As of July 8 I will be posting on Crooked Timber. This blog will keep running, but it will be more focussed on metaphysics, epistemology and philosophy of language than it used to be, with other posts going to Crooked Timber.
John Turri alerted me to this very interesting site on counterfactual research. Not much philosophy there (despite an intro quote from David Lewis about what counterfactual possibilities are) but lots that’s really interesting for those of us who care about all aspects of the role of conditionals.
posted by Brian Weatherson 11/30/2002 08:24:00 PM
Keith Jackson doesn’t seem to believe in mereological essentialism. Here’s a quote from his intro to the Notre Dame-USC game.
“The first game was played in 1926. It was played on the same turf, not the same grass mind you.”
Good for Jackson. I’ve always liked watching games he’s doing, and not just because he has good commonsensical philosophical views.
(Pedantic postscript: There are a few other ways to interpret Jackson’s comment other than as a denial of mereological essentialism, such as for instance interpreting him as accepting Geachian relative identity, but no such interpretation sounds very charitable to my ear.)
posted by Brian Weatherson 11/30/2002 08:19:00 PM
I just got a book voucher for a moderately sizeable amount (actually a rather large amount if only spent on paperback books). As they’d put it on an SAT test, Brian is to internet bookshops as kid is to ______.
posted by Brian Weatherson 11/26/2002 11:55:00 AM
I’ve got much more to (eventually) write about privileged access, including responding to some comments on the previous post, but for now let me just note something that may be of interest to those who come here looking for vagueness stuff. (I haven’t read it, so I don’t know it’s interesting.) Eugene Volokh, of UCLA Law School (and a prominent blog) has a paper on slippery slope arguments in legal reasoning. I hope to read this soon. If anyone here gets to it before me, let me know if it’s any good!
posted by Brian Weatherson 11/26/2002 09:00:00 AM
Narrow content and privileged access.
I assume (at least here) that there is such a thing as narrow mental content. And I assume that all mental representations, not just beliefs, have narrow content. In particular, I imagine that conceivings or imaginings have narrow content, and that often this content differs radically from the wide content of those very same conceivings or imaginings. So if I imagine the world having atomic stuff in its rivers, lakes and oceans, the narrow content of my imagination is that water is atomic, and the wide content of it is that there is no water in the rivers, lakes and oceans.
So something distinguishes narrow content from wide content. What might it be? An obvious solution is that I have privileged access to the narrow content of my imaginings, but not to their wide content. Some people claim I do have privileged access to the wide content of my mental states - this position is bizarre even by philosophical standards, so I’ll ignore that here. I think privileged access doesn’t produce a distinction between narrow and wide content because we don’t have privileged access to narrow content either. Here’s an example to prove this.
Cian, Hilary and Ted are all philosophy professors. Today they are all, at different spots along Highway 95, teaching about the identity of indiscernibles, and Max Black’s objection to it. So they are all imagining a world consisting of naught but two duplicate atoms. They aren’t thinking about this right now, but they all have quite different views about whether (1) is true in the world they are imagining. And if asked they would tell you what they think of whether (1) or (2) are true in the world at the drop of a hat.
(1) $x$y"z (z = x Ú z = y)
(2) ~$x$y"z (z = x Ú z = y)
Ted thinks that (1) is false in that world. He thinks that there are three objects in the world, the two atoms and their fusion, so (1) couldn’t be true. Cian thinks that (1) is true in the world, because atoms never fuse, so these atoms don’t fuse. And Hilary thinks there is no fact of the matter as to whether (1) is true in such a world. All of them would, if asked, think similar things about the contents of their imaginings. Ted thinks that (2) is part of the content of what he is imagining, Cian thinks that (1) is part of the content of what he is imagining, and Hilary thinks that there is no fact of the matter as to whether it is part of the content of what he is imagining is that (1) is true or(2) is true. Note that while there are other attitudes one could take towards the question of whether (1) and (2) are part of the content of what is being imagined, Cian, Ted and Hilary presumably exclude the range of attitudes one could take towards the question of whether the two atoms in question have a fusion.
If that example is possible (and I am pretty confident it is, being so close to actual examples) then the following principles cannot all be true.
Strong Privileged Access (SPA) - For all imaginings i and all propositions p, if x imagines i, and x’s introspective faculties are properly functioning, then x can know by introspection whether p is part of the narrow content of i.
Disbelief Excludes Knowledge (DEK) - If x believes that Øp, then x does not know that p.
Stability of the Logical Constants (SLC) - Any sentence consisting entirely of logical vocabulary (quantifiers, connectives, variables and identity) is semantically stable.
Stability implies Common Content (SCC) - If a sentence s is semantically stable, then s is part of the narrow content of i iff s is part of the wide content of i.
Mereological Necessity (MN) - If there is a world w in which there exist two atoms and nothing else and those two atoms do not have a fusion, then in any world in which there exists two atoms and nothing else, those two atoms do not have a fusion.
Closure of Content Under Immediate Implication (CCI) - If x explicitly imagines that p, and q is an immediate consequence of p, then q is part of the wide content of what x imagines.
Immediacy of Mereological Facts (IMF) - If it is a necessary truth that two objects have a fusion, then the existence of that fusion is an immediate consequence of the existence of those objects. Similarly, if it is a necessary truth that they do not have a fusion, or that it is indeterminate whether they have a fusion, then the non-existence, or indeterminate existence, of that fusion is an immediate consequence of the existence of those objects.
Here’s the argument that these claims are not compatible. First, assume that Ted is right and the atoms have a fusion, so (1) is false. By (MN), it is either necessarily true if there are two atoms in the world and no other distinct objects, then (2) is true. By (IMF), (2) is an immediate consequence of the existence of those atoms. By (CCI), (2) is part of the content of the imagining. By (SLC), (2) is semantically stable. So by (SCC), (2) is part of the narrow content of the imagining. By (SPA), Cian knows that (2) is part of the narrow content of what he is imagining. But Cian believes that (2) is not part of the content of the imagining. He believes, in fact, that he is imagining something coherent and that part of its content is (1). So by (DEK) he does not know the content of what he is imagining. If Cian is right and the atoms don’t have a fusion, a similar argument shows that Ted does not know the content of what he is imagining. If Hilary is right, then both Cian and Ted do not know what they are imagining, because they believe that one of (1) and (2) is part of the content of what’s being imagined.
The above argument assumes that Ted and Cian’s introspective faculties are properly functioning. This may or may not be true in reality, but there’s no reason to assume it is not true in the example. One of them has a false mereological belief, but this can hardly be sufficient to make their introspective faculties dysfunctional, unless we think that true philosophical beliefs are required for introspection.
Most of the other assumptions here apart from (SPA) should be fairly self-explanatory, but I want to make brief notes about my notion of ‘immediate consequence’ and about how I’ve phrased privileged access.
Sometimes the content of what we imagine goes beyond a simple description of the state of imagining. If I imagine holding three apples in my left hand, and two apples in my right hand, then I imagine that I am holding five apples. On the other hand, imagination is not closed under entailment generally. If I imagine holding three apples then I do not imagine holding a number of apples n such that xn + yn = zn has no solutions in integers x, y, z. More generally, we do not want every mathematical truth to be part of the content of every imagining. There is obviously quite a bit of work to be done to specify just which entailments ‘get in’ to the content of the imagining. I assume that one of the crucial factors that determines whether q is part of the content of an imagining that is explicitly an imagining that p, is how many steps it takes to infer q from p in a properly designed proof theory. Assuming (as might be contested) that the true theory of mereology licences particular rules of proof, (IMF) will be more or less a triviality.
It seems clear that it will often be indeterminate whether q is an immediate consequence, in this sense, of p. But that is no challenge to (CCI). For all it shows is that it will often be indeterminate whether q is part of the content of what is being imagined. And we know full well that the content of a particular act of imagination is often indeterminate.
It is not entirely common to provide a quantified version of privileged access. It is more common to write things like the following (from McLaughlin and Tye’s Phil Review paper)
When our faculty of introspection is working properly, we can know what we are thinking by introspection.
Of course, I’ve extended this to imaginings, if that wasn’t meant to be included already in ‘thinking’. But I don’t think the use of quantifiers does more than spell out what is involved in McLaughlin and Tye’s definition. In general (as Lewis says in “Whether Report”) know wh- claims are quantified claims. If I know who’s coming to the party, I know for each person whether they are coming to the party. If I know which teams are in the playoffs, I know for each team whether they are in the playoffs. And if I know what the governor is doing, I know for each action whether the governor is performing that action. So by analogy I think that if I know what I’m imagining, I should know for every proposition whether I am imagining that proposition.
There is a weaker interpretation of know wh- claims that might be more appropriate here. Imagine that the playoff teams are the Cats, the Dogs, the Rabbits and the Kangaroos, and for each of those teams I know that they are in the playoffs. But there are other teams, not in the playoffs, such that I don’t know whether they are in. Perhaps I don’t know how many teams make the playoffs, or perhaps I’ve forgotten which teams there are, so I don’t have propositional attitudes towards them. Then there’s still a sense in which I know which teams make the playoffs, for it is true for each team making the playoffs that I know it makes the playoffs. A similar account can be given of privileged access. I know what I’m imagining iff for every proposition that I am imagining, I know that I am imagining it.
If we adopt this account of privileged access, and we adopt Hilary’s account of the two-atom world, then possibly we can avoid the argument above. Even if, for example, Ted thinks that (2) is part of the content of what he is imagining, but it is not, that is no threat to privileged access under its current interpretation, for privileged access only has implications for the content of his imagination.
It might be worried that even if we adopt all this, there will still be propositions that are part of the content of what is being imagined that Ted believes are not part of its content. For instance, it will be part of the content of the imagining that it is indeterminate whether (1) is true. But there are a few moves that will block that position. First, it might be denied that we can genuinely form propositions using an ‘determinately’ operator. Secondly, Hilary’s position might be altered so that it is indeterminate ‘all the way up’, whether (1) is true in the world in question. That is, no proposition formed by prefixing strings of determinately operators and negations to (1) is determinately true in that world. It is not so hard to build formal models such that this is the case as long as we put few formal constraints on the determinately operator, although it is sometimes hard to see the philosophical motivation for the position.
The real objection to this way of saving privileged access, I think, is that Hilary’s position is incoherent. (1) and (2) recall, are constructed entirely out of logical vocabulary. As Ted Sider has stressed in a few places, it is implausible that such claims are indeterminate. Indeterminacy arises in normal language because there are too many competitors to be the meaning of a particular term, and considerations of Lewisian naturalness do not settle the issue. But this is not the case when a sentence is constructed entirely from logical vocabulary, for there are very natural candidate meanings for the logical terms. If the only way out for the defender of privileged access with respect to narrow content is to claim that (1) is indeterminate, then things look very bad indeed for privileged access.
posted by Brian Weatherson 11/23/2002 06:26:00 PM
The results of the vagueness experiment were quite encouraging. Here’s the philosophically interesting part of what happened. The subjects were asked whether they thought n minutes after midday was late (for the relevant appointment) for increasing n until they finally said Yes at some point, call it k. Then they were asked again about whether k-1 minutes after midday was late. 18 out of 19 respondents (I know it’s a small sample, but it’s something) said No, just like they had when asked the question the first time, and despite having just said that k minutes was late, and despite that answer being displayed in boldface just above the question. Various contextualists (I don’t have the references with me, but I’ll try and find them later and update this post) have claimed that saying that k minutes after midday is late creates a context where it is no longer true that k-1 minutes after midday is not late, and so when this question is asked the common answer should be Yes. But only 1 respondent so far has said that. Some contextualists have been relatively cautious about what the empirical consequences of their views should be, but some have been relatively bold about what they think will happen in experiments with just this design. It would be good to do this test more rigorously, with random sampling and a larger sample, but 18-1 is a pretty big split even allowing for those design flaws. Much thanks, of course, to everyone who has taken the experiment. I will keep it up, and keep the counters running, though now that I've said what the experiment was testing for the flaws in the experimental design are even more alarming.
UPDATE: It is actually 17-1 in favour of being consistent, not 18-1 as I reported above. My apologies.
posted by Brian Weatherson 11/22/2002 04:58:00 PM
I’m trying to write something up about narrow content and privileged access, and I noticed two things while doing a bit of web surfing as background. First, a rather long, though from what I’ve read quite good, piece on narrow content has just been published in the Stanford Encyclopedia by Curtis Brown. Secondly, as I remember John Hawthorne telling me years ago, it is possible to get arthritis in the thigh. I know you shouldn’t trust everything, you read on the web, but scroll down these definitions of types of arthritis until you get to Fibromyalgia. If you can’t be bothered following the link, the text is: “Usually affecting women, fibromyalgia is a condition that affects the muscles at their attachments to bones.” I don’t know about you, but I’d say that’s something that one could have in one’s thigh. For more details, see these links.
posted by Brian Weatherson 11/22/2002 04:23:00 PM
Say your preferred account of the a priori is that “S is a priori iff it knowable just on the basis of one’s understanding of S”, as Stephen Yablo suggests in his paper in the Gendler and Hawthorne volume. And say that you also think, not unreasonably, that understanding the logical connectives just means finding their elimination and introduction rules primitively compelling. And say that you also think (as I’m not sure that I do) that the relevant rules are those for a Gentzen style single conclusion natural deduction system. So the introduction and elimination rules for ® are given by the equivalence of the following two sequents.
(1) S, A: B
(2) S: A ® B
I use S as a variable over pluralities of propositions, A and B as variables over propositions, and : for the consequence relation. Nothing above is utterly unreasonable, and indeed everything is close to majority opinion amongst the relevant theorists, though this being philosophy nothing in uncontroversial. Now it is well known that these rules do not let us prove (3)
(3) ((p ® q) ® p) ® p
(3) can be proven using the standard rules for the connectives, but you have to use the rules for negation, not just the rules for ®.
If you accept all the assumptions in the first paragraph, then you have a dilemma. Either (3) is not a logical truth, despite being a truth-functional tautology, or some logical truths are not a priori. Dummett accepts all of the initial assumptions (I think) and concludes that (3) is not a logical truth. Yablo I think is committed to (3) not being a priori, despite being a logical truth. This isn’t an unintelligible position, but it might be grounds for rejecting his account of what it is to be a priori.
posted by Brian Weatherson 11/22/2002 02:19:00 PM
Simon Blackburn doesn’t much like Steven Pinker’s most recent book on nativism. The most amusing part (among many) is where Blackburn starts using plot details from The Flintstones to work out what the world was like in hunter-gatherer days, and hence derive some quick’n’dirty results in evolutionary psychology. But the most alarming part was when Blackburn said, “it is not for its cultural history that people are buying Pinker's book in alarming numbers, but for the promise of a new synthesis”. Alarming?! Pinker’s book is over the top, and as Blackburn points out the enemy under attack is a strawman even by high school debating standards, but I don’t know that makes it alarming that his book sells well. If only more academic books would do so.
posted by Brian Weatherson 11/20/2002 11:44:00 PM
There’s been a David Chalmers sighting on Instapundit. Traffic to his site should crash the University of Arizona system by mid-afternoon.
On a related note, my Sims paper, which I first started thinking about after reading something else on Instapundit, got a positive sounding revise and resubmit today! Whether this means a publication, I don’t know, but it is progress.
On principle I’d rather not link to sites as conservative as Instapundit, but it’s a bit childish to not mention things that are philosophically interesting just because they may be, to a greater or lesser degree, politically distasteful. (Just reading that over, it seems to imply that I have childish principles but I’m ‘mature’ enough to disobey them. Not the best state to be in perhaps, but not the worst either.)
posted by Brian Weatherson 11/20/2002 03:23:00 PM
The Binding Argument
Jason Stanley claims that the following kind of argument is generally sound.
(1) It is possible to interpret “In every room in John’s house, every bottle is in the corner” as being true iff in every room in John’s house, every bottle in that room is in the corner.
(2) Hence the logical form of “Every bottle is in the corner” includes a quantifier domain restrictor, as it might be the property being in this room, which is bound by the outermost quantifier in the longer sentence.
This is a move in a dispute between those who say that “Every bottle is in the corner” expresses the proposition that every bottle whatsoever is in the corner, or perhaps expresses no proposition at all, and only conveys the proposition that every bottle in this room is in the corner. Jason thinks that the restriction to bottles in this room is not pronounced, but it is articulated - it is a genuine feature of the syntax of the sentence, and of the proposition that sentence expresses.
This proposal has come in for some criticism recently, especially in Ernest Lepore and Herman Cappelen’s paper in the most recent Analysis. Let me add my own little objection, mostly due to a conversation with Europa Malynicz. (The examples are very close to ones she suggested, as I guess is the argument, but the usual disclaimer that all the faults are mine applies.) (3) is a well-formed sentence, and the quantifier here does not feel like a null quantifier. It is just the kind of thing that could be said by a rather cautious traveller.
(3) Everywhere I go, I only drink bottled water.
Jason’s argument is that the quantifier here is not a null quantifier, so it must be binding something, so the embedded sentence must have syntactic element that is bindable. Hence I guess (4) really expresses the proposition (5).
(4) I only drink bottled water.
(5) I only drink bottled water at place x.
But it is quite implausible that this is what (4) means. I don’t think this is implausible for the reason Lepore & Cappelen think it is implausible, that it puts too many variables into (4). Maybe they are there, maybe they aren’t. I think it is implausible because it suggests, falsely, that one could use (4) when at place x to express the proposition that one only drinks bottled water at that place, even though you drink tap water anywhere else. So I could use (4) here and now to express the proposition that in Providence I only drink bottled water.
This argument needs one qualification. In some contexts it is possible to use (4) to express the proposition that I only drink bottled water in Providence. If I have just been asked a question about Providence and especially its water quality, and I respond with (4), it will be natural to view my utterance as being elliptical for the claim that I only drink bottled water in Providence. But what Jason needs (I think) and what he can’t have (I also think) is a situation where I could use (4) to express that proposition without it being simply elliptical.
posted by Brian Weatherson 11/18/2002 10:15:00 PM
David Fickling makes a few sound points here about the quirks of the Australian character, but there are a couple of errors that suggest he might be new to the Australian beat. For one thing, Ned Kelly was more the bank-robbing than the sheep-shearing kind of larrikin. (I guess nowadays he’d be thought of as a terrorist by some.) For another it’s a wee bit more than 200 miles from Brisbane to Sydney. These kinds of errors won’t happen once you’ve been in the country long enough.
There’s something rather nice about having one’s national identity be based around partying, even if it is grating to see a conservative like Howard try and adopt that for his own image. In general I think Australians are doing rather better at the pursuit of happiness thing than Americans, despite not having deigned to adopt it as a constitutional policy. I hadn’t realised quite how distinctive the larrikin figure is. Maybe that’s why no one’s been able to figure out the point of the pranks paper.
On a different topic, everyone who has responded has had the same result in the vagueness experiment. I can’t say what that is without biasing the experiment even more than I already have, which would be a bad thing. So take the experiment yourself and I’ll let you know how it all turns out.
posted by Brian Weatherson 11/18/2002 09:56:00 PM
Probably very few readers here are interested in the minutiae of Victorian opinion polls, but I thought this was particularly striking. The Age’s poll taken last weekend for the upcoming Victorian state election has some surprising number. One surprising, and too good to be true, number is that Labor is ahead by 22 points on two-party preferred. If only that were true. But what seemed more interesting were the numbers about the Liberal Party’s speeding policy. Traditionally in Australia, like in most other places, if you were within 10% of the speed limit you wouldn’t get ticketed. The Labor government abandoned this policy, directly police to ticket anyone who was measured to exceed the speed limit by more than the margin of error of the radar detectors (about 3 km/h). The Liberals claimed this was just a revenue raising policy (which was probably true, even if it has a nice public safety side effect) and promised to abandon it.
Now I’d expect this would be a vote winner for the Libs. And I wouldn’t have expected much of a demographic split in the results, except maybe a slightly higher support for it in non-metro areas. Well, that was all mistaken. Here are the relevant numbers, with the support for the policy listed first.
Good thing I’m not a political advisor, huh?! The last two lines were a complete shock though. I don’t recall seeing that big a gender gap on any polling question in Australia for a long time. Even on issues where one traditionally expects a gender gap, like child care or abortion rights, there’s usually nothing this big. In fact it’s very rare for an Australian poll to get numbers this lopsided on any partisan question. Speed limits are obviously a very minor issue, but maybe it signals a wider gulf in attitudes towards the proper balance between safety and liberty. If I was a political scientist looking at Australians’ attitudes about the role of government in setting this balance, I’d start polling on a few other related issues to find out.
posted by Brian Weatherson 11/18/2002 03:19:00 PM
I previously posted on the existence of a Buffy conference in Norwich that looked like it would be dire, but turned out apparently to be pretty good. Now there’s a Buffy conference in Melbourne.
posted by Brian Weatherson 11/18/2002 02:42:00 PM
I’ve done one of these experiments before, but I didn’t run the experiment in HTML, and I didn’t have as many readers then as I have now, and I realised something new about the experimental design that should be controlled for, so I’m running another vagueness experiment. If you’d be ever so kind as to follow that link and answer all the questions that get thrown at you as honestly as is possible, I’d be most appreciative. I’m keeping of count of who gets to what pages when, so I’ll be able to interpret the results reasonably accurately, though I may have to do some interpreting at some stages.
Anyway, I’ve been ever so annoyed at contextualist claims about what will and won’t happen in forced march Sorites for a while now that I thought I should do something serious about testing them. Then I realised I knew nothing about experimental design, so I’m doing this instead.
UPDATE: This is a little embarrassing to admit, but I didn’t transfer the webcounter code to the website last night when I set up the experiment. So I haven’t been able to keep track of the results, which is a large part of the point. So could everyone who has taken the experiment before midday east coast time (1700 GMT) please either take the experiment again or, if you couldn’t be bothered clicking through all those things again, email me a summary of your choices and I’ll enter them by hand.
posted by Brian Weatherson 11/18/2002 01:33:00 AM
Some quick reports on journal articles of interest. (Sorry for the lack of links, but everything is subscriber only.)
It’s a little old now, but I only just found out that Legal Theory last year ran a symposium on law and vagueness. I haven’t read it all, but I guess I’ll have to when I ever get back to writing the vagueness book. Two quick points to note. Reading Dorothy Edgington’s paper made me realise that her position is a little closer to mine than I’d previously acknowledged. She says that there are numerical degrees of belief, but they ‘compose’ in the way that probability values do. The effect is much as if you’d taken a range of precisifications, put a measure on them, and let the degree of truth of p be the measure of the set of precisifications at which p. I don’t know why we don’t just get rid of the numbers, since they don’t play a role in the compositional theory, or how this extends to the intensional, but it is similar enough to my theory that I should comment on this eventually. And the Joseph Raz comment on Roy Sorensen’s paper reads more like a pro wrestling smackdown than like a scholarly interchange. Sorensen’s tendency to never say something straight if he can say it as a joke can be infuriating from time to time, but I’m not sure that this is the right response.
There looks like there’s a potentially interesting article on conditionals in the latest Notre Dame Journal of Formal Logic, but since it isn’t online it may as well not exist from this blog’s perspective.
The August Philosophical Studies has two articles from the Syracuse-Rutgers crew. John Hawthorne’s article on ‘blockers’ has finally been published, though I think it should have been edited a little more closely so it didn’t look quite so much like a part of a longer piece. Hint: starting an article with ‘As we have seen’ is usually a bit of a give away. And Ted Sider’s second article on time travel is also included. By the way, that link is to the free copy of Ted’s article on his webpage. (More public domain discussion on time travel can be found here, though of course it can’t be guaranteed that the content will be Sideresque.)And the September Phil Studies has an article by Brown’s Juan Comesaña, on how we can resolve some tricky problems for certain reliabilist theories of justification by going two-dimensionalist. Of course if you’re reading this site you probably already believe that all philosophical problems can be solved somehow by going two-dimensionalist, so this won’t necessarily be much of a surprise.
There’s a few interesting new papers up on the Stanford Encyclopaedia of Philosophy. Michael Zimmerman’s entry on Intrinsic Value is particularly comprehensive, as you’d expect from someone who’s just written a book on the subject. (And it’s probably a useful resource for those looking to my entry on intrinsic properties for something about value.) Michael Dickson’s entry on Modal Interpretations of Quantum Mechanics is a fascinating survey of a field that I (at least) knew very little about. The Stanford Encyclopaedia is getting a pretty good coverage of QM - perhaps science-y types are better at meeting deadlines than us humanities-oriented hacks. As you’d expect, Alan Hájek’s entry on Interpretations of the Probability Calculus is first-rate, a great introduction to the field for those who wonder what philosophers of probability argue with each other about. On the other hand, Anat Biletzki and Anat Matar’s entry on Wittgenstein was rather disappointing. There’s next to no discussion of any books other than the Tractatus and the Investigations. Actually, there was little there that I didn’t know, and when it comes to Wittgenstein I know nothing. Maybe they can get some more specialist entries on, say, Wittgenstein on mathematics or ethics. Expect to see soon my mammoth (and, to be honest, a little too self-centred) entry on The Problem of the Many.
posted by Brian Weatherson 11/17/2002 02:02:00 PM
After my previous post on the paradoxes, Hud Hudson reminded me that there are some much simpler paradoxes involving validity rather than soundness. These don’t appeal to anything as controversial as excluded middle, so they are a little more forceful.
A1. Argument A is valid
AC. Santa Claus is coming to town.
The argument that this leads to paradox is as follows.
(1) If Argument A is valid, then if Argument A is valid, then Santa Claus is coming to town.
(By the definition of validity)
(2) If Argument A is valid, then Santa Claus is coming to town.
(Contraction from (1))
(3) Necessarily, if Argument A is valid, then Santa Claus is coming to town.
(By (2), since all the premises we used to get there are necessary truths.)
(4) Argument A is valid
(From (3), and the definition of validity)
(5) Santa Claus is coming to town.
(Modus Ponens on (2) and (4).)
Well, that was a little easy. Anyway, here’s the serious problem. The obvious way to block the paradox here is to say that (2) doesn’t really follow from (1). And Hartry Field has been arguing just that for a while now, with I think some success. But it seems to me that it’s much more plausible to say that p ® (p ® q) doesn’t entail p ® q when the arrow denotes ordinary ‘if…then’ than when it denotes entailment. When ® means ‘entails’, contraction seems much more plausible. (I could be wrong about the relative plausibility of the claims here - I think contraction is still quite plausible for ordinary conditionals, but I think it is if anything stronger for entailment conditionals.) Anyway, then the argument to paradox goes as follows. (Using ® for the entailment conditional.)
(6) (Argument A is valid) ® ((Argument A is valid) ® Santa Claus is coming to town))
Assuming here that an analysandum entails its analysans
(7) (Argument A is valid) ® Santa Claus is coming to town)
Contraction on (6)
(8) Argument A is valid
(7), connection between validity and entailment
(9) Santa Claus is coming to town.
Modus Ponens on (7), (8)
Of course, none of this is original to moi. I only mention it here because I had forgotten there were proof-theoretical paradoxes, and it is not entirely obvious that the solutions that work for other paradoxes also work for these.
posted by Brian Weatherson 11/15/2002 05:26:00 PM
The Brown Alumni Magazine has a front-page feature on Steven Emerson, who has for many years now been one of the more outspoken voices proclaiming that we face a grave danger from Islamic terrorists. (Why? I hear you ask. Well, he’s a Brown Alum, he’s in the news, he does good interview, and I suppose we can’t put Chris Berman on the cover of every alumni magazine.) Emerson doesn’t come off too well in this story about the firing of Professor Al-Arian from Salon. Considering the source, you might not think that it’s necessarily fair to Emerson, so the puff-piece from Brown might serves as a kind of balance.
posted by Brian Weatherson 11/15/2002 03:04:00 PM
I meant to add earlier when writing about Wo’s latest entry that it would be fun if many more people in philosophy had blogs, so there could be a rolling public permanent discussion. EPhilosopher has discussion boards, but blogs seem to encourage slightly more careful commentary. (Bracket here my comments below about McGinn and darts.) On the other hand, if everyone had blogs, I’d probably do nothing but write responses to things I see on blogs. On the third hand though, there might be nothing wrong with that - I’d probably produce much more philosophy this way than I would writing one or two papers per semester (or year, or decade) for journals.
posted by Brian Weatherson 11/14/2002 11:37:00 AM
Tomorrow Mohan Matthen will be presenting a paper called “Sensing and Doing”. The talk will be in the Philosophy Department at 5.30.
Also tomorrow, a play about robots and consciousness, “Judy, or what is it like to be a robot” will be presented at AS220, in downtown Providence, at 8pm. It costs $7, but it looks kinda interesting. (The promo I got sent for it had glowing quotes from Dennett and Hofstadter, which probably tells you something about the line it is taking.)
Finally, Harvey Pitt (yes, that Harvey Pitt) will be speaking at Brown next week, presenting the Noah Krieger Memorial Lecture. I imagine the tone will be relatively polite, even respectful, as befits a memorial lecture, but does not in any way befit Pitt.
posted by Brian Weatherson 11/14/2002 11:22:00 AM
From Wo’s Weblog (a seemingly endless source of good ideas):
Suppose one day I'll meet Swampman and the brain in a vat. We will be able to communicate perfectly well. How could this be possible if we spoke completely different languages? Perhaps there are aspects of meaning which aren't directly relevant for understanding and communication, but this certainly can't be true for all aspects.
I just realized that this account resembles what Lewis says about naming the colours in 'Naming the Colours'.
Two quick thoughts. First, George Bealer (in his paper in the totally wonderful volume on Conceivability and Possibility) thinks that similar cases are bad news for two-dimensionalism. The idea is that since the inhabitants of ‘Dune’ and ‘Waterworld’ share almost no platitudes about water, according to the two-dimensionalist they should not be able to understand each other, since understanding involves sharing of platitudes. But, says Bealer, they certainly could understand each other. (We could question that but let’s not.) Now if the theory in ‘Naming the Colours’ works, we should be able to treat the Dune crew and the Waterworld crew on a par with the footy people and the rugby people, and explain their cross-communication the same way.
Secondly, I’m not so sure the theory in ‘Naming the Colours’ is all that clear. I think I think it ends up being something like this.
- ‘Red’ (in the mouth of an English speaker) is a name for whatever fills the red role in the theory of redness common to all English speakers.
- The theory of redness common to all speakers says, inter alia, that for each community, the theory of redness of that community includes paradigms of redness.
- The theory of redness of the footy people includes the claim that the stripe on the Essendon jumper is actually red.
So I think the upshot of this is that one of the platitudes about redness is that it is the best deserver of the name ‘red’ in the footy people’s theory of redness, and in the rugby people’s theory of redness, and in the arty people’s theory of redness, and so on. There’s no reason to think that this iterated Ramsey-sentence approach doesn’t make sense. But I do worry a bit about including something so explicitly metalinguistic in the platitudes. Only a bit, mind you. If the platitudes do have to be metalinguistic, and metaRamsified, that would explain why Lewis includes a rather long footnote defending causal descriptivism about proper names, somewhat without warning, earlier in the paper. But it didn’t seem entirely clear to me at first reading that the game was going to get this complicated, and Lewis is normally upfront about matters like that, so I’m worried that I’m misinterpreting something here.
Bealer has a final worry about this kind of approach, that I’m not quite sure how to respond to. Assume that one of the platitudes fixing the reference of my term ‘red’ is that it is the colour that fills the redness role in the rugby people’s theory of colour. And assume that I know nothing about the rugby people’s platitudes. Then, Bealer sort of suggests (sort of because he’s not addressing this particular proposal) I don’t understand my own term. But this is wrong since I do understand it. Now I think the (implicit) response in ‘Naming the Colours’ is that since I’m a footy person, and hence have tacit knowledge of the footy people’s theory of colour, and that theory suffices to fix the reference more or less, that combined with the knowledge that everyone who speaks English knows some theory that latches onto more or less the same property is sufficient for understanding. And I think if that’s the response I believe it, though I can see the worry Bealer is pointing to - the Lewisian theory suggests that learning the platitudes of the rugby folk would improve my understanding of the term ‘red’, but really that wouldn’t improve my understanding at all.
Did you know: the first platitude listed in the OED to fix the reference of ‘red’ is that it is the colour of British Empire countries on traditional maps?
posted by Brian Weatherson 11/14/2002 11:01:00 AM
The Bernard Williams chat on the Guardian wasn’t particularly exciting. Lots of Williams reminding people that there are things that are objectively true. Exciting things mostly, like that it is raining outside, or that England hasn’t won the World Cup since ’66. Actually, he didn’t say the last thing, which prompted one of the more amusing questions:
Not since Freddy Ayer has there been a prominent football-supporting philosopher. Karl Miller, admittedly a mere former UCL English professor - although by all accounts a bright lad – has kept the flame alive with his “Gazza was like a bronzed God, resplendent in the Mediterranean sun.” But that old lag Honderich can't tell his Liverpool from his liver sausage. Parfit reckons he knows a thing or two about the continuity of self, but has consistently been fucking terrible on the flat back four debate. Nussbaum just bursts into tears when she’s asked to explain the offside ruling; and McGinn thinks we’re all too innately stupid to understand anything more complicated than darts.
What's wrong with philosophers nowadays? Have you no sense of priorities?
Surprisingly enough, Williams did not answer that question.
Why can’t more American’s ask questions like that of philosophers? The comment about Nussbaum is horribly unfair of course, but the McGinn comment is much closer to the target. And can I just remind you that while it’s not football, Marc Lange did have a very good paper in the latest Analysis which revealed a rather subtle understanding of some important issues in baseball. He may have made some comments about how this bore on the issue of whether current scientific theories are true, and including afterthoughts like this shows that he has his priorities in exactly the right order. So not everywhere do philosophers have misplaced affections.
The really depressing thing to come out of the chat is that after doing a survey of the literature, Williams concluded that there are people who need to be reminded that there are objective truths like this in the world. Fixing up some belief systems is a rough old job, and I’m glad he’s trying to do it and not I.
Postscript: in the intro to the chat the editor described Williams as “this country’s greatest living philosopher”. Huh? What does this say about the rest of the philosophical scene there? Michael Dummett’s just an old commie hack? Tim Williamson’s a mere logic-wielding showoff? I’d probably vote Mike Martin above Williams in terms of great British philosophers, but I’m probably just being ageist there.
posted by Brian Weatherson 11/13/2002 11:25:00 PM
Wo is on a roll at the moment. This post about rigidity and counterpart theory is actually I think much more interesting than it may first look. (Or, I should say, may first look if you're a lazy reader who reflexively assumes that counterpart theory can solve all the traditional problems concerning de re modality without breaking a sweat.) So at first, I thought the issue of how do you define rigidity without assuming trans-world identity wasn't that deep. Here’s how you define rigidity if you’re a counterpart theorist
(CR) t rigidly denotes a iff for all a´, w´, if t denotes a´ in w´, then a´ is a counterpart of a in w´.
This doesn’t cover the issue about how to define rigidity for natural kind terms if you’re a trope theorist, but I suppose something similar could be done. So on first glance I thought, nothing to see here, move along. But on second thought I thought maybe I’d gone a little too far. After all, any fool can put the definition of rigidity through the ‘counterpart-theoretic-equivalent’ generating machine and come up with something like (CR). The philosophically interesting question is whether what we get out really deserves to be called rigidity. And on third thought, I came up with a little argument that it doesn’t. To get to it, consider the following argument:
The Rigidity Argument
R1. Possibly, t1 is t2
R2. ‘t1’ is a rigid designator
R3. ‘t2’ is a rigid designator
RC. So, t1 is t2
(The round quotes here should be corner quotes, but I’ve got no idea about how to do them in HTML.)
I think that it’s a platitude about rigidity that The Rigidity Argument is valid. If you don’t immediately agree, here’s a little argument to convince you. Assume that possibly t1 is t2. So in some world, t1 and t2 denote the same object. Since t1 is rigid, it denotes the same object here as it does in that world. And since t2 is rigid it denotes the same object here as it does in that world. But that means that t1 and t2 denote the same object here, so the sentence ‘t1 is t2’ must be true, and by semantic descent t1 is t2.
Now let’s recall some of the special features of counterpart theory. Two objects, a and b, in this world, can have the same counterpart, c in another world w. Assume that this is the case, and assume that F is some (quite precise) property instantiated only by a in this world, and G another (also quite precise) property instantiated only by b. Then for the counterpart theorist, it’s true in w that the actual F is the actual G. So, it’s possible that the actual F is the actual G. But it’s not true that the actual F is the actual G. But I thought ‘the actual F’ and ‘the actual G’ were rigid designators if anything was. It looks like one of the following three things has to go.
1 A counterpart-theoretic treatment of de re modality
2 The view that ‘the actual F’ is a rigid designator
3 The view that The Rigidity Argument is valid
It’s a pity that we have to give up one of these, because until a few hours ago I’d have probably endorsed all three. And I’d still like to endorse all three, if I didn’t think they were mutually contradictory.
It would be no good to ‘solve’ the problem by finding a version of ‘counterpart theory’ that eliminated the possibility that a and b could have a counterpart in common. I know this would be technically possible, and I could even whip up a theory that did it quicker than I could fry an egg (though maybe not quicker than you could fry an egg) but it’s hard to see the philosophical point. Counterpart theory is a substantive philosophical view, not a technical apparatus, and if you start putting those kind of restrictions into the formalism, saying that a and b can’t have a common counterpart, you’ve effectively abandoned the philosophical view. As I said, this could be done technically, and could even be done technically with the veneer of counterpart theory, but I’d regard it as giving up 1.
So what should we do? I think we should recognise two notions of rigidity. There’s a strong notion of rigidity, according to which a rigid designator really names the same damn object in every possible world. On that notion of rigidity, The Rigidity Argument is valid, and ‘the actual F’ simply isn’t a rigid designator according to counterpart theory. And there’s a weak notion of rigidity, given by (CR) on which ‘the actual F’ is rigid, and The Rigidity Argument is invalid. And it’s a substantive thesis, one of the many substantive yet somehow plausible theses advocated by counterpart theorists, that apparently rigid designators are only weakly rigid, not strongly rigid. (Some terms, such as numerals, may be strongly rigid de facto, but no term is strongly rigid de jure.) This ‘two kinds of rigidity’ solution may look pretty ugly, but I can’t try and be Solomon all the time without sometimes splitting the baby. (I got the last bit of pop philosophy from Law & Order, which is I think a step up from stealing philosophical examples from Budweiser commercials.)
Anyway, this is all a mess, but if anything things get worse. I’d have sworn, before thinking too hard about this, that (4) and (5) were equivalent, but of course this isn’t true. (4) is a contingent falsehood and (5) a necessary falsehood.
(4) The actual F is the actual G.
(5) Actually, the F is the G.
If it makes you feel any better, the biconditional (4) iff (5) is still a priori, last I checked, just not necessarily true.
I planned to write something more on the paradoxes, but it’s late and I’m tired, and in a little philosophical shock.
posted by Brian Weatherson 11/13/2002 01:55:00 AM
From Wo’s Weblog:
1. If the conclusion of argument Z is true, then argument Z isn't sound.
2. If the conclusion of argument Z is not true, then argument Z isn't sound.
Therefore: Argument Z isn't sound.
Is argument Z sound? (If not, which premise is false?)
There is a paradox here, but maybe this question isn’t the best way to get at it. After all, the paradox can be tightened up a little. Premise 2 is an analytic truth, so it can be dropped from the argument. Hence the following should be just as paradoxical.
1. If the conclusion of argument Z´ is true, then argument Z´ isn't sound.
Therefore: Argument Z isn't sound.
But now it’s clear what the untrue premise must be, it’s premise 1. So I think premise 1 is also untrue in argument Z. That may be paradoxical, but at least we’ve located the paradox.
posted by Brian Weatherson 11/12/2002 08:36:00 AM
Conservative webpundits often accuse the Guardian of employing faulty logic. And normally I’m not inclined to believe them; I generally like the Guardian more than any other newspaper in the world, even if they do occasionally err on the side of publishing somewhat extremist lefty positions. But when they start running headlines like How England can do the Impossible, I start to think that maybe there are grounds for complaints about their logical acumen.
By the way, I got the time of the chat with Bernard Williams wrong. It is 10am EST not 9am.
posted by Brian Weatherson 11/11/2002 06:36:00 PM
I’ve finished a draft of the many paper! Apart from adding bibliography, internet resources, etc, this is close to the version I intend to send to Stanford. So comments are extremely welcome. This only took about five times as long as I expected. That the paper is about two and a half times as long as expected might have something to do with this, as might the growing gap between the speed I think I can write and the speed I can actually write.
posted by Brian Weatherson 11/11/2002 06:15:00 PM