Dilemma re: (Platonist) Structuralism

I've got to go reread my Shapiro. But before his smooth writing bewitches me, let me note down the very simple objection that I am currently unable to see how he would answer.

Structuralism is traditionally motivated by the desires to address a problem from Benacerraf: that there are multiple equally good ways of interpreting talk of numbers as referring to sets, so that either answer to "what set is the number 3" seems unprincipled. But now:

If you are not OK with plentiful abstract objects, you can't believe there are abstracta called structures.

If you are OK with plentiful abstract objects, then you can address this worry by just saying that the numbers and sets are different items. Certain mathematics textbooks find it useful to speak as though 3 were literally identical to some set, but this is just a kind of "abuse of notation" motivated by the fact that we can see in advance that any facts about the numbers will carry over in a suitable way to facts about the relevant collection of sets named in honor of those numbers. One might argue that analogous abuse of notation happens all the time in math e.g. writing a function that applies to Fs where you really mean the corresponding function that applies to equivalence classes of the Fs. This route seems like a much less radical move than claiming that basic laws about identity fail to apply to positions in a structure e.g. there is no fact of the matter about whether positions in two distinct structures (like the numbers and the sets) are identical.

Cog Sci Question

[edited after helpful conversation with OE where I realize my original formulation of the worries was very unclear]

I was just looking at this cool MIT grad student's website, and thinking about the project of a) reducing other kinds of reasoning to Baysean inference and b) modeling what the brain does when we reason on other ways in terms of such conditionalization.

This sounds pretty good, but now I want to know:

a) What is a good model for how the brain might do the conditionalization? Specifically: how could it store all the information about the priors? If you picture this conditionalization in terms of a space of possible worlds, with prior probability spread over it like jelly to various depths, it is very hard to imagine how *that* could be translated to something realizable in the brain. It seems like there wouldn't be enough space in the brain to store separate assignments of prior probabilities for each maximally specific description of a state of the world (even assuming that there is a maximum "fineness of grain" to theories which we can consider, so that the number of such descriptions would be finite).

b) How do people square basing everything on Baysian conditionalization with psychological results about people being terrible at dealing with probabilities consciously?

Google turns up some very general results that look relevant but if any of you know something about this topic and can recommend a particular model/explain how it deals with these issues...

Putnam Indeterminacy Dilemma

Putnam uses Skolem's theorem (every consistent first-order theory has a model whose domain is the integers or some subset thereof) to argue that the meanings of our sentences are indeterminate.

If considerations of elegance CAN make something a more natural candidate for the meaning of a given word (e.g. someone with behavior that doesn't distinguish between plus and quus means plus), then the mere existence of some (clumsly and arbitrary) Skolem model doesn't pose a problem for our meaning something definite - since the Skolem model's interpretation of expressions like "all possible subsets" will be much less elegant than the natural one.

If considerations of elegance CAN'T make something a more natural candidate for the meaning of a given word, then Putnam is wrong to assume that even the meanings of the first order logical connectives which his perverse Skolem model captures are pinned down. For why think that we mean 'or' rather than a quus like version of 'or' that starts behaving like `and' in sentences longer than a billion words long?

Old Evidence and Apologies

If the problem of old evidence for Bayesian epistemology is just the following, then I don't think it's a problem:

Sometimes it seems like we should change our probabilities based on discovering logical consequences of a theory, but Bayesian updating only involves changing probabilities when you make a new observation.

For (it seems to me) this objection has the same ultimate structure as the following, surely bad, objection:

Sometimes it seems like we should apologize, but obeying so-and-so's moral theory involves never wronging anyone - and hence never apologizing.

If old evidence E is logically incompatible with hypothesis H, then Bayesianism says that you should *already* have ruled out all the worlds where H is true, and changed your probabilities accordingly, whenever you observed that E. So, I see no problem for the Bayesian epistemologist in saying that when you discover that you have failed to update in the way required by the theory (by not noticing a logical incompatibility), you should fix the mistake and change your probabilities accordingly.

[Compare this with the following popular intuition in ethics: you should promise to visit your grandmother and then visit her, but given that you aren't going to visit you shouldn't promise to visit her.]

Obvious vs. embarassing mistakes

As you've probably noticed, this blog has been on a bit of a hiatus. I'm going on the jobmarket this year so things have been very busy. I do have a little time now though, to note something about the relationship between two phenomena that are ubiquitous in my life :)

Not all obvious mistakes are embarrassing mistakes. Any mistake you make while adding two numbers will be an obvious mistake, but nearly everyone doing calculations makes such mistakes some fair fraction of the time, and these errors are not (intuitively) embarrassing mistakes.

further questions:
-Is being obvious once pointed out a necessary condition for being an embarrassing mistake? [edit: appropriately enough, i had originally put "sufficient" :)]
-Is the mere fact that a mistake is made with high frequency in some community sufficient to prevent it from being an embarrassing mistake? (maybe inferring the consequent is made with high frequency yet also embarrassing).
-Will trying and failing to give principled necessary and sufficient conditions for a mistake being embarrassing make one feel less embarrassed by embarrassing mistakes?

[hat tip to E.M. for suggesting this would make a cute post]

On Moral Philosophers' Library Fines

I just listened to this neat conversation, which summarizes some empirical research into the question of whether thinking about moral philosophy makes you any better at behaving morally. It turns out moral philosophers are actually slightly more likely to steal library books than philosophers in other areas, and political philosophers are no more likely to vote than people in other profession.

The speakers mention that these results are surprising, since they conflict with the hope that researching moral philosophy will have morally good effects.

Now I'm pretty skeptical about moral philosophy myself, for other reasons, but here's what the moral philosophers would/could say for themselves on this score:

"The phenomenon of weakness of the will, means that there are two components to doing what's good: the epistemic component of figuring out what's morally better/required in a given case, and then the practical component of actually doing that.

Moral philosophy only pretends to address the first component. Thinking hard about weird trolley cases, and abstract moral principles helps you figure out what you ought to do in cases where this is unclear. It doesn't address the second component of acting well - working up the will power to actually do what you ought to.

In this way, moral philosophers are like scientists who study fistfights not professonal boxers. They spend a long time studying the differences between different principles that only make a difference to what one should in principle do in certain rare cases. They don't spend this time practicing up their personal ability to implement the overall art of fighting well.

For this reason, testing whether moral philosophers are more virtuous in cases where it's *obvious*/uncontroversial what's virtuous (you should return library books, you should vote) exactly fail to capture the benefits that doing moral philosophy brings. Studying moral philosophy helps society make the world better, because the moral philosophers work out what we should do in novel, or controversial cases. This doesn't mean that it makes moral philosophers themselves substantially more virtuous. For, in most of the cases where ordinary people have a chance to act badly (adultery, embezzlement, falsifying data, refusing charitable aid) the limiting factor isn't *figuring out* what the right thing to do is, but rather summoning the willpower to sacrifice individual pleasure and benefit to do whats right."

Maybe this was obvious to everyone else

If Fodor thinks that elements in the language of thought get their meaning from counterfactuals about assymetric dependence (HORSE means horse, not horse-or-cow-on-a-dark-night, because if tokenings of HORSE hadn't tracked horses they wouldn't have tended to track horses-or-cows-on-a-dark-night either), what does he say about Swampman?

Since Swampman is supposed to have come into being from random electrical activity, none of these counterfactuals about different response patterns which Swampman could have had seem well defined. Does Fodor say that Swampman wouldn't be thinking?

I guess Davidson (who came up with the example) bites this bullet. But it seems like the exact kind of intuitions that motivate accepting mental representation in the first place (you could have just the same phenomenology, if you were paralyzed so you had no dispositions to use any external language; surely this should suffice for you to count as having thoughts) rebel at the idea that Swampman wouldn't be thinking.