tag:blogger.com,1999:blog-6432111.post836409575165894954..comments2017-04-19T13:03:57.282+01:00Comments on Theories 'n Things: Degrees of belief and supervaluationsRobbie Williamshttp://www.blogger.com/profile/02081389310232077607noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-6432111.post-56747944546380725882009-11-23T13:35:28.661+00:002009-11-23T13:35:28.661+00:00Cool story as for me. It would be great to read a ...Cool story as for me. It would be great to read a bit more concerning this topic.<br />By the way look at the design I've made myself <a href="http://www.admirableescorts.com/high_class_escorts_london.html" rel="nofollow">High class escorts</a>123 123http://www.blogger.com/profile/09096049486330095076noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-18724015006855450542007-11-06T19:10:00.000+00:002007-11-06T19:10:00.000+00:00Thanks for explaining: I'd kind of guessed that th...Thanks for explaining: I'd kind of guessed that that's what you meant by 'measure' but always best to get these things spelled out when, like me, you aren't a mathmo. I'm really glad that you think that accepting (2) ends up undercutting lots of the motivation for standard supervaluationism - that's my impression too. <BR/><BR/>I guess that supervaluationists who go for (1) will have a choice: they can either accept something like degrees of intendedness for precisifications to explain the patterns of our credences in the kind of case I describe, or else they can appeal to uncertainty about the admissibility of precisifications, which is the option precluded by (2). But really the first option seems much better, since it avoids some higher-order vagueness stuff. And anyone accepting degress of intendedness should probably just go along with (2) anyway - thus even accepting (1) is going to lead to some pressure towards (2).<BR/><BR/>I really want to hear the degreed story about conventions of truthfulness sometime, 'cos I get the feeling that I'm not too keen on the implicit direction of explanation. But that can wait till you can explain in person.<BR/><BR/>One final comment: it may just be a quirk of philosophical etymology, but the phrase 'degree of intendedness' sounds very congenial to projectivism about meaning and vagueness...Daniel Elsteinnoreply@blogger.comtag:blogger.com,1999:blog-6432111.post-1385307429104152072007-11-05T22:34:00.000+00:002007-11-05T22:34:00.000+00:00Hi Daniel. I'm very unsure about supervaluationist...Hi Daniel. <BR/><BR/>I'm very unsure about supervaluationist sociology here. The idea that p&~Dp is a contradiction is a pretty entrenched doctrine, among those who think that supertruth is truth. And as I emphasised above, it would seem really peculiar to combine *that* with anything other than the non-classical handling of probabilities. So if they do go for (2), then I think there's some tension in their views unless they want to say the sort of things I do about the logic. Quite a few people with supervaluationist sympathies that I've spoken to also have sympathy for the Jeffrey idea about representing credence with sets of probability functions. As Ant and Kenny emphasize, its a very supervaluationist-sounding idea. As far as I can see, the principled way to fit that into the framework here is to go for (1). It'd be interesting to find examples where supervaluationists discuss this. I don't know of many places where its discussed.<BR/><BR/>I'm personally sympathetic to (2), and to the idea that credences of an ideal agent should match the degree of truth in the proposition (contra Edgington, from what you were telling me). But I guess I start to wonder about the utility of even talking about truth/supertruth once we've got degrees of truth on the table. If we need to go for (2) anyway, and so become a degree-supervaluationist, I think that undercuts the motivation for lots that standard supevaluationism usually says. <BR/><BR/>I think you're right to emphasize that we can't expect to be able to define degrees of truth by anything like "counting the number of precisifications" on which a given sentence is true.<BR/><BR/>The way I think of this, the basic notion of the degree-supervaluationist (a la Edgington, Kamp, Lewis) is not that of a class of admissible precisifications, but of the measure of an arbitrary set of classical interpretations. In the finite case, you can think of the measure of a single interpretation as its "degree of intendedness".<BR/><BR/>In the first instance, this gets you degrees of truth (as the measure of the set of precisifications where the sentence is true). There's then a question of whether and how to analyze the notion of truth simpliciter. On some options, you might end up agreeing with the letter if not the spirit of standard supervaluationism. And that's sort of the position I had in mind for (2) above. <BR/><BR/>If we're a degree-supervaluationist, we face the foundational question: what establishes degrees of intendedness? And that's exactly parallel to the question that faces a classic semanticist: what fixes one interpretation as the intended one; and the foundational question facing the standard supervaluationist: what fixes a set of of interpretations as admissible?<BR/><BR/>One answer, that you allude to, would be to appeal to some kind of projective story from the credences assigned by ideal agents. Another, which I've thought about a bit, appeals to a degreed story about conventions of truthfulness and trust in uttering sentences. I suppose a robust anti-reductionist could just take the measure as a metaphysical primitive. I'm sure there are other options.Robbiehttp://www.blogger.com/profile/02081389310232077607noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-65019349456533890342007-11-05T20:42:00.000+00:002007-11-05T20:42:00.000+00:00Robbie, I think I'd always assumed that supervalua...Robbie, I think I'd always assumed that supervaluationists would go for classical probability and your option (2), which probably goes to show how little I understand the motivations of supervaluationists.<BR/><BR/>A strange consequence though: if we interdefine degrees of truth with a measure on the admissible precifications, and also with expert degrees of belief, what we get is that an admissible precisification is just one which an expert would not assign credence 0 to being the correct precisification.<BR/><BR/>But that makes me think that supervaluationism is introducing problems which weren't there before. For instance, it seems pretty harmless to think that even an expert would have >0 (though very small) credence that a man with a billion hairs is bald. (I.e. the view that expert credence should be asymptotic to 0 as number of hairs tends to infinity.) But if we buy the measure on precisifications thing that will mean that precisifications counting billion-haired men as bald are admissible, and thus most admissible precifications make million-haired men bald.<BR/><BR/>We want to avoid the result that 'A man with a million hairs is bald' has a degree of truth close to 1, so I guess that for the measure on the precisifications to give the right answer the precisifications have to have something like intensities (corresponding to the credences that experts assign to them). But it doesn't seem to me that such intensities are part of a natural story about precisifications which doesn't see them as defined by credences. So in the unified credences-verities-supervaluationist position, it looks to be credences that wear the trousers.<BR/><BR/>Apologies if that's either obvious or obviously wrong, but I really struggle to see what work supervaluationism ends up doing.Daniel Elsteinnoreply@blogger.comtag:blogger.com,1999:blog-6432111.post-42845346266836960512007-11-05T15:56:00.000+00:002007-11-05T15:56:00.000+00:00Robbie: yep, your second thought was right, I was ...Robbie: yep, your second thought was right, I was thinking of doing it all locally. The point about global consequence is well taken; not being an expert on this, or particularly enamoured of supervaluationism, I'm tempted to concede it.Anthttp://users.ox.ac.uk/~sfop0118/noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-46380159879239712902007-11-04T15:05:00.000+00:002007-11-04T15:05:00.000+00:00Ant:Rereading your comment, I noticed that your su...Ant:<BR/><BR/>Rereading your comment, I noticed that your suggestion was that the probabilistic constraint be applied on a precisification-by-precisification level.<BR/><BR/>First question about this: what's the notion of validity with which the credences in precisifications must cohere? If it's one on which p&~Dp comes out contradictory, then (I guess) it'll be tricky to find any classical probability function to plausibly do the job.<BR/><BR/>An alternative reading is that the probabilities must cohere with e.g. a locally defined consequence relation (=guaranteed truth preservation on each precisification). It's well known that local validity is fully classical, and in particular doesn't make p&~Dp a contradiction. <BR/><BR/>I guess at this point I'd like to ask whether what we end up saying about credences in vague sentences simpliciter should impose any constraints on consequence, simpliciter, for a vague language? Of course our language *is* vague, and so the arguments we want to consider (and evaluate for validity/assess whether we believe the premises) *are* usually formulated in terms vaguely expressed premises and conclusions. So it's extremely natural, I think, to think that the constraint must apply at this level too.<BR/><BR/>If that's conceded, the dialectic sketched out in the previous comment can get going. <BR/><BR/>Even if it's not conceded (e.g. if we think that all logical constraints on credences can be captured "locally") then I think we still have some traction on the debate about what formal construction deserves the name "consequence" simpliciter. For something which is a Q-contradiction can (rationally, determinately) get credence 1/2, I think we've got a big pro tanto case for Q being a formal construction that doesn't play the consequence-role. <BR/><BR/>In the case at hand, global consequence as traditionally defined looks like it's in this situation. And local consequence (I argue in the paper) looks like it doesn't play the consequence-role for other reasons (you can get a locally valid argument all of whose premises you should accept; and all of whose conclusions you should reject).Robbiehttp://www.blogger.com/profile/02081389310232077607noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-2695940080085170602007-11-04T13:37:00.000+00:002007-11-04T13:37:00.000+00:00That's very interesting; I was meaning to think ab...That's very interesting; I was meaning to think about how the sets-of-probability functions thingy fitted in. I agree with Ant that they've got some independent appeal (I quite like the old and outdated operationalization of this sort of stuff, too!)<BR/><BR/>The interactions are far from transparent to me though, so I'd really appreciate guidance/references on this stuff.<BR/><BR/>Let's take as a setup the following: propositions (sets of possible worlds) are the primary bearers of probability, and that no vagueness afflicts propositions. If a sentence expresses a unique proposition, one can obviously straightforwardly associate the sentence with a unique probability. But if the sentence corresponds to many different propositions with different probabilities, then there's obviously some slack (just as there is when a sentence corresponds to propositions with different truth values). <BR/><BR/>I take it the analogue of the truth=supertruth idea is to define the probability (=superprobability) of a sentence to be the minimum of probability of the propositions partially expressed by the sentence. A truth=subtruth idea would be to define the probability (=subprobability) of a sentence to be the maximum probability of the propositions partially expressed by the sentence. (Or am I misinterpreting the suggestion?)<BR/><BR/>I'm still unsure of the interactions. I'm about to flip a fair coin. Consider the proposition (H) that the fair coin will land heads; and the proposition (T) that the fair coin will land tails. The probability of each proposition is 1/2. We can suppose it's probability 1 that the disjunctive proposition, H or T, obtains. <BR/><BR/>Now introduce the word "heils" to be indeterminate in reference between heads and tails. Then the sentence "the fair coin will land heils" will partially express two propositions that are each probability 1/2. So it looks that the sentence has probability 1/2 whether we calculate that by super or by sub-probability recipes.<BR/><BR/>What proposition is expressed by the sentence "it is not determinately the case that the fair coin will land heils"? The proposition obtains iff at least one of the propositions expressed by the embedded sentence fails to obtain. So the proposition expressed by this sentence, I reckon, is the proposition that either the fair coin lands heads, or the fair coin lands tails. And we've got probability 1 invested in this proposition, ex hypothesi. <BR/><BR/>So it seems to me that the upshot of all of this will be that we've got a sentence "S" which is probability 1/2, such that "it is indeterminate whether S" is probability 1. And, working things through, both the propositions expressed by "S and it is indeterminate whether S" are probability 1/2. So, whichever way we choose to interpret probability talk in this sort of setting, it looks like that sentence will get probability 1/2. <BR/><BR/>Of course, none of that fits with the idea that "S and it is indeterminate whether S" is a logical contradiction (together with the probabilistic constraint on validities I mentioned). So if this is the right way to go, it strikes me that the supervaluationist will need to go against orthodoxy and deny that "S and it is indeterminate with S" is a logical contradiction. (They don't have to do this in the way that I sketch in the paper: they might take it as an argument for a local definition of supervaluational logical consequence, for example).<BR/><BR/>In any case, this looks to me like a different sort of proposal from the particular implementation of Shafer-function machinery that Brian Weatherson describes as "probability theory for supervaluationists" in the paper I linked to. That way of going gives us probability 0 in the sentence I mentioned, not probability 1/2. <BR/><BR/>But maybe I've messed up or misinterpreted something here.Robbiehttp://www.blogger.com/profile/02081389310232077607noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-69944020367345436192007-11-03T22:27:00.000+00:002007-11-03T22:27:00.000+00:00To follow up on Ant's point - I'm prettty sure tha...To follow up on Ant's point - I'm prettty sure that using Dempster-Shafer functions is in some sense equivalent to using sets of probability functions, though I can't remember if they're required to be convex sets, or satisfy some other condition. And since Dempster-Shafer functions naturally give you both upper and lower credences, you might think these should somehow correspond to super- and sub-valuations.Kennyhttp://www.blogger.com/profile/09588770173317316837noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-74887456715302427772007-11-03T16:18:00.000+00:002007-11-03T16:18:00.000+00:00Maybe the right thought is that for every admissib...Maybe the right thought is that for every admissible precisification there will be a classical probability function which respects the probabilistic constraints on coherence with validity. So we would allow the supervaluationist to supervaluate truth over classical assignments, and to supervalute credence over classical credence functions. <BR/><BR/>This will cohere too with the models of imprecise credence that Jeffrey, van Fraassen, et al, have defended, basically the idea that (at least) we should model actual credences by a family of credence functions. (Usually they end up using upper and lower credences in each proposition, which leads to prima facie difficulties if you think that we should model higher-order vagueness this way.) One argument that can be given for this treatment on very classical lines is as follows. Note that Dutch-book arguments justify the thesis that credences are probabilities by pointing to a connection between credences and betting behaviour. However, if one takes this seriously, one will note that if betting behaviour is supposed to operationally define credences, observed betting behaviour is compatible with a great many credences, not the unique function assumed by the classical theory. So we should, all along, have been modelling credence by at least a family of probability functions. Note that, old-fashioned and dodgy as an appeal to operational definitions clearly is, it nevertheless aims to provide a vagueness-independent reason to accept imprecise credences.<BR/><BR/>How this maps onto regular full belief is even more complicated than in the original case. And whether supervaluating over classical credences yields anything that deserves the name 'credence' strikes me as even more vexed than whether supervaluating over classical assignments yields anything that deserves the name 'truth'. But on first glance a parallel treatment would seem to have something to recommend it for supervaluationists, especially if there are independent reasons apart from vagueness to move to a richer framework for credences.Anthttp://users.ox.ac.uk/~sfop0118/noreply@blogger.com