So Graham Priest believes that change is impossible without contradiction. I bogged about that a while back, glossing Priest's argument and presenting three objections to it:
(1) Priest's theory, formulated as it is in terms of paraconsistent tense logic, assumes the A-Theory of time, which conflicts with our best current science, given that Einstein's Special Theory of Relativity seems to entail the B-Theory.
(2) The contradiction theory of change seems to undermine Priest's "classical re-capture," since too many statements would be dialetheias for comfort, given that the re-capture relies on the claim that this is only true of a small minority of statements, &
(3) His argument centrally relies on the intuition that change exists and that Russellian "cinematic change" wouldn't count as real change, but we have no reason from any plausible theory of intuitions to suppose that if unobservable, instantaneous contradictory states of change existed, our intuitions would track them.
All of these points are explained in the original post. One important point to note here is that, unlike other critics of Priest's views about change (see, for example, the Tahko article discussed in this post, or Fracis Jeffry Pelletier's comments a while back in the Bulletin of Symbolic Logic), I take seriously Priest's claim that he's *not* talking about vagueness, either in language or in the world, or problems relating to the extensions of vague predicates.
The discussion in the comment thread focused on (2). Rafal Urbaniak suggested that dialetheism about change might be rendered compatible with the classical re-capture by some mechanism like:
(a) Differentiating between contexts involving change and those that do not involve it, and regarding only the latter as the target for the classical re-capture, and/or
(b) Interpreting ordinary statements that might be dialetheic in the light of Priest's theory of change in a somewhat static way, so that we can reason about them as part of the 'contexts not involving change' category.
Deleet seconded these concerns, while raising a quite separate concern about the whole notion of the classical re-capture, which is that it seems hard to make sense of talking about percentage of infinite categories. What does it mean to say that the percentage of statements which are both true and false is very low?
At the time, I planned to do a follow-up post on all that, and for a variety of reasons (moving back and forth from California to Florida, road-tripping, dissertating, yadayadayada), it never happened, although while I was dithering, the post was more widely noticed and various people said nice things about it.
So...much later, and with more than a little embarrassment, here's a reply to all of that, working backwards from Deleet's point to Rafal's. Here's what I have to say about former in a footnote in my dissertation:
"One might be concerned that, if we are wondering about the proportion of claims that are true and false, or of contradictions that are true, we will face problems about performing statistical calculations on categories with transfinite numbers of members. It’s not clear to me, however, that this is what’s going on. First of all, if one does not accept Platonism about propositions—the claim that claims that no one has ever made and will never made still, in some sense, exist—then the problem goes away, and even if it doesn’t, there may be a fix in terms of looking a the hypothetical limiting frequency of arbitrarily selected members of that transfinite set of claims, or of contradictory claims, or whatever one takes the relevant category to be."
As far as Rafal's points go, I'd say about (a) that the problem is that change is a constant feature of the properties of the sorts of objects that ordinary reasoning is usually about, and so it seems to me that much of the point of the classical re-capture goes is lost if we restrict ourselves to contexts not involving change. What would those be? Perhaps a certain sort of mathematical Platonist would claim that the properties of mathematical objects are eternal and unchanging, but of course Priest postulates all sorts of contradictions involving *those*, from Russell's Paradox in naïve set theory to his incompleteness-theorem-based argument for the inconsistency of arithmetic. Moreover, it is the ordinary, garden-variety reasoning cases to which the classical re-capture is supposed to apply.
For (a) to really work, then, we need (b) to work. It seems to me that there's a deep tension between Zeno's Principle's formulation in terms of *tense* logic--a formulation, moreover, that is not a happenstance but seems to be conceptually basic to the idea--and the claim that statements have their truth-value statically. The whole point of tense logic is that statements that are currently false were true, that statements that are true will be false, etc. In other words, the *very same statement* changes truth value over time. As such, I see no plausible way to avoid the conclusion (on Priest's premises) that an ordinary statement like "Graham is in the room" uttered as he is changing from being in the room to not being in the room, is dialetheic, and the problem persists.
Of course, I'm not confident that this gets us to the point where there are enough true contradictions to definitely invalidate the classical re-capture, but it certainly seems to be too many for comfort for anyone who's hopes for rendering dialetheism compatible with the intuitive role of rules like Disjunctive Syllogism in what we normally regard as good reasoning about garden-variety cases are bound up with the classical re-capture.