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:

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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:

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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?

David Gawthorne said...

These are great questions and I would be interested to see the answers.

Emil said...