So, first things first, we will be back to more standard fare on Wednesday, with a post on J.C. Beall's discussion of the difficulties dialetheists have with saying that some things are "just false."
Meanwhile...
Remember What's Wrong With The World? That's the blog where Ed Feser said that a doctor murdered by a domestic terrorist had it coming (because, y'know, every sperm is sacred), then accused me and a few others of "libel" for pointing out that he'd said what he said.
So, as you can imagine, the recent decision by the APA to kind-of-sort-of-penalize institutions that discriminate against gays and lesbians didn't go over particularly well over at W4. In a discussion over at Philosophy Smoker, a question was raised about whether the sorts of views regularly expressed at W4 are typical of Christians in philosophy. Given that the great majority of philosophy academics are atheists or agnostics, and that the bloggers at W4 make a huge deal of the alleged Christian basis of their extreme misogyny, support for institutional discrimination against gay and lesbian job applicants, etc., etc., it's natural for people to start wondering whether these views are actually typical of their theist colleagues. Fortunately, the answer to that question mostly seems to be "no."
Brian Leiter quoted the questions a commenter at the Philosophy Smoker asked about whether other Christians in philosophy agreed with the hateful interpretation of Christianity spouted by folks like Professor Feser, as well as a sample of answers that other commenters gave. (The gist of all of which was 'no, no we don't.') Feser responded by interpreting Leiter's quoting and linking to this discussion as Leiter attempting to "smear" W4. (What the "smear" is supposed to be, I have no idea. One of the funny things about Feser is that he blogs at a place that advertises itself as being on a "crusade" to save "the remains of Christendom" from "liberalism and the jihad," but whenever Christendom's enemies notice the existence of W4 and say something critical about it, instead of wading into the fray as a happy warrior for Christ, he tends to whine about how he's been misrepresented, he's being stalked, the critics must be "obsessed" with him and his co-bloggers and so on.) In any case, the ever-so-clever response he endorsed (from an anonymous correspondent) goes like this:
I think it might be fun if you all decided to simply respond in kind. That is, ask your Atheist friends some questions and see whether Leiter's views fall within the "mainstream" of atheist philosophers. Maybe some questions like the following:
1) Did you think the collapse of the Soviet Union was unfortunate, politically and morally speaking?
2) Do you think that there is a noteworthy moral difference between heteronormative sexual morality and believing that homosexuals should be executed?
3) Do you believe there is a noteworthy moral difference between the Taliban and people who think it should be legal to voluntarily pray in public schools?
4) Do you think it is morally appropriate for a notable professional philosopher to personally attack graduate students and untenured faculty in a highly public and visible forum?
5) Do you think it is misogyny to acknowledge genetic differences between men and women?
6) Do you think it would have been a gross exaggeration to say that George W. Bush is a theocrat and/or a fascist who was planning to "imminently" reinstate the draft or "imminently" bomb Iran?
7) Do you think it would be a gross exaggeration to compare Bill O'Reilly with Joseph Goebbels?
8) Did the clips of Jeremiah Wright's sermons make you more favorably disposed towards Obama?
Now, the clumsiness of all of this, and the extreme disanalogy between asking Christians if they agree with the views of academics who constantly use Christianity to justify their bigotry, and asking atheists if they agree with the unrelated political views of a blogger who rarely references his atheism, is striking. That said, just for the hell of it:
(1) Stalinism was bad, and free speech and multi-party elections are good. That said, the impoverishment of the Russian people as their country's resources were sold off to a tiny handful of, basically, mafia families, was not so good. During the Cold War, the domestic regime of the Soviet Union was, of course, vastly more authoritarian and objectionable than that of the United States, but, on the other hand, the brutality of the American management of the U.S. sphere of influence in Latin America greatly exceeded that of the Soviet management of their sphere of influence in Eastern Europe. (When Lech Walensa spoke to Congress after the fall of the USSR about how the U.S. is a beacon of freedom for the world, a Jesuit priest whose response I saw pointed out that, if Walensa had tried to organize Solidarnosc in El Salvador, he wouldn't have been imprisoned. The death squads would have left him in little pieces on the side of the road.) I'd also point out that, for example, the war in Iraq would have never happened in a two-superpower, Cold War world. Whether Russia ultimately ends up being sufficiently less authoritarian under Putin than it was under Gorbachev to make the fall of the USSR "worth it" despite the human costs of economic "shock therapy," the bodies piling up in Iraq, the risks involved in massive post-Soviet nuclear proliferation, etc., is, I'd think, a question on which reasonable people can disagree.
(2) Sure, the same way I think there's a significant difference between garden-variety anti-Semitism and gas chambers. That said, both are things that I'm against, and Feser & Co.'s support for institutional discrimination against gay people doesn't start to sound reasonable just because he stops short of advocating their extermination.
(3) It is legal to voluntarily pray in public schools. Go to a public school cafeteria, get some food, and say grace before you eat it. See if anyone stops you. School-sponsored prayer, prayer that's institutionalized as part of the school day, even if student participation is nominally 'voluntary,' is (and should be) illegal. The Constitutional ban on state promotion of religion is a very good thing.
Now, taken by itself, the proposal that we go back to the days where you either stuck around for the prayers or you had to mark yourself for social isolation by leaving the room with the Jewish kids, as vile as it is, obviously isn't nearly as bad as what the Taliban did. On the other hand, a good many of the people who most fervently support that proposal--like, say, Ed Feser--support it as a small part of a much larger and scarier theocratic agenda, parts of which (like executing abortion doctors) would quite properly inspire Taliban analogies.
(4) Yes, I do. If a graduate student or untenured professor says something ridiculous in a visible public forum, then they can't turn around and whine that it's not appropriate for people who find it ridiculous to say so because of their professional status. As a graduate student who blogs, I've never thought I had some special protection against tenured professors (or anyone else) saying unkind things about me.
(5) Nope. Then again, put like that, no one else does either. Now, for the sake of contrast, I do think it's misogyny to want to legally force women to bring every pregnancy to term regardless of their wishes, and I think that objecting on principle to your city council hiring a female chief of police, because this means that a woman will be exerting authority over men, displays an almost psychotic level of misogyny.
(6) Those predictions would have been mistaken. As it turned out, in the eight years he had to work with, Bush "only" cluster-bombed, invaded and occupied two nations full of people whose children will now grow up hating us. Of course, he did endorse as his would-be successor a man known to gleefully sing "bomb bomb bomb, bomb bomb Iran," so it's safe to say that Bush wasn't, like, horribly opposed to thought of bombing Iran. And, given how thin our military is already stretched by occupying various other countries, if we were to attack Iran, a re-instatement of the draft might be the only way to fill all the necessary boots. Obviously, this would give a massive shot in the arm to the anti-war movement, on the streets and (as in Vietnam) in the military itself, so this would be a tactical decision I'd imagine that the war-makers would be very reluctant to make if they thought they could get enough fresh bodies some other way.
(7) It's not a comparison I would make. On the other hand, I think it's a whole lot less ridiculous than comparing a secular Jewish political economist who never held state power, who never killed anyone, and who consistently spoke out against things like censorship and the death penalty to Adolf Hitler because you disagree with him about public vs. private ownership of the means of production.
(8) They certainly didn't make me less favorably disposed to him. Some of what Wright said was dumb (endorsing conspiracy theories, etc.), but in most of the clips I saw, he was saying true and important things about the history and current reality of racism and imperial bullying of the third world. (Many of these true and important things, sadly, seem to have been lost on parishioner Obama, given the depressing degree of continuity between the foreign policies of the Bush and Obama administrations.) Now, as a Christian, Wright mixed in his message with a theology that says that God "damns"/punishes nations whose leaders do sinful things. Obviously, as an atheist, this is a place where my views diverge from those of the Reverend. On the other hand, I don't understand how anyone who considers themselves to be a Christian, and who has even casually skimmed the Old Testament prophets, could find that theological stance objectionable. And yes, presumably, a just God would object greatly to cluster-bombing Iraqi civilians, torturing people picked up on suspicion and holding them for years without charges, etc., etc., etc., and if (for reasons of whatever your favorite theodicy might be) He still allowed these things to occur, He'd certainly damn the perpetrators.
So, no, Obama's former Reverend having these views doesn't make me think less of Obama. This is not to say, of course, that there's nothing that could have gone on in that Church in Chicago that would make me think less of the guy. For example, if there was a youtube video of Jeremiah Wright laying hands on Barack Obama to give him a blessing to protect him against "witchcraft," while Obama had his head bowed and his arms upraised and was generally giving every indication that he thought what was going on was perfectly sane and reasonable, then that would make me think a lot less of him. Not to put too fine a point on it, it would make me think that he was fucking crazy and that he probably shouldn't be trusted with the amount of power and authority vested in a local police chief, much less the Presidency of the United States.
Monday, February 8, 2010
Wednesday, February 3, 2010
Some More Stuff About The Analytic/Synthetic Distinction
[The last paragraph of the first--and thus far only--Amazon.com customer review of Graham Priest's new book made me smile. And, obviously, I'd love to write that book.]
OK, so analyticity...
One of the funny things about the philosophical debate about analyticity is that it's often framed as a debate about "the analytic/synthetic distinction." Now, philosophy is sometimes characterized as the art of making distinctions, and even if this over-states things, it's still undoubtedly true that distinction-making is a central activity of philosophers, and that sentences of the form "Philosopher X denies the Y-Z distinction" tend to sound a bit odd. Moreover, this formulation tends to tilt the playing field heavily in favor of those defending the X-Y distinction. After all, they win the argument as long as there's some difference between X's and Y's. Those criticizing the distinction have the daunting task of trying to argue against all claims that X's and Y's are in any way different.
(Some friends of mine have this very nerdy running joke about starting a bar called "The Two Dogmas Of Alcoholism." We'd serve a shot called "The Analytic" and a shot called "The Synthetic" and both of them would be Jose Cuervo. When patrons had one of each and then asked what the difference was, the bar-tenders would all be trained to respond with, "ex-actly!")
Moreover, in the case of the analytic/synthetic distinction, given standard ways of categorizing all true statements into one column or the other, it's surely not the case that there are no differences between the things in the column where we write down various things that can be accurately translated into logical tautologies ("All bachelors are married"), mathematical truths and so on and the column where we write down the rest of the true statements. For one thing, trivially, the things in Column A have the property of "being the sort of statements that philosophers tend to refer to as analytic" and those in Column B lack that property. Depending on exactly how one carves up the lists, there might be more substantive differences as well--for example, the statements in Column A (but not the statements in Column B) might be instances of general logical claims. Whether those distinctions exist, or whether it can be useful to be clear on them, surely isn't at issue when people argue about the analytic-synthetic distinction.
What's at issue instead seems to be whether the true statements that are instances of general logical or mathematic truths have any of the special features that have often been imputed to them by philosophers, features related to how they become true, what sort of epistemic access we have to their truth, or some combination of the two. (As such, I generally think it might be better if instead of presenting it as an argument about "the analytic/synthetic distinction," we talked about it as an argument about "analyticity.") A while back, I made some objections to the claim that there's a distinction between the way that analytic statements are made true and the way that synthetic statements are, but of course, even if one rejects that distinction, that still leaves the much larger issue of whether there's some sort of epistemic distinction.
While I reject both, I tend to think the case for an epistemic distinction is much harder to respond to than the case for a truth-making distinction. (One of the interesting things about the debate is that often times even people who are vocally loyal to analyticity in one of the standard senses often find the other senses a bit incomprehensible. For example, in the session on "New Waves In The Philosophy Of Mathematics" at the Eastern APA, Roy Cook, who's defends a neo-Fregean program in the philosophy of math, said that he "didn't even know what it would mean" to say that true mathematical and other 'analytic' statements are made true in some special way that's different from how ordinary statements are made true.) Really getting into that involves tackling the issue of whether the elements of our overall package of beliefs about the world are confirmed or disconfirmed individually or holistically, how we can tell and what's at stake in the argument about all of that, and I'm not particularly keen to get into that right now.
For the moment, instead, I want to talk about a strange sort of intermediate sense of analyticity people often seem to appeal to, where the distinction is framed in terms of belief-revision. In the case of synthetic claims, belief-revision is a matter of refutation, whereas in the case of analytic claims, it's a matter of a change in meaning....we're just deciding to use words in different ways. Hence, maybe, the Newtonian claim that time and space are absolute has been refuted, whereas when we switch from Euclidean to non-Euclidean contexts and thus change our minds about whether there can be more than one straight line between any two points, we're just using the words "point" and "line" in new ways.
Without getting too deeply into the specific examples, this picture raises a lot of strange questions. Start with a particularly basic question:
Is all of this supposed to be descriptive or normative?
If the idea is supposed to be that, as a matter of fact, when we change our minds about an analytic claim, we're just changing the meaning of the terms involved, that seems to suggest that it's impossible for us to have incorrect beliefs about analytic matters, which seems to be fantastically implausible. Of course we sometimes believe contradictions, ocassionally explicitly (especially if you're named "Graham Priest" or "J.C. Beall") but more often implicitly. It's plausible that everyone's overall belief set is internally inconsistent all the time--maybe being a rational person means trying to recognize and correct the inconsistencies as efficiently as possible, but that doesn't mean that they aren't there.
But wait. If the two-tiered picture of belief revision supposed to be normative--that is to say, it's about how people *should* revise their beliefs--does that mean that, when you realize that you're wrong about an analytic matter (given how you're using the terms, you have some beliefs that jointly yield a contradiction), you shouldn't revise your beliefs to correct the inconsistency? Because, if you should, then your change-of-belief on the analytic matter is *not* a matter of deciding to use your terms in a new way, it's a matter of using them in the old way and substantively changing your mind. If someone used the word "bachelor" in the standard way, and believed that some bachelors were married, then when the inconsistency was pointed out to them, *shouldn't* they (while continuing to use the word "bachelor" to refer to unmarried males) move to reject their old belief that some bachelors were married? And wouldn't this be a matter of their old belief being refuted rather than them now making a decision to use the words in a new way?
It could be objected that, realistically, no one would hold this strange belief about bachelors, but:
(1) Let's not be too quick about that. In In Contradiction, Graham Priest argues for legal true contradictions. Given strangely-worded marriage laws, and the belief that legal dialetheias are possible, one could in fact see how a dialetheist could convince themselves that there are some married bachelors--men who both are and are not married under the inconsistency-generating law.
(2) Abstract from the example. After all, once you understand that "bachelor" means "unmarried" male, the logical inference from "John is a bachelor" to "John is unmarried" is an extremely simple and intuitive, since all it involves is a single instance of conjunction-elimination. However, lots of "analytic" truths can only be discovered as a result of much more complicated and less intuitively obvious chains of inference. For example, if you go with Frege (and against Kant) in thinking of mathematical truths as being "analytic," it's very obviously possible for people who understand the meanings of all the terms involved in a mathematical sentence to fail to grasp its truth.
Often times, in Intro classes, I'll spend a while explaining what "set" is, what it means for two sets to "have the same cardinality" and so on and no one will be lost. Then I'll show them that (and why), for example, the set of all whole numbers has the same cardinality as the set of all even numbers, and again, no one will be lost. Then I'll ask them if they think that all transfinite sets will have the same cardinality, and they'll either be unsure or raise their hands to say yes, absolutely, that should be true. Then I'll show them Cantor's diagonal proof that not all transfinite sets have the same cardinality, and, despite the fact that the proof is delightfully simple and straight-forward, some of them won't get it, or in fact will resist the counter-intuitive conclusion, despite having seen all the steps in the proof, and try to poke holes in it. So, we have a putatively "analytic" matter (do all transfintie sets have the same cardinality?) about which, even when they understand all the terms perfectly, many people will come to the wrong conclusion.
Are the students who get it and thus change their minds about whether all transfinite sets have the same cardinality somehow being irrational? If not, then not only is the claim that belief revision is a matter of change-of-meaning in analytic cases unworkable as a universal descriptive claim, it looks equally problematic as a normative claim.
Now, someone could say at this juncture of the argument that the claim isn't that revising away beliefs about analytic matters is (or even should be) a matter of change-of-meaning rather than refutation. Rather, perhaps, the claim could be that revising away analytic *truths* should be a matter of change of meaning rather than refutation--i.e. if you start with a *true* statement about analytic issues and you want to end up with another *true* statement, that seems to contradict it (e.g. you go from "there is always one and only one straight line between two points" to "there are infinitely many straight lines between two points"), then the belief-change must have been merely a matter of using the terms in a different way. Put that way, whatever you think about the specific examples (Putnam has a good discussion about the geometry case in "Is Logic Empirical?" that makes clear that this particular example isn't as straightforward as it seems), it's hard to argue. The only kind of "belief revision" that gets you from a true statement to another true statement that employs the same terms and seems to contradict the first one is a change of meaning.
But, wait, this is just as true if we're talking about "synthetic" claims! If I stop believing that it was raining at 3:01 on January 3rd in South Miami and I start believing that it wasn't raining then, and both statements are true, and there are no true contradictions, I must have started using the word "rains" in a different way, so that the light drizzle on January 3rd counted under the first definition and didn't count under the second one.
So, given that, what's the difference?
Or am I just missing something fundamental about what people are getting at when they claim that there's a distinction in terms of modes of belief revision?
OK, so analyticity...
One of the funny things about the philosophical debate about analyticity is that it's often framed as a debate about "the analytic/synthetic distinction." Now, philosophy is sometimes characterized as the art of making distinctions, and even if this over-states things, it's still undoubtedly true that distinction-making is a central activity of philosophers, and that sentences of the form "Philosopher X denies the Y-Z distinction" tend to sound a bit odd. Moreover, this formulation tends to tilt the playing field heavily in favor of those defending the X-Y distinction. After all, they win the argument as long as there's some difference between X's and Y's. Those criticizing the distinction have the daunting task of trying to argue against all claims that X's and Y's are in any way different.
(Some friends of mine have this very nerdy running joke about starting a bar called "The Two Dogmas Of Alcoholism." We'd serve a shot called "The Analytic" and a shot called "The Synthetic" and both of them would be Jose Cuervo. When patrons had one of each and then asked what the difference was, the bar-tenders would all be trained to respond with, "ex-actly!")
Moreover, in the case of the analytic/synthetic distinction, given standard ways of categorizing all true statements into one column or the other, it's surely not the case that there are no differences between the things in the column where we write down various things that can be accurately translated into logical tautologies ("All bachelors are married"), mathematical truths and so on and the column where we write down the rest of the true statements. For one thing, trivially, the things in Column A have the property of "being the sort of statements that philosophers tend to refer to as analytic" and those in Column B lack that property. Depending on exactly how one carves up the lists, there might be more substantive differences as well--for example, the statements in Column A (but not the statements in Column B) might be instances of general logical claims. Whether those distinctions exist, or whether it can be useful to be clear on them, surely isn't at issue when people argue about the analytic-synthetic distinction.
What's at issue instead seems to be whether the true statements that are instances of general logical or mathematic truths have any of the special features that have often been imputed to them by philosophers, features related to how they become true, what sort of epistemic access we have to their truth, or some combination of the two. (As such, I generally think it might be better if instead of presenting it as an argument about "the analytic/synthetic distinction," we talked about it as an argument about "analyticity.") A while back, I made some objections to the claim that there's a distinction between the way that analytic statements are made true and the way that synthetic statements are, but of course, even if one rejects that distinction, that still leaves the much larger issue of whether there's some sort of epistemic distinction.
While I reject both, I tend to think the case for an epistemic distinction is much harder to respond to than the case for a truth-making distinction. (One of the interesting things about the debate is that often times even people who are vocally loyal to analyticity in one of the standard senses often find the other senses a bit incomprehensible. For example, in the session on "New Waves In The Philosophy Of Mathematics" at the Eastern APA, Roy Cook, who's defends a neo-Fregean program in the philosophy of math, said that he "didn't even know what it would mean" to say that true mathematical and other 'analytic' statements are made true in some special way that's different from how ordinary statements are made true.) Really getting into that involves tackling the issue of whether the elements of our overall package of beliefs about the world are confirmed or disconfirmed individually or holistically, how we can tell and what's at stake in the argument about all of that, and I'm not particularly keen to get into that right now.
For the moment, instead, I want to talk about a strange sort of intermediate sense of analyticity people often seem to appeal to, where the distinction is framed in terms of belief-revision. In the case of synthetic claims, belief-revision is a matter of refutation, whereas in the case of analytic claims, it's a matter of a change in meaning....we're just deciding to use words in different ways. Hence, maybe, the Newtonian claim that time and space are absolute has been refuted, whereas when we switch from Euclidean to non-Euclidean contexts and thus change our minds about whether there can be more than one straight line between any two points, we're just using the words "point" and "line" in new ways.
Without getting too deeply into the specific examples, this picture raises a lot of strange questions. Start with a particularly basic question:
Is all of this supposed to be descriptive or normative?
If the idea is supposed to be that, as a matter of fact, when we change our minds about an analytic claim, we're just changing the meaning of the terms involved, that seems to suggest that it's impossible for us to have incorrect beliefs about analytic matters, which seems to be fantastically implausible. Of course we sometimes believe contradictions, ocassionally explicitly (especially if you're named "Graham Priest" or "J.C. Beall") but more often implicitly. It's plausible that everyone's overall belief set is internally inconsistent all the time--maybe being a rational person means trying to recognize and correct the inconsistencies as efficiently as possible, but that doesn't mean that they aren't there.
But wait. If the two-tiered picture of belief revision supposed to be normative--that is to say, it's about how people *should* revise their beliefs--does that mean that, when you realize that you're wrong about an analytic matter (given how you're using the terms, you have some beliefs that jointly yield a contradiction), you shouldn't revise your beliefs to correct the inconsistency? Because, if you should, then your change-of-belief on the analytic matter is *not* a matter of deciding to use your terms in a new way, it's a matter of using them in the old way and substantively changing your mind. If someone used the word "bachelor" in the standard way, and believed that some bachelors were married, then when the inconsistency was pointed out to them, *shouldn't* they (while continuing to use the word "bachelor" to refer to unmarried males) move to reject their old belief that some bachelors were married? And wouldn't this be a matter of their old belief being refuted rather than them now making a decision to use the words in a new way?
It could be objected that, realistically, no one would hold this strange belief about bachelors, but:
(1) Let's not be too quick about that. In In Contradiction, Graham Priest argues for legal true contradictions. Given strangely-worded marriage laws, and the belief that legal dialetheias are possible, one could in fact see how a dialetheist could convince themselves that there are some married bachelors--men who both are and are not married under the inconsistency-generating law.
(2) Abstract from the example. After all, once you understand that "bachelor" means "unmarried" male, the logical inference from "John is a bachelor" to "John is unmarried" is an extremely simple and intuitive, since all it involves is a single instance of conjunction-elimination. However, lots of "analytic" truths can only be discovered as a result of much more complicated and less intuitively obvious chains of inference. For example, if you go with Frege (and against Kant) in thinking of mathematical truths as being "analytic," it's very obviously possible for people who understand the meanings of all the terms involved in a mathematical sentence to fail to grasp its truth.
Often times, in Intro classes, I'll spend a while explaining what "set" is, what it means for two sets to "have the same cardinality" and so on and no one will be lost. Then I'll show them that (and why), for example, the set of all whole numbers has the same cardinality as the set of all even numbers, and again, no one will be lost. Then I'll ask them if they think that all transfinite sets will have the same cardinality, and they'll either be unsure or raise their hands to say yes, absolutely, that should be true. Then I'll show them Cantor's diagonal proof that not all transfinite sets have the same cardinality, and, despite the fact that the proof is delightfully simple and straight-forward, some of them won't get it, or in fact will resist the counter-intuitive conclusion, despite having seen all the steps in the proof, and try to poke holes in it. So, we have a putatively "analytic" matter (do all transfintie sets have the same cardinality?) about which, even when they understand all the terms perfectly, many people will come to the wrong conclusion.
Are the students who get it and thus change their minds about whether all transfinite sets have the same cardinality somehow being irrational? If not, then not only is the claim that belief revision is a matter of change-of-meaning in analytic cases unworkable as a universal descriptive claim, it looks equally problematic as a normative claim.
Now, someone could say at this juncture of the argument that the claim isn't that revising away beliefs about analytic matters is (or even should be) a matter of change-of-meaning rather than refutation. Rather, perhaps, the claim could be that revising away analytic *truths* should be a matter of change of meaning rather than refutation--i.e. if you start with a *true* statement about analytic issues and you want to end up with another *true* statement, that seems to contradict it (e.g. you go from "there is always one and only one straight line between two points" to "there are infinitely many straight lines between two points"), then the belief-change must have been merely a matter of using the terms in a different way. Put that way, whatever you think about the specific examples (Putnam has a good discussion about the geometry case in "Is Logic Empirical?" that makes clear that this particular example isn't as straightforward as it seems), it's hard to argue. The only kind of "belief revision" that gets you from a true statement to another true statement that employs the same terms and seems to contradict the first one is a change of meaning.
But, wait, this is just as true if we're talking about "synthetic" claims! If I stop believing that it was raining at 3:01 on January 3rd in South Miami and I start believing that it wasn't raining then, and both statements are true, and there are no true contradictions, I must have started using the word "rains" in a different way, so that the light drizzle on January 3rd counted under the first definition and didn't count under the second one.
So, given that, what's the difference?
Or am I just missing something fundamental about what people are getting at when they claim that there's a distinction in terms of modes of belief revision?
Monday, February 1, 2010
No Monday Post This Week
...or at least not a real one. Sorry.
But stay tuned for some stuff about the analytic/synthetic distinction on Wednesday.
But stay tuned for some stuff about the analytic/synthetic distinction on Wednesday.
Wednesday, January 27, 2010
Truth-Values For Quantum Logic?
Quantum logicians* claim that there are cases where the behavior of true statements about the properties of subatomic particles fails to conform to the distribution of conjunction over disjunction in classical logic (i.e. the rule that lets us go from P & (Q v R) to (P & Q) v (P & R)). Now, for there to be a counter-example to this law, we'd need a case where P was true, (Q v R) was true, but both Q and R had some status other than "true."**
After all (holding the truth of P constant in all of these cases), if Q was true and R wasn't, then the premise of the relevant instance of Distribution would be true, but so would the conclusion. The same would be true if R was true and Q wasn't. And, of course, it would still be true if P and Q were both true. If, on the other hand, Q and R were both false, then once again, we wouldn't have a counter-example to Distribution, because the premise would be false.
Fair enough, you might think, but that just shows you that the old bivalent conception of truth is wrong, and that's exactly the sort of thing we should expect to be shown once we've really absorbed the quantum revolution, really exposed the ancient dogmas encoded in classical logic to the searing light of empirical revision.
OK. Maybe. But postulating a third truth-value, by itself, doesn't clarify much here. What third truth-value would get the job done? A natural first thought is that what we're talking about here is a truth-value gaps--i.e. the joint absence of the two classical values--but that's not going to get it done. If Q is neither true nor false, and R is neither true nor false, then why should (Q v R) be true rather than neither true nor false itself? Now, if we think of third truth-value not as a gap but as a glut--the joint presence of the two classical values--the situation might seem to be a little bit better. Now, after all, the premise of the instances of Distribution where Q and R are both oddly-valued comes out true (whatever else it might be). The problem, of course, is that the conclusion also comes out true.
One might say that the third value is not a matter of being definitely neither or definitely both but being in some sense vague or ambiguous or indeterminate between the two. Fine. But why, then, wouldn't both the premise and the conclusion come out as vague or ambiguous or indeterminate or whatever? If it's ambiguous whether or not Q is true, and ambiguous whether or not R is true, but P is unambiguously true, shouldn't it be ambiguous whether (Q v R) is true, and also ambiguous whether (P & Q) is true, whether (P & R) is true, and whether ((P & Q) v (P & R)) is true?
One might set up the truth tables differently here, but its hard to see how one could do so, in a principled way and without opening oneself up to some "change of meaning" charges. Of course, some people routinely level those charges against all heterodox proposals about the behavior of logical connectives, but it would be much harder to answer them here. To see why, think of it likes this:
In classical logic, "either P or Q is true" and "at least one of the following things is true: P, Q" are different ways of saying the same thing. Now, if a heterodox logician comes along and says "sometimes it's ambiguous whether P is true, and it's equally ambiguous whether Q is true," and then concludes that in those cases it's ambiguous whether at least of the two is true, then the "change of meaning" charge seems unfair. It seems more natural to say that they mean the same thing by "or" as the classical logician, but that they admit possibilities that the classical logician rejects. If, by contrast, they say that it's ambiguous whether P is true, and ambiguous whether Q is true (and not epistemically ambiguous, but in terms of its objective truth-status), but that "either P or Q" is unambiguously true, it really does start to seem like they're using "or" in a new way.
...or maybe not. A more radical move yet would be to simply reject truth-functionality entirely here. Just as "for any collection of numbers, there is a sum of those numbers" is true (and might even seem so obvious as to follow from the meaning of "number" or "collection") so long as we restrict our focus to finite (and countably infinite) collections of numbers, but it breaks down when we get to uncountably infinite collections (like the collection of all real numbers), to which addition simply doesn't apply, one could argue that "the truth-value of disjunctions is a function of the truth-values of their disjuncts" holds when we restrict our attention to normal situations, but that it breaks down when we turn our attention to the outer edges of logical possibility that are physically actualized by quantum weirdness.
OK, fair enough, but if they do choose to take that line, it's surely incumbent on the quantum logician to give us a clear account of exactly what exactly the distinction is between normal and non-normal situations. If the distinction is simply a matter of shifting truth-values, then this isn't a proposal about a break-down of truth-functionality, it's simply about non-standard truth-functionality, and given the failure of the third truth-value to transfer from the disjuncts to the disjunction, the change of meaning question looms large. If the distinction between normal and non-normal situation is about something other than truth-values--e.g. we have a situation where Q and R are both false but where (Q v R) somehow manages to be true, or where P, Q and R are all true but (P & Q) v (P & R) somehow fails to be true--then they really owe us a very clear explanation of how the inclusive "or" of formal logic can retain its customary meaning at the same time as two false disjuncts somehow jointly yield a true disjunction, or two true disjuncts can fail to yield a true disjunction, and exactly what the difference is between situations where logical connectives behave in this strange way and the situations in which they don't, and exactly how to distinguish between which situations are which.
Now, from an orthodox perspective, it's tempting to conclude from the whole mess that the proposal that Distribution fails in quantum contexts is just deeply confused, and that might even be the right answer here, but I'd be far more interested in hearing attempts to resolve it and explain just how the trick can be turned--e.g. exactly how we can conceptualize a third truth-value that would plausibly behave in the right way, or how to make sense of the idea that the standard truth-values would in the relevant situations stop combining in the standard ways.
Thoughts?
*For our purposes here, the phrase "quantum logicians" refers to full-on, 1970s-Putnam-style, realist, monist quantum logicians, not the namby-pamby kind that just take quantum logic to be an interesting mathematical representation of certain experimental results and leave it at that. The latter might be far easier to plausibly argue for, but it's also far more boring.
**Note that, for the sake of simplicity, in everything that follows I'm assuming that conjunction behaves in the standard way. If anyone wants to get into that in the comments, and provide a quantum-logical motivation for questioning that, that's fine too.
After all (holding the truth of P constant in all of these cases), if Q was true and R wasn't, then the premise of the relevant instance of Distribution would be true, but so would the conclusion. The same would be true if R was true and Q wasn't. And, of course, it would still be true if P and Q were both true. If, on the other hand, Q and R were both false, then once again, we wouldn't have a counter-example to Distribution, because the premise would be false.
Fair enough, you might think, but that just shows you that the old bivalent conception of truth is wrong, and that's exactly the sort of thing we should expect to be shown once we've really absorbed the quantum revolution, really exposed the ancient dogmas encoded in classical logic to the searing light of empirical revision.
OK. Maybe. But postulating a third truth-value, by itself, doesn't clarify much here. What third truth-value would get the job done? A natural first thought is that what we're talking about here is a truth-value gaps--i.e. the joint absence of the two classical values--but that's not going to get it done. If Q is neither true nor false, and R is neither true nor false, then why should (Q v R) be true rather than neither true nor false itself? Now, if we think of third truth-value not as a gap but as a glut--the joint presence of the two classical values--the situation might seem to be a little bit better. Now, after all, the premise of the instances of Distribution where Q and R are both oddly-valued comes out true (whatever else it might be). The problem, of course, is that the conclusion also comes out true.
One might say that the third value is not a matter of being definitely neither or definitely both but being in some sense vague or ambiguous or indeterminate between the two. Fine. But why, then, wouldn't both the premise and the conclusion come out as vague or ambiguous or indeterminate or whatever? If it's ambiguous whether or not Q is true, and ambiguous whether or not R is true, but P is unambiguously true, shouldn't it be ambiguous whether (Q v R) is true, and also ambiguous whether (P & Q) is true, whether (P & R) is true, and whether ((P & Q) v (P & R)) is true?
One might set up the truth tables differently here, but its hard to see how one could do so, in a principled way and without opening oneself up to some "change of meaning" charges. Of course, some people routinely level those charges against all heterodox proposals about the behavior of logical connectives, but it would be much harder to answer them here. To see why, think of it likes this:
In classical logic, "either P or Q is true" and "at least one of the following things is true: P, Q" are different ways of saying the same thing. Now, if a heterodox logician comes along and says "sometimes it's ambiguous whether P is true, and it's equally ambiguous whether Q is true," and then concludes that in those cases it's ambiguous whether at least of the two is true, then the "change of meaning" charge seems unfair. It seems more natural to say that they mean the same thing by "or" as the classical logician, but that they admit possibilities that the classical logician rejects. If, by contrast, they say that it's ambiguous whether P is true, and ambiguous whether Q is true (and not epistemically ambiguous, but in terms of its objective truth-status), but that "either P or Q" is unambiguously true, it really does start to seem like they're using "or" in a new way.
...or maybe not. A more radical move yet would be to simply reject truth-functionality entirely here. Just as "for any collection of numbers, there is a sum of those numbers" is true (and might even seem so obvious as to follow from the meaning of "number" or "collection") so long as we restrict our focus to finite (and countably infinite) collections of numbers, but it breaks down when we get to uncountably infinite collections (like the collection of all real numbers), to which addition simply doesn't apply, one could argue that "the truth-value of disjunctions is a function of the truth-values of their disjuncts" holds when we restrict our attention to normal situations, but that it breaks down when we turn our attention to the outer edges of logical possibility that are physically actualized by quantum weirdness.
OK, fair enough, but if they do choose to take that line, it's surely incumbent on the quantum logician to give us a clear account of exactly what exactly the distinction is between normal and non-normal situations. If the distinction is simply a matter of shifting truth-values, then this isn't a proposal about a break-down of truth-functionality, it's simply about non-standard truth-functionality, and given the failure of the third truth-value to transfer from the disjuncts to the disjunction, the change of meaning question looms large. If the distinction between normal and non-normal situation is about something other than truth-values--e.g. we have a situation where Q and R are both false but where (Q v R) somehow manages to be true, or where P, Q and R are all true but (P & Q) v (P & R) somehow fails to be true--then they really owe us a very clear explanation of how the inclusive "or" of formal logic can retain its customary meaning at the same time as two false disjuncts somehow jointly yield a true disjunction, or two true disjuncts can fail to yield a true disjunction, and exactly what the difference is between situations where logical connectives behave in this strange way and the situations in which they don't, and exactly how to distinguish between which situations are which.
Now, from an orthodox perspective, it's tempting to conclude from the whole mess that the proposal that Distribution fails in quantum contexts is just deeply confused, and that might even be the right answer here, but I'd be far more interested in hearing attempts to resolve it and explain just how the trick can be turned--e.g. exactly how we can conceptualize a third truth-value that would plausibly behave in the right way, or how to make sense of the idea that the standard truth-values would in the relevant situations stop combining in the standard ways.
Thoughts?
*For our purposes here, the phrase "quantum logicians" refers to full-on, 1970s-Putnam-style, realist, monist quantum logicians, not the namby-pamby kind that just take quantum logic to be an interesting mathematical representation of certain experimental results and leave it at that. The latter might be far easier to plausibly argue for, but it's also far more boring.
**Note that, for the sake of simplicity, in everything that follows I'm assuming that conjunction behaves in the standard way. If anyone wants to get into that in the comments, and provide a quantum-logical motivation for questioning that, that's fine too.
Monday, January 25, 2010
Dialetheism and Scientific Reasoning
As paraconsistentists of all stripes are fond of pointing out, historically well-accepted scientific theories have often entailed various inconsistencies. There seems to be some sense of “accept” in which working scientists are often willing to accept implicitly inconsistent theories (or pairs of mutually inconsistent theories, like classical formulations of relativistic and quantum physics) while they search for consistent alternatives. Partisans of what one can call “paraconsistency-lite”—the view that classical logic is wrong in holding that everything follows from every contradiction, but not because this “explosion” of inferences has true counter-examples (i.e. not because any contradictions are true)—are particularly fond of these sorts of examples. After all, by their lights, the scientists’ attitude is exactly the rationally correct one: accept the inconsistency, don’t accept triviality, and don’t lose sight of the fact that the inconsistent theory you’ve provisionally accepted must ultimately be wrong, because contradictions are never true. People who, for example, accepted Bohr’s theory of the atom in the formulation that relied on Maxwell’s equations, were, implicitly and without having the logical formalism to explain why they were right, proto-paraconsistentists.
Or so goes the argument. I have a lot of issues with the whole line of thought, not least of which is the fact that, while I’m as naturalistic in my epistemic stance as the next guy (actually, in my Department, I tend to be way more naturalism-friendly than the next guy), I think that this sort of thing tends to devolve into a sort of exaggerated hyper-naturalism where the empirical sciences are taken not just as pretty good tools for getting to the truth in the long run, but as nearly flawless paragons of rationality in all of their day-to-day epistemic practices—the speed at which the scientific community actually arrives at a conclusion must be the correct speed, etc. There’s a lot to be said about this—I’ve blogged here about these sorts of “retroactive implicit paraconsistency” arguments more than once before, and I certainly will again—but right now I want to focus on another subject entirely.
From the perspective of the paraconsistency-lite crowd, the attitude of those scientists willing to temporarily swallow inconsistency while looking for the right theories (which they assume must be consistent) makes perfect sense, but what about dialetheism? (To switch from beer to cigarettes, we can think of the views we’ve been discussing as Paraconsistency Lights and dialetheist positions as Paraconsistency Reds.) I’ve read many passages in which Graham Priest basically makes the classical Paraconsistency Lights argument and leaves at that, but only one where he makes the obvious Paraconsistency Reds twist on it.
It comes on pp. 149-150 of my edition of Doubt Truth To Be A Liar:
“It is here that the impact of paraconsistent logic is revisionary—indeed, revolutionary. The Law of Non-Contradiction has been well-entrenched in Western thought—and so science—since the canonization of Aristotle, whose defence of the Law has rarely been challenged. Hence, scientists and philosophers have not been prepared to brook the thought that an inconsistent theory of any kind might be true. But subscribing to the law is not rationally mandatory, as I argued in Chapter 7, and as the development of paraconsistent logics has played a large role in showing. Once this fact is digested, scientists may—justifiably—take a different attitude to inconsistent theories of the appropriate kind. Indeed, they may even develop inconsistent theories, if these have the right empirical consequences, just as paraconsistent logicians have developed inconsistent theories of semantics to handle the paradoxes of self-references.”
…and that’s pretty much all he has to say about it. (To be fair, in a couple of other places in DBTL he gives a couple of hypothetical examples of ways this might happen, but this is pretty much what he has to say on the epistemic issue.) So, to sum up:
(1) Scientists have been in the thrall of the Aristotelian dogma of non-contradiction, which explains their bias that inconsistent theories can never be true, but
(2) Philosophical work on the self-references paradoxes, the development of inconsistency-tolerant formalisms, etc., shows us that this dogma should be rejected, so
(3) Now, one hopes, they'll start being less dogmatic.
This is certainly a far cry from the extreme deference to scientific practice you tend to get with the paraconsistency-lite foks, and it raises a lot of strange and awkward questions. Given that, as his less radical comrades are always pointing out, temporary inconsistency is not that rare a situation in the history of science, and that these are presumably situations where inconsistency is pulling in one direction (showing that the theory must be false) but happy empirical consequences are pulling in the other (giving the scientific community good reason to continue to provisionally accept the theories in question), what sort of retroactive advice should someone who agrees with Priest give scientists in this position? What scientific progress would have been lost by researchers agreeing with Priest, and what future progress would be lost if the contemporary scientific community were to be won over to his position?
To switch gears for a second, consider a traditional criticism that defenders of neo-Darwinian biological orthodoxy level against “Intelligent Design” creationists: that, if their views were generally adopted, researchers would be content to put God in the gaps in their understanding, and future explanatory progress would be stunted.
Now, here’s my question for readers more sympathetic to dialetheism than I am:
Does an analogous criticism apply to what Priest is advocating here? If not, why not? What’s the difference?
Certainly, as a sociological matter, most dialetheists are atheists (although, as I’ve mentioned before, I think that the appropriation of dialetheism by at least some philosophically aware Christian theologians is a historical inevitability), so part of their answer here might just be that there is no good reason to believe that God exists (the central philosophical arguments for God all being fairly spectacularly unconvincing), whereas the paradoxes of self-reference do give us good reason to believe in true contradictions.
Fair enough. If so, though, how about the counterfactual? If there were a good, convincing argument for the existence of God (e.g. some bright young grad student at Notre Dame came up with an absolutely unanswerable re-formulation of the Ontological Argument), would Intelligent Design theory be a rationally acceptable option for biological science, or would the stunting-future-inquiry objection still be a good one, and as such would the stance of those theologically liberal Christians who accept God but categorically reject ID be the right one? If so, is there an epistemically relevant difference between the ID creationist’s suggestion that gaps in our understanding should at least sometimes simply be accepted as evidence of divine intervention and Priest’s suggestion that inconsistent theories should at least sometimes not just be provisionally accepted while everyone assumes they can’t possibly be true and tries to find a consistent alternative, but actually accepted as true? If so, what is it?
Or so goes the argument. I have a lot of issues with the whole line of thought, not least of which is the fact that, while I’m as naturalistic in my epistemic stance as the next guy (actually, in my Department, I tend to be way more naturalism-friendly than the next guy), I think that this sort of thing tends to devolve into a sort of exaggerated hyper-naturalism where the empirical sciences are taken not just as pretty good tools for getting to the truth in the long run, but as nearly flawless paragons of rationality in all of their day-to-day epistemic practices—the speed at which the scientific community actually arrives at a conclusion must be the correct speed, etc. There’s a lot to be said about this—I’ve blogged here about these sorts of “retroactive implicit paraconsistency” arguments more than once before, and I certainly will again—but right now I want to focus on another subject entirely.
From the perspective of the paraconsistency-lite crowd, the attitude of those scientists willing to temporarily swallow inconsistency while looking for the right theories (which they assume must be consistent) makes perfect sense, but what about dialetheism? (To switch from beer to cigarettes, we can think of the views we’ve been discussing as Paraconsistency Lights and dialetheist positions as Paraconsistency Reds.) I’ve read many passages in which Graham Priest basically makes the classical Paraconsistency Lights argument and leaves at that, but only one where he makes the obvious Paraconsistency Reds twist on it.
It comes on pp. 149-150 of my edition of Doubt Truth To Be A Liar:
“It is here that the impact of paraconsistent logic is revisionary—indeed, revolutionary. The Law of Non-Contradiction has been well-entrenched in Western thought—and so science—since the canonization of Aristotle, whose defence of the Law has rarely been challenged. Hence, scientists and philosophers have not been prepared to brook the thought that an inconsistent theory of any kind might be true. But subscribing to the law is not rationally mandatory, as I argued in Chapter 7, and as the development of paraconsistent logics has played a large role in showing. Once this fact is digested, scientists may—justifiably—take a different attitude to inconsistent theories of the appropriate kind. Indeed, they may even develop inconsistent theories, if these have the right empirical consequences, just as paraconsistent logicians have developed inconsistent theories of semantics to handle the paradoxes of self-references.”
…and that’s pretty much all he has to say about it. (To be fair, in a couple of other places in DBTL he gives a couple of hypothetical examples of ways this might happen, but this is pretty much what he has to say on the epistemic issue.) So, to sum up:
(1) Scientists have been in the thrall of the Aristotelian dogma of non-contradiction, which explains their bias that inconsistent theories can never be true, but
(2) Philosophical work on the self-references paradoxes, the development of inconsistency-tolerant formalisms, etc., shows us that this dogma should be rejected, so
(3) Now, one hopes, they'll start being less dogmatic.
This is certainly a far cry from the extreme deference to scientific practice you tend to get with the paraconsistency-lite foks, and it raises a lot of strange and awkward questions. Given that, as his less radical comrades are always pointing out, temporary inconsistency is not that rare a situation in the history of science, and that these are presumably situations where inconsistency is pulling in one direction (showing that the theory must be false) but happy empirical consequences are pulling in the other (giving the scientific community good reason to continue to provisionally accept the theories in question), what sort of retroactive advice should someone who agrees with Priest give scientists in this position? What scientific progress would have been lost by researchers agreeing with Priest, and what future progress would be lost if the contemporary scientific community were to be won over to his position?
To switch gears for a second, consider a traditional criticism that defenders of neo-Darwinian biological orthodoxy level against “Intelligent Design” creationists: that, if their views were generally adopted, researchers would be content to put God in the gaps in their understanding, and future explanatory progress would be stunted.
Now, here’s my question for readers more sympathetic to dialetheism than I am:
Does an analogous criticism apply to what Priest is advocating here? If not, why not? What’s the difference?
Certainly, as a sociological matter, most dialetheists are atheists (although, as I’ve mentioned before, I think that the appropriation of dialetheism by at least some philosophically aware Christian theologians is a historical inevitability), so part of their answer here might just be that there is no good reason to believe that God exists (the central philosophical arguments for God all being fairly spectacularly unconvincing), whereas the paradoxes of self-reference do give us good reason to believe in true contradictions.
Fair enough. If so, though, how about the counterfactual? If there were a good, convincing argument for the existence of God (e.g. some bright young grad student at Notre Dame came up with an absolutely unanswerable re-formulation of the Ontological Argument), would Intelligent Design theory be a rationally acceptable option for biological science, or would the stunting-future-inquiry objection still be a good one, and as such would the stance of those theologically liberal Christians who accept God but categorically reject ID be the right one? If so, is there an epistemically relevant difference between the ID creationist’s suggestion that gaps in our understanding should at least sometimes simply be accepted as evidence of divine intervention and Priest’s suggestion that inconsistent theories should at least sometimes not just be provisionally accepted while everyone assumes they can’t possibly be true and tries to find a consistent alternative, but actually accepted as true? If so, what is it?
Thursday, January 21, 2010
This Is Only Sort Of A Post
....and mostly only here to re-assure you, gentle reader, that missing two scheduled posts in a row doesn't actually mean this blog has gone gentle into that good night night. Just normal wear and tear to the schedule from flying back to Miami on Monday, starting to teach on Tuesday, fighting with the power company and gearing up for (what I really hope will be) the final round of dissertation revisions in the next couple weeks.
That said, I should be back to the regular schedule on Monday. So, for anyone who's actually reading this, I'm open to audience requests. Anything you'd be particularly interested in hearing about for the next few weeks?
That said, I should be back to the regular schedule on Monday. So, for anyone who's actually reading this, I'm open to audience requests. Anything you'd be particularly interested in hearing about for the next few weeks?
Wednesday, January 13, 2010
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