APA Blogging: Relativism

31 03 2006

(Anyone who is not familiar with contextualist and relativist semantics might want to read the last three paragraphs here first.)

The last day of the APA saw an interesting session on relativism by Bob Stalnaker, John MacFarlane, and John Hawthorne. I had unfortunately slept through the morning session on relativism with Michael Glanzberg, Thony Gillies, and Andy Egan. And since it was at the end of the conference, I wasn’t at peak form in catching what was said. But what I got out of it was that Stalnaker gave a good summary of the New Relativist position (together with some challenges about “ambivalence” towards propositions that I didn’t quite catch), MacFarlane gave the start of an account of how it is that an assertion of P by one person can disagree with a denial of P by another person if the relevant context of assessment has changed between people, and Hawthorne gave some arguments to challenge standard intuitions that are taken to motivate the relativist move.

When John says, “rotting flesh is not tasty”, I will agree with him. But it seems that I will disagree with Vinny the Talking Vulture who says “rotting flesh is tasty”. This would be an argument against standard (indexical) contextualism – an indexical account would say there is no more disagreement here than there is when I say “My name is Kenny” and you say “My name is not Kenny”. But Hawthorne suggested that this intuition just doesn’t exist here, so there is no need to reject contextualism for something more radical. Because John (having seen some roadkill a little bit back) can then go to Vinny and say “there’s something tasty down the road” – and it seems both that he is agreeing with Vinny, and that he hasn’t changed his mind from earlier, so his original statement and Vinny’s original statement aren’t really contraries, as the relativist (but not the contextualist) would suggest. I think this example is a bit beside the point, because it seems to me that there’s some odd pragmatic move going on when John says “there’s something tasty down the road”. (I think John MacFarlane pointed this out best by asking what John Hawthorne would say if the vulture said “Aha! So you agree with me now! Rotting flesh is tasty!”) But there may well be challenges in the vicinity.

I think it was a bit unfortunate that so much of the discussion was focused on predicates of personal taste (like “fun”, “funny”, “tasty”, and the like), because it’s generally seemed to me that the relativist’s best case is for epistemic modals (“might” in the sense that’s roughly similar to “as far as I know”), though Branden Fitelson might have convinced me that future contingent statements (“I will go shopping tomorrow”, when nothing about the world guarantees that this either will or won’t be the case) are a better case. All the relativist needs to do is point out that at least some area of discourse is best modeled with their semantics.

In general, it seems that there is a family of problems and a family of solutions available for them. The problem cases include future contingents, epistemic modals, predicates of personal taste, gradable adjectives (like “tall” and “flat” – which Gil Harman pointed out may well fall into two categories depending on whether or not they have an absolute at one end), knowledge, indexicals (“I”, “here”, “tomorrow”), demonstratives (“this”, “that”), and probably others. The solutions that have been proposed include saying that the effect is (1) merely pragmatic, (2) subject-sensitive invariantism (or something similar), (3) indexical contextualism, (4) non-indexical contextualism, and (5) relativism.

(1) attempts to explain away the data by appeal to non-literal speech or conversational practices. (2) says the relation discussed is more complicated than it seems, but ultimately only depends on the status of the situation being talked about, not the circumstance it is mentioned in. The other three suggest that some additional sort of contextually supplied parameter is important in the assessment of sentences involving the relevant concept. The question is just whether the parameter is necessary to find out what proposition is expressed, as in (3), or to find out whether or not the proposition is true, as in (4) and (5). The distinction between (4) and (5) is whether the parameter is taken from the circumstance of utterance or the circumstance of assessment. Since an utterance typically expresses a unique proposition, any parameter needed to find out what that proposition is will need to come from the circumstance of utterance. But when assessing an utterance for truth, we have an extra circumstance available to us, so both (4) and (5) are theoretically options (despite the problems one might find with (5)).

I think we have fairly decisive evidence that the best way to treat indexicals and demonstratives is with (3), and people have generally agreed that a proposition gives not just an individual truth-value, but a function from worlds to truth-values, so that the world of utterance must show up in the parameter needed for (4). Perhaps this means that non-indexical contextualism should be called bicontextualism, and relativism should actually be called tricontextualism! However, it’s a somewhat open question whether anything other than person, time, location, and world appear in (3), anything other than world appears in (4), and whether anything at all shows up in the parameter for (5). A debate about one specific parameter for predicates of personal taste will be relevant to whether anything shows up in (5), but it is by no means decisive about relativism.


Sets of Worlds

29 03 2006

One question about subjective probability that I’ve received a few times is how necessarily false propositions can get a non-zero probability. It’s a consequence of any form of the axioms of probability that any tautologically false proposition must get probability zero, but depending on which form of the axioms one takes, this won’t have to be the case even for first-order logically false propositions, much less metaphysically impossible ones. The reason I say “depending on which form of the axioms one takes” is because there are several different forms that are generally considered to be equivalent.

For instance, Kolmogorov says that probability (1) is a non-negative function on sets of possible worlds (2) that assigns the value 1 to the complete set (3) and is (finitely or countably) additive on disjoint sets of worlds. Another formulation replaces (2) and (3), saying instead that logical truths get probability 1, and that probability adds on logically incompatible statements. Yet another (which I get from Brian Weatherson) replaces all four by saying that logical truths and falsehoods get probability 1 and 0 respectively, that if A entails B then P(A)≤P(B), and that P(A)+P(B)=P(A and B)+P(A or B).

The reason for this equivalence (and also, I think, the motivation behind the original questions) is that most people take a probability function (subjective, epistemic, logical, objective, or whatever) to be a function from sets of possible worlds to real numbers. (I’ve also heard of some proposals that would restrict to rationals, expand to complex numbers, or change to p-adics or some other number system. However, I think most of these suggestions occur for purely mathematical reasons and just encode certain similarities to probabilities, but aren’t really considered to be probabilities themselves.) The later formulations I give above talk about logical truths and the like, but it is very easy (and relatively standard) to talk about propositions as just being sets of worlds. And if the set of all possible worlds is taken to include all logically possible worlds (rather than metaphysically possible worlds), then I believe all the above formulations are equivalent. This slip between logical and metaphysical possibility is I think why people worry about whether impossible statements must get probability 0.

However, in many cases it seems natural to take a more neutral stance (as Brian Weatherson did) and just think of a probability function as an assignment of real numbers to propositions or even just statements in a language rather than sets of possible worlds. This was pursued by Karl Popper in appendices *iv and *v to The Logic of Scientific Discovery, where he tries to give an account of conditional probability on antecedents of probability zero. (I happen to think his particular approach is wrong, but he has the right general idea.) Popper’s axioms are quite nice, in that he can prove for any two tautologically equivalent statements that they get the same probability from the probability axioms alone, without making any assumptions about what the logical connectives mean or what propositions are.

I think that for dealing with tricky logics, or statements containing essential indexicals, this sort of distinction is important to make. People try to modify the “sets of possible worlds” approach by talking about “sets of centered possible worlds”, but I’m skeptical about how much can be accomplished in this way.

APA Blogging: Blogging Panel

27 03 2006

One interesting but not totally related point – during the second half of last week, the number of hits on my blog dropped by about 1/3 to 1/2 (it’s hard to tell, because the ordinary traffic ranges from about 65 to about 90 views a day, while several days last week were between 45 and 70). I’m not sure if it’s because everyone else was at the APA in Portland too, or a whole bunch of spring breaks lining up at this time, or something else. (I suspect it’s not the spring break thing, because the number of hits recovered today, when at least Berkeley and Stanford started spring break.)

The panel on blogging was a lot of fun, even though it almost didn’t happen, because Jon was an hour late due to flight delays, and Brian, Gillian and I only managed to get through the lineup to register (and incidentally find out what room we were in) about two minutes before it started. And in the end, since it was the first session on the first day, there were only about six people in the audience.

Some good suggestions did come out of the discussion though. Brian recommended blogging as a tool for grad students to practice writing for public consumption – though with an interesting caveat. He suggested that one start a blog but not publicize it, so that one doesn’t necessarily expect people to read, but makes things a little bit more polished in case anyone does randomly find it through Google or whatever. Coincidentally, this is basically what I did with my blog – for basically the first three months of its existence, I don’t think anyone knew about it except me and one or two friends, until I left a comment on Gillian’s blog. Some advantages of this approach are that it gives you time to decide if you really want a blog (a lot of people decide in a week or a month that it’s not really for them), it means that when people first find the blog they’ll have several posts to look at rather than just one (so they find something interesting and decide to keep coming back), and gives you a chance to practice a few times and figure out what you’ll want to write about and how you’ll want to say it before really facing a public.

Here are some tips for starting a philosophy blog (which I suppose should apply to any academic blog). I’ve put a little thought into this, but not so much that I can’t be convinced some of them are bad ideas, so leave a comment if you have different thoughts.

  • Never blog drunk!
  • Start the blog secretly (as I mentioned above), and possibly anonymously – you can always move to publicity and add your name, but you can’t really go the other direction.
  • When you do decide to publicize the blog, do it by mentioning some relevant post in the comments of a blog on relatively similar topics, or by e-mailing the author of such a blog, or something like that. While a link from Brian Weatherson or Brian Leiter would be the easiest way to get wide publicity, you’re more likely to gain readers by appealing to people who already read a somewhat less widely-read blog and have shown some interest in your subject area.
  • Try to stay within a relatively well-defined subdiscipline and away from “metaphilosophy” – while a wide range of subject areas, and discussion of how to do philosophy, might be interesting, one isn’t generally likely to have interestingly new ideas on that wide an area, and it’s easier to attract an audience if they know that almost every post will be on topics close to their interests.
  • Link to books on Amazon, papers that are publicly available online, and posts on other interesting blogs whenever possible – it makes it easier for people who aren’t already familiar with the literature to get fully up to speed on the discussion.
  • Try to maintain a relatively stable posting frequency – if you normally post about once a month (as several of the blogs I read do), then posting four times in one day makes it easy for people to miss the first two posts, since they’re not expecting more below the newest one.
  • Assign categories to your posts and have category archives available, so that new visitors later on can easily find posts on a particular topic.
  • Post about papers you read (especially ones that are publicly available online) and conference talks you go to, so other people can benefit from what you’ve learned (and so you can consolidate your own thoughts on the matter). Posting about colloquia and seminars is probably fine, though you might want to get permission from the person or people involved. Posting about ideas that came up in more informal conversations you should definitely ask permission from the people involved, and/or leave out their names in case they don’t want to be publicly associated with off-the-cuff remarks.
  • Don’t post much about strictly personal issues. (You can have a LiveJournal or something similar for that.) People who are there for your ideas won’t generally care about what happened to your brother on the way to work yesterday. Of course, there are exceptions. If you get married or get a new job, by all means post that. If anything comes up that will get in the way of your regular blogging schedule, mention that too. And there seems to be a common blogospheric tradition of “Friday Cat Blogging” (any other day of the week only has a couple hundred hits, except Monday, which has about 1/10 as many as Friday) – I suppose that only makes sense though if your regular posting frequency is at least a couple times a week.
  • Try to encourage comments, especially from people in neighboring fields that might have interesting perspectives on your ideas – this is probably the biggest benefit of putting one’s ideas on a blog, apart from name-recognition.
  • Don’t blog drunk!

Any other suggestions?

APA Blogging: Jason Stanley, Knowledge and Practical Interests

27 03 2006

I should start this post by pointing out that I haven’t read Stanley’s book, I didn’t have anything to take notes at the session, and all I know about subject-centered invariantism (which I believe is Stanley’s position on knowledge) is what I learned in John MacFarlane’s seminar last year, and occasional discussions with other people. But even given all that, it was quite an interesting session – and other people seem to agree on that, given that it seemed to have the largest audience. (I was sitting on the floor most of the time, with about a dozen other people – there were two other sessions with similar-sized audiences in even smaller rooms, so they were even more crowded.)

Stanley’s position is “invariantism” in that he denies that the situation of the asserter plays any important role in the proposition expressed by “A knows that p” or its truth value (unlike, say, Keith DeRose and others, some of whom suggest that the salience of relevant alternatives in the context of utterance can make “Jane knows that she has hands” go from true (in most contexts) to false (if one has just considered that she has no way to rule out being a brain in a vat)). However, it is “subject-centered”, because having made exactly the same observations, A can know that p while B doesn’t, if something of extreme urgency for B (but not for A) depends on whether p. (Stanley pointed out that there is a connection between “evidence” and “knowledge”, so we have to talk about something more like observations than evidence.)

I don’t remember too many details of the session (though I know I’d like to get a copy of Stephen Schiffer’s handout, since he made a bunch of very interesting points, and seemed to have handed out something like a full transcript of his remarks), but there was one interesting objection raised in the question period by Ryan Wasserman. Jason Stanley had already bitten the bullet and agreed that if John and Jane are on the same airplane, and have the same information about windspeeds and departure time and the like, but Jane has an important talk to give very soon after arrival, then John can know that the plane will arrive on time even though Jane doesn’t. This seems somewhat odd, and Ryan Wasserman pushed it further by pointing out that on Stanley’s position, this can even be possible if Jane has gathered more information about the weather, history of the airline’s performance, and the like.

After Jason Stanley’s response, Delia Graff (who was chairing the session) tried to defuse the worry that the theory makes such predictions by pointing out a related prediction of a related theory. It seems perfectly fine for her to say that her 9-year-old cousin is really really good at playing basketball, and that Ryan Wasserman plays basketball even better than her cousin, but that Ryan Wasserman is not very good at basketball (despite being better than someone that’s really really good at it). The fact that this prediction is perfectly fine for subject-centered invariantism about “good at basketball” (rather than “knows”) seems to support subject-centered invariantism.

At first I agreed with her, but now I think that this piece of evidence actually counts against Stanley’s theory. I think (correct me if I’m wrong) the intuitions suggest that the basketball case sounds much better than the knowledge case. If subject-centered invariantism about both predicates predicts that both should be acceptable, then this suggests that something like subject-centered invariantism may well be true for “good at basketball”, but probably isn’t true about “knows”. If it did apply to both, then in addition to explaining away the intuition in the case of “knows”, Stanley would have to explain why the intuition reappears for the basketball case. Now, it’s possible that such an explanation will emerge (as it will have to if one thinks that subject-centered invariantism is wrong for both predicates, as I think that I do), but it’s quite a convoluted way to get at the data from Stanley’s theory, and starts to disconnect the theory somewhat from the evidence.

Anyway, it’s interesting stuff.


18 03 2006

I see that at LanguageLog they’ve put up two jokes. One of my students told me a philosophy joke the other day that I figure I might as well share:

Q: How did the philosopher deal with the awkward sexual advances of the student?

A: By denying the existence of the proposition!

Anyone else have any jokes to share?

Also, I’ll be spending most of the coming week in Portland at the Pacific APA meeting, participating both in a panel on blogging, and commenting on a paper by Otávio Bueno on MacBride’s criticism of Resnik’s structuralism. So I probably won’t post until afterwards, but I may have some conference blogging to do when I get back.

Blogging as a Tool for Philosophical Discourse: the State of the Art

15 03 2006

Next week in Portland, I’ll be on a panel with Jonathan Kvanvig, Gillian Russell, and Brian Weatherson, with the title as above. Since Brian has already said something about what he’ll say, I figured I’ll post a bit as well, especially to elicit more suggestions.

I figured, since I’m still in graduate school, and therefore know less about the profession at large than the other panelists, I’ll mainly talk about blogging per se. (Most of the data below I gathered by using the list of blogs that Dave Chalmers maintains.)

When I began graduate school, only 6 of the blogs currently on Chalmers’ list existed, and half of them were non-philosophy oriented. Projecting current trends, by the time I graduate there will almost certainly be over 200, with over 150 on philosophical topics.

There have been some changes in the pattern of blog creation – in the first two years, there were only 6 or so blogs (out of 25) that focus on a particular topic (Will Wilkinson, Brian Weatherson, Greg Restall, Wo Schwartz, Clark Goble, and Jeremy Pierce – to the extent that BW and WS can be said to be topical), and more than half of the blogs were primarily non-philosophical. But in early ’04, a few more topical blogs were formed, and there was a burst in May/June ’04 as 17 topical blogs (and four others) were formed. This brought the total of all blogs from 38 to 59, with almost half of them topical.

Interestingly enough, the second half of 2004 had about the same rate of blog creation as the period before May/June, and was again about equally split between philosophical and non-philosophical blogs, mostly non-topically focused. However, in 2005, the pace of blog creation picked up (with another burst in January, that included my blog) and has tended to be more topically focused.

Interestingly, the topics have grown more specialized. Whereas blogs from before May ’04 that I counted as “topical” often talked about general language/epistemology/metaphysics/mind topics, some more recent ones have focused on philosophy of “real mathematics”, science ethics, and contextualism in epistemology.

Another interesting development has been the rise of group blogs. The first group blogs in philosophy appear to be the grad student blogs at Rochester, Brown, Syracuse, and Arizona as part of the burst in April and May of ’04, followed in June by topical group blogs on free will, religion, epistemology, experimental philosophy, ethics, art, and biology.

It’s interesting to compare the development of blogging in philosophy with that in other academic disciplines. In physics, the major blogs I glanced at mostly seemed to get started in ’04 and ’05, a bit later than in philosophy (though John Baez has been posting This Week’s Finds in Mathematical Physics since 1993!), while the major linguistics blogs seemed to get started around ’02 and ’03, just as in philosophy. I know less about where to look in other academic disciplines, but maybe Brian can use some of his connections at Crooked Timber (established in July ’03) to find out more about the history of blogging in other academic disciplines.

I’ve certainly found it quite interesting glancing through all these different blogs to find out when they were started; whether they focus on a particular topic, are about general philosophy, or primarily non-philosophical topics; and who writes them. The main philosophical benefits I’ve gotten (besides some quite useful comments on ideas I post!) are running into people at conferences who already have some idea of what I work on, and starting up e-mail conversations with people about my interests. I don’t think anything I’ve first written in a blog post has (yet) ended up in a larger paper, but some of it probably will before too terribly long.

Anyway, if other people have thoughts, I’d be glad to hear them (and possibly share them next week, if you can’t make it to the discussion in Portland yourself!)

Kanamori on the Need for Foundations

11 03 2006

I’ve been reading Akihiro Kanamori’s The Higher Infinite to make sure that I know enough about what’s going on in Hugh Woodin’s class on determinacy and woodin cardinals. It’s really an extremely well-written book, giving enough mathematical detail that it’s not quite as dense as Jech’s set theory book, and has more content than Kunen’s. And it also has much more historical detail than any other set theory book that I know of, including citations to the papers where each notion was first introduced, and papers where important use was made of the concepts.

But given that this book is primarily an exploration of axioms extending ZFC, it’s interesting to see the polemical “Appendix (with apologies to Burton Dreben)”. He pushes some Wittgensteinian ideas suggesting that the search for explanations of mathematical practice are misguided, and thus that set theory is best when it is pursued as just another branch of mathematics, rather than attempting to give a “foundation” for the other branches. I think I generally disagree with this point of view, but he tells a lovely story that I heard third-hand reference to coincidentally just the day before from some of the other logic grad students. I’ll quote the entire thing here:

To pursue an analogy, the world of mathematics is like a great cathedral. The thick stone walls along the stately aisles still show the lines of the ancient church that predated the grand edifice. The central dome is supported by high arches of vaulting stone, resilient reminders of the anonymous master masons. Whatever their design, the arches have easily supported the elegant latter-day spires reaching high into the sky. The first adornments can still be seen in the oldest chapels; there in continuing communion with the past steady additions are made, each new age imparting its own distinctive style. In recent memory large new side chapels have been constructed, and new flying buttresses for extra support. Every day the curious enter through the great door of polished wood with the attractive inset figures. Several venture down the long nave seeking instruction, and a few even initiation, quite taken by the order and beauty of the altar. And the work continues: The architects attempt to chart out large parts of the cathedral, some even proposing vast renovations. The craftsman [sic] continue the steady work on the new wood paneling, the restoration of the sculpture, and the mortaring of the cracks that appear with age. And supported by high scaffolding, the artisans continue to work on the fine stained glass. They try to coordinate with their colleagues in the adjoining frames, but sometimes the heady heights inpire them to produce new gems. Those who step back see a larger scheme, but they cannot see across the whole breadth. And they are so high up that they can no longer see their supports. Nevertheless, they are sustained as a community, as part of the ongoing human adventure.

To append an apocryphal tale: A host of industrious spiders started to build an elaborate network of webs in newly excavated vaults beneath the cathedral. It quickly grew so thick and complex that no one could venture across without getting enmeshed. One day, a fearful wind came howling in and blew a gaping hole through the network, and in a desperate response the spiders worked frantically to reestablish the connections. For you see, the spiders had become convinced that their carefully constructed webbing was the foundation without which the entire cathedral would totter. Of course, the craftsmen above hardly raised an eyebrow.

I think he’s right that the large mathematical endeavor has proven so useful and coherent that it is not in any danger of falling. If someone were to prove that ZFC is inconsistent, there would be some scrambling to come up with a new theory (or a move to some alternative old theory, like Quine’s New Foundations, or Russell’s ramified theory of types), but within a decade or so, 95% of mathematics would be shown to be representable in the new foundational picture as well. This happened several times in the early 20th century (though a few of those times didn’t involve a proof of inconsistency, but just a change in fashion about which system to use).

But this doesn’t mean that the cathedral supports itself. I (and others who work in foundations) would like to know how it is in fact supported – there’s no need to think that it is actually supported by our work. A predecessor of this cathedral was the church of analysis built on the work of Newton and Leibniz, and brought to many of its greatest heights by the master craftsman Euler. However, Bishop Berkeley had pointed out to Newton that he was building his edifice directly on a major fault line. Mathematicians responded as Kanamori seems to. In the early 19th century it became clear that Berkeley was right, as Fourier and Cauchy “proved” both that the sum of a series of continuous functions is continuous, and that many discontinuous functions were the sums of Fourier series of continuous functions. [Edited for clarity.] Fortunately, the resulting tremors only damaged a few pieces of work, and Cauchy and Weierstrass were able to restructure the base of the church with epsilons and deltas, finally taking the load off the fault line that Berkeley had pointed out. (Kanamori discusses this entire history in his appendix.)

Just because mathematics has generally withstood the problems of the past doesn’t mean that there are no remaining problems – just that these problems are likely to be only relatively minor. Unlike Kanamori, I think this means we should be continuously vigilant about the foundations. And there are still metaphysical questions. He seems to conflate the desire to do metaphysics with the desire for platonism (which I suppose is something I’ve also done in the title and subtitle of this blog!) but I think many of the foundational programs of Hatry Field, Stewart Shapiro, Michael Resnik, and the like are worth studying, and may result in important foundational gains. Kanamori objects, saying that this drive, “along with the more traditional musings about the starry heavens above or the moral law within, are not in the world but of the mystical, part of the feeling for the unity of experience in the large.” He closes with a couple quotes from the Tractatus and the Tao Te-Ching, saying this is one of those things that must just be shown, not said.

But if this is all right, then the desire for explanation is a sort of mysticism, which would seem to undermine the entire scientific program for understanding the world. Maybe some readers of Wittgenstein would approve of that result, but I think this is an overreaction against workers in the foundations of mathematics, saving mathematics from a lack of foundations in a way that threatens all of science.