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!
Monday, March 21, 2011
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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