Thursday, November 29, 2007

Limitations vs Generality Constraint?

If I understod it right, in the first part of Pepa’s yesterday seminar Oscar talks about there was an argument from the limitation of discriminative powers of a given perceptual system of representation to the failure of generality constraint. I wasn’t clear however how the argument could succeed.

Suppose the pigeons discriminate between 40 pecks and 50 pecks but fail to discriminate between 48 pecks and 50 pecks, so that are able to think:

(1) 40 pecks is different from 50 pecks.

(2) 40 pecks is different from 48 pecks.

It seems true that due to the limits alluded to the pigeons can not think

(3) 48 pecks is different from 50 pecks

as opposed to

(3#) 50 pecks is different from 50 pecks.

But in order for generality constraint to be put in jeopardy it seems one would need the lack of ability to think (3) (and thus (3#)) period, and nothing about the limitation mentioned seems enough to substantiate this latter contention.

I might be misconstruing something in the situation, can anyone help?

Wednesday, November 28, 2007

On inference relations and constituents of representations

Today Pepa Toribio gave a thoughtful and dense talk on nonconceptualism, and the very beginning of it she told us that
"For to contentful mental states to be inferentially related, they ought to have at least one constituent in common"
That puzzled me, because it seems easy to give examples of inferences in which none of the premises share a constituent with the conclusion. Take for example the inference from "b is red" to "There are non-blue things". The inference works because "red things are not blue" is analitically true (though not being logically true, or true in virtue of the sintax alone.) Does anyone else shares my feelings?

Saturday, November 24, 2007

St. Petersburg Paradox -Where are you?

During our last sesion on Decision theory, we were discusing on St. Peterburg paradox.

We, at least partially, agree that there is a paradox even if there is no infinite utilities. I will briefly defend that this position does not resist a simple mathematical analysis.

On the asumption that there are no infinite utilities the St. Peterburg game is perfectly acceptable:
I would bet 2utilities for getting 2utilities if the coin lands heads and 4utilities if the second time that I flip the coin it lands heads again. The game seems to be completelly fair. And so are the following games where:

The fist column represents the maximum price of the game. This would be 2utilities if the coin is flipped only once, 4 if it is flipped at most 2 times, and so on. In general 2 to the power of n where n is the number of times that the coin can as much be flipped.
The second represents the probability of each case.

The third column represents the expected utility (how many utilities should I pay to play the game).

Premium Probability % EU Result
0 50,0000000000 0 -20
2 50,0000000000 1 -18
4 25,0000000000 2 -16
8 12,5000000000 3 -12
16 6,2500000000 4 -4
32 3,1250000000 5 12
64 1,5625000000 6 44
128 0,7812500000 7 108
256 0,3906250000 8 236
512 0,1953125000 9 492
1024 0,0976562500 10 1004
2048 0,0488281250 11 2028
4096 0,0244140625 12 4076
8192 0,0122070313 13 8172
16384 0,0061035156 14 16364
32768 0,0030517578 15 32748
65536 0,0015258789 16 65516
131072 0,0007629395 17 131052
262144 0,0003814697 18 262124
524288 0,0001907349 19 524268
1048576 0,0000953674 20 1048556

For the example assumme that I have a lineal utility function regarding money between 0 and 1million euro (hard to believe but assumme that that is the case) and that the utility of 100M € equals the utility of 1M for me. The function saturates at 1M. (if you are not convince, for 30€ you can earn up to 1billion €, and I think that that is enought to saturate definitely the utility function of all of us).
The fouth column shows the money I would win or lose depending on the result of the game.
If you are having doubts on whether to play the game or not is because the utility of money is not linal for you and therefore: U(1M€) is not equal to 50000*U(20€).

In this case you would pay less money to play the game, but this is completely compatible with decision theory. Think of something wich utility is lineal in this range and you accpet the game (psichological reasons to avoid betting are out of the question) as you clearly see when the game is propossed to win just 4€.
The paradox is expressed in terms of utilities so have to find something which utility is lineal between 0 and 1M.

The real problem arises just in case we consider infinite utilities (no matter whether they are lineal or not). Imagine that more money has always a higher utility, so the utility function of money is a monotonically strictly increasing function in any interval. Then there is a problem, because at the limit the price is infinite...
The expected utility of any lottery involving an infinite price cost infinite no matter what the probability is. This two lotteries has the same cost (infinite):









You should prefer the second lottery to all that you have and that is obviously unacceptable. The solution: there are not infinite utilities.

The problem with lower probabilities is just that we are not able to find any utility that satisfies that lottery and therefore it is difficult to find an interpretation of paying 250 utilities to play this lottery.



But that says absolutely nothing against the decision theory.

The St. Petersburg game is only a problematic if we consider infinite utilities.

Friday, November 23, 2007

C&R Zeman: A Closet Contextualist?

According to David Lewis (1980), a context is a location (spatiotemporally centered world) where a sentence may be said (but need not contain any utterance nor speaker at the center etc.), and thus has countless features, and an index is an n-tuple of shiftable features of context. Moderate views have it that a sentence s is true at a context c iff s is true at c with respect to the index of that context i_c; and radical relativist views such as MacFarlane's depart from that.

With respect to this framework, one can characterize contextualist versions of moderate relativism endorsing the appearances of sentence s being true at c (wrt i_c) while false at c* (wrt i_c*); and in turn one can distinguish indexical contextualism (having it that this is true in virtue of s having a different content at c than c*) from non-indexical contextualism (having it that s has the same content at c and c* but that determines a different value wrt i_c than wrt i_c*.

Contexts in this sense are very rich. In particular, there is nothing as the epistemic situation (or standard or whathaveyou) of the context. There is that of the speaker at the center of the context (if one), that of the attributee of the utterance at the center of the context (if one), that which is salient in the conversation that takes place near the center of the context (if one), and so on and so forth. As Dan Z points out, this richness of contexts tends to be neglected in some discussions about knowledge attributions, and more sophisticated versions of indexical contextualism would presumably exploit this. (He still thinks that the view suffers from other “quite serious” difficulties so that it is “likely” that it will fail. I’m not convinced, but let’s discuss that in some other occasion.)

As I understand his own positive proposal, he claims that the attributions have the same semantic value across context, but are evaluated differently with respect to different indices of these context—where the epistemic standard of the context that figures as a coordinate in the index need not be that of the subject at the center of the context, nor the attributee, but is the highest (I guess among those that are relevant in the conversation that takes place near the center). But thus his seems to me to be a version of non-indexical contextualism and not radical relativism proper!

Wednesday, November 21, 2007

Ways of Doing Otherwise?

Today, at the LOGOS Colloquium, Carlos Moya (València) presented his views on how to defend the principle of of alternate possibilities (PAP) from Frankfurt-like cases, which he published as chapter 2 of his Moral Responsability (Routledge 2006).

In a nutshell, and if I didn't misunderstand his presentation (I haven't read the chapter), the main idea was the following one. John's being responsible for murdering Smith doesn't contradict PAP, for John could have done otherwise after all: he could have merely involuntarily killed Smith.

(Carlos originally stated this in terms of unintentionally killing Smith, but as issued in discussion with Prades, the notion of intentional action in place cannot be merely that of action appropriately caused by beliefs/desires, and Carlos replied he was happy rephrase it in terms of (in)voluntary action.)

I worried, in connection with Jose's, that this seemed to be dangerously close to the following (unsatisfactory, I take it) general way of dispelling any possible counterexample to PAP: if the agent is responsible, s/he could always have done otherwise, for s/he could always have done the "corresponding" thing without being responsible. It was hard for me to see how the sense in which the act of murdering and the act of involuntary killing someone (in the Frankfurt situation) were "different actions" could fail to vindicate that same sense in the latter, trivializing case.

Thursday, November 15, 2007

Imagining Scientific Models?

Yesterday, at the LOGOS Seminar, Roman presented his views on scientific models (see also Manolo M’s discussion).

I was very sympathetic to Roman’s contention that “going fictionalist” in debates in metaphysics or the philosophy of mathematics of the philosophy of science need not help much—unless, of course, one has an illuminating general theory on fictions, and is in a position to substantiate the claim that the problematic entities are indeed fictions, in the sense of the theory.

This was indeed the aim of Roman’s paper, dwelling upon the “pretense theory.” As he himself acknowledged, there might be general problems with the view—what if the key normative notions employed ultimately make no sense—and specific problems with the intended application to scientific models—what if the sensible generation principles are relatively trivial, and the only truths in fiction are very close to the surface?—. In particular, I worried that there seemed to be a crucial disanalogy between literary works and descriptions of scientific models: although talk about imagination makes perfectly good sense in the former case, it seems to be at best metaphorical in the latter. As Roman seemed to agree in discussion, the relevant kind of act seems to be more that of consideringas opposed to imagining, I would say. But then the worry was that the contrast with the alternative so-called “formal” approaches turn out to be much less clear after all, as also pointed out by Jose.

Roman on fiction and models

In yesterday's session of the Logos Seminar, Roman Frigg made the interesting suggestion that scientific models -such as ball-and-stick molecular models or simple pendula, with their massless strings and their point masses- should be understood as being similar in kind to literary fictions -such as Sherlock Holmes or Godzilla. Furthermore, he proposed that the best treatment for these is one along the lines of Walton's acts of make-believe.
I had doubts about one of the arguments he presented for treating models as fictions:

(The Semantic Argument) The simple pendulum equations are not true of anything -they would only apply to pendula with a massless string and a point mass, shielded from all forces but a uniform gravitational field, or something like that. Therefore, between the equations and real pendula we must postulate an imaginary something -a scientific model- to which the equations would faithfully applied, if it existed.

In fact, Roman's aim for the talk was to consider the relation between ourselves and the scientific model -relation he spelled out in terms of acts of make-believe- and not the relation between model and world.

But I would have said there is another option to deal with the lack of conformity between the simple pendulum equation and real pendula: the relevant singular terms in the equations do really refer to pendula; it is just that the equations misrepresent them. Actually, they don't misrepresent them that much; this is why the equations are useful. Wouldn't this get rid of models-as-fictions in the case of pendula?
A way to drive this point home, maybe, is to consider a history book in which several things are said about World War II, some of which are false: that Spain sent troops to Germany, maybe. Couldn't we mount an analogue to the Semantic Argument above to the effect that there is a fictional war involved in our understanding of the text?

(The Semantic Argument - WWII version) The sentences in the history book are not true of anything -they would only apply to a war in which Spain did send troops to Germany. Therefore, between the book and the real war we must postulate an imaginary something -a fictional war- to which the sentences would faithfully applied, if it existed.

But we feel no temptation to postulate such a fictional war: it is just that the book misrepresents WWII.

Another question in this connection: does it follow, if Roman is right, that there is a fictional model between ball-and-stick molecular mock-ups and real molecules, one in which atoms are spherical and rigidly bonded to one another? I'm not sure that it follows, but if it does, that is surely less natural than simply say that such a ball-and-stick mock-up truly represents the molecule of, say, cyclohexane, just like a map of the London Tube truly represents the London Tube.

Thursday, November 08, 2007

(How) Is the Present Special?

Yesterday, at the LOGOS Seminar, Sven presented his views on how to account for the intuition that the present is special, taking anti-presentism for granted.

Unfortunately, I’m very unfamiliar with debates on these extremely complicated issues in the philosophy of time—so that for instance it wasn’t clear which was exactly the content of the invoked intuition, nor thus what would qualify as vindicating it, and in particular why it didn’t work the proposal that it consisted in the present time exemplifying the irreducible property of being present. In any case, I worried how Sven proposal in terms of the present times occupying the object NOW ultimately differed from the considered proposal. In discussion, some other people seemed to share this concern. (If I don’t misremember, Sven suggested that his could work without the metaphor of “occupying” that object, by invoking relations of variable temporal distance to an object (which is therefore not a time). But as it issued in discussion with Sebas, it’s not clear that the latter notion is more illuminating than the former.)

On reflection, I also share Manolo M’s other concern: there seems to be as much reason to posit NOW as to posit also TOMORROW, TWO DAYS AGO, and so on. Thus, at each moment, every time occupies one of these “transcendental” positions. The original worry would then reappear: in which sense is NOW special?

Any thoughts?

Thursday, November 01, 2007

Teleology and Indeterminacy

Yesterday, at the LOGOS Seminar, Manolo M presented two ideas for responding to Fodor on teleological/functional solutions to the “Disjunction Problem.”

I haven’t (re-?)read Fodor’s stuff yet, but if I followed correctly, Fodor's general point was that there arguably are pairs of distinct properties such that, nonetheless, there is no fact of the matter as to whether a given mental state has the function of signalling one as opposed to the other. (As Oscar remarked, plausible examples might be harder to come with if a restriction to natural (enough) properties is in place.)

This sounds right. But, as Sebas also worried, it’s not clear in which sense the resulting indeterminacy is not precisely one the defender of the teleological/functional proposal would independently predict and willingly embrace.

Any views?