It's a fun paradox, and Peter Eldridge-Smith argues (convincingly, by my lights) that it creates problems for the claim that 'semantic' contradictions can be true, but not 'metaphysically' substantive ones. JC Beall's half of the exchange is available for free here.
(Eldridge Smith's half is available for free too, but if you're reading this on a computer at an institution with an online subscription to Analysis.)
One problem I have with Beall's response is that it's far from clear what sort of "impossibility" he has the resources to assign to base-language contradictions. It's one thing to say that the actual world lacks them--it certainly seems to!--but Beall, of course, can hardly claim that non-trivial worlds containing base-language contradictions are *logically* impossible. As he himself convincingly argues in Spandrels of Truth, dialetheists can hardly go around claiming that some falsehoods are 'more false' than others, such that contradictions involving them really would be explosive, since one could always construct a paradoxical 'spandrel' which attributed precisely this sort of extra-special-super-falseness to itself. If the claim is that they're metaphysically-but-not-logically impossible, I think that requires considerable fleshing out. *Why* would they be metaphysically impossible?
Someone with orthodox views would say that they're metaphysically impossible *because* they're logically impossible. Once we've blocked off that route by accepting (even "purely semantic") true contradictions, an alternative explanation is required.
Wednesday, August 31, 2011
Monday, August 29, 2011
Wednesday, May 11, 2011
Analysis
I just had a paper, entitled "Paracompleteness and Revenge," accepted for publication at Analysis.
It's about revenge problems for "paracomplete" solutions to the Liar Paradox, a topic which of course I've discussed in this space before.
It's about revenge problems for "paracomplete" solutions to the Liar Paradox, a topic which of course I've discussed in this space before.
Wednesday, April 27, 2011
Singapore
I just gave a talk at the National University of Singapore, entitled "Liar Paradox II: Revenge of the Liar Paradox." Singapore, by the way, is lovely, and I'm going to be sorry to leave on Thursday. On the surface it feels enough like Miami to make me feel nostalgic--humid, windy, full of palm trees and outdoor bars and a mishmash of different languages and cultures--while having a lot of appealing un-Miami-ish traits, like being chock-full of restaurants serving delicious Indian food. (The strangest thing I've seen here to date has been Haw Par Villa, a "moral instruction" theme park based on Confucianism and Chinese mythology put up by some early-twentieth-century Chinese millionaires who'd made a killing in the tiger balm trade. The main attraction is the Ten Courts of Hell, where lurid statues and signs depict the punishments sinners are sentenced to by the Emperors of Hell. For example, "cheating on examinations" gets you your intestines ripped out by demons.) While I've been in Singapore, I've been staying with NUS prof Neil Sinhababu, of Possible Girls fame, who will henceforth always have a special place in my heart for saying, when I came in on Saturday night, "I made sure to save some Laphroaig for your visit."
As far as the talk itself, here's the abstract:
Dialetheists like Graham Priest and JC Beall conclude from the Liar Paradox that sentences like “This sentence is not true” are fact both true and untrue, and that we must therefore revise our logic to accommodate the existence of true contradictions. Similarly, “paracomplete” theorists like Hartry Field avoid the contradiction posed by the Liar Paradox by rejecting one of the central elements of classical logic, the Law of the Excluded Middle. A more conservative solution starts from the claim that sentences that attempt to attribute truth or untruth to themselves are meaningless, and therefore simply not the kinds of things we can logically symbolize or apply truth talk to without committing a nonsensical category mistake. The most common objections to this move are (1) that the “meaninglessness solution” is refuted by the existence of “revenge paradoxes” like the one revolving around the sentence “This sentence is either false or meaningless”, and that (2) the sentences involved are so obviously meaningful that it’s just not possible to take seriously the claim that they’re literally meaningless in any ordinary sense, like “Blorks geblork” or “Colorless green ideas sleep furiously,” whereas the dialetheist and paracomplete approaches have the advantages that they (1*) make room for the perfectly obvious fact that, in any language with normal expressive resources, we can construct perfectly meaningful sentences that attribute untruth to themselves, and (2*) are immune to refutation by means of “revenge paradoxes.” I will argue that (1), (2), (1*) and (2*) are all completely wrong.
In terms of the talk itself, I'm never 100% sure what to think about the ethics of blogging in-person discussions, given that I'm sure I wouldn't want to be represented by someone else's half-clear recollection of what I said on the spur of the moment, so I'll pretty well stick to representing what I said myself, with one exception (one hopes, a benign one): In the talk, I spent a few minutes hammering the standard Priest/Beall/Field sort line on Curry's Paradox. In the Q&A, NUS prof Ben Blumson took issue with some of that, and later in the day I ended up spending a couple of hours in his office genially arguing about Curry and related issues, and if I'm still not utterly convinced, I will definitely say that he did a better job of presenting a fairly plausible defense of the approach to Curry I was criticizing than any other defense of that approach I've seen or read before, and in future I will be scaling back at least some of my initial objections in light of some of the points he made.*
In any case, Curry aside, a lot of the ground I covered should be familiar to regular readers here. While I briefly presented my disquotationalist argument for the claim that ungrounded truth talk is literally meaningless, including the Greenness Paradox as a way of defusing the worry that, since we are able to reason about the Liar, we know what follows from it, thus what it means and thus that it means something, my main focus was on revenge paradoxes. (A paper I'm working on making some of these points is tentatively entitled 'Who Among Us Is Safest From The Liar's Revenge?') Conventional wisdom says that the dialetheist and paracomplete approaches to the Liar, given their willingness to engage in radical surgery to our basic logical notions, gain immunity from the revenge paradoxes that typically plague classical solutions to the paradoxes, of which a particularly clear case is supposed to be the problem posed by (1) for those of us who take these sentences to be meaningless:
(1) Sentence (1) is either false or meaningless.
Since paracompletists don't assert anything about the semantic status of such sentences, but rather reject the relevant instances of Excluded Middle, reject the negation of those instances and so on 'all the way down the line,' they seem to be immune from danger from sentences that attribute to themselves the status paracompletists attribute to such sentences. Even more so, dialetheists seem to be immune from any revenge problems, because any 'revenge' liar would at worst just generate yet another true contradiction, and true contradictions don't generate triviality, given the dialetheist's claim that Disjunctive Syllogism isn't universally truth-preserving.
My claim is that (1) is not a problem for the meaninglessness solution at all. A meaningless sentence does not become meaningful once we attach the word "or" to it and paste (what would otherwise be) a meaningful sentence to its tail. Just because a meaningless sentence has the syntactic form of a disjunction and a true second disjunct does not mean that it's meaningful, much less true.
On the other hand, I argue that the paracompletist has a real problem about sentence (2) and that the dialetheist has a real problem about sentence (3).
(2) An ideally rational being who did not lack any relevant information would not accept sentence (2).
(3) It is not the case that sentence (3) is related to truth.
Regular readers will recognize that (2) is the latest form of a revenge paradox for paracompletism I've been tinkering with for some time. The problem, as I see it, is that, if (2) is true, we have the starkly counter-intuitive result that an ideally rational being would not accept a sentence it knew to be true, if (2) is false, we have the equally counter-intuitive result that an ideally rational being would accept a sentence it knew to be false, and if (2) is one of the sentences about which the most rational option is to 'go paracomplete' and reject both the sentence and its negation, then its a sentence that any ideally rational being would not accept (it would reject the sentence instead of accepting it!) and the sentence is true, and, once again, we have the conclusion that an ideally rational being would fail to accept a sentence it knew to be true.
(3) is a familiar problem, but as I argued here, the exact nature of the biggest problem it poses doesn't seem to be widely realized. If being-related-to-truth and not-being-related-to-truth overlap, just as being-related-to-truth and being-related-to-falsehood overlap, then when the dialetheist shows that (given the assumption of dialetheism) there are cases in which all the premises of Disjunctive Syllogism are related to truth and the conclusion is not, they have no more shown that DS is not universally truth-preserving than they would if they'd 'just' showed that all the premises of DS were true and the conclusion was false. No one thinks that "all the premises of argument A are true and the conclusion is false" is a dialetheistically-acceptable way of establishing a failure of truth-preservation. Why should "all the premises of A are related to truth and the conclusion is not" be even a little bit different? Without a better answer to that question, the dialetheist claim that Liars can be both true and false without triviality following simply doesn't hold up.
*On a similar note, I should include a quick shout-out to Brandon Watson for giving me a hard time recently about my error theory about the mistakenness of ordinary competent speakers who take Liars to be meaningful. My preferred way of putting the point now, which I used in the talk, goes about like this: Self-referential sentences are often meaningful--e.g. 'This sentence has seven words in it'--and sentences with precisely the same wording as the Liar sentence are meaningful in other context--'This sentence is false' said while pointing at a sentence about some substantive subject written on a chalkboard. To realize that it's meaningless when the intended reference of the 'this' is that very sentence is a conclusion that takes careful philosophical argumentation. Given those two facts, its quite natural that most people don't realize that it's true. By analogy, if an object is far away and looks a certain (misleading) way from a great distance, and out of a whole crowd of people watching the object, only Bob has a telescope, it's utterly unsurprising that most competent-users-of-functioning-human-eyes end up having a mistaken impression about the object. All Bob needs to do by way of explanation of the disconnect is to say, "yeah, you don't have a telescope. But, hey, look through it yourselves and you'll see where you went wrong here."
As far as the talk itself, here's the abstract:
Dialetheists like Graham Priest and JC Beall conclude from the Liar Paradox that sentences like “This sentence is not true” are fact both true and untrue, and that we must therefore revise our logic to accommodate the existence of true contradictions. Similarly, “paracomplete” theorists like Hartry Field avoid the contradiction posed by the Liar Paradox by rejecting one of the central elements of classical logic, the Law of the Excluded Middle. A more conservative solution starts from the claim that sentences that attempt to attribute truth or untruth to themselves are meaningless, and therefore simply not the kinds of things we can logically symbolize or apply truth talk to without committing a nonsensical category mistake. The most common objections to this move are (1) that the “meaninglessness solution” is refuted by the existence of “revenge paradoxes” like the one revolving around the sentence “This sentence is either false or meaningless”, and that (2) the sentences involved are so obviously meaningful that it’s just not possible to take seriously the claim that they’re literally meaningless in any ordinary sense, like “Blorks geblork” or “Colorless green ideas sleep furiously,” whereas the dialetheist and paracomplete approaches have the advantages that they (1*) make room for the perfectly obvious fact that, in any language with normal expressive resources, we can construct perfectly meaningful sentences that attribute untruth to themselves, and (2*) are immune to refutation by means of “revenge paradoxes.” I will argue that (1), (2), (1*) and (2*) are all completely wrong.
In terms of the talk itself, I'm never 100% sure what to think about the ethics of blogging in-person discussions, given that I'm sure I wouldn't want to be represented by someone else's half-clear recollection of what I said on the spur of the moment, so I'll pretty well stick to representing what I said myself, with one exception (one hopes, a benign one): In the talk, I spent a few minutes hammering the standard Priest/Beall/Field sort line on Curry's Paradox. In the Q&A, NUS prof Ben Blumson took issue with some of that, and later in the day I ended up spending a couple of hours in his office genially arguing about Curry and related issues, and if I'm still not utterly convinced, I will definitely say that he did a better job of presenting a fairly plausible defense of the approach to Curry I was criticizing than any other defense of that approach I've seen or read before, and in future I will be scaling back at least some of my initial objections in light of some of the points he made.*
In any case, Curry aside, a lot of the ground I covered should be familiar to regular readers here. While I briefly presented my disquotationalist argument for the claim that ungrounded truth talk is literally meaningless, including the Greenness Paradox as a way of defusing the worry that, since we are able to reason about the Liar, we know what follows from it, thus what it means and thus that it means something, my main focus was on revenge paradoxes. (A paper I'm working on making some of these points is tentatively entitled 'Who Among Us Is Safest From The Liar's Revenge?') Conventional wisdom says that the dialetheist and paracomplete approaches to the Liar, given their willingness to engage in radical surgery to our basic logical notions, gain immunity from the revenge paradoxes that typically plague classical solutions to the paradoxes, of which a particularly clear case is supposed to be the problem posed by (1) for those of us who take these sentences to be meaningless:
(1) Sentence (1) is either false or meaningless.
Since paracompletists don't assert anything about the semantic status of such sentences, but rather reject the relevant instances of Excluded Middle, reject the negation of those instances and so on 'all the way down the line,' they seem to be immune from danger from sentences that attribute to themselves the status paracompletists attribute to such sentences. Even more so, dialetheists seem to be immune from any revenge problems, because any 'revenge' liar would at worst just generate yet another true contradiction, and true contradictions don't generate triviality, given the dialetheist's claim that Disjunctive Syllogism isn't universally truth-preserving.
My claim is that (1) is not a problem for the meaninglessness solution at all. A meaningless sentence does not become meaningful once we attach the word "or" to it and paste (what would otherwise be) a meaningful sentence to its tail. Just because a meaningless sentence has the syntactic form of a disjunction and a true second disjunct does not mean that it's meaningful, much less true.
On the other hand, I argue that the paracompletist has a real problem about sentence (2) and that the dialetheist has a real problem about sentence (3).
(2) An ideally rational being who did not lack any relevant information would not accept sentence (2).
(3) It is not the case that sentence (3) is related to truth.
Regular readers will recognize that (2) is the latest form of a revenge paradox for paracompletism I've been tinkering with for some time. The problem, as I see it, is that, if (2) is true, we have the starkly counter-intuitive result that an ideally rational being would not accept a sentence it knew to be true, if (2) is false, we have the equally counter-intuitive result that an ideally rational being would accept a sentence it knew to be false, and if (2) is one of the sentences about which the most rational option is to 'go paracomplete' and reject both the sentence and its negation, then its a sentence that any ideally rational being would not accept (it would reject the sentence instead of accepting it!) and the sentence is true, and, once again, we have the conclusion that an ideally rational being would fail to accept a sentence it knew to be true.
(3) is a familiar problem, but as I argued here, the exact nature of the biggest problem it poses doesn't seem to be widely realized. If being-related-to-truth and not-being-related-to-truth overlap, just as being-related-to-truth and being-related-to-falsehood overlap, then when the dialetheist shows that (given the assumption of dialetheism) there are cases in which all the premises of Disjunctive Syllogism are related to truth and the conclusion is not, they have no more shown that DS is not universally truth-preserving than they would if they'd 'just' showed that all the premises of DS were true and the conclusion was false. No one thinks that "all the premises of argument A are true and the conclusion is false" is a dialetheistically-acceptable way of establishing a failure of truth-preservation. Why should "all the premises of A are related to truth and the conclusion is not" be even a little bit different? Without a better answer to that question, the dialetheist claim that Liars can be both true and false without triviality following simply doesn't hold up.
*On a similar note, I should include a quick shout-out to Brandon Watson for giving me a hard time recently about my error theory about the mistakenness of ordinary competent speakers who take Liars to be meaningful. My preferred way of putting the point now, which I used in the talk, goes about like this: Self-referential sentences are often meaningful--e.g. 'This sentence has seven words in it'--and sentences with precisely the same wording as the Liar sentence are meaningful in other context--'This sentence is false' said while pointing at a sentence about some substantive subject written on a chalkboard. To realize that it's meaningless when the intended reference of the 'this' is that very sentence is a conclusion that takes careful philosophical argumentation. Given those two facts, its quite natural that most people don't realize that it's true. By analogy, if an object is far away and looks a certain (misleading) way from a great distance, and out of a whole crowd of people watching the object, only Bob has a telescope, it's utterly unsurprising that most competent-users-of-functioning-human-eyes end up having a mistaken impression about the object. All Bob needs to do by way of explanation of the disconnect is to say, "yeah, you don't have a telescope. But, hey, look through it yourselves and you'll see where you went wrong here."
Sunday, April 24, 2011
Some Objections to the Meaninglessness Solution to the Liar Paradox, Part IV of IV
(Is it Wednesday already? Oh well, better late than never....)
I've argued that, if (as I think) the truth predicate/operator is just a device used to assert things (just as the falsehood predicate/operator is just a device used to assert their negations), it can pretty clearly only be meaningfully applied when there is something there to be asserted--thus, it can only be meaningfully applied to claims about something other than truth. Thus, for example, in a Yablo-like series of sentences where each sentence ascribes truth to the next sentence in the series,
T1: T2 is true.
T2: T3 is true.
T3: T4 is true.
....and so on forever, all the sentences in the infinite series are literally as devoid of meaning as strings of nonsense syllables, or 'Colorless green ideas sleep furiously.' If, on the other hand, sentence T1000000 is "Snow is white," the rest of the sentences inherit their meanings (and, thus, truth-values) from that.
A semantic property pretty clearly *unlike* truth in this respect is meaningfulness itself. If the meaningfulness predicate only applied to meaningful sentences, it wouldn't fulfill its sole communicative function of separating out the meaningful sentences from the meaningless ones. This is important when we consider (18), which, by analogy to the Liar, we can call The Babbler:
(18) Sentence (18) is meaningless.
If (18) is true, it's both true and meaningless, therefore both meaningful and meaningless, and, of course, if it's meaningless, it's both true and meaningless, therefore both meaningful and meaningless. As such, on pain of contradiction, (18) had better just be false.
Fortunately, in light of the above, we have a good principled reason to think that this is indeed the case. If the function of the meaningfulness predicate is to separate out the meaningful from the meaningless sentences, it has to apply to all sentences. Therefore, it's meaningful to say of any sentence that it's meaningful or meaningless, regardless of the nature of the sentence we're talking about. As such, if all a sentence does is assert a view about the meaningfulness of some sentence, even itself, there's no reason for it not to be meaningful. Thus, (18) is false and (19):
(19) Sentence (19) is meaningful.
...is true.
One important principle, underlying the whole business of revenge-paradoxology, is worth calling attention to here, since I've been implicitly using it a lot. Given these sorts of examples, or, better yet, cased like (20) and (21):
(20) This sentence has seven words in it.
(21) This sentence has twenty words in it.
....where it would be clearly absurd to assert about sentence (20), for example, that is seven words long, without granting that sentence (21) is true, we have what we can call the Meaningfulness of Self-Reference Principle: "If Sentence X has property Y, and Sentence X *states* that Sentence X has property Y, then Sentence X is true (and thus, of course, meaningful)."
With all that in mind, and the demonstrations in Parts II and III that it clearly is possible to engage in apparent reasoning about even the most clearly meaningless sentences--meaning that it's not a problem for meaninglessness solutions to the Liar that it's "clearly possible to reason about it, and we all know what does and doesn't follow from it"--let's turn to the apparently troubling revenge paradox for my view that I ended with last time:
(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.
So, playing along with the game of treating it as meaningful for a moment, an obvious first question is this:
Does (17) take a stand on the question of its own meaningfulness? In other words, does it (a) say of itself that it's meaningful, (b) say of itself that it's meaningless, or (c) remain neutral on that topic?
The wording strongly suggests that (a) would be the wrong gloss--talk of treating it 'as meaningful' and 'going through the motions' strongly suggests that the point is to, at the very least, keep open the possibility that it's meaningless, if not to actively assert it. That said, if (a) is right--it's taking a stand on its own meaningfulness in the directing of asserting it--then to say that, if one went through the motions of reasoning about it, one would make something we would regard in other contexts--i.e. really reasoning about meaningful things--as a mistake, is to say that, if one reasoned about it and failed to come to the conclusion that it was false, one would be making a real, full-fledged mistake in reasoning--a factual mistake, landing us with the wrong answer. In other words, given (a), (17) is just a normal if un-usually phrased Liar sentence, the normal meaninglesness solution applies to it, and the Principle of the Meaningfulness of Self-Reference is not violated if we simultanneously say of it that, although meaningless, going through the motions seems to get us the result that it's false (and true), given that what it's saying is that this isn't a matter of going through the motions in an empty context, because it really is false. (It can be neutral about its own falsehood, given that it asserts its own meaningfulness and thus converts the neutral-sounding language about apparent mistakes into, in effect, the positive claim that one would be making a substantive mistake and getting the wrong result.)
If (b) is the case, then we have a disguised conjunction of two claims: (i) a claim about its alleged meaninglessness, and (ii) a claim about whether any possible analysis of it that (1) took it as meaningful and (2) failed to include any mistakes unrelated to the meaningfulness question would therefore (3) diagnose (17) as false. There's a lot to untangle here, but suffice to say that if it is meaningless, then the true 'first conjunct' asserting as much doesn't make the whole thing meaningful, for reasons examined when we looked at (2), above, and if it's not meaningless, the falsity of the first conjunct guarantees the falsity of the whole thing without fear of contradiction. Really, though, I think the most natural reading is (c), and that's where the real problem seems to be.
If (c) is, then, the case, as should be clear by now, (17) really amounts to a disguised disjunction between the claim that (i*) reasoning about (17) and failing to come to the conclusion that it's false would be a *factual* mistake, and (ii*) that 'reasoning' about (17) leads us to the apparent conclusion that it is false, but only because we're indulging a nonsensical category mistake. In other words, given (c), what we end up with is a disguised version of sentence (2), above:
(2) The sentence marked (2) is either false or meaningless.
...which we already dealt with in Part I. Since I enjoy the circularity of ending by directing back to the first post in the series, I think I'll just leave off there and throw open the floor to questions, comments and devastating objections.
I've argued that, if (as I think) the truth predicate/operator is just a device used to assert things (just as the falsehood predicate/operator is just a device used to assert their negations), it can pretty clearly only be meaningfully applied when there is something there to be asserted--thus, it can only be meaningfully applied to claims about something other than truth. Thus, for example, in a Yablo-like series of sentences where each sentence ascribes truth to the next sentence in the series,
T1: T2 is true.
T2: T3 is true.
T3: T4 is true.
....and so on forever, all the sentences in the infinite series are literally as devoid of meaning as strings of nonsense syllables, or 'Colorless green ideas sleep furiously.' If, on the other hand, sentence T1000000 is "Snow is white," the rest of the sentences inherit their meanings (and, thus, truth-values) from that.
A semantic property pretty clearly *unlike* truth in this respect is meaningfulness itself. If the meaningfulness predicate only applied to meaningful sentences, it wouldn't fulfill its sole communicative function of separating out the meaningful sentences from the meaningless ones. This is important when we consider (18), which, by analogy to the Liar, we can call The Babbler:
(18) Sentence (18) is meaningless.
If (18) is true, it's both true and meaningless, therefore both meaningful and meaningless, and, of course, if it's meaningless, it's both true and meaningless, therefore both meaningful and meaningless. As such, on pain of contradiction, (18) had better just be false.
Fortunately, in light of the above, we have a good principled reason to think that this is indeed the case. If the function of the meaningfulness predicate is to separate out the meaningful from the meaningless sentences, it has to apply to all sentences. Therefore, it's meaningful to say of any sentence that it's meaningful or meaningless, regardless of the nature of the sentence we're talking about. As such, if all a sentence does is assert a view about the meaningfulness of some sentence, even itself, there's no reason for it not to be meaningful. Thus, (18) is false and (19):
(19) Sentence (19) is meaningful.
...is true.
One important principle, underlying the whole business of revenge-paradoxology, is worth calling attention to here, since I've been implicitly using it a lot. Given these sorts of examples, or, better yet, cased like (20) and (21):
(20) This sentence has seven words in it.
(21) This sentence has twenty words in it.
....where it would be clearly absurd to assert about sentence (20), for example, that is seven words long, without granting that sentence (21) is true, we have what we can call the Meaningfulness of Self-Reference Principle: "If Sentence X has property Y, and Sentence X *states* that Sentence X has property Y, then Sentence X is true (and thus, of course, meaningful)."
With all that in mind, and the demonstrations in Parts II and III that it clearly is possible to engage in apparent reasoning about even the most clearly meaningless sentences--meaning that it's not a problem for meaninglessness solutions to the Liar that it's "clearly possible to reason about it, and we all know what does and doesn't follow from it"--let's turn to the apparently troubling revenge paradox for my view that I ended with last time:
(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.
So, playing along with the game of treating it as meaningful for a moment, an obvious first question is this:
Does (17) take a stand on the question of its own meaningfulness? In other words, does it (a) say of itself that it's meaningful, (b) say of itself that it's meaningless, or (c) remain neutral on that topic?
The wording strongly suggests that (a) would be the wrong gloss--talk of treating it 'as meaningful' and 'going through the motions' strongly suggests that the point is to, at the very least, keep open the possibility that it's meaningless, if not to actively assert it. That said, if (a) is right--it's taking a stand on its own meaningfulness in the directing of asserting it--then to say that, if one went through the motions of reasoning about it, one would make something we would regard in other contexts--i.e. really reasoning about meaningful things--as a mistake, is to say that, if one reasoned about it and failed to come to the conclusion that it was false, one would be making a real, full-fledged mistake in reasoning--a factual mistake, landing us with the wrong answer. In other words, given (a), (17) is just a normal if un-usually phrased Liar sentence, the normal meaninglesness solution applies to it, and the Principle of the Meaningfulness of Self-Reference is not violated if we simultanneously say of it that, although meaningless, going through the motions seems to get us the result that it's false (and true), given that what it's saying is that this isn't a matter of going through the motions in an empty context, because it really is false. (It can be neutral about its own falsehood, given that it asserts its own meaningfulness and thus converts the neutral-sounding language about apparent mistakes into, in effect, the positive claim that one would be making a substantive mistake and getting the wrong result.)
If (b) is the case, then we have a disguised conjunction of two claims: (i) a claim about its alleged meaninglessness, and (ii) a claim about whether any possible analysis of it that (1) took it as meaningful and (2) failed to include any mistakes unrelated to the meaningfulness question would therefore (3) diagnose (17) as false. There's a lot to untangle here, but suffice to say that if it is meaningless, then the true 'first conjunct' asserting as much doesn't make the whole thing meaningful, for reasons examined when we looked at (2), above, and if it's not meaningless, the falsity of the first conjunct guarantees the falsity of the whole thing without fear of contradiction. Really, though, I think the most natural reading is (c), and that's where the real problem seems to be.
If (c) is, then, the case, as should be clear by now, (17) really amounts to a disguised disjunction between the claim that (i*) reasoning about (17) and failing to come to the conclusion that it's false would be a *factual* mistake, and (ii*) that 'reasoning' about (17) leads us to the apparent conclusion that it is false, but only because we're indulging a nonsensical category mistake. In other words, given (c), what we end up with is a disguised version of sentence (2), above:
(2) The sentence marked (2) is either false or meaningless.
...which we already dealt with in Part I. Since I enjoy the circularity of ending by directing back to the first post in the series, I think I'll just leave off there and throw open the floor to questions, comments and devastating objections.
Wednesday, April 13, 2011
Fatalism, Part I of II (Diet Soap Nit-Pickery)
A little while ago, I mentioned that I was interviewed for a second appearance on philosophy-oriented podcast Diet Soap. (First one is here.) Anyway, I think the episode with the second appearance on it is going to be coming out within the next couple weeks.
As I emphasized then, I'm happy to be on there. Diet Soap is a podcast I listen to regularly--in fact, lately, it's been the one I've listened to the most regularly that isn't about hockey--and I almost always find it interesting, entertaining and thought-provoking. You should listen.
Anyway, despite having been a normal weekly listener for most of the last bunch of weeks, I somehow missed Episode 91, which was (among other things) about Deluze. Since the most recent episode was a different perspective on Deluze, and the show notes referred to the previous one, I thought I might as well go back and listen to the first Deluze discussion.
...most of which was interesting enough, but towards the end, the host and his guest touched on fatalism and free will in a way that made me want to rip my iPod out of my ears and throw it against the nearest wall in frustration. (I didn't. It's an expensive iPod--one of those tiny little "nano touch" thingies--and what with me being in Korea and all, it'd be even more expensive to replace. Plus, of course, despite my frustration on this particular point, I was still interested to hear the rest of what they had to say.) I've touched on this complaint before, after host Doug Lain brought it up in a previous episode, but I want to take another, more careful crack at it here. Here's what I said about it before:
(2) In the discussions about free will and fatalism, there's a lot of running together of two quite distinct claims:
(i) That there are facts about what will happen in the future, such that some statements about the future are true and some are false, and
(ii) That some being knows which statements about the future are true and which ones are false.
Clearly (at least given the orthodox assumption that truth is a necessary condition for knowledge), (ii) entails (i), but (i) can absolutely and obviously be true without (ii) being true. By analogy, consider Claim C (about the past, rather than the future):
C: "Alexander the great's maternal grandmother's paternal grandmother accidentally cut her toe on a rock when she was six years old."
C is pretty clearly either true or false. Whatever one thinks about reference failures and all of that (i.e. whether a statement like "the present King of France is bald" is true, false or neither, given that there is no present King of France), Alexander the Great clearly had a maternal grandmother, and she clearly had a paternal grandmother, and at one point she was six years old. During that year, that lady either did accidentally cut her toe on a rock--in which case C is true--or she didn't (in which case the negation of C is true), and none of this is remotely philosophically controversial. Given atheism (and the absence of time machines) no one is in any position to have epistemic access to the fact of the matter here, but no one thinks that there isn't a fact of the matter about this issue. Why on earth should it be any different, re: future facts and the absence of any being with epistemic access to those facts?
(In the comments on that post, a friend of mine who's working on free will for his doctoral dissertation put the point rather more vehemently than I would.)
Expanding a bit now:
Lain expresses the point in terms of "truth claims", which I find slightly confusing, just because it's not terminology that I'm used to, but I think it's fairly clear in context that it just means "claims that are true." (For the sake of simplicitly, let's make that "true statements.") He's responding to Taylor's classic argument for fatalism (the idea that the future is "fixed" in some way that gets in the way of some important intuitive idea of free will). That argument is spelled out formally by Taylor, and Lain is looking for a way out. So far, so good.
On the philosophical substance here, my own very strong view is that (a) there are lots of ways out, even if Lain's favored one is as problematic as I think it is, but that (b) no matter what your favorite conception is of free will, "fatalism" shouldn't be a problem. We can come back to that in a bit. Meanwhile....
Lain's move is, basically, to leverage atheism against fatalism. If Taylor's picture has it that there is an infinite set of every true statement about the future--and therefore that, for every prediction you could make about the future, either its in that set or its not, but one way or the other, there's a fixed fact of the matter about whether the prediction's going to come true--Lain wants to dispute the claim that there is such a set of true statements. After all, in the absence of an omniscient God, no one is in a position to claim all the infinitely many true things about the future.
In his most recent statement of all this, in Episode 91, Lain made a special point of saying that something can only be a statement if someone has said it, written it down or thought it. I think this might have been a way of side-stepping the way I'd previously expressed my objection, quoted above--in terms of "some statements being true and others being false" vs. "some entity being in a position to know which statements are true and which are false"--and I guess it does, but in a way that I think misses the point.
Think about the past. That's definitely "fixed" and at this point unchangeable in just the sense that anyone worried about fatalism is worried that the future is "fixed", right? Well, even if the past is finite (different physical cosmologies have importantly different results on that point), in a universe without any God-like entities, surely no one is in any position to know, or state, every true statement about the past, right? That is, however, just obviously utterly irrelevant to the pasts' "fixed"-ness.
The reason its irrelevant is that the issue isn't so much about statements as it is about facts. Even if I hadn't come up with the particular example I used in the comments--C: "Alexander the great's maternal grandmother's paternal grandmother accidentally cut her toe on a rock when she was six years old."--and indeed if no one had ever said or thought of that statement (as is extremely likely that no one would have) the lady in question, and all events in her life, would still exist, and either include or fail to include the described incident. Even if one thinks that sentences per se rather, than say, propositions, are the only things that can be "true" or "false", and even if a sentence describing the incident doesn't exist, either the incident occurred or it didn't.
Now, one could make a really radical move here and just deny the existence of un-described facts--if no one has ever commented on or thought about the number of empty bottles on the floor of the basement of the frat house, then there isn't a certain, definite, objective number of bottles there!--and that would sort-of-help here, but, in the end, it wouldn't help much. Not only would this move distance you so much from any remotely recognizable sense of the meaning of the word "truth" as it's used pre-philosophically in ordinary everyday conversations that it's no longer clear to me what we're talking about when we talk about whether some statement is "true" or "false", but even if we make this move, it won't get us off the fatalist hook.
For one thing, we can always reconstruct the fatalistic stuff in terms of hypothetical statements--e.g. "for any possible future event, if one were to make a prediction about it, that prediction would either be a true prediction or it wouldn't be"--and for another, even if we couldn't (and, again, we pretty clearly can), that wouldn't matter very much.
Here's why:
Forget "the future" as a vast (possibly infinitely extended) category, and re-ask yourself why you're concerned with fatalism in the first place. Presumably, it's because we want to think we have the power to change things with our idividual or collective choices, or at the very least that (even if we don't think it's a matter of choice) certain future possibilities we care about are still "open."
The problem is that, for any given future possibility we care about the openness of, we can just construct a sentence about it. For example:
"Doug Lain's great-grandchildren will live under precisely the sort of anarchist-socialist utopia he advocates."
or
"An anarchist-socialist utopia will never come about."
or
"Doug Lain will murder someone on July 15th, 2058, and be executed for that crime."
or
"Doug Lain will never kill anyone."
....or whatever. Whether or not there's an infinite set of true statements for any of these these statements to be part of (if any of them are true) or to be fail to be part of, we hardly need an infinite, omniscient mind for these particular statements to exist. (Check them out! I just wrote them up!) Given that they exist, they're either true or they're not, which is presumably just as much (or, of course, just as little) of a problem for the "openness" or undecidness or whatever of these future possibilities as them being or not being part of some infinite set of true statements would be.
Now, like I said earlier, I tend to think that both (a) if one thinks that its important to avoid this fatalistic result, there are plenty of moves you could make that do so, even if the move under consideration has prospects as dim as I think they are, and that (b) it's actually not important to avoid it (the future is every bit as much "up to us" and to our free choices with or without the kind of 'openness' anti-fatalists tend to be concerned with). That is, though, as they say, a-whole-nother discussion, and one probably best reserved for a blog post of its own, this one being as long as it is already.
So let's do that in a couple weeks. Meanwhile, stay tuned for the long-delayed Part IV of the Liar Pardox posts next Wednesday!
As I emphasized then, I'm happy to be on there. Diet Soap is a podcast I listen to regularly--in fact, lately, it's been the one I've listened to the most regularly that isn't about hockey--and I almost always find it interesting, entertaining and thought-provoking. You should listen.
Anyway, despite having been a normal weekly listener for most of the last bunch of weeks, I somehow missed Episode 91, which was (among other things) about Deluze. Since the most recent episode was a different perspective on Deluze, and the show notes referred to the previous one, I thought I might as well go back and listen to the first Deluze discussion.
...most of which was interesting enough, but towards the end, the host and his guest touched on fatalism and free will in a way that made me want to rip my iPod out of my ears and throw it against the nearest wall in frustration. (I didn't. It's an expensive iPod--one of those tiny little "nano touch" thingies--and what with me being in Korea and all, it'd be even more expensive to replace. Plus, of course, despite my frustration on this particular point, I was still interested to hear the rest of what they had to say.) I've touched on this complaint before, after host Doug Lain brought it up in a previous episode, but I want to take another, more careful crack at it here. Here's what I said about it before:
(2) In the discussions about free will and fatalism, there's a lot of running together of two quite distinct claims:
(i) That there are facts about what will happen in the future, such that some statements about the future are true and some are false, and
(ii) That some being knows which statements about the future are true and which ones are false.
Clearly (at least given the orthodox assumption that truth is a necessary condition for knowledge), (ii) entails (i), but (i) can absolutely and obviously be true without (ii) being true. By analogy, consider Claim C (about the past, rather than the future):
C: "Alexander the great's maternal grandmother's paternal grandmother accidentally cut her toe on a rock when she was six years old."
C is pretty clearly either true or false. Whatever one thinks about reference failures and all of that (i.e. whether a statement like "the present King of France is bald" is true, false or neither, given that there is no present King of France), Alexander the Great clearly had a maternal grandmother, and she clearly had a paternal grandmother, and at one point she was six years old. During that year, that lady either did accidentally cut her toe on a rock--in which case C is true--or she didn't (in which case the negation of C is true), and none of this is remotely philosophically controversial. Given atheism (and the absence of time machines) no one is in any position to have epistemic access to the fact of the matter here, but no one thinks that there isn't a fact of the matter about this issue. Why on earth should it be any different, re: future facts and the absence of any being with epistemic access to those facts?
(In the comments on that post, a friend of mine who's working on free will for his doctoral dissertation put the point rather more vehemently than I would.)
Expanding a bit now:
Lain expresses the point in terms of "truth claims", which I find slightly confusing, just because it's not terminology that I'm used to, but I think it's fairly clear in context that it just means "claims that are true." (For the sake of simplicitly, let's make that "true statements.") He's responding to Taylor's classic argument for fatalism (the idea that the future is "fixed" in some way that gets in the way of some important intuitive idea of free will). That argument is spelled out formally by Taylor, and Lain is looking for a way out. So far, so good.
On the philosophical substance here, my own very strong view is that (a) there are lots of ways out, even if Lain's favored one is as problematic as I think it is, but that (b) no matter what your favorite conception is of free will, "fatalism" shouldn't be a problem. We can come back to that in a bit. Meanwhile....
Lain's move is, basically, to leverage atheism against fatalism. If Taylor's picture has it that there is an infinite set of every true statement about the future--and therefore that, for every prediction you could make about the future, either its in that set or its not, but one way or the other, there's a fixed fact of the matter about whether the prediction's going to come true--Lain wants to dispute the claim that there is such a set of true statements. After all, in the absence of an omniscient God, no one is in a position to claim all the infinitely many true things about the future.
In his most recent statement of all this, in Episode 91, Lain made a special point of saying that something can only be a statement if someone has said it, written it down or thought it. I think this might have been a way of side-stepping the way I'd previously expressed my objection, quoted above--in terms of "some statements being true and others being false" vs. "some entity being in a position to know which statements are true and which are false"--and I guess it does, but in a way that I think misses the point.
Think about the past. That's definitely "fixed" and at this point unchangeable in just the sense that anyone worried about fatalism is worried that the future is "fixed", right? Well, even if the past is finite (different physical cosmologies have importantly different results on that point), in a universe without any God-like entities, surely no one is in any position to know, or state, every true statement about the past, right? That is, however, just obviously utterly irrelevant to the pasts' "fixed"-ness.
The reason its irrelevant is that the issue isn't so much about statements as it is about facts. Even if I hadn't come up with the particular example I used in the comments--C: "Alexander the great's maternal grandmother's paternal grandmother accidentally cut her toe on a rock when she was six years old."--and indeed if no one had ever said or thought of that statement (as is extremely likely that no one would have) the lady in question, and all events in her life, would still exist, and either include or fail to include the described incident. Even if one thinks that sentences per se rather, than say, propositions, are the only things that can be "true" or "false", and even if a sentence describing the incident doesn't exist, either the incident occurred or it didn't.
Now, one could make a really radical move here and just deny the existence of un-described facts--if no one has ever commented on or thought about the number of empty bottles on the floor of the basement of the frat house, then there isn't a certain, definite, objective number of bottles there!--and that would sort-of-help here, but, in the end, it wouldn't help much. Not only would this move distance you so much from any remotely recognizable sense of the meaning of the word "truth" as it's used pre-philosophically in ordinary everyday conversations that it's no longer clear to me what we're talking about when we talk about whether some statement is "true" or "false", but even if we make this move, it won't get us off the fatalist hook.
For one thing, we can always reconstruct the fatalistic stuff in terms of hypothetical statements--e.g. "for any possible future event, if one were to make a prediction about it, that prediction would either be a true prediction or it wouldn't be"--and for another, even if we couldn't (and, again, we pretty clearly can), that wouldn't matter very much.
Here's why:
Forget "the future" as a vast (possibly infinitely extended) category, and re-ask yourself why you're concerned with fatalism in the first place. Presumably, it's because we want to think we have the power to change things with our idividual or collective choices, or at the very least that (even if we don't think it's a matter of choice) certain future possibilities we care about are still "open."
The problem is that, for any given future possibility we care about the openness of, we can just construct a sentence about it. For example:
"Doug Lain's great-grandchildren will live under precisely the sort of anarchist-socialist utopia he advocates."
or
"An anarchist-socialist utopia will never come about."
or
"Doug Lain will murder someone on July 15th, 2058, and be executed for that crime."
or
"Doug Lain will never kill anyone."
....or whatever. Whether or not there's an infinite set of true statements for any of these these statements to be part of (if any of them are true) or to be fail to be part of, we hardly need an infinite, omniscient mind for these particular statements to exist. (Check them out! I just wrote them up!) Given that they exist, they're either true or they're not, which is presumably just as much (or, of course, just as little) of a problem for the "openness" or undecidness or whatever of these future possibilities as them being or not being part of some infinite set of true statements would be.
Now, like I said earlier, I tend to think that both (a) if one thinks that its important to avoid this fatalistic result, there are plenty of moves you could make that do so, even if the move under consideration has prospects as dim as I think they are, and that (b) it's actually not important to avoid it (the future is every bit as much "up to us" and to our free choices with or without the kind of 'openness' anti-fatalists tend to be concerned with). That is, though, as they say, a-whole-nother discussion, and one probably best reserved for a blog post of its own, this one being as long as it is already.
So let's do that in a couple weeks. Meanwhile, stay tuned for the long-delayed Part IV of the Liar Pardox posts next Wednesday!
Monday, April 11, 2011
Wednesday, April 6, 2011
Some Objections to the Meaninglessness Solution to the Liar Paradox, Part III of IV
My view is that, as my boy Willard Van put it, truth is disquotation. When I prefix the words 'it's true that' to a quoted sentence, the effect of what I've done is to remove the quotation marks. Moreover, I see no principled distinction between this way of ascribing truth to a sentence (quoting it within the larger sentence in which one applies the truth operator to it), or other standard ways of ascribing truth, like saying "that's true" in response to someone else's statement, or the more formal device of writing down a pair of numbered sentences like (14) and (15):
(14) Snow is white.
(15) Sentence (14) is true.
In all of these, the function of the truth predicate/operator is exactly the same.
A good analogy in contemporary informal English is "What he said."
Imagine the following, fairly mundane interaction:
An evolutionary biologist, Jane, is drinking at a bar with her boyfriend John (a humanities major with a shaky but more or less accurate grasp on her field) and her loveable-but-frustrating cousin Jack, a fundamentalist Christian (who's just ordering coca cola and bar nachos while his heathen cousin and the man she's living in sin booze up). At some point, Jack brings up evolution and runs through some creationist talking point about missing links in the fossil record or some such. Jane sighs, orders another drink and carefully runs through the scientific explanation of what Jack's talking about. In the end, both cousins stop talking and turn to John, who just tilts his head towards his girlfriend and says "What she said."
This is a normal and immediately familiar usage--note, BTW, that John's sentence isn't syntactically "well-formed", but it's meaningful all the same, "well-formed"-ness in natural language contexts not being necessary for, sufficient for, or even especially relevant t meaningfulness--and we all get what's going on here. "What she said" is a linguistic device John is using as a shorthand method of asserting exactly what Jane just asserted. He could be using it for a variety of reasons--most obviously, using this handy abbreviation is far easier than repeating the entire explanation Jane just gave, but it could also (in this case quite plausibly) be that he doesn't remember every detail of what he means to be asserting. Certainly, there's very little temptation here to think that John means anything above and beyond, or different from, what Jane said. The point of the phrasing is, in fact, to draw attention to the fact that he means to say exactly what, well, "she said."
The word 'true' has various advantages over its functionally kindred linguistic device 'what she said'--for one thing, one can use it on written sentences, and more tellingly, on sentences whose source is unclear--but the point, I think, is the same. Instances of "what she said" are presumably meaningful if the sentence it's applied to are meaningful and meaningless otherwise (John: "Colorless green ideas sleep furiously", Jane: "What he said"), and the same goes, I would argue for truth. The general principle is that truth talk is only *parasitically* meaningful. Prefixing "it's true that" to a *quoted* sentence has the effect of removing the quotation marks--i.e. "it's true that 'snow is white'" means precisely the same thing as "snow is white"--but putting "it's true that" at the beginning of a sentence already outside of quotation marks has no semantic impact at all. (It might add emphasis, but it doesn't change the meaning.) "(16) is true" has no independent meaning not supplied by whatever sentence (16) means. An obvious consequence of this view is that if "(16) is true" inherits no meaning from sentence (16), then it means nothing at all. Hence, if sentence (16) is "snow is white", "(16) is true" does nothing but attribute whiteness to snow, and if (16) is (16) is true, it means nothing at all. Putting a "not" in the mix is never, of course, enough to change a meaningless jumble of words into a meaningful one.
At the end of Part I, I considered one of the most worrying objections to this position. Isn't it manifestly possible to 'reason' about these sentences? Doesn't someone like me, who takes Liar sentences to be meaningless, come to this position on the basis of careful consideration of various other approaches to the paradox? Isn't part of the process of arguing for this solution going to be a matter of arguing against competing solutions, and won't that, in turn, be to a considerable extent a matter of arguing about "what follows" from various Liar sentences, in combination with added premises taken from a proposed solution? (For example: "You say that standard Liar sentences are meaningful but that they do not express propositions. What, then, about a sentence that says of itself that it does not express a true proposition? Surely, if it doesn't express a proposition at all, it doesn't express a true one, right?" or "I don't see how a gap theorist can get around the revenge paradox about a sentence that says of itself that it's either false or gappy" or "How does the dialetheist deal with a sentence that says of itself that it is just false and not true?") If one plays this game as well as anyone, doesn't that show that, like everyone else one grasps the meaning of the sentences in question? After all, isn't this game of generating unappetizing inferences from alternate solutions a matter of drawing out the entailments of the content of these sentences?
In Part II, I responded to this objection by pointing out that the same problem could arise for sentences that everyone takes to be meaningless, drawing out a scenario in which many people might infer contradictions from the sentence "Colorless green ideas sleep furiously" and ways that the hypothetical philosophical debate about this "Greenness Paradox" could closely mimic the actual philosophical debate about the Liar Paradox.
One possible problem here might have to do with distinctions among meaningless sentences. In the comments on Part I, ParisW suggested that there might be quantitative degrees of, or qualitatively different types of meaningfulness, and that different meaningless sentences might interact with logic in different ways. Now, I don't words in his mouth, and the line of thought would have to be developed a bit first anyway, but the general idea could be that it's not legitimate to pick out a meaningless sentence, show how it interacts with logic, and make sweeping generalizations about how Liars interact with logic or fail to do so if they are meaningless.
Now, personally I have trouble seeing how this could get off the ground--"means something"/"means nothing" look pretty clearly binary to me--but maybe the possibility of the "Greenness Paradox" is a consequence of "Colorless green ideas sleep furiously", despite its distinguished history as a stock example of a meaningless sentence, just isn't meaningless enough. How about "blorks geblork"? We could have the following conversation:
Person 1: "Blorks geblork!"
Person 2: "That's false."
Person 1: "So you think blorks don't geblork?"
Person 3: "That doesn't follow from what 2's point that it's not the case that blorks geblork. It could be that there are no blorks."
Clearly, there's something absurd about these three people going through the motions of reasoning about a combination of nonsense syllables. Equally, clearly, Person 1's gloss on Person 2's statement commits some sort of further mistake, correctly highlighted by Person 3's comment, and this further mistake is something that goes above beyond the basic category mistake of applying truth talk to a meaningless string of nonsense syllables and going on to "reason" about them.
Again, one might think this has something to do with degrees or kinds of meaninglessness. The string of nonsense syllables in question, after all, still has an apparent subject-predicate form, which is the entry point for all this.
Take a different example. Let's say I just sneezed. I've made a sound that doesn't sound at all subject-predicate-ish, and that no one who heard it and understood what it was would mistake for a claim about anything. Now, if some strange person did say that my sneeze was "true", a tempting way to correct them would be to say, "no no no, it wasn't true or false. Sneezes are just the wrong kind of thing to be able to count as either."
Once we combine a natural way of symbolizing the first sentence of my "correction" with two banally orthodox assumptions about truth and logic, we have all the ingredients of what we can call the Sneeze Paradox:
Premise 1: For every P, T(P) iff P..
Premise 2: For every P, T(P) or F(P).
Premise 3: Ben's sneeze (S) is neither true nor false. [~T(S) & ~F(S)]
By a series of relative simple steps I'll leave as an exercise for the reader, we get to:
Conclusion: S & ~S
One could imagine an (unlikely) scenario where no one ever figured out what was wrong here, and dialetheists used the Sneeze Paradox to argue for true contradictions, gap theorists used it to argue against Bivalence, sophisticated logicians with mostly orthodox premises found all kinds of ingenious ways of twiddling with or conceptually re-thinking the rational role of the logical architecture to avoid the conclusion and so on. Inevitably, various participants in this debate would make various reasoning mistakes.
Of course, we know that the at-bottom mistake underlying the whole debate is a nonsensical category mistake, not a factual mistake of any kind. If my statement "my sneeze wasn't true or false" is true, it's because I don't mean to literally assert the negation of the disjunction of the claim that it is true and the claim that it is false. If I'm talking sense in any sense, it's because what I really mean by the sloppy shorthand "it's not true or false" is "it's not the kind of thing to which 'true' and 'false' can be meaninfully applied, which is a different kettle of fish entirely. Still, on he way to realizing this, we'd doubtless want to nit-pick the arguments of the normal participants in the debate, catch them out on 'errors.'
So, how can we possibly conceptualize these 'errors'? And won't any analysis we give of the nature of these apparent "errors in reasoning" inevitably spawn new revenge problems for the meaningless solution, along the lines of (17)?
(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.
To which all I can say is, stay tuned for the exciting conclusion of our quadrilogy to find out!
(14) Snow is white.
(15) Sentence (14) is true.
In all of these, the function of the truth predicate/operator is exactly the same.
A good analogy in contemporary informal English is "What he said."
Imagine the following, fairly mundane interaction:
An evolutionary biologist, Jane, is drinking at a bar with her boyfriend John (a humanities major with a shaky but more or less accurate grasp on her field) and her loveable-but-frustrating cousin Jack, a fundamentalist Christian (who's just ordering coca cola and bar nachos while his heathen cousin and the man she's living in sin booze up). At some point, Jack brings up evolution and runs through some creationist talking point about missing links in the fossil record or some such. Jane sighs, orders another drink and carefully runs through the scientific explanation of what Jack's talking about. In the end, both cousins stop talking and turn to John, who just tilts his head towards his girlfriend and says "What she said."
This is a normal and immediately familiar usage--note, BTW, that John's sentence isn't syntactically "well-formed", but it's meaningful all the same, "well-formed"-ness in natural language contexts not being necessary for, sufficient for, or even especially relevant t meaningfulness--and we all get what's going on here. "What she said" is a linguistic device John is using as a shorthand method of asserting exactly what Jane just asserted. He could be using it for a variety of reasons--most obviously, using this handy abbreviation is far easier than repeating the entire explanation Jane just gave, but it could also (in this case quite plausibly) be that he doesn't remember every detail of what he means to be asserting. Certainly, there's very little temptation here to think that John means anything above and beyond, or different from, what Jane said. The point of the phrasing is, in fact, to draw attention to the fact that he means to say exactly what, well, "she said."
The word 'true' has various advantages over its functionally kindred linguistic device 'what she said'--for one thing, one can use it on written sentences, and more tellingly, on sentences whose source is unclear--but the point, I think, is the same. Instances of "what she said" are presumably meaningful if the sentence it's applied to are meaningful and meaningless otherwise (John: "Colorless green ideas sleep furiously", Jane: "What he said"), and the same goes, I would argue for truth. The general principle is that truth talk is only *parasitically* meaningful. Prefixing "it's true that" to a *quoted* sentence has the effect of removing the quotation marks--i.e. "it's true that 'snow is white'" means precisely the same thing as "snow is white"--but putting "it's true that" at the beginning of a sentence already outside of quotation marks has no semantic impact at all. (It might add emphasis, but it doesn't change the meaning.) "(16) is true" has no independent meaning not supplied by whatever sentence (16) means. An obvious consequence of this view is that if "(16) is true" inherits no meaning from sentence (16), then it means nothing at all. Hence, if sentence (16) is "snow is white", "(16) is true" does nothing but attribute whiteness to snow, and if (16) is (16) is true, it means nothing at all. Putting a "not" in the mix is never, of course, enough to change a meaningless jumble of words into a meaningful one.
At the end of Part I, I considered one of the most worrying objections to this position. Isn't it manifestly possible to 'reason' about these sentences? Doesn't someone like me, who takes Liar sentences to be meaningless, come to this position on the basis of careful consideration of various other approaches to the paradox? Isn't part of the process of arguing for this solution going to be a matter of arguing against competing solutions, and won't that, in turn, be to a considerable extent a matter of arguing about "what follows" from various Liar sentences, in combination with added premises taken from a proposed solution? (For example: "You say that standard Liar sentences are meaningful but that they do not express propositions. What, then, about a sentence that says of itself that it does not express a true proposition? Surely, if it doesn't express a proposition at all, it doesn't express a true one, right?" or "I don't see how a gap theorist can get around the revenge paradox about a sentence that says of itself that it's either false or gappy" or "How does the dialetheist deal with a sentence that says of itself that it is just false and not true?") If one plays this game as well as anyone, doesn't that show that, like everyone else one grasps the meaning of the sentences in question? After all, isn't this game of generating unappetizing inferences from alternate solutions a matter of drawing out the entailments of the content of these sentences?
In Part II, I responded to this objection by pointing out that the same problem could arise for sentences that everyone takes to be meaningless, drawing out a scenario in which many people might infer contradictions from the sentence "Colorless green ideas sleep furiously" and ways that the hypothetical philosophical debate about this "Greenness Paradox" could closely mimic the actual philosophical debate about the Liar Paradox.
One possible problem here might have to do with distinctions among meaningless sentences. In the comments on Part I, ParisW suggested that there might be quantitative degrees of, or qualitatively different types of meaningfulness, and that different meaningless sentences might interact with logic in different ways. Now, I don't words in his mouth, and the line of thought would have to be developed a bit first anyway, but the general idea could be that it's not legitimate to pick out a meaningless sentence, show how it interacts with logic, and make sweeping generalizations about how Liars interact with logic or fail to do so if they are meaningless.
Now, personally I have trouble seeing how this could get off the ground--"means something"/"means nothing" look pretty clearly binary to me--but maybe the possibility of the "Greenness Paradox" is a consequence of "Colorless green ideas sleep furiously", despite its distinguished history as a stock example of a meaningless sentence, just isn't meaningless enough. How about "blorks geblork"? We could have the following conversation:
Person 1: "Blorks geblork!"
Person 2: "That's false."
Person 1: "So you think blorks don't geblork?"
Person 3: "That doesn't follow from what 2's point that it's not the case that blorks geblork. It could be that there are no blorks."
Clearly, there's something absurd about these three people going through the motions of reasoning about a combination of nonsense syllables. Equally, clearly, Person 1's gloss on Person 2's statement commits some sort of further mistake, correctly highlighted by Person 3's comment, and this further mistake is something that goes above beyond the basic category mistake of applying truth talk to a meaningless string of nonsense syllables and going on to "reason" about them.
Again, one might think this has something to do with degrees or kinds of meaninglessness. The string of nonsense syllables in question, after all, still has an apparent subject-predicate form, which is the entry point for all this.
Take a different example. Let's say I just sneezed. I've made a sound that doesn't sound at all subject-predicate-ish, and that no one who heard it and understood what it was would mistake for a claim about anything. Now, if some strange person did say that my sneeze was "true", a tempting way to correct them would be to say, "no no no, it wasn't true or false. Sneezes are just the wrong kind of thing to be able to count as either."
Once we combine a natural way of symbolizing the first sentence of my "correction" with two banally orthodox assumptions about truth and logic, we have all the ingredients of what we can call the Sneeze Paradox:
Premise 1: For every P, T(P) iff P..
Premise 2: For every P, T(P) or F(P).
Premise 3: Ben's sneeze (S) is neither true nor false. [~T(S) & ~F(S)]
By a series of relative simple steps I'll leave as an exercise for the reader, we get to:
Conclusion: S & ~S
One could imagine an (unlikely) scenario where no one ever figured out what was wrong here, and dialetheists used the Sneeze Paradox to argue for true contradictions, gap theorists used it to argue against Bivalence, sophisticated logicians with mostly orthodox premises found all kinds of ingenious ways of twiddling with or conceptually re-thinking the rational role of the logical architecture to avoid the conclusion and so on. Inevitably, various participants in this debate would make various reasoning mistakes.
Of course, we know that the at-bottom mistake underlying the whole debate is a nonsensical category mistake, not a factual mistake of any kind. If my statement "my sneeze wasn't true or false" is true, it's because I don't mean to literally assert the negation of the disjunction of the claim that it is true and the claim that it is false. If I'm talking sense in any sense, it's because what I really mean by the sloppy shorthand "it's not true or false" is "it's not the kind of thing to which 'true' and 'false' can be meaninfully applied, which is a different kettle of fish entirely. Still, on he way to realizing this, we'd doubtless want to nit-pick the arguments of the normal participants in the debate, catch them out on 'errors.'
So, how can we possibly conceptualize these 'errors'? And won't any analysis we give of the nature of these apparent "errors in reasoning" inevitably spawn new revenge problems for the meaningless solution, along the lines of (17)?
(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.
To which all I can say is, stay tuned for the exciting conclusion of our quadrilogy to find out!
Monday, April 4, 2011
Singapore Talk & Revenge Problems for Dialetheism
So I just bought a roundtrip ticket to Singapore.
Three weeks from tomorrow, I'll be delivering a talk at the Philosophy Department at the National University of Singapore (NUS) entitled "Liar Paradox II: Revenge of the Liar Paradox." In lieu of Part III of the ongoing series on the same subject, here's the abstract I sent them for the talk (and then a quick explanation of where I'm going with it):
Dialetheists like Graham Priest and JC Beall conclude from the Liar Paradox that sentences like “This sentence is not true” are fact both true and untrue, and that we must therefore revise our logic to accommodate the existence of true contradictions. Similarly, “paracomplete” theorists like Hartry Field avoid the contradiction posed by the Liar Paradox by rejecting one of the central elements of classical logic, the Law of the Excluded Middle. A more conservative solution starts from the claim that sentences that attempt to attribute truth or untruth to themselves are meaningless, and therefore simply not the kinds of things we can logically symbolize or apply truth talk to without committing a nonsensical category mistake. The most common objections to this move are (1) that the “meaninglessness solution” is refuted by the existence of “revenge paradoxes” like the one revolving around the sentence “This sentence is either false or meaningless”, and that (2) the sentences involved are so obviously meaningful that it’s just not possible to take seriously the claim that they’re literally meaningless in any ordinary sense, like “Blorks geblork” or “Colorless green ideas sleep furiously,” whereas the dialetheist and paracomplete approaches have the advantages that they (1*) make room for the perfectly obvious fact that, in any language with normal expressive resources, we can construct perfectly meaningful sentences that attribute untruth to themselves, and (2*) are immune to refutation by means of “revenge paradoxes.” I will argue that (1), (2), (1*) and (2*) are all completely wrong.
#
On (2)/(1), of course, see Part I and Part II of the series of posts I've been doing on that here. (And, of course, stay tuned for Part III on Wednesday!) To get a sense of what I'm talking about on (1)/(2*), see (on the paracomplete side) here. On the dialetheist side, the problem, as I see it, is this*:
The dialetheist wants to argue that Disjunctive Syllogism fails to be universally truth-preserving (given true contradictions), and so it cannot be used to infer triviality after the dialetheist has embraced the contradictions entailed by the various paradoxes.
What does it mean to fail to be universally truth-preserving?
Given logical orthodoxy, the obvious answer is that an inference fails to be universally truth preserving iff there are possibilities on which the premises are all true and the conclusion is false. The dialetheist, obviously, can't conceive of it that way. Given the possibility of true contradictions, we can have possibilities where the premises of an argument are all true and the conclusion is false....but also true. On dialetheist assumptions, the mere fact that we've inferred a false conclusion from true premises is insufficient to establish that the the inference form fails to be universally truth-preserving.
Graham Priest's solution is to conceive of failures-of-truth-preservation as cases where the premises all 'relate to truth' and the conclusion fails to do so. (For technical reasons of his own, he prefers to think of truth as a relation rather than a function--so sentences 'relate' to truth or 'relate' to falsehood or both--but that's not really relevant right now. Talk of sentences relating to truth can translate to talk of them being true with no loss of nuance relevant to our discussion here.) The problem is that, obviously, it's always possible to come up with a Liar that says of itself that it fails to relate to truth. If normal Liars establish the possibility of sentences being simultaneously true and false, these anti-dialetheist revenge Liars should equally well establish the possibility of sentences simultaneously relating to truth and failing to relate to truth. Given this, establishing the possibility of all of the premises of an instance of Disjunctive Syllogism relate to truth while the conclusion fails to relate to truth should be not a single bit more relevant to showing that it fails to be universally truth-preserving than establishing the possibility of all the premises of an instance of Disjunctive Syllogism being true while the conclusion is false.
More generally, it looks like for any Status S such that the dialetheist could try to turn to in order to say "an argument fails to be universally truth preserving iff the premises are all true and the conclusion has Status S", we can always construct a revenge Liar of the form "This sentence has Status S" that will, on dialetheist assumptions, establish that true sentences can also have Status S. Once we've established this, it's not clear why Status S is a better candidate for a definition of failures-of-truth-preservation than mere falsity.
Many people have noticed the possibility of such sentences, shredding up distinctions dialetheists seem to find important--e.g. between sentences that are false-and-also-true and those that are "just" false ("This sentence is just false and not true")--and felt that in some way this was a problem for the dialetheist position on the Liar. Graham Priest, at least, has a standard response, found in multiple books and papers. He'll analyze the Liar sentence in question, show how the contradiction is derived from it, show how triviality fails to be entailed by the contradiction in his favored system of paraconsistent logic, and make some variation of a quip about how his point was never to avoid contradictions, but merely to contain them.
The problem, if I'm right about this, is that dialetheism's revenge problems don't just deliver more contradictions, they tear down the bars dialetheists want to use to contain them.
Three weeks from tomorrow, I'll be delivering a talk at the Philosophy Department at the National University of Singapore (NUS) entitled "Liar Paradox II: Revenge of the Liar Paradox." In lieu of Part III of the ongoing series on the same subject, here's the abstract I sent them for the talk (and then a quick explanation of where I'm going with it):
Dialetheists like Graham Priest and JC Beall conclude from the Liar Paradox that sentences like “This sentence is not true” are fact both true and untrue, and that we must therefore revise our logic to accommodate the existence of true contradictions. Similarly, “paracomplete” theorists like Hartry Field avoid the contradiction posed by the Liar Paradox by rejecting one of the central elements of classical logic, the Law of the Excluded Middle. A more conservative solution starts from the claim that sentences that attempt to attribute truth or untruth to themselves are meaningless, and therefore simply not the kinds of things we can logically symbolize or apply truth talk to without committing a nonsensical category mistake. The most common objections to this move are (1) that the “meaninglessness solution” is refuted by the existence of “revenge paradoxes” like the one revolving around the sentence “This sentence is either false or meaningless”, and that (2) the sentences involved are so obviously meaningful that it’s just not possible to take seriously the claim that they’re literally meaningless in any ordinary sense, like “Blorks geblork” or “Colorless green ideas sleep furiously,” whereas the dialetheist and paracomplete approaches have the advantages that they (1*) make room for the perfectly obvious fact that, in any language with normal expressive resources, we can construct perfectly meaningful sentences that attribute untruth to themselves, and (2*) are immune to refutation by means of “revenge paradoxes.” I will argue that (1), (2), (1*) and (2*) are all completely wrong.
#
On (2)/(1), of course, see Part I and Part II of the series of posts I've been doing on that here. (And, of course, stay tuned for Part III on Wednesday!) To get a sense of what I'm talking about on (1)/(2*), see (on the paracomplete side) here. On the dialetheist side, the problem, as I see it, is this*:
The dialetheist wants to argue that Disjunctive Syllogism fails to be universally truth-preserving (given true contradictions), and so it cannot be used to infer triviality after the dialetheist has embraced the contradictions entailed by the various paradoxes.
What does it mean to fail to be universally truth-preserving?
Given logical orthodoxy, the obvious answer is that an inference fails to be universally truth preserving iff there are possibilities on which the premises are all true and the conclusion is false. The dialetheist, obviously, can't conceive of it that way. Given the possibility of true contradictions, we can have possibilities where the premises of an argument are all true and the conclusion is false....but also true. On dialetheist assumptions, the mere fact that we've inferred a false conclusion from true premises is insufficient to establish that the the inference form fails to be universally truth-preserving.
Graham Priest's solution is to conceive of failures-of-truth-preservation as cases where the premises all 'relate to truth' and the conclusion fails to do so. (For technical reasons of his own, he prefers to think of truth as a relation rather than a function--so sentences 'relate' to truth or 'relate' to falsehood or both--but that's not really relevant right now. Talk of sentences relating to truth can translate to talk of them being true with no loss of nuance relevant to our discussion here.) The problem is that, obviously, it's always possible to come up with a Liar that says of itself that it fails to relate to truth. If normal Liars establish the possibility of sentences being simultaneously true and false, these anti-dialetheist revenge Liars should equally well establish the possibility of sentences simultaneously relating to truth and failing to relate to truth. Given this, establishing the possibility of all of the premises of an instance of Disjunctive Syllogism relate to truth while the conclusion fails to relate to truth should be not a single bit more relevant to showing that it fails to be universally truth-preserving than establishing the possibility of all the premises of an instance of Disjunctive Syllogism being true while the conclusion is false.
More generally, it looks like for any Status S such that the dialetheist could try to turn to in order to say "an argument fails to be universally truth preserving iff the premises are all true and the conclusion has Status S", we can always construct a revenge Liar of the form "This sentence has Status S" that will, on dialetheist assumptions, establish that true sentences can also have Status S. Once we've established this, it's not clear why Status S is a better candidate for a definition of failures-of-truth-preservation than mere falsity.
Many people have noticed the possibility of such sentences, shredding up distinctions dialetheists seem to find important--e.g. between sentences that are false-and-also-true and those that are "just" false ("This sentence is just false and not true")--and felt that in some way this was a problem for the dialetheist position on the Liar. Graham Priest, at least, has a standard response, found in multiple books and papers. He'll analyze the Liar sentence in question, show how the contradiction is derived from it, show how triviality fails to be entailed by the contradiction in his favored system of paraconsistent logic, and make some variation of a quip about how his point was never to avoid contradictions, but merely to contain them.
The problem, if I'm right about this, is that dialetheism's revenge problems don't just deliver more contradictions, they tear down the bars dialetheists want to use to contain them.
Wednesday, March 30, 2011
Some Objections to the Meaninglessness Solution to the Liar Paradox, Part II of IV
Imagine a world where the predicates 'is green' and 'is colored' were considered much more philosophically interesting than it is in the actual world, interesting enough that philosophers and logicians worried about what formal rules related these predicates. One fairly crushingly obvious rule about them would what we can call the G-out rule, allowing us to infer 'X is Colored' from any instance of 'X is Green.'
Now, imagine that there was one other big difference between that world and this world. In our world, the classical example of a syntactically correct but clearly meaningless sentence is C:
C: "Colorless green ideas sleep furiously."
In the imaginary world, this sentence is treated rather different. The humans in this world have made contact with unfathomably intelligent alien entity, capable of speaking English (perhaps with the aid of a universal translator). Every time the entity has been asked a question, and it has deigned to answer, its answer has been proven correct. Sometimes it has taken humans many years, and full-fledged scientific revolutions, to understand *how* what the entity said could have been true, but in the end, there's never been any room for serious doubt. The entity has never once been shown to have (or even been widely suspsect to have) misunderstood a question. At some point, for some strange reason, someone asks the entity about C and it points to the paper where the questioner has written down C and says "this is true."
As often happens when the alien entity says something interesting, ripples of immediate change go through entire fields of study. A few philosophers think that in this case the entity got confused and make a strange sort of category mistake--after all, as in our world, any position, no matter how odd, always has a few philosophical backers--but there's a wide consensus now that C must be true (and therefore meaningful) after all. Almost immediately, some clever theorists notice that this revelation has created a new problem, which they call the "Greenness Paradox." Pretty soon, the dialetheists in this world seize on the Greenness Paradox as an argument for the existence of true contradictions. Here's how it goes:
Start with the formalization of C, given classical logic and orthodox assumptions about how to read the existential quantifier:
1: "There exists an X such that X is green and it is not the case that X is colored and X is an idea and X sleeps furiously."
It clearly follows from 1 that:
2: "There exists an X such that X is green and it is not the case that X is colored."
Apply existential instantiation to 2 to get:
3: "P is green and it is not the case that P is colored."
Apply conjunction elimination to 3 to get:
4: "P is green."
Apply our G-out rule to 4 to get:
5: "P is colored."
Apply conjunction elimination to 3 once again to get:
6: "It is not the case that P is colored."
Apply conjunction addition to 5 & 6 and we get:
7: "P is colored and it is not the case that P is colored."
.....which, the dialetheists of this world argue, is a true contradiction! Viola.
Of course, the dialetheist take on the Greenness Paradox isn't the only game in town. For example, one would imagine that a more conservative solution to the Greenness Paradox would be to deny "the naive theory of greenness" and to restrict G-out in some way. An obvious non-classical but non-dialetheist solution would be to deny that the existential quantifier is ontologically loaded after all. Proponents of this Meinongian solution to the Greenness Paradox would argue that some things can be true of colorless green things ideas without there being colorless green ideas. The Hofweber of this world will argue that, while the existential quantifier is ontologically loaded, and classical logic and the naive theory of greenness are true, and we shouldn't be so arrogant as to reject the superior wisdom of the alien entity by denying C, truth preservation should be understood in a generic rather than universal way. Just as "bears are dangerous" can be true without every bear being dangerous, "valid logical inferences are truth preserving" can be true even if not every valid inference from a true premise preserves truth. The Greenness Paradox, Bizarro-Hofweber would argue, shows us that the universal reading of the notion of truth preservation represents an airy "ideal of validity" that has an obvious appeal, but that the paradox falsifies the ideal.
At this point, it should be pretty easy to come up with a variety of other such philosophically sophisticated solutions to the paradox and to have a pretty good idea of how the argument between proponents of various competing solutions would proceed. Inevitably, some solutions would seem to work better than others, to contain hidden inconsistencies, and so on, and everyone, including the few extreme skeptics who didn't think the unfathomably intelligent alien entity at the source of all this was on the level when it uttered the words "this is true" about C, would be able to do so perfectly easily. "You try to solve it by saying that the colorless, furiously sleeping ideas are red rather than green, but red things are just as colored as green ideas, so you haven't gotten around the original problem." "You forgot a negation sign in Step 5. Once you add it in, you can see that a contradiction is entailed later, when you say...." Etc., etc., etc.
Now, imagine that they were right, and that the entity actually had the same take on C as Chomsky and most of the rest of us citizens of the actual world. He was simply messing with the puny humans out of boredom by pointing to a meaningless sentence and saying the words "this is true." He'd never done this before--he'd always given good and helpful responses to the rest of their inane little queries--but there's a first time for everything. Certainly, from the perspective of the humans, it's understandable that they would never catch on. Having been shown so many amazing things by the entity--remember, scientific revolutions are sparked off by it's statements on a regular basis--it seems utterly plausible to them that a sentence they thought was definitely meaningless actually has a meaning that their puny monkey minds cannot fully grasp. From there, given the function of phrases like 'is green' and 'is colored' in meaningful sentences (G-out is clearly a good rule), the equivalence of 'colorless' with the negation of 'colored', and the ways that we translate into logical lingo sentences of the form "X-ish things do Y", the apparent possibility of reasoning from a contradiction to Y.
Now, assuming that we and the imaginary aliens are right about C, we now have a problem. It is, in fact, the same problem we ended Part I with. We know that nothing "follows" from C. It's meaningless, not the kind of thing we can logically symbolize or apply truth-talk to without committing a nonsensical category mistake. The idea that anything really "follows" from C is deeply confused, like saying that something 'follows' from a string of nonsense syllables, or a bit of burning candle wax. Somehow, though, we seem to be perfectly capable of 'reasoning' about it, as we've been doing for the last few paragraphs.
In the beginning of Part I, I argued that the diquotationalist "nothing above and beyond" principle about truth--"to say that 'P' is true is to say nothing above and beyond P", or to put it differently, "to prefix a quoted sentence with the words 'it is true that' has the semantic effect of simply removing the quotation marks" (the claim, remember, from which the word "disquotationalism" is derived)-is best explained by a general view that the truth predicate/operator is only parasitically meaningful. Of course, the original claim is about sentences that ascribe truth to sentences quoted within them and my claim broadens this to all ascriptions of truth, but I would argue that the former claim, in the absence of the latter, has some awkward consequences. For example, consider the following three sentences*:
(11) "It's true that 'snow is white.'"
(12) Sentence (13) is true.
(13) Snow is white.
I'd submit that there's something a bit strange about arguing that (11) and (12) have distinct meanings. If one asserts meaning-parasiticalness for sentences that ascribe truth to an internally quoted sentence and rejects meaning-parasiticalness for sentences that ascribe truth to other sentences in other ways, one has to explain what substantive difference the *method* of applying the predicate/operator to the claim to which truth is being ascribed makes. Moreover, the obvious explanations of *why* the "nothing above and beyond" principle would be true--most obviously, general philosophical stories like "the word 'true' doesn't pick out some substantive feature of the world, but rather functions as a time-saving way of saying other things, especially useful for cases where we aren't entirely sure *what* we're saying (i.e. blind endorsements)"--would seem to apply equally well, to sentences like (11), sentences like (12), to sentences like "everything John just said is true", to the one-word exclamation "true!" uttered in response to something one's friend has just said, and so on. The syntactic form the truth-ascription takes seems to make no difference. All sentences that do nothing but ascribe truth to a sentence inherit their meanings from the meanings of the sentences to which they ascribe truth. If a sentence S1 tries to ascribe truth to another sentence S2 that has no meaning, S1 will have no meaning either. It has nowhere to get it.
A happy consequence of this view is that, given some other plausible assumptions (e.g. that adding the word "not" to a meaningless sentence does not convert it into a meaningful one), it entails that sentences like "this sentence is not true" are meaningless. This lets us solve the Liar Paradox without having to give up on "the naive theory of truth"--a unitary truth predicate obeying all the standard rules about truth, etc.--or the unrestricted power of classical logic, or much of anything else except many people's initial intuition that the sentences involved are meaningless. At the end of Part I, though, we confronted what sounds like a serious problem:
Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)
(8) The sentence marked as (8) does not express a true proposition.
If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.
Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):
(9) The sentence marked as (9) has some status other than 'true.'
....or the familiar anti-dialetheist revenge paradox (10):
(10) This sentence is just false, rather than being both true and false.
.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?
Now, there's a lot more to be said about all this--particularly about the thorny question of what sort of mistake someone can be accused of when they 'reason' about something meaningless in a 'bad' way and 'contradict' themselves about it, above and beyond the original sin of treating the something in question as if it were meaningful--but I take the example at the beginning of this post to pretty definitively answer the question I ended the last post with in the negative. Someone who (as we would all agree here in the actual world, correctly) characterized C as meaningless would be faced with precisely the same problem that a pardadox-solver who takes the Liar to be meaningless is faced with in our world. Although it's still somewhat unclear *why* the objection doesn't work in either case--we'll say more about that--it's failure in the closely parallel imaginary Greenness Paradox case would seem to show that it fails when it comes to the actual Liar Paradox as well.
Now, imagine that there was one other big difference between that world and this world. In our world, the classical example of a syntactically correct but clearly meaningless sentence is C:
C: "Colorless green ideas sleep furiously."
In the imaginary world, this sentence is treated rather different. The humans in this world have made contact with unfathomably intelligent alien entity, capable of speaking English (perhaps with the aid of a universal translator). Every time the entity has been asked a question, and it has deigned to answer, its answer has been proven correct. Sometimes it has taken humans many years, and full-fledged scientific revolutions, to understand *how* what the entity said could have been true, but in the end, there's never been any room for serious doubt. The entity has never once been shown to have (or even been widely suspsect to have) misunderstood a question. At some point, for some strange reason, someone asks the entity about C and it points to the paper where the questioner has written down C and says "this is true."
As often happens when the alien entity says something interesting, ripples of immediate change go through entire fields of study. A few philosophers think that in this case the entity got confused and make a strange sort of category mistake--after all, as in our world, any position, no matter how odd, always has a few philosophical backers--but there's a wide consensus now that C must be true (and therefore meaningful) after all. Almost immediately, some clever theorists notice that this revelation has created a new problem, which they call the "Greenness Paradox." Pretty soon, the dialetheists in this world seize on the Greenness Paradox as an argument for the existence of true contradictions. Here's how it goes:
Start with the formalization of C, given classical logic and orthodox assumptions about how to read the existential quantifier:
1: "There exists an X such that X is green and it is not the case that X is colored and X is an idea and X sleeps furiously."
It clearly follows from 1 that:
2: "There exists an X such that X is green and it is not the case that X is colored."
Apply existential instantiation to 2 to get:
3: "P is green and it is not the case that P is colored."
Apply conjunction elimination to 3 to get:
4: "P is green."
Apply our G-out rule to 4 to get:
5: "P is colored."
Apply conjunction elimination to 3 once again to get:
6: "It is not the case that P is colored."
Apply conjunction addition to 5 & 6 and we get:
7: "P is colored and it is not the case that P is colored."
.....which, the dialetheists of this world argue, is a true contradiction! Viola.
Of course, the dialetheist take on the Greenness Paradox isn't the only game in town. For example, one would imagine that a more conservative solution to the Greenness Paradox would be to deny "the naive theory of greenness" and to restrict G-out in some way. An obvious non-classical but non-dialetheist solution would be to deny that the existential quantifier is ontologically loaded after all. Proponents of this Meinongian solution to the Greenness Paradox would argue that some things can be true of colorless green things ideas without there being colorless green ideas. The Hofweber of this world will argue that, while the existential quantifier is ontologically loaded, and classical logic and the naive theory of greenness are true, and we shouldn't be so arrogant as to reject the superior wisdom of the alien entity by denying C, truth preservation should be understood in a generic rather than universal way. Just as "bears are dangerous" can be true without every bear being dangerous, "valid logical inferences are truth preserving" can be true even if not every valid inference from a true premise preserves truth. The Greenness Paradox, Bizarro-Hofweber would argue, shows us that the universal reading of the notion of truth preservation represents an airy "ideal of validity" that has an obvious appeal, but that the paradox falsifies the ideal.
At this point, it should be pretty easy to come up with a variety of other such philosophically sophisticated solutions to the paradox and to have a pretty good idea of how the argument between proponents of various competing solutions would proceed. Inevitably, some solutions would seem to work better than others, to contain hidden inconsistencies, and so on, and everyone, including the few extreme skeptics who didn't think the unfathomably intelligent alien entity at the source of all this was on the level when it uttered the words "this is true" about C, would be able to do so perfectly easily. "You try to solve it by saying that the colorless, furiously sleeping ideas are red rather than green, but red things are just as colored as green ideas, so you haven't gotten around the original problem." "You forgot a negation sign in Step 5. Once you add it in, you can see that a contradiction is entailed later, when you say...." Etc., etc., etc.
Now, imagine that they were right, and that the entity actually had the same take on C as Chomsky and most of the rest of us citizens of the actual world. He was simply messing with the puny humans out of boredom by pointing to a meaningless sentence and saying the words "this is true." He'd never done this before--he'd always given good and helpful responses to the rest of their inane little queries--but there's a first time for everything. Certainly, from the perspective of the humans, it's understandable that they would never catch on. Having been shown so many amazing things by the entity--remember, scientific revolutions are sparked off by it's statements on a regular basis--it seems utterly plausible to them that a sentence they thought was definitely meaningless actually has a meaning that their puny monkey minds cannot fully grasp. From there, given the function of phrases like 'is green' and 'is colored' in meaningful sentences (G-out is clearly a good rule), the equivalence of 'colorless' with the negation of 'colored', and the ways that we translate into logical lingo sentences of the form "X-ish things do Y", the apparent possibility of reasoning from a contradiction to Y.
Now, assuming that we and the imaginary aliens are right about C, we now have a problem. It is, in fact, the same problem we ended Part I with. We know that nothing "follows" from C. It's meaningless, not the kind of thing we can logically symbolize or apply truth-talk to without committing a nonsensical category mistake. The idea that anything really "follows" from C is deeply confused, like saying that something 'follows' from a string of nonsense syllables, or a bit of burning candle wax. Somehow, though, we seem to be perfectly capable of 'reasoning' about it, as we've been doing for the last few paragraphs.
In the beginning of Part I, I argued that the diquotationalist "nothing above and beyond" principle about truth--"to say that 'P' is true is to say nothing above and beyond P", or to put it differently, "to prefix a quoted sentence with the words 'it is true that' has the semantic effect of simply removing the quotation marks" (the claim, remember, from which the word "disquotationalism" is derived)-is best explained by a general view that the truth predicate/operator is only parasitically meaningful. Of course, the original claim is about sentences that ascribe truth to sentences quoted within them and my claim broadens this to all ascriptions of truth, but I would argue that the former claim, in the absence of the latter, has some awkward consequences. For example, consider the following three sentences*:
(11) "It's true that 'snow is white.'"
(12) Sentence (13) is true.
(13) Snow is white.
I'd submit that there's something a bit strange about arguing that (11) and (12) have distinct meanings. If one asserts meaning-parasiticalness for sentences that ascribe truth to an internally quoted sentence and rejects meaning-parasiticalness for sentences that ascribe truth to other sentences in other ways, one has to explain what substantive difference the *method* of applying the predicate/operator to the claim to which truth is being ascribed makes. Moreover, the obvious explanations of *why* the "nothing above and beyond" principle would be true--most obviously, general philosophical stories like "the word 'true' doesn't pick out some substantive feature of the world, but rather functions as a time-saving way of saying other things, especially useful for cases where we aren't entirely sure *what* we're saying (i.e. blind endorsements)"--would seem to apply equally well, to sentences like (11), sentences like (12), to sentences like "everything John just said is true", to the one-word exclamation "true!" uttered in response to something one's friend has just said, and so on. The syntactic form the truth-ascription takes seems to make no difference. All sentences that do nothing but ascribe truth to a sentence inherit their meanings from the meanings of the sentences to which they ascribe truth. If a sentence S1 tries to ascribe truth to another sentence S2 that has no meaning, S1 will have no meaning either. It has nowhere to get it.
A happy consequence of this view is that, given some other plausible assumptions (e.g. that adding the word "not" to a meaningless sentence does not convert it into a meaningful one), it entails that sentences like "this sentence is not true" are meaningless. This lets us solve the Liar Paradox without having to give up on "the naive theory of truth"--a unitary truth predicate obeying all the standard rules about truth, etc.--or the unrestricted power of classical logic, or much of anything else except many people's initial intuition that the sentences involved are meaningless. At the end of Part I, though, we confronted what sounds like a serious problem:
Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)
(8) The sentence marked as (8) does not express a true proposition.
If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.
Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):
(9) The sentence marked as (9) has some status other than 'true.'
....or the familiar anti-dialetheist revenge paradox (10):
(10) This sentence is just false, rather than being both true and false.
.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?
Now, there's a lot more to be said about all this--particularly about the thorny question of what sort of mistake someone can be accused of when they 'reason' about something meaningless in a 'bad' way and 'contradict' themselves about it, above and beyond the original sin of treating the something in question as if it were meaningful--but I take the example at the beginning of this post to pretty definitively answer the question I ended the last post with in the negative. Someone who (as we would all agree here in the actual world, correctly) characterized C as meaningless would be faced with precisely the same problem that a pardadox-solver who takes the Liar to be meaningless is faced with in our world. Although it's still somewhat unclear *why* the objection doesn't work in either case--we'll say more about that--it's failure in the closely parallel imaginary Greenness Paradox case would seem to show that it fails when it comes to the actual Liar Paradox as well.
Monday, March 28, 2011
Diet Soap Interview & Apologies
I'm once again putting off Part II. I've written about half of it, but (i) I have tests to write and classes to prep, and (ii) I just finished writing what, on copying and pasting all of my comments into a Word file and running a word count, turned out to be a bit over 2500 words in response to Colin, Brandon and ParisW's thoughts and objections to Part I. If you're desperate for more material on Liars and meaninglessness, I'll direct you to that discussion-in-progress. Meanwhile, I'll mention that this last weekend I was interviewed for a second appearance on the philosophy-themed Diet Soap podcast. Sounds like I might Episode 100. We didn't really skip to this script (plenty of questions not on the list, not all of the list questions asked), and in any case the interview lasted long enough that only a fraction of it should survive the cutting process and make it into the podcast, but to give at least an approximate flavor of the interview, here are the questions that host Doug Lain sent me in advance...
#
You have a doctorate in philosophy and you specialize in philosophical systems of logic. As an American philosopher and a logician it strikes me that you'd fall in with Analytic philosophers. Is this correct?
How do you consider the division or distinction between continental and analytic philosophy?
How important is Frege, Russell and Wittgenstein to you and your philosophical work.
Do you hold to a deflationary account of truth claims?
It seems to me that Analytic philosophy might share something in common with instrumental reason. That is, that the deflationary accounts of truth claims have the impact of limiting our ability to challenge the logic of our historical moment or culture, whereas Continental philosophers like Hegel and Neitzche were primarily interested in thinking about how philosophy was tied to culture and history.
#
You have a doctorate in philosophy and you specialize in philosophical systems of logic. As an American philosopher and a logician it strikes me that you'd fall in with Analytic philosophers. Is this correct?
How do you consider the division or distinction between continental and analytic philosophy?
How important is Frege, Russell and Wittgenstein to you and your philosophical work.
Do you hold to a deflationary account of truth claims?
It seems to me that Analytic philosophy might share something in common with instrumental reason. That is, that the deflationary accounts of truth claims have the impact of limiting our ability to challenge the logic of our historical moment or culture, whereas Continental philosophers like Hegel and Neitzche were primarily interested in thinking about how philosophy was tied to culture and history.
Wednesday, March 23, 2011
A More Succinct Proof
No time for a second post in the series on the meaninglessness solution to the Liar Paradox just now--my apologies, dear reader, but you'll have to wait until Monday for that--but, to reward you for checking back for one, here's a link to a comic that the sort of people who read this blog might enjoy.
(And, on the other end of P.F. Snow's 'Two Cultures', this one's good too.)
(And, on the other end of P.F. Snow's 'Two Cultures', this one's good too.)
Monday, March 21, 2011
Some Objections to the Meaninglessness Solution to the Liar Paradox, Part I of IV
Elsewhere (and in my dissertation), I've argued at length that "Liar sentences", like:
(1) The sentence marked (1) is not true.
or
(2) The sentence marked (2) is either false or meaningless.
...and, for precisely, the same reason, "Truth-Teller" sentences, like:
(3) The sentences marked (3) is true.
....and, of course, conditionalized truth-tellers (better known as "Curry sentences"), like
(4) If this sentence is true, the author of the blog post it appears in is a dialetheist.
.....are quite literally meaningless. "Wait," I can hear you asking, "doesn't that make (2) true?" I've written extensively about that question in the past, but the short answer is "no." A sentence with the grammatical form of a disjunction and a "second disjunct" that, if the same words in the same order were split off into a sentence of their own, would constitute a meaningful-and-true sentence, does not thereby become a meaningful sentence, much less a true one. For example, take (5), adapted from the classical example of a meaningless-but-"well-formed" sentence:
(5) Either colorless green ideas sleep furiously or snow is white.
There is, clearly, no contradiction in asserting both (6):
(6) (5) is meaningless.
....and (7):
(7) Snow is white.
....at the same time. Now, this is a very unpopular solution to the paradoxes--which is part of what makes it interesting enough to spend years developing arguments for!--but one which there are few extensive arguments against. Many theorists interested in the paradoxes--especially those interested in non-classical approaches--just brush it off out of hand as not worth taking seriously. Graham Priest derisively refers to it in In Contradiction as "the heroic solution." Hartry Field says in the introduction to Saving Truth From Paradox that people who endorse meaninglessness solutions must mean the term "meaningless" in "some special technical way", so that what they're saying must amount to a strangely-expressed version of his own paracomplete solution.
(I've always tried to be clear that I mean the word "meaningless" is precisely the ordinary mundane sense. As a result of my version of extreme deflationism about truth, I take the sentences that JC Beall calls "TTruth-inelimable" to be literally meaningless in precisely the same sense as a string of nonsense syllables, or "Colorless green ideas sleep furiously." Click on the link above for a less abbreviated explanation, but, basically, I agree with and take literally Quine's claim that sentences that ascribe truth to other sentences mean nothing above and beyond what the original sentences mean--that's the original metaphor behind the term "disquotationalism," that the upshot of prefixing a quoted sentence with the words 'it is true that' is to "remove the quotation marks"--and I generalize this to the claim that all truth-ascribing sentences necessarily inherit their meaning from the sentences to which they ascribe it. Thus, for example, "'colorless green ideas sleep furiously' is true" ends up being meaningless, because it inherits no meaning from the sentence to which it tries to ascribe truth. For precisely the same reason, "this sentence is true" is meaningless. And, of course, as Carnap was fond of pointing out, the negation of nonsense is nonsense.)
In the same spirit as Field's disguised-paracompleteness objection, when I met a regular reader of this blog, at the Eastern APA before last, we chatted about the Liar Paradox and he said he'd have to wait to "see the technical details" before he knew if it would "work."
I have, of course, a philosophical argument for the claim, and a lot of responses to various actual and potential objections, by the very nature of the solution, there aren't and can't be any "technical details." (There's plenty of nit-picky precision work--particularly when it comes to formulating and responding to "revenge paradoxes"--but that's not what most Liar specialist mean when they talk about "technical details.") The necessary absence of technical details strike right at the heart of the difference between the meaninglessness solution and more standard ones--that nothing technical needs to be revised in any way, shape or form on account of the semantic pardoxes is one of the chief selling points of the solution! We get to keep "the naive theory of truth" rather than any of the elaborate 'technical' theories that have proliferated in the post-Tarski/post-Kripke era. We get to keep classical logic, classical T-in and T-out rules, and, in short, we get to keep everything except for the intuition that many professional philosophers report having about the semantic status of the sentences in question.
So no, no "technical details" of the kind fashionable in theories of the Liar. There are not and could not be special rules (whether thought of as logicially revisionary or placed 'on top of' the logical edifice regulating particular predicates or operators related to truth or meaninglessness) about, say, the precise behavior of M(P) and ~M(P), because, if a sentence is meaningless, to symbolize it with a letter and trying to perform logical operations on it is to commit the same nonsensical category mistake which would be committed if some very confused logician tried to do the same to a cough or a string of nonsense syllables or a bit of burning candle wax.
The most common argument against the meaninglessness sentence is a simple foot-stamping appeal to intuition. Sadly, X-phi has not yet provided us with any empirical evidence about how widely shared the intuitions in question are, so it's hard to know whether those who take it as obvious that such sentences are meaningful are right when they assert that it's generally obvious to everyone pre-philosophically, but whether they're right or wrong, it's clearly possible for competent speakers of a natural language to be mistaken about questions of meaningfulness. For example, the philosophers of the Vienna Circle were competent speakers of German, but they mistakenly took many perfectly meaningful German sentences about metaphysical subjects to be meaningless. In fact, even if we *wanted* to be semantic Cartesians, holding idealized views about the privileged access of competent speakers to the status of sentences as meaningful or meaningless, we couldn't, because there are disputes in which, whoever is right, someone is a competent speaker making this mistake. For example, Graham Priest and I are both competent speakers of English, and we disagree about the meaningfulness of Liar sentences. Whichever one of us is right, the other one is a competent speaker of a natural language who has made a mistake about meaningfulness.
Of course, there's nothing wrong with appeals to intuition--we can hardly do without them entirely--but, given a good argument and a good error theory, initial intuitive assessments are often shown to be false. Arrogantly enough, of course, I take myself to have both.
What about, however, the following more sophisticated variant on this sort of objection? (It was presented to me by a junior faculty member at the University of Miami a year or so ago, and I don't think I took it seriously enough at the time.) Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)
(8) The sentence marked as (8) does not express a true proposition.
If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.
Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):
(9) The sentence marked as (9) has some status other than 'true.'
....or the familiar anti-dialetheist revenge paradox (10):
(10) This sentence is just false, rather than being both true and false.
.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?
To which I say.......
Good question. Tune in on Wednesday!
(1) The sentence marked (1) is not true.
or
(2) The sentence marked (2) is either false or meaningless.
...and, for precisely, the same reason, "Truth-Teller" sentences, like:
(3) The sentences marked (3) is true.
....and, of course, conditionalized truth-tellers (better known as "Curry sentences"), like
(4) If this sentence is true, the author of the blog post it appears in is a dialetheist.
.....are quite literally meaningless. "Wait," I can hear you asking, "doesn't that make (2) true?" I've written extensively about that question in the past, but the short answer is "no." A sentence with the grammatical form of a disjunction and a "second disjunct" that, if the same words in the same order were split off into a sentence of their own, would constitute a meaningful-and-true sentence, does not thereby become a meaningful sentence, much less a true one. For example, take (5), adapted from the classical example of a meaningless-but-"well-formed" sentence:
(5) Either colorless green ideas sleep furiously or snow is white.
There is, clearly, no contradiction in asserting both (6):
(6) (5) is meaningless.
....and (7):
(7) Snow is white.
....at the same time. Now, this is a very unpopular solution to the paradoxes--which is part of what makes it interesting enough to spend years developing arguments for!--but one which there are few extensive arguments against. Many theorists interested in the paradoxes--especially those interested in non-classical approaches--just brush it off out of hand as not worth taking seriously. Graham Priest derisively refers to it in In Contradiction as "the heroic solution." Hartry Field says in the introduction to Saving Truth From Paradox that people who endorse meaninglessness solutions must mean the term "meaningless" in "some special technical way", so that what they're saying must amount to a strangely-expressed version of his own paracomplete solution.
(I've always tried to be clear that I mean the word "meaningless" is precisely the ordinary mundane sense. As a result of my version of extreme deflationism about truth, I take the sentences that JC Beall calls "TTruth-inelimable" to be literally meaningless in precisely the same sense as a string of nonsense syllables, or "Colorless green ideas sleep furiously." Click on the link above for a less abbreviated explanation, but, basically, I agree with and take literally Quine's claim that sentences that ascribe truth to other sentences mean nothing above and beyond what the original sentences mean--that's the original metaphor behind the term "disquotationalism," that the upshot of prefixing a quoted sentence with the words 'it is true that' is to "remove the quotation marks"--and I generalize this to the claim that all truth-ascribing sentences necessarily inherit their meaning from the sentences to which they ascribe it. Thus, for example, "'colorless green ideas sleep furiously' is true" ends up being meaningless, because it inherits no meaning from the sentence to which it tries to ascribe truth. For precisely the same reason, "this sentence is true" is meaningless. And, of course, as Carnap was fond of pointing out, the negation of nonsense is nonsense.)
In the same spirit as Field's disguised-paracompleteness objection, when I met a regular reader of this blog, at the Eastern APA before last, we chatted about the Liar Paradox and he said he'd have to wait to "see the technical details" before he knew if it would "work."
I have, of course, a philosophical argument for the claim, and a lot of responses to various actual and potential objections, by the very nature of the solution, there aren't and can't be any "technical details." (There's plenty of nit-picky precision work--particularly when it comes to formulating and responding to "revenge paradoxes"--but that's not what most Liar specialist mean when they talk about "technical details.") The necessary absence of technical details strike right at the heart of the difference between the meaninglessness solution and more standard ones--that nothing technical needs to be revised in any way, shape or form on account of the semantic pardoxes is one of the chief selling points of the solution! We get to keep "the naive theory of truth" rather than any of the elaborate 'technical' theories that have proliferated in the post-Tarski/post-Kripke era. We get to keep classical logic, classical T-in and T-out rules, and, in short, we get to keep everything except for the intuition that many professional philosophers report having about the semantic status of the sentences in question.
So no, no "technical details" of the kind fashionable in theories of the Liar. There are not and could not be special rules (whether thought of as logicially revisionary or placed 'on top of' the logical edifice regulating particular predicates or operators related to truth or meaninglessness) about, say, the precise behavior of M(P) and ~M(P), because, if a sentence is meaningless, to symbolize it with a letter and trying to perform logical operations on it is to commit the same nonsensical category mistake which would be committed if some very confused logician tried to do the same to a cough or a string of nonsense syllables or a bit of burning candle wax.
The most common argument against the meaninglessness sentence is a simple foot-stamping appeal to intuition. Sadly, X-phi has not yet provided us with any empirical evidence about how widely shared the intuitions in question are, so it's hard to know whether those who take it as obvious that such sentences are meaningful are right when they assert that it's generally obvious to everyone pre-philosophically, but whether they're right or wrong, it's clearly possible for competent speakers of a natural language to be mistaken about questions of meaningfulness. For example, the philosophers of the Vienna Circle were competent speakers of German, but they mistakenly took many perfectly meaningful German sentences about metaphysical subjects to be meaningless. In fact, even if we *wanted* to be semantic Cartesians, holding idealized views about the privileged access of competent speakers to the status of sentences as meaningful or meaningless, we couldn't, because there are disputes in which, whoever is right, someone is a competent speaker making this mistake. For example, Graham Priest and I are both competent speakers of English, and we disagree about the meaningfulness of Liar sentences. Whichever one of us is right, the other one is a competent speaker of a natural language who has made a mistake about meaningfulness.
Of course, there's nothing wrong with appeals to intuition--we can hardly do without them entirely--but, given a good argument and a good error theory, initial intuitive assessments are often shown to be false. Arrogantly enough, of course, I take myself to have both.
What about, however, the following more sophisticated variant on this sort of objection? (It was presented to me by a junior faculty member at the University of Miami a year or so ago, and I don't think I took it seriously enough at the time.) Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)
(8) The sentence marked as (8) does not express a true proposition.
If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.
Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):
(9) The sentence marked as (9) has some status other than 'true.'
....or the familiar anti-dialetheist revenge paradox (10):
(10) This sentence is just false, rather than being both true and false.
.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?
To which I say.......
Good question. Tune in on Wednesday!
Wednesday, March 16, 2011
Michael Sandel
One of the classes I'm teaching this year is, basically, a political philosophy class for Sociology majors. Following the Sociology Department's recommendation, I'm assigning Michael Sandel's book "Justice: What's The Right Thing To Do?"
It has some important secondary advantages--e.g. it's available in Korean translation--and, to be fair, it's reasonably well-written. Sandel uses lots of nice, vivid historical examples. But in some ways.....Jesus.
To steal a line from Jay Rosenberg, Sandel's critique of utilitarianism commits genocide against an entire race of straw men.
It has some important secondary advantages--e.g. it's available in Korean translation--and, to be fair, it's reasonably well-written. Sandel uses lots of nice, vivid historical examples. But in some ways.....Jesus.
To steal a line from Jay Rosenberg, Sandel's critique of utilitarianism commits genocide against an entire race of straw men.
Monday, March 7, 2011
Wednesday, March 2, 2011
Graham Priest Interview, Part II
I talked about Part I on Monday. Part II just went up. My questions were the last four included. I also contributed the clarification to the next-to-last question, obviously.
There's a lot of interesting stuff here, a good bit of which I haven't really had a chance to digest yet. One thing, however, does jump out at me immediately as a problem:
His answer to my clarification on the next-to-last question would seem to fly in the face of any intuitive understanding of the notion of 'truth-preservation.'
For background, click through to the interview. The question provides a lot of detailed background on this. "ArT" means "A relates to Truth", which is a fancy way of saying "A is True." The idea here, as Priest has explained in other contexts, such as his article What is so bad about contradictions?, is that truth is conceived, not as a function, as classical logicians understand it, but as a relation, such that a proposition can be related to truth, to falsity or to both. In What is so bad about contradictions?, he includes a fourth option--A is related to neither truth nor falsity--but that option would seem to made superfluous by his arguments against the possibility of truth-value gaps in In Contradiction, and in any case the existence or non-existence of the fourth option isn't relevant to this discussion. DS is, of course, Disjunctive Syllogism, the classical inference from ~p and (pvq) to q. Since DS, plus the dialetheist's claim that p and ~p can sometimes both be true, quickly generates triviality, Priest and other dialetheists reject it. Priest's argument is, basically, that it isn't universally truth-preserving (and hence, isn't valid) because, given the assumption that some (but not all) contradictions are true, there can be cases in which ~p is true and (pvq) is true but in which q is not.
As he says in his response to me, "The DS can be show to be invalid is the semantics of LP as follows. (The semantics has many presentations. Let us use the version in which evaluations are relations, R, between formulas and the values t and f.
"Consider the inference ~p, pvq / q. Take an interpretation where pRt, pRf, qRf, and it is not the case that qRt. By the truth and falsity conditions for negation and disjunction, (~p)Rt and (pvq)Rt. Hence there is an evaluation where the premises of the inference relate to t and the conclusion does not. Hence the inference is invalid."
"Note that this argument...[is not] undercut if it turns out that there are formulas, A, such that ARt and it is not the case that ARt - even if you could show by some argument (goodness knows what), that this held when A is the p in question. Deductive reasoning is, after all, monotonic. (Valid arguments are never made invalid by the addition of extra premises.)"
So, why do I think all of this flies in the face of any intuitive notion of 'truth-preservation'?
Well, first of all, it seems to me that Professor Priest is being a bit coy when he speaks neutrally about the possibility of "ArT" and "it is not the case that ArT" being shown to be compatible--"if it turns out that there are formulas, A, such that ARt and it is not the case that ARt..." Given Priest's assumptions, *of course* there are such formulas! After all, we can always construct a sentence A such that A="It is not the case that ArT."
Secondly--and to the point--given that such formulas would seem to have to exist on Priest's account, when he's told us that there's an interpretation on which (~p)rT and (pvq)rT but it's not the case that qrT, he hasn't precluded the possibility that qrT--in other words, he hasn't precluded the possibility that, in this case, as in all other cases, true premises, fed into DS, generate a true conclusion!
Think of it this way--Priest would not claim that the mere existence of a case in which (~p)rT and (pvq)rT but in which qrF constituted a counter-example to DS, right? Given that it's as easy to generate a formula that both does and does not relate to truth as it is to generate one that relates to both truth and falsehood, why should truth-preservation be any more violated by the existence of a case in which q doesn't relate to truth than by a case in which it does relate to falsehood?
There's a lot of interesting stuff here, a good bit of which I haven't really had a chance to digest yet. One thing, however, does jump out at me immediately as a problem:
His answer to my clarification on the next-to-last question would seem to fly in the face of any intuitive understanding of the notion of 'truth-preservation.'
For background, click through to the interview. The question provides a lot of detailed background on this. "ArT" means "A relates to Truth", which is a fancy way of saying "A is True." The idea here, as Priest has explained in other contexts, such as his article What is so bad about contradictions?, is that truth is conceived, not as a function, as classical logicians understand it, but as a relation, such that a proposition can be related to truth, to falsity or to both. In What is so bad about contradictions?, he includes a fourth option--A is related to neither truth nor falsity--but that option would seem to made superfluous by his arguments against the possibility of truth-value gaps in In Contradiction, and in any case the existence or non-existence of the fourth option isn't relevant to this discussion. DS is, of course, Disjunctive Syllogism, the classical inference from ~p and (pvq) to q. Since DS, plus the dialetheist's claim that p and ~p can sometimes both be true, quickly generates triviality, Priest and other dialetheists reject it. Priest's argument is, basically, that it isn't universally truth-preserving (and hence, isn't valid) because, given the assumption that some (but not all) contradictions are true, there can be cases in which ~p is true and (pvq) is true but in which q is not.
As he says in his response to me, "The DS can be show to be invalid is the semantics of LP as follows. (The semantics has many presentations. Let us use the version in which evaluations are relations, R, between formulas and the values t and f.
"Consider the inference ~p, pvq / q. Take an interpretation where pRt, pRf, qRf, and it is not the case that qRt. By the truth and falsity conditions for negation and disjunction, (~p)Rt and (pvq)Rt. Hence there is an evaluation where the premises of the inference relate to t and the conclusion does not. Hence the inference is invalid."
"Note that this argument...[is not] undercut if it turns out that there are formulas, A, such that ARt and it is not the case that ARt - even if you could show by some argument (goodness knows what), that this held when A is the p in question. Deductive reasoning is, after all, monotonic. (Valid arguments are never made invalid by the addition of extra premises.)"
So, why do I think all of this flies in the face of any intuitive notion of 'truth-preservation'?
Well, first of all, it seems to me that Professor Priest is being a bit coy when he speaks neutrally about the possibility of "ArT" and "it is not the case that ArT" being shown to be compatible--"if it turns out that there are formulas, A, such that ARt and it is not the case that ARt..." Given Priest's assumptions, *of course* there are such formulas! After all, we can always construct a sentence A such that A="It is not the case that ArT."
Secondly--and to the point--given that such formulas would seem to have to exist on Priest's account, when he's told us that there's an interpretation on which (~p)rT and (pvq)rT but it's not the case that qrT, he hasn't precluded the possibility that qrT--in other words, he hasn't precluded the possibility that, in this case, as in all other cases, true premises, fed into DS, generate a true conclusion!
Think of it this way--Priest would not claim that the mere existence of a case in which (~p)rT and (pvq)rT but in which qrF constituted a counter-example to DS, right? Given that it's as easy to generate a formula that both does and does not relate to truth as it is to generate one that relates to both truth and falsehood, why should truth-preservation be any more violated by the existence of a case in which q doesn't relate to truth than by a case in which it does relate to falsehood?
Monday, February 28, 2011
Graham Priest Interview, Part I
A few weeks back, Edgar Aroutiounian told me on Facebook that he was planning to interview Graham Priest for the Florida Student Philosophy Blog, and he asked me if I had any questions I'd like asked. I gave him some, then blogged my questions here, since I figured they were detailed enough to double as a pretty decent (if incomplete) snapshot of a lot of my objections to Priest's version of the dialetheist project. Anyway, the interview's been split into two parts, and my questions are all in the second part, which hasn't been posted yet, but Part I is available here.
Most of the questions in Part I are relatively light and biographical in nature (nothing wrong with that--some of his answers are quite interesting), but the most philosophically interesting question was the last one, a somewhat confusingly-worded question about "consistent physicalism." Priests answer included the following passage:
"Functionalism, and materialist views of the mind in general, of course have problems. The most obvious is what to say about 'raw feels' (though the problem of intentionality is also a hard one). There are different possibilities about what to say about this. I guess that most of them are consistent, but how adequate they are is much debated. (I’ve never heard anyone suggest that dialetheism might help with the matter.)"
........which, of course, amused me because I do know someone who has publicly suggested just that!
More seriously, though, Ryan's comic raises a good point:
Why on earth hasn't Priest or anyone else floated a dialetheic theory of mind and the (ir)reducibility of raw feels to functional states? The arguments for both halves of the relevant contradiction are independently extremely powerful and compelling (and often felt to be that way even by philosophers who unambiguously put themselves in one or the other camp), the problem has been with us for a long time, and it seems to exhibit much the same sort of intuitive intractability as Priest's favorite paradoxes.
Most of the questions in Part I are relatively light and biographical in nature (nothing wrong with that--some of his answers are quite interesting), but the most philosophically interesting question was the last one, a somewhat confusingly-worded question about "consistent physicalism." Priests answer included the following passage:
"Functionalism, and materialist views of the mind in general, of course have problems. The most obvious is what to say about 'raw feels' (though the problem of intentionality is also a hard one). There are different possibilities about what to say about this. I guess that most of them are consistent, but how adequate they are is much debated. (I’ve never heard anyone suggest that dialetheism might help with the matter.)"
........which, of course, amused me because I do know someone who has publicly suggested just that!
More seriously, though, Ryan's comic raises a good point:
Why on earth hasn't Priest or anyone else floated a dialetheic theory of mind and the (ir)reducibility of raw feels to functional states? The arguments for both halves of the relevant contradiction are independently extremely powerful and compelling (and often felt to be that way even by philosophers who unambiguously put themselves in one or the other camp), the problem has been with us for a long time, and it seems to exhibit much the same sort of intuitive intractability as Priest's favorite paradoxes.
Monday, February 14, 2011
Happy Valentine's Day!
Cheerful V-Day information, via Brian Leiter:
"[A]ccording to a new report approximately 60 percent of all flowers sold in the United States come from Colombia. A third of Ecuador’s yearly production is exported to the U.S. for Valentine’s Day. Flower workers in these countries earn poverty-level wages, work long hours, and suffer significant health problems due to pesticides. The report also finds that over half of women workers in the flower industry in Colombia and Ecuador have been subjected to sexual harassment...."
Now that you're in a nice romantic mood from reading about that, enjoy the rest of your night!
"[A]ccording to a new report approximately 60 percent of all flowers sold in the United States come from Colombia. A third of Ecuador’s yearly production is exported to the U.S. for Valentine’s Day. Flower workers in these countries earn poverty-level wages, work long hours, and suffer significant health problems due to pesticides. The report also finds that over half of women workers in the flower industry in Colombia and Ecuador have been subjected to sexual harassment...."
Now that you're in a nice romantic mood from reading about that, enjoy the rest of your night!
Wednesday, February 9, 2011
Getting Back On Track/Questions for Graham Priest
Well, I won't bore anyone with excuses for the long unplanned blogging hiatus. First year as a full-time prof, adjusting to life in the far East, yadayada. You know the drill. Anyway, I'm going to try like hell to get back to a regular Monday/Wednesday schedule here.
Anyway, last week, a grad student I'm friends with on Facebook told me he was going to be interviewing Graham Priest soon, and asked if I had any questions to suggest. It occurred to me that the questions I came up with pretty much double as explanations of a lot of my main objections to Priest's version of the dialetheist project, so I could do worse than just re-post them here by way of new content. Here goes, copied and pasted from my Facebook message:
#
I'm not sure what kind of interview we're talking about here, but if it's OK that they be a bit long-winded (I'm trying to be very careful about spelling out the ...assumptions to maximize the chances of getting philosophically interesting answers), here are my top 4 questions:
#
Dr. Priest,
(1) When it comes to giving similar paradoxes "uniform solution," you've endorsed five different claims that seem to be in tension with each other:
(a) The Principle Of Uniform solution dictates that all paradoxes of the same "type" be solved in a uniform fashion, &
(b) That the Inclosure Schema delineates a "type," and indeed
(c) That, if someone were to embrace one of the standard consistent solutions to the Liar Paradox but get around Russell's Paradox by an appeal to mathematical nominalism, then the POUS would be violated. Moreover, you've granted that:
(d) The Barber Paradox can be seen to fall under the Inclosure Schema. (It would be surprising if this were not so, given that it was invented to illustrate the structure of Russell's Paradox, which is in turn one of your favorite IS paradoxes!) Despite this, you've argued that:
(e) The POUS does not dictate that we solve Barber in the same way as we solve the main IS paradoxes.
You have justified (e) by saying that it is not enough that a proposed paradox structurally conform to the IS, but also that we have good reason to think that all of its premises are true. (You very reasonably deny that we have any good reason to believe in the existence of a barber who succeeds in shaving everyone in the town in which he lives who does not shave himself.) Why, however, couldn't the mathematical nominalist say precisely the same thing about the Russell Set (since the nominalist denies the existence of sets in general!), use the various standard arguments for nominalism--Benacerraf, etc.--to deny the Existence component of Russell's Paradox in a non-question-begging matter, and thus be perfectly entitled by your own standards to solve the Liar Paradox in a different way, without thus violating the POUS?
(2) On the same subject--Let's assume that the IS does delineate which paradoxes are "of a type" and thus must be given uniform solution. You've argued (quite plausibly) that "evading the Schema" isn't sufficiently fine-grained to satisfy the requirement of uniform solution, while your own dialetheist solution does. On the other hand, on the level of abstraction at which the Schema operates, wouldn't someone who denied the Existence component of Russell's Paradox for nominalist reasons, the Existence component of the Liar Paradox on the basis of considerations derived from their favored views about the philosophy of language and so on be just as "unified" as the dialetheist, who, after wading through various arguments about the particulars of each case, embraced all three Schema components (Existence, Closure and Transcendence) in every case?
(3) You have argued in various places that Disjunctive Syllogism is not universally truth-preserving, because it has counter-examples--cases where P is both true and false, making (P v Q) and ~P true, but in which Q fails to be true. Given the importance of rejecting rules like Disjunctive Syllogism to your overall case for dialetheism (after all, a dialetheist who thought Disjunctive Syllogism *was* universally truth-preserving would be a trivialist!), it might seem to be a a problem for your view that (a) the argument just sketched out relies on a distinction between false claims that are also true and false claims that are just false, but (b) as you are, of course, aware, many critics have pointed out that any phrase that one devises to express this distinction can be recycled in fresh paradoxes (e.g. "this sentence is just false and fails to be true", etc.) Some dialetheists, like JC Beall, lean heavily on the vocabulary of acceptance and rejection to get around these sorts of problems. (For example, in "Spandrels of Truth," he constantly uses the language of rejection to distinguish dialetheias from ordinary falsehoods.) This move is, however, not available to you, given your argument in "Doubt Truth To Be A Liar" that dialetheists should accept that the grounds for rational rejection and rational acceptance might sometimes overlap. One might think this concession deprives you of your last available tool for expressing the distinction needed for your argument against the validity of Disjunctive Syllogism. Do you see this as a problem?
(4) Your argument for the "classical re-capture" in "In Contradiction" relies on the notion that the statistical frequency of true contradictions is very low, and in particular that few statements that arise in ordinary contexts can reasonably be thought to be dialetheias. Elsewhere in the same book, however, you argue for a paraconsistent theory of change, whereby (a) as in standard tense logic, statements truth-values change over time, and more radically that (b) at any point where the subject of a statement is changing from being the way the statement asserts that it is to not being that way or vice versa, the statement is both true and false. (You formally express (b) as Zeno's Principle.) Given that theory of change, and the fact that, as Heraclitus and Engels are quick to remind us, change is a constant, pervasive feature of practically all discernible reality, doesn't it suddenly seem quite plausible that ordinary statements are dialetheic, not just in slightly contrived cases like contingent Liars or Kriple's Nixon case, but in a wide variety of contexts? If I say "the cat is on the mat" while the cat is on the mat, won't that statement be both true and false at the inevitable moment when the cat is in the process of departing from the mat? Won't, indeed, a large, stastically significant number of ordinary statements be both true and false at any given time? (One might think that, given all this, the one domain of reliably contradiction-free statements would be the domain of statements about changeless things. Historically, perhaps, the most popular candidate for changeless truths would be the mathematical one, but of course, you postulate all sorts of contradictions there as well!) In light of all this, how can we be confident that the frequency of true contradictions is very low?
Anyway, last week, a grad student I'm friends with on Facebook told me he was going to be interviewing Graham Priest soon, and asked if I had any questions to suggest. It occurred to me that the questions I came up with pretty much double as explanations of a lot of my main objections to Priest's version of the dialetheist project, so I could do worse than just re-post them here by way of new content. Here goes, copied and pasted from my Facebook message:
#
I'm not sure what kind of interview we're talking about here, but if it's OK that they be a bit long-winded (I'm trying to be very careful about spelling out the ...assumptions to maximize the chances of getting philosophically interesting answers), here are my top 4 questions:
#
Dr. Priest,
(1) When it comes to giving similar paradoxes "uniform solution," you've endorsed five different claims that seem to be in tension with each other:
(a) The Principle Of Uniform solution dictates that all paradoxes of the same "type" be solved in a uniform fashion, &
(b) That the Inclosure Schema delineates a "type," and indeed
(c) That, if someone were to embrace one of the standard consistent solutions to the Liar Paradox but get around Russell's Paradox by an appeal to mathematical nominalism, then the POUS would be violated. Moreover, you've granted that:
(d) The Barber Paradox can be seen to fall under the Inclosure Schema. (It would be surprising if this were not so, given that it was invented to illustrate the structure of Russell's Paradox, which is in turn one of your favorite IS paradoxes!) Despite this, you've argued that:
(e) The POUS does not dictate that we solve Barber in the same way as we solve the main IS paradoxes.
You have justified (e) by saying that it is not enough that a proposed paradox structurally conform to the IS, but also that we have good reason to think that all of its premises are true. (You very reasonably deny that we have any good reason to believe in the existence of a barber who succeeds in shaving everyone in the town in which he lives who does not shave himself.) Why, however, couldn't the mathematical nominalist say precisely the same thing about the Russell Set (since the nominalist denies the existence of sets in general!), use the various standard arguments for nominalism--Benacerraf, etc.--to deny the Existence component of Russell's Paradox in a non-question-begging matter, and thus be perfectly entitled by your own standards to solve the Liar Paradox in a different way, without thus violating the POUS?
(2) On the same subject--Let's assume that the IS does delineate which paradoxes are "of a type" and thus must be given uniform solution. You've argued (quite plausibly) that "evading the Schema" isn't sufficiently fine-grained to satisfy the requirement of uniform solution, while your own dialetheist solution does. On the other hand, on the level of abstraction at which the Schema operates, wouldn't someone who denied the Existence component of Russell's Paradox for nominalist reasons, the Existence component of the Liar Paradox on the basis of considerations derived from their favored views about the philosophy of language and so on be just as "unified" as the dialetheist, who, after wading through various arguments about the particulars of each case, embraced all three Schema components (Existence, Closure and Transcendence) in every case?
(3) You have argued in various places that Disjunctive Syllogism is not universally truth-preserving, because it has counter-examples--cases where P is both true and false, making (P v Q) and ~P true, but in which Q fails to be true. Given the importance of rejecting rules like Disjunctive Syllogism to your overall case for dialetheism (after all, a dialetheist who thought Disjunctive Syllogism *was* universally truth-preserving would be a trivialist!), it might seem to be a a problem for your view that (a) the argument just sketched out relies on a distinction between false claims that are also true and false claims that are just false, but (b) as you are, of course, aware, many critics have pointed out that any phrase that one devises to express this distinction can be recycled in fresh paradoxes (e.g. "this sentence is just false and fails to be true", etc.) Some dialetheists, like JC Beall, lean heavily on the vocabulary of acceptance and rejection to get around these sorts of problems. (For example, in "Spandrels of Truth," he constantly uses the language of rejection to distinguish dialetheias from ordinary falsehoods.) This move is, however, not available to you, given your argument in "Doubt Truth To Be A Liar" that dialetheists should accept that the grounds for rational rejection and rational acceptance might sometimes overlap. One might think this concession deprives you of your last available tool for expressing the distinction needed for your argument against the validity of Disjunctive Syllogism. Do you see this as a problem?
(4) Your argument for the "classical re-capture" in "In Contradiction" relies on the notion that the statistical frequency of true contradictions is very low, and in particular that few statements that arise in ordinary contexts can reasonably be thought to be dialetheias. Elsewhere in the same book, however, you argue for a paraconsistent theory of change, whereby (a) as in standard tense logic, statements truth-values change over time, and more radically that (b) at any point where the subject of a statement is changing from being the way the statement asserts that it is to not being that way or vice versa, the statement is both true and false. (You formally express (b) as Zeno's Principle.) Given that theory of change, and the fact that, as Heraclitus and Engels are quick to remind us, change is a constant, pervasive feature of practically all discernible reality, doesn't it suddenly seem quite plausible that ordinary statements are dialetheic, not just in slightly contrived cases like contingent Liars or Kriple's Nixon case, but in a wide variety of contexts? If I say "the cat is on the mat" while the cat is on the mat, won't that statement be both true and false at the inevitable moment when the cat is in the process of departing from the mat? Won't, indeed, a large, stastically significant number of ordinary statements be both true and false at any given time? (One might think that, given all this, the one domain of reliably contradiction-free statements would be the domain of statements about changeless things. Historically, perhaps, the most popular candidate for changeless truths would be the mathematical one, but of course, you postulate all sorts of contradictions there as well!) In light of all this, how can we be confident that the frequency of true contradictions is very low?
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