if super-blueness instantiates itself. If it does, we get the same problem. If it doesn't, we get the second horn of the dilemma at the 'super' level.

If blueness doesn't instantiate itself, then presumably neither does redness. So, there is something that blueness and redness have in common, namely non-self-instantiation. So, we can ask: does the property of non-self-instantiation instantiate itself? Now, we get a Russell's Paradox.

Here are three quick replies:

(i) Bite the bullet and say that what blueness and a blue car have in common just is blueness.

(ii) Hold that universals themselves do not instantiate universals.

(iii) Allow universals to instantiate other universals, but claim that non-self-instantiation is not a genuine universal. Perhaps you can point to the fact that it leads to a paradox as reason to make this claim.

Thoughts?

Josh May

Is seems to me that abstracts are much less common in philosophy than in other disciplines. Whenever I look into, say, some psychology literature, nearly every paper on ingenta, etc. has an abstract. It's way helpful when you're sifting through a bunch of literature and trying to figure out whether to read the article or not.

Of course, there are philosophers who house drafts of their own papers with abstracts on their own sites. Take Richard Holton or Stephen Finlay, for example. (Thanks guys!) But I'd really like to see the movement more widespread in the discipline.

Am I way off on my claim about the lack of abstracts in philosophy? If so, I still maintain that abstracts should be more common in any discipline. But if I'm not wrong, then why are there not more abstracts in places where philosophy articles are housed? I know journals very often require an abstract with submission, but then they just dump the abstract and publish the article. Is the abstract the philosopher's kryptonite? Is there something inherently evil about abstracts?

Justin Snedegar

Check out the new site that Andrew Cullison is putting together. It's a social bookmarking site which allows users (professional philosophers and graduate students) to submit and vote-up philosophy-related blog posts, unpublished papers, and journal articles. There is a ton of stuff on there already, and it's awesome.

Also, I hope everyone is OK after the earthquake today. Lewis and I were together here in LA, and didn't even notice. One of my friends from back east called to check on us, and that's how I found out about it.