Against Causal Decision Theory?

Too bad I missed last session of LOGOS RG on DT, where people discussed Andy Egan's 'Some Counterexamples to Causal Decision Theory'. Did anyone get why exactly CDT predicts that Paul should press the button?

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?

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?

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):

1,00%	99,00%
0	infinite
99,99%	0,01%
0	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.

99,99%->0

0,01%->25000000

But that says absolutely nothing against the decision theory.

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

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!

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.

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 considering—as 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.

(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?

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?

New e-Discussion Group on Contextualism & Relativism

In addition to the regular LOGOS Reading Groups, we are planning to run an informal e-discussion group on contextualism and relativism.

Following the format of last year e-RG on meta-metaphysics, the idea would be to have the discussion every two or three weeks here at The bLOGOS, so everybody is welcome to participate, regardless of whether you are sited near Barcelona.

We would be mainly discussing papers by ourselves. It is my pleasure to announce that the first paper to get this started will be Dan Zeman's 'Knowledge Attributions and Relevant Contexts'. New posts discussing this paper are to be expected around 2 November, with titles starting with ‘C&R Zeman.’

As for further e-sessions, I’d like to suggest López de Sa 2007 and Kölbel 2007 exchange (on Kölbel 2004, to which Dan Z also refers). Any other suggestions? Please give them in comments, and add links if available.

DT RG: Carcel Confusion

This pertains to the reading group on decision theory, but any comments are welcome.
It's my version of the Three Prisoners Paradox. I read about the original paradox years ago in a book about the Monty Hall Problem, and I always assumed that it was created as a variant of this problem. However, Wikipedia recently taught me that it's much older than the MHP, and that it's due to Martin Gardner.
Here goes the story (I assume you know about the Monty Hall Problem; otherwise, read the wikipedia entry first):
Three prisoners, A, B and C, are awaiting their execution. It's known to them that one of them will be pardoned, but part of their punishment is that they may not know who prior to the day of the execution. They are kept in separate cells in different buildings.
One day, as the prison guard comes to check on prisoner A, A begs him to give him a hint concerning his fate. Of course the guard declines, but A keeps begging. At least, A suggests, the guard could tell him the name of only one of the others who will be executed for sure. That way A would still not know whether he will die or live, and the guard wouldn't have disobeyed his orders.
The guard thinks it through and mercifully agrees to give the required information: B will die. A thanks the guard and thinks to himself: "Well, at least I know that my chances to get out alive are 50% now."
So far, so good. Anyone familiar with Monty Hall will see that A is wrong. His chances are still 33%, the guard's revelation has gained him nothing. To draw the analogy to Monty Hall, he should switch fates with C if only he could. If we, the audience, were the type of people who bet on people's lives and deaths, we should put our money on C's staying alive.
That's the Three Prisoners Paradox as I remember reading it in the book. Now my appendix:
The guard passes by the cell of poor B, who is sound asleep, and finally comes to C. Here, a similar scene as before unfolds. C implores the guard to tell him something about his situation. The guard recalls his talk with A, goes through the reasoning once again to make sure he's not disobeying his orders, and tells C that B is going to die. "Whoopy!", thinks C, "So my chances to survive are 50%!!" But of course we know that this is false, his chances are 33%.
To sum up, we have A at a survival-chance of 33%, doomed B at 0% and C at 33% as well. But that seems a bit odd...
I've been puzzled by this for a long time, and I've asked a bunch of people and received a bunch of interesting and interestingly different answers. I think I know what's wrong, but I'm never quite sure (about 66% most of the time), so I await clarification(s)!

CFP: LOGOS Conference on Meta-Metaphysics

LOGOS Conference on Meta-Metaphysics
Barcelona , 19-21 June 2008

First Call for Papers

Do numbers, sets, and other abstract entities, exist? Does mereological composition ever occur? Does it always occur? How do objects persist through time? In recent years, there has been an increasing interest in the status of certain traditional debates in metaphysics such as these. Some think that some of these turn out to be genuine disputes but of a semantic or conceptual character. Some think that some of these turn out to be pseudo-disputes that should be just dismissed. (Some others think, of course, that the disputes are indeed genuine, but not of a semantic or conceptual character.) Reflection of these issues promises to shed light on the nature of philosophical inquiry in general.

LOGOS—Grup de Recerca en Lògica, Llenguatge i Cognició is organizing a conference on meta-metaphysics. Invited and submitted papers will be made available to participants one month before the conference. Participants are expected to read them in advance, as there will be no presentation of them during the conference. Sessions will start with a critical commentary (lasting 20 minutes at most), followed by a response by the author(s) (lasting 10 minutes at most) and a general open discussion period.

Proposals to participate as a speaker and/or as a commentator should be sent by e-mail to logos@pcb.ub.es by 1 April 2008. Full papers in suitable form for blind refereeing should be submitted in order to participate as a speaker, and a short CV is to be supplied as to participate as a commentator. We expect to notify accepted proposals within four weeks of the deadline.

Participants other than invited speakers will have to rely on their own institutions to defray the cost of travel and accommodation.

Confirmed Invited Speakers:

John Hawthorne (Oxford )
Amie Thomasson (Miami)
Stephen Yablo (MIT)

Organizing Committee:

Manuel García-Carpintero (Barcelona)
Dan López de Sa (NYU/St Andrews)
Pablo Rychter (Barcelona)

Scientific Committee:

Fabrice Correia (Rovira i Virgili)
Manuel García-Carpintero (Barcelona)
John Hawthorne (Oxford)
Max Kölbel (Birmingham)
Dan López de Sa (NYU/St Andrews)
Sven Rosenkranz (Barcelona/St Andrews)
Pablo Rychter (Barcelona)
Amie Thomasson (Miami)
Gabriel Uzquiano (Oxford)
Timothy Williamson (Oxford)
Stephen Yablo (MIT)

Further information:

logos@pcb.ub.es
www.ub.edu/grc_logos

Power-points to the point

This video reminds me some power-point presentations I've recently seen. Enjoy!

Nussbaum on India

Martha Nussbaum has written a surprisingly well-informed and insightful essay on the rise of fascism in India. Surprising, that is, for someone like me who isn't following her work very closely; she has just published a whole book about this issue. You have to give it to her, her scope is impressive.
Reading through the piece brought back memories of some downright scary discussions about this guy that I had in India. There is not much that is more distressing to a German than to be congratulated for this part of his country's history.
In case you're neither interested in Martha, Adolf nor India, read it for the sake of the good point she makes against over-pragmatically inclined educational systems.

MetaMetaphysics e-Reading Group: next session

Logos’ e-reading group on MetaMetaphysics is resuming, after a short period of inactivity. During the next e-session we will discuss “Fundamental and derivative truths”, a work in progress by Robbie Williams, available here. The e-session will start around May 30, here in the bLOGOS. Posts belonging to this session should be tilted “MM Williams: your title”

UPDATE: This has been postponed until the beginning of next semester.

Call for Intuitions

This came up the other day when I was talking with Brenda Laca over at the UAB. Consider:

We had lunch at twelve.

I agree (tentatively) with Prof. Laca that this means, as a matter of semantics, that the actual eating started at twelve. Thus it would be wrong to assert this sentence if the lunch went from eleven to one; in that case the right thing to say would be

We were having lunch at twelve.


Still, it seems to me that even in these circumstances, it wouldn't be right to contest the first assertion, at least not by saying something like

No you didn't!

If anyone shares these intuitions or has different ones, I'd be grateful to read about them!

Contexts and their Centers

According to David Lewis (1980), in order to capture how the truth of a sentence depends on features of contexts and its contribution to the value of longer sentences in which it is embedded, we need a semantically basic two-dimensional relation of a sentence s being true at a context c at an index i. A context is a location—time, place, and possible world, or centered world for short—where a sentence might be said. It has countless features, determined by the character of the location. An index is an n-tuple of features of context, but not necessarily features that go together in any possible context. Thus an index might consist of a speaker, a time before his birth, a world where he never lived at all, and so on. The coordinates of an index are features that can be shifted independently, unlike those of a context, and are used to systematize the contribution of sentences embedded under sentence operators, such as ‘possibly’ or, more controversially, ‘somewhen,’ ‘strictly speaking,’ and so on. Given a context c, however, there is the index of the context, i_c: that index having coordinates that match the appropriate features of c. Hence the basic two-dimensional relation can be abbreviated in this special case: sentence s is true at context c iff s is true at context c at index i_c.

According to David Chalmers (2006), there is a contextual understanding and an epistemic understanding of two-dimensional semantics. Although I am not familiar with the details of “this monster paper” (so described by his author ;-{)}), it seems to me clear that the Lewisian should be counted among the “contextual understanding” approaches, if any does: “the first dimension represents possible contexts of utterance, and the intension involved in the first dependence represents the context-dependence of an expression’s extension” (Chalmers 2006, p. 65) (This is not to say that it cannot be count as also being among the “epistemic understanding” approaches, but never mind this now.)

Notice, however, that Lewis’s contexts are worlds centered at spatiotemporal points, which may or may not be occupied by linguistic tokens, utterances thereof, thoughts, or whathaveyou. Thus, for Lewis, contexts are locations where a sentence might be uttered, but not necessarily locations which contain any utterance of any sentence. (Thus the models for contexts offered in (Chalmers 2006, p. 66) are not appropriate in general.)

One of the two general problems David Chalmers identifies against the contextual understanding of two-dimensional semantics concerns precisely the need to evaluate sentences such as ‘Language exists’ as false with respect to language-free contexts. Thus it seems to me to be directed only against particular versions of the contextual understanding which, unlike Lewis’s, restrict themselves to contexts with specific linguistic/mental centers.

Am I wrong? And anyway is there any reason why, on the contextual understanding, one should so restrict the contexts, against Lewis?

(I think Oscar will be arguing for such a restriction at the LOGOS Seminar. Maybe he’ll also share his reasons here…)

MM Chalmers: Schaffer on Furnishing Functions

In a part of ‘Ontological Anti-Realism’ which I didn’t comment on (§§8-11), David Chalmers considers an objection against anti-realism based on the idea that the absolute unrestricted quantifier has an objective, determinate semantic value. I don’t want to assess his response to the objection here (see related discussion here, and references there).

In order to analyse existence assertions, however, he tentatively introduces the notion of a furnished world—an ordered pair of a world and a domain—and a furnishing function—a mapping from worlds to domains—(see the end of §8).

In his comments to the paper, Jonathan Schaffer objects:

The argument for heavyweight realism about fundamental structure: Furnishing functions are maps from a world to a domain. But a function is a map from one structure (‘the input’) to another (‘the output’). One cannot have a well-defined function without there being some articulated structure to the input. In particular we must be able to specify the arguments of the function. Any function is either complete or partial. It is either injective or not. It is either surjective or not. None of these classifications would make sense unless the input (‘the world’) already comes with some fundamental articulated structure inbuilt, to feed into the function. … I conclude that the framework that Chalmers actually supplies is at least half-realist, in the sense that it presupposes heavyweight realism about fundamental structure. (pp. 2-3)

I am probably missing something here. For I understood that a furnishing function was a map from the class of worlds to the class of domains, whose arguments were precisely just worlds. Thus I don’t see why there being such mappings requires in any sense any “articulated structure” in the items to which the function is applied. Can anyone help?

Online Graphical Dictionary

http://www.visuwords.com/. Interesting ;-{)}!

(Thanks to E.B. for the link.)