[Note: For the sake of continuing a thread of the last discussion, I'm pushing back the already-written-and-scheduled post on the use of the negation-revenge distinction in discussions about revenge problems until Monday.]
A couple of days ago, I talked a bit about the overlap between the Liar and Curry Paradoxes. The standard dialetheist line is that Liar sentences (sentences that, in one form or another, deny their own truth) are both true and false, whereas Curry sentences (sentences that say of themselves that if they are true, some other claim P is true) that they are (just) false. After all, if such sentences were either (just) true or both true and false, given that "P" can be anything, triviality would ensue.
Of course, the problem with Curry sentences is that even if one says that they're false, if one acknowledges that (a) their truth conditions are given by the relevant instances of the T-Schema, and (b) that contraction--the inference from "if P, then if P, then Q" to "if P, then Q"--is valid, it follows that such sentences are true. Since a dialetheist (who argues for dialetheism on the basis of the Liar Paradox) is hardly likely to accept that the T-Schema ever fails (given its role in arguments from contradictions from standard Liars), so, unsurprisingly, they pick (b).
Now, contraction certainly sounds valid, but it's a bit obscure--on first consideration, we might think that it's not something that comes up a lot in important non-paradoxical contexts. (Of course, given the assumption that conditionals are truth-functional and that all sentences are true, false or both, it's hard to get around contraction's validity, but we have other good reasons to reject the idea that conditionals are entirely truth-functional anyway.)
Whether or not all of this is plausible, notice that in order for contraction to fail, either Modus Ponens or conditionalization must fail as well, and conditionalization is one of the most basic rules related to the conditional that there is, one that one might be forgiven for describing as basic to the very notion of a conditional. Assume the antecedent. Prove the consequent. Conclude that if the antecedent is true, so is the consequent. Intuitively, this an Modus Ponens are two sides of the same coin--Modus Ponens tells us that, given "if P, then Q," P entails Q, whereas conditionalization tells us that, given that P entails Q, "if P, then Q." This intuitive symmetry is routinely honored in introductory logic textbooks that refer to Modus Ponens as "conditional-elimination" and conditionalization as "conditional-introduction," and by philosophers and logicians who think nothing of casually talking about the "rule form" and "conditional form" of various rules.*
...all of which is to say the intuitive cost is considerable, but at least the paradox is blocked.
Now, in the last post, I raised the question of "lying Curries," paradoxical sentences that combine features of traditional Liar and Curry sentences, like LC, below.
LC: "If LC is true, then LC is false."
...I suggested that, even given the ways in which standard dialetheist solutions to Curry restrict the power of conditionals, standard Liar reasoning might get us the result that LC is both true and false. Thus, the dialetheist might be deprived of their ability to have a uniform policy whereby Curry sentences are always (just) false.
In the discussion in the comment thread, I was convinced that the reasoning I employed relied on contraction at a crucial step. Thus, contrary to my original claim, the standard dialetheist Curry-solver does have the formal resources for blocking a contradiction about the LC.
Of course, I still think that the dialetheist who says that Curry sentences are invariably false has to recognize at least one glutty Curry, namely the Truth-Telling Curry (TTC), below.
TTC: "If this sentence is true, this sentence is true."
Given the law of identity (still universally validated with the "suitable conditionals" favored by dialetheists like Priest and Beall), and Capture (the rule that says that we can infer "'A' is true" from A), TTC must be true. Thus, if the dialetheist Curry-solver says that all Curry sentences are false, they have to acknowledge that this is both true and false. If they abandon it in the face of this example, the TTC is still (just) true. One way or the other, they aren't entitled to a unified policy of regarding Curry sentences as (just) false. How big a deal this is depends on how compelling you find the sorts of symmetry considerations that lead people to seek out unified policies.
All that said, I think the LC itself nicely demonstrates quite a different objection to standard dialetheist solutions to Curry. Pre-philosophically, "this sentence is false" and "if this sentence is true, it's false" look just the same. They seem confusing in the same way, they seem to be saying almost exactly the same thing, and the same steps--the assumption that they must be either true or false, the realization that either answer generates the other and so on--seem to be the same, even if, once one sits down with the kind of formal logic one learns in an introductory class and works out the derivations of the contradictions, one proof is a bit longer than the other.
Given all of this, one can imagine someone in this position--no familiarity with the higher-level literature on paradoxes, but quick on their feet and equipped with good enough proficiency in (orthodox) formal logic to follow the moves--having the following conversation with a dialetheist paradox-solver.
(We'll call the pre-philsophical Worrier About Paradox WAP and the dialetheist paradox-solver DPS.)
WAP: "I'm really worried by these paradoxical sentences."
DPS: "Which ones?"
WAP: "This sentence is false" and "if this sentence is true, it's false."
DPS: "Well, for that second sentence you mentioned, we can actually solve the paradox by weakening the inferential power of our conditionals. See, there's this rule called contraction..."
DPS goes on to explain about contraction and "suitable conditionals" and the rest.
WAP: "Cool! So which rule about conditionals do I have to reject to get around the first sentence?"
DPS: "Oh, you can't solve that one by doing anything with the conditional. That one actually forces us to acknowledge that some sentences are both true and false."
WAP: "What?!? Really?"
DPS: "Yep."
WAP: "Hold on. What about this rule that we used to get a contradiction out of that first sentence, the one that says that from two conditionals with the same consequent and the disjunction of their antecedents, you can derive the consequent? If conditionals aren't truth-functional, like you explained to me when we were going over that second sentence, and we're messing around with what we can infer from them to get around these paradoxes anyway, why don't we reject this rule, too, just like we rejected that contraction rule? That way, we could still say that if first sentence is true, it's false, and we could still say that if it's false, it's true, and we could still say that the first sentence was just false, just like we got to say that the second sentence was just false when we got rid of contraction. And, just like you explained to me when we talked about contraction, we still get to keep the most basic rules about conditionals, like Modus Ponens and identity. Wouldn't my way be better than just accepting the contradiction?"
DPS: "No, that would be ad hoc."
WAP: "Huh?"
*Note too that standard explanations of the conditionals crucial for the derivation of a contradiction from the Liar Paradox look suspiciously like instances of conditionalization. After all, if someone asks why they should believe that the Liar is true iff it's false, a standard explanation would start with "well, look, let's say that it's false. Well, that's what it says, so it must be true. Alternately, let's say that it's true..."
Of course, this point doesn't quite show that no one who rejects conditionalization is entitled to argue for dialetheism from the Liar Paradox, since they can get the relevant conditionals straight from the T-Schema. Still, in terms of the intuitive justification, if someone asked why they should accept the relevant T-Schema instance rather than taking the paradox to show that some instances of the T-Schema are wrong, the obvious way to explain it to them would be the one just mentioned.
This still doesn't quite show that conditionalization-rejecters are deprived of the argument for dialetheism from the Liar Paradox, since they could go about justifying their adherence to T-Schema absolutism in other ways, but it does show that, without conditionalization, the argument from the Liar to contradiction loses a good bit of its original intuitive force.
Wednesday, February 24, 2010
Monday, February 22, 2010
A Basic Question: Lying Curries?
What follows takes us a bit off-course from the recent discussion about J.C. Beall's maneuvers about "just true," but we'll return to that on Wednesday, with a discussion about a problem for his claim that "just true" can be made sense of through acceptance/rejection talk....which is also, I think, a problem for the general use of acceptance/rejection talk by many contemporary paradox-solvers (particularly parcomplete theorists). In any case, stay tuned for that on Wednesday. For today, let's talk about Curry...
#
Dialetheists take sentences like:
"This sentence is false."
"This sentence is not true."
"This sentence is false or gappy."
...etc., etc., to be both true and false, as a result of the following familiar argumentative steps (which, given bivalence, and the background assumption that such sentences are meaningful, truth-evaluable, etc., are pretty hard to find fault with):
(1) If the sentence in question is true, it's false, so it's both.
(2) If the sentence in question is false, it's true, so it's both.
(3) It must be one or the other, so it really is both.
Now, sentences like:
"If this sentence is true, the moon is made of green cheese."
"If this sentence is true, Hitler won World War II."
...etc., etc., are in quite a different category. Generally speaking, dialetheists try to get around the Curry Paradox by fiddling with the rules for their conditionals, and I've extensively criticized that strategy here in the past, but right now the question I want to focus on is a more basic one.
Besides weakening their conditionals, a necessary part of any dialetheist solution to Curry is that sentences like the ones above are just false. After all, such sentences can be constructed with anything you like in their consequents, so if the antecedents are true (whether they're just true or both true and false), then everything is true and all possible reasoning goes up in flames. Given the assumption that self-referential truth talk is meaningful, truth-evaluable, etc., the claim that Curry sentences are just false is the only way to avoid triviality here.
Hence, for example, in his book Spandrels Of Truth, JC Beall starts by classifying all "ttruth-ineliminable sentences"--i.e. sentences where the talk of truth and falsity doesn't ground out in a subject other than truth--as being both true and false. Then, when he gets to Curry, he qualifies this by saying that it's only his position on the the "conditional-free" fragment of his language.
OK. But wait.
What about the following combined Liar/Curry sentence?
Sentence LC: "If LC is true, then it's false."
Apply exactly the steps discussed earlier.
(1) Obviously, if LC is false, it's true, so it's both.
(2) Less obviously, if LC is false, it's true, so it's both.
(3) It must be one or the other, so it's both.
The second step is less obvious because one might think that it's possible to say that LC is false, but to deny that if it's true, it's false. (After all, in this case, to say that the sentence is false just is to deny that, right?) Sure. Of course, if the "if...then" is understood as the simple truth-functional conditional of classical logic, then the fact that the antecedent is false would suffice to make the conditional true, so step (2) would be obvious.
The problem, of course, is that in any of the sorts of logics suitable for adoption by a dialetheist, the conditionals won't be truth-functional. (One reason is that, in classical logic, "if P, then Q" has the same truth-table as "either not-P or Q."* Given double negation, that makes Modus Ponens logically equivalent to Disjunctive Syllogism. If dialetheism is right, Disjunctive Syllogism isn't universally truth-preseving unless everything is true, but if "if P, then Q" and "P" are going to be true in all the same circumstances that "either not-P or Q" and "not-not-P" are true, then Disjunctive Syllogism can't fail to be universally truth-preserving without Modus Ponens failing to be truth-preserving in all the same contexts.) So (2) is less obvious than all that.**
That said, it looks to me like (2) still goes through. To see why, assume for the sake of argument that the LC does somehow manage to be(just) false. Given that assumption, what do we want to say about it's status if it's true? In other words, do we want to say...
(I) The LC's (just) false, and if it's true, it's false.
...or...
(II) The LC's (just) false, and if it's true, it's true.
It's pretty obvious that we don't want to say (I), since the second conjunct is just what the LC hence, hence, if (I) is right, the LC's both (just) false and true, and hence not really "just" anything.
So let's try (II). If you say that if the LC's true, it's true, then if it's true, then what it says is right. What it says is that if it's true, it's false. Hence, from the assumption that if it's true, it's true, it follows that if it's true, it's false, which is all LC says!
Hence, if it's false, it's true, whether (I) or (II) is correct.
Maybe we could try to argue that neither (I) nor (II) is right. The dialetheist can hardly deny Excluded Middle, given its central role in delivering dialetheias from standard liar sentences, but once we stop accepting that conditionals are entirely truth-functional, we can pry apart "either Q or ~Q" from "either 'if P, then Q' or 'if P then ~Q'". For example, if we put relevance constraints on conditional formation, then it could be the case that P and Q simply don't have the right relationship with each other for either "if P, then Q" or "if P, then ~Q" to be true. Fair enough. The problem is that in this case, P=Q, so by the law of identity (for any sentence P, "if P, then P" is true), "if P, then Q" must be true, from which, as we've seen, "if P, then ~Q" follows, and "if P, then ~Q" simply is the content of LC.
In every discussion I've seen by a dialetheist about what a suitable conditional is for their system, universally satisfying identity is always part of their criteria, and, given identity, (II) must be the right choice, and (I) follows from (II) in any case, and the fact that (I) entails that LC is both true and false is the uninterestingly obvious part.
Now, to be honest, I'm not sure how big a problem this is for the dialetheist. Nothing I've said shows that they can't continue to say that most Curry sentences--i.e. sentences of the format "if this sentence is true, then P"--are (just) false. It does, however, show that any dialetheist who bases their dialetheism on standard Liar reasoning can't insist that all such conditionals are (just) false. They can't, in other words, have a unified policy on Curry sentences.
How much of a problem that is, of course, depends on just what on what you take the virtue of a unified policy to be. For example, in In Contradiction, Graham Priest admits that the Truth-Teller intuitively looks like an excellent status for "gap" status (unlike, he thinks, the more obviously glutty Liar), but argues that both are gluts on the basis of "symmetry" considerations. If one finds such considerations compelling, the issue about lying Curries looks like a bit of an embarrassment.
*This is often put by unsympathetic critics as the claim that "in classical logic, the conditional is 'either not-p or q," but in the absence of a persuasive argument for identifying meaning with truth conditions, this strikes me as a considerable over-statement.***
**One might think that we can construct a lying Curry for which we get (2) on the cheap by specifying that the conditional is a classical one. The problem is that, even if one keeps around the classical conditional in a dialetheist logic along with a more suitable conditional, that conditional won't detach--i.e. Modus Ponens will fail for it. When it comes to Curry sentences constructed with a classical conditional in a dialetheic logical setting, calling them true doesn't commit you to embracing their consequents.
***Interestingly enough, in "Spandrels...", Beall both explicitly rejects--on deflationist grounds--the identification of meaning with truth conditions, and claims that "the hook" (i.e. the conditional of classical logic) just is (~P v Q). Go figure.
#
Dialetheists take sentences like:
"This sentence is false."
"This sentence is not true."
"This sentence is false or gappy."
...etc., etc., to be both true and false, as a result of the following familiar argumentative steps (which, given bivalence, and the background assumption that such sentences are meaningful, truth-evaluable, etc., are pretty hard to find fault with):
(1) If the sentence in question is true, it's false, so it's both.
(2) If the sentence in question is false, it's true, so it's both.
(3) It must be one or the other, so it really is both.
Now, sentences like:
"If this sentence is true, the moon is made of green cheese."
"If this sentence is true, Hitler won World War II."
...etc., etc., are in quite a different category. Generally speaking, dialetheists try to get around the Curry Paradox by fiddling with the rules for their conditionals, and I've extensively criticized that strategy here in the past, but right now the question I want to focus on is a more basic one.
Besides weakening their conditionals, a necessary part of any dialetheist solution to Curry is that sentences like the ones above are just false. After all, such sentences can be constructed with anything you like in their consequents, so if the antecedents are true (whether they're just true or both true and false), then everything is true and all possible reasoning goes up in flames. Given the assumption that self-referential truth talk is meaningful, truth-evaluable, etc., the claim that Curry sentences are just false is the only way to avoid triviality here.
Hence, for example, in his book Spandrels Of Truth, JC Beall starts by classifying all "ttruth-ineliminable sentences"--i.e. sentences where the talk of truth and falsity doesn't ground out in a subject other than truth--as being both true and false. Then, when he gets to Curry, he qualifies this by saying that it's only his position on the the "conditional-free" fragment of his language.
OK. But wait.
What about the following combined Liar/Curry sentence?
Sentence LC: "If LC is true, then it's false."
Apply exactly the steps discussed earlier.
(1) Obviously, if LC is false, it's true, so it's both.
(2) Less obviously, if LC is false, it's true, so it's both.
(3) It must be one or the other, so it's both.
The second step is less obvious because one might think that it's possible to say that LC is false, but to deny that if it's true, it's false. (After all, in this case, to say that the sentence is false just is to deny that, right?) Sure. Of course, if the "if...then" is understood as the simple truth-functional conditional of classical logic, then the fact that the antecedent is false would suffice to make the conditional true, so step (2) would be obvious.
The problem, of course, is that in any of the sorts of logics suitable for adoption by a dialetheist, the conditionals won't be truth-functional. (One reason is that, in classical logic, "if P, then Q" has the same truth-table as "either not-P or Q."* Given double negation, that makes Modus Ponens logically equivalent to Disjunctive Syllogism. If dialetheism is right, Disjunctive Syllogism isn't universally truth-preseving unless everything is true, but if "if P, then Q" and "P" are going to be true in all the same circumstances that "either not-P or Q" and "not-not-P" are true, then Disjunctive Syllogism can't fail to be universally truth-preserving without Modus Ponens failing to be truth-preserving in all the same contexts.) So (2) is less obvious than all that.**
That said, it looks to me like (2) still goes through. To see why, assume for the sake of argument that the LC does somehow manage to be(just) false. Given that assumption, what do we want to say about it's status if it's true? In other words, do we want to say...
(I) The LC's (just) false, and if it's true, it's false.
...or...
(II) The LC's (just) false, and if it's true, it's true.
It's pretty obvious that we don't want to say (I), since the second conjunct is just what the LC hence, hence, if (I) is right, the LC's both (just) false and true, and hence not really "just" anything.
So let's try (II). If you say that if the LC's true, it's true, then if it's true, then what it says is right. What it says is that if it's true, it's false. Hence, from the assumption that if it's true, it's true, it follows that if it's true, it's false, which is all LC says!
Hence, if it's false, it's true, whether (I) or (II) is correct.
Maybe we could try to argue that neither (I) nor (II) is right. The dialetheist can hardly deny Excluded Middle, given its central role in delivering dialetheias from standard liar sentences, but once we stop accepting that conditionals are entirely truth-functional, we can pry apart "either Q or ~Q" from "either 'if P, then Q' or 'if P then ~Q'". For example, if we put relevance constraints on conditional formation, then it could be the case that P and Q simply don't have the right relationship with each other for either "if P, then Q" or "if P, then ~Q" to be true. Fair enough. The problem is that in this case, P=Q, so by the law of identity (for any sentence P, "if P, then P" is true), "if P, then Q" must be true, from which, as we've seen, "if P, then ~Q" follows, and "if P, then ~Q" simply is the content of LC.
In every discussion I've seen by a dialetheist about what a suitable conditional is for their system, universally satisfying identity is always part of their criteria, and, given identity, (II) must be the right choice, and (I) follows from (II) in any case, and the fact that (I) entails that LC is both true and false is the uninterestingly obvious part.
Now, to be honest, I'm not sure how big a problem this is for the dialetheist. Nothing I've said shows that they can't continue to say that most Curry sentences--i.e. sentences of the format "if this sentence is true, then P"--are (just) false. It does, however, show that any dialetheist who bases their dialetheism on standard Liar reasoning can't insist that all such conditionals are (just) false. They can't, in other words, have a unified policy on Curry sentences.
How much of a problem that is, of course, depends on just what on what you take the virtue of a unified policy to be. For example, in In Contradiction, Graham Priest admits that the Truth-Teller intuitively looks like an excellent status for "gap" status (unlike, he thinks, the more obviously glutty Liar), but argues that both are gluts on the basis of "symmetry" considerations. If one finds such considerations compelling, the issue about lying Curries looks like a bit of an embarrassment.
*This is often put by unsympathetic critics as the claim that "in classical logic, the conditional is 'either not-p or q," but in the absence of a persuasive argument for identifying meaning with truth conditions, this strikes me as a considerable over-statement.***
**One might think that we can construct a lying Curry for which we get (2) on the cheap by specifying that the conditional is a classical one. The problem is that, even if one keeps around the classical conditional in a dialetheist logic along with a more suitable conditional, that conditional won't detach--i.e. Modus Ponens will fail for it. When it comes to Curry sentences constructed with a classical conditional in a dialetheic logical setting, calling them true doesn't commit you to embracing their consequents.
***Interestingly enough, in "Spandrels...", Beall both explicitly rejects--on deflationist grounds--the identification of meaning with truth conditions, and claims that "the hook" (i.e. the conditional of classical logic) just is (~P v Q). Go figure.
Wednesday, February 17, 2010
Dialetheism's Trivialism Problems
Dialetheists think that some contradictions are true.
Trivialists think that everything is true (and false).
Here's a trivialism problem that everyone has:
You can't express your rejection of trivialism in a way that isn't compatible with trivialism by the trivialist's lights. For example, if you say "trivialism is false," the trivialist will agree with you.
Here's a trivialism problem that only the dialetheist has:
They can't express their rejection of trivialism in a way that isn't compatible with trivialism by *their own* lights.
Here's what I mean:
If an ordinary nondialetheist says "trivialism is false," they've just said something that they think rules out the possibility that trivialism is true.
In a dialetheist says "trivialism is false," they've said something they *don't* think rules out the possibility that trivialism is true.
If they say "trivialism is (just) false" or "trivialism fails to be true in any sense" or "trivialism has an alethetic status that rules out the possibility that it could be true," they still haven't said anything that can be (by their lights) incompatible with the truth of trivialism.
...at least assuming that they take Liar sentences to be both true and false.*
After all, we can always construct Liars like:
"This sentence is (just) false."
"This sentence fails to be true in any sense."
"This sentence as an alethic status that rules out the possibility that it could be true."
....etc., etc., etc. This is, I take it, one of the reasons why the dialetheist's difficulties with making sense of claiming that some sentences are "just true" or "just false" are philosophically significant, a subject we'll be returning to next week. So that's dialetheism's trivialism problem (1).
While we're at it, though, here are two other special trivialism problems that the dialetheist has that no one else has:
(2) The Curry Paradox bears exactly the same relation to trivialism that the Liar Paradox bears to dialetheism. In both cases, we have paradoxical sentences involving self-referential truth talk, such that if we take such sentences to be meaningful, truth-evaluable, etc., the philosophical position in question simply follows. When it comes to the Liar, the dialetheist can accept all of those things, accuse anyone who tries to tamper with otherwise intuitive inferential rules involved in the paradox in order to avoid the paradoxical result of begging the question, etc. When it comes to Curry, they're forced into an awkward double standard. If they want to avoid trivialism, they have to start making exactly the sorts of moves they rail against when it comes to the Liar.
(3) A classical proof in classical logic shows that we can infer anything and everything from any contradiction.
It's easy to show that the dialetheist has a good, principled response to (3).
But, given (1) and (2), this shouldn't be taken as meaning that dialetheism doesn't have any trivialism problems that the rest of us don't.
*It would, technically, be possible to be a dialetheist without taking Liars to be both true and false--one could, for example, be convinced by Graham Priest's arguments about "the paradoxes of motion and change" but not by any of his other arguments--but I know of no dialetheist who doesn't analyze Liars dialethically. In every actual case of people who argue for dialetheism, the argument from the Liar and related semantic paradoxes is their *central* argument.
Trivialists think that everything is true (and false).
Here's a trivialism problem that everyone has:
You can't express your rejection of trivialism in a way that isn't compatible with trivialism by the trivialist's lights. For example, if you say "trivialism is false," the trivialist will agree with you.
Here's a trivialism problem that only the dialetheist has:
They can't express their rejection of trivialism in a way that isn't compatible with trivialism by *their own* lights.
Here's what I mean:
If an ordinary nondialetheist says "trivialism is false," they've just said something that they think rules out the possibility that trivialism is true.
In a dialetheist says "trivialism is false," they've said something they *don't* think rules out the possibility that trivialism is true.
If they say "trivialism is (just) false" or "trivialism fails to be true in any sense" or "trivialism has an alethetic status that rules out the possibility that it could be true," they still haven't said anything that can be (by their lights) incompatible with the truth of trivialism.
...at least assuming that they take Liar sentences to be both true and false.*
After all, we can always construct Liars like:
"This sentence is (just) false."
"This sentence fails to be true in any sense."
"This sentence as an alethic status that rules out the possibility that it could be true."
....etc., etc., etc. This is, I take it, one of the reasons why the dialetheist's difficulties with making sense of claiming that some sentences are "just true" or "just false" are philosophically significant, a subject we'll be returning to next week. So that's dialetheism's trivialism problem (1).
While we're at it, though, here are two other special trivialism problems that the dialetheist has that no one else has:
(2) The Curry Paradox bears exactly the same relation to trivialism that the Liar Paradox bears to dialetheism. In both cases, we have paradoxical sentences involving self-referential truth talk, such that if we take such sentences to be meaningful, truth-evaluable, etc., the philosophical position in question simply follows. When it comes to the Liar, the dialetheist can accept all of those things, accuse anyone who tries to tamper with otherwise intuitive inferential rules involved in the paradox in order to avoid the paradoxical result of begging the question, etc. When it comes to Curry, they're forced into an awkward double standard. If they want to avoid trivialism, they have to start making exactly the sorts of moves they rail against when it comes to the Liar.
(3) A classical proof in classical logic shows that we can infer anything and everything from any contradiction.
It's easy to show that the dialetheist has a good, principled response to (3).
But, given (1) and (2), this shouldn't be taken as meaning that dialetheism doesn't have any trivialism problems that the rest of us don't.
*It would, technically, be possible to be a dialetheist without taking Liars to be both true and false--one could, for example, be convinced by Graham Priest's arguments about "the paradoxes of motion and change" but not by any of his other arguments--but I know of no dialetheist who doesn't analyze Liars dialethically. In every actual case of people who argue for dialetheism, the argument from the Liar and related semantic paradoxes is their *central* argument.
Monday, February 15, 2010
One Of These Names Is Not Like The Others
In a scene set in the far future in Ken MacLeod's novel The Sky Road, a character starts running through a list of "names of the One and names of prophets" in a moment of superstitious fear. The names he goes through include Allah, Buddha, Christ....and Quine.
Wednesday, February 10, 2010
Beall And "Just True" (Part I)
So J.C. Beall devotes a full chapter of "Spandrels of Truth" to dealing with the difficulties that dialetheists' have with making sense of the claim that, while some sentences are both true and false, some sentences are "just true." I've dealt with this question here before, since the claim just made is one that it's very important for the dialetheist to make, so they can differentiate their position from trivialism, and the difficulties involved (given their position) are enormous. And at some point soon, I do want to dissect Beall's discussion of "just true." For now, though, I want to make a much quicker point about a place where Beall (it seems to me) accidentally brushes up against a closely related issue.
In "Spandrels of Truth", Beall argues that all "ttruth-ineliminable sentences" (what, in more familiar Kripkean terms, are called "ungrounded" sentences) should be treated as gluts. Thus, not only Liars, but also variants on the Truth-Teller, like the sentence marked with the dollar sign below....
$ The sentence marked with the dollar sign in Ben's blog post, "Beall and 'Just True' (Part I)" is true.
...are both true and false.
(In section 1.5.2, he discusses these cases explicitly, and says, "For present purposes, I treat all such sentences as gluts."
He also discusses the question of whether being grounded is a pre-condition for being truth-evaluable, in section 1.5.3:
"According to the driving picture, ttruth is a constructed see-through device, one brought in to overcome practical difficulties that we otherwise confront with our (otherwise quite sufficient) base language. Given that the device is constructed to be entirely transparent, one expects a certain supervenience to hold. In particular, one expects ttruth to supervene on base-language facts--the base language ttruths.
"The expectation of such supervenience, I think, is natural. If one were to insist on such supervenience across the board, then one would need to reject that some of the given spandrels are gluts, since such sentences are ttrue without their ttruth 'depending' on base-language ttruths. But I see no reason to so insist.... Why insist as much when the constructed device that might yield spandrels that buck supervenience?"
The combination of his stance on Truth-Tellers and his stance on the supervenience requirement, I think, yields an embarassment that (while slightly different than the "just truth" issue) constitutes a fairly good introduction to our eventual discussion of his take on "just truth."
In his discussion on supervience, Beall, it seems to me, is making a distinction between two types of true sentences, true sentences of the kind whose truth Ultimately Depends on the truth of some base language sentence (let's call them udtruths, a category that would include all true base language sentences as well as true sentences that are "ttruth-eliminable"), and true sentences whose truth ultimately Fails to Depend on the truth of some base language sentence (let's call them fdtruths, a category that would include all "ttruth-ineliminable" sentences). Now that we've introduced this terminology (which Beall can hardly object to, since it's a conceptual distinction that he himself makes), we can see that it gives rise to the following "spandrel":
# The sentence marked with the number sign in Ben's blog post "Beall And 'Just True' (Part I)" is udtrue.
If Truth-Tellers are gluts, as Beall wants them to be, and # is a recognizable Truth-Teller (albeit one that attributes a particular sort of truth to itself rather than truth simpliciter), then it seems like we have no choice but to say that it's true (because it's both true and false) that # is true in a way that ultimately depends on the truth of some base-language sentnece, which it certainly doesn't seem to be.
I'm not sure how much to conclude from this, but at the very least, if he is in fact forced to this conclusion, this looks like an embarassment for Beall's position. More so because he says elsewhere in "Spandrels..." that he doesn't think there are any gluts in the base language, and that this seems difficult to square with there being a glut whose truth ultimately depends on the truth of a base-language sentence. At the very least, to reconcile those two claims, we have to say about # that (somehow) it's truth relies on the truth of some base-language sentence, but it's falsity comes from a different source, which is...at the very least...strange.
In "Spandrels of Truth", Beall argues that all "ttruth-ineliminable sentences" (what, in more familiar Kripkean terms, are called "ungrounded" sentences) should be treated as gluts. Thus, not only Liars, but also variants on the Truth-Teller, like the sentence marked with the dollar sign below....
$ The sentence marked with the dollar sign in Ben's blog post, "Beall and 'Just True' (Part I)" is true.
...are both true and false.
(In section 1.5.2, he discusses these cases explicitly, and says, "For present purposes, I treat all such sentences as gluts."
He also discusses the question of whether being grounded is a pre-condition for being truth-evaluable, in section 1.5.3:
"According to the driving picture, ttruth is a constructed see-through device, one brought in to overcome practical difficulties that we otherwise confront with our (otherwise quite sufficient) base language. Given that the device is constructed to be entirely transparent, one expects a certain supervenience to hold. In particular, one expects ttruth to supervene on base-language facts--the base language ttruths.
"The expectation of such supervenience, I think, is natural. If one were to insist on such supervenience across the board, then one would need to reject that some of the given spandrels are gluts, since such sentences are ttrue without their ttruth 'depending' on base-language ttruths. But I see no reason to so insist.... Why insist as much when the constructed device that might yield spandrels that buck supervenience?"
The combination of his stance on Truth-Tellers and his stance on the supervenience requirement, I think, yields an embarassment that (while slightly different than the "just truth" issue) constitutes a fairly good introduction to our eventual discussion of his take on "just truth."
In his discussion on supervience, Beall, it seems to me, is making a distinction between two types of true sentences, true sentences of the kind whose truth Ultimately Depends on the truth of some base language sentence (let's call them udtruths, a category that would include all true base language sentences as well as true sentences that are "ttruth-eliminable"), and true sentences whose truth ultimately Fails to Depend on the truth of some base language sentence (let's call them fdtruths, a category that would include all "ttruth-ineliminable" sentences). Now that we've introduced this terminology (which Beall can hardly object to, since it's a conceptual distinction that he himself makes), we can see that it gives rise to the following "spandrel":
# The sentence marked with the number sign in Ben's blog post "Beall And 'Just True' (Part I)" is udtrue.
If Truth-Tellers are gluts, as Beall wants them to be, and # is a recognizable Truth-Teller (albeit one that attributes a particular sort of truth to itself rather than truth simpliciter), then it seems like we have no choice but to say that it's true (because it's both true and false) that # is true in a way that ultimately depends on the truth of some base-language sentnece, which it certainly doesn't seem to be.
I'm not sure how much to conclude from this, but at the very least, if he is in fact forced to this conclusion, this looks like an embarassment for Beall's position. More so because he says elsewhere in "Spandrels..." that he doesn't think there are any gluts in the base language, and that this seems difficult to square with there being a glut whose truth ultimately depends on the truth of a base-language sentence. At the very least, to reconcile those two claims, we have to say about # that (somehow) it's truth relies on the truth of some base-language sentence, but it's falsity comes from a different source, which is...at the very least...strange.
Monday, February 8, 2010
Just For The Hell Of It...My Answers To Feser's Questions
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 Salvadoran Jesuit priest pointed out that, if Walensa had tried to organize Solidarnosc in El Salvador instead of Poland, he wouldn't have been put in prison. 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 would 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.
(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 factories.
(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, torture, etc., etc, etc.
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.
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 Salvadoran Jesuit priest pointed out that, if Walensa had tried to organize Solidarnosc in El Salvador instead of Poland, he wouldn't have been put in prison. 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 would 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.
(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 factories.
(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, torture, etc., etc, etc.
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.
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.
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