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.
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But then again, I appear to be a Platonist about the carriers of truth. I think that there are numerous problems with sentence theories (as the one you seem to favor). See Swartz and Bradley (1979) chapter 2 for a defense of my point of view that I particularly like.
I think that 'math' has some solution to the worry that I stated earlier, but I don't know it. I need to read up on transfinite math.
In my view there is never any change of truth values. What changes with time is which proposition is expressed by an utterance such as "Priest is in the room". Propositions are omnitemporally true/false; they feature a time operator such as "on the 19th October 2009, at 20:00:00 o'clock". Was Priest in the room at that precise moment? Then the proposition is true. Was he not? Then it is false.
If you think sentences are omnitemporally true or false, then you've rejected tense logic, the A-Theory of time, etc., and you've ruled out Priest's views about change just on those grounds alone. As you should, of course. (I'm a B-Theorist too, for reasons that I mentioned in the original post.)
As far as the separate question, though, of whether Priest's *also* going to get into trouble (given Platonism about unexpressed propositions or whatever) because of the worry you expressed earlier, as far as I know, you can't perform statistical operations on transfinite collections. (I.e. to adapt an example used by William Lane Craig, if you imagine an infinite library where every other book is black and every other book is red, so it goes red book, black book, red book, black book, throughout its infinite extent, even if you checked out every red book from the library, such that between every two black books, there was an empty spot, it wouldn't be the case that there were only half as many books in the library as there were before. Rather, the set of red books has the same cardinality as the set of all red and black books, so technically speaking, there are exactly as many books on the shelves as there were before, not 50% less.) Now, that said, I think that Priest's "classical re-capture" could probably be made compatible with Platonism about propositions by taking the talk of the statistical frequency of true contradictions to not be a matter of the proportion of contradictions that are true, but rather a matter of the proportion of randomly selected contradictions that turn out to be true over the course of a hypothetical limiting frequency, just like, when we say (if we're frequentists about probability) that the chances of a flipped coin coming up heads are fifty/fifty, we aren't claiming anything about the actual proportion of total coin flips by everyone ever that come up heads (which, surely, varies all the time as new coins are flipped and at any given time, may very well not be precisely fifty percent). Rather, we're claiming that, over the course of a hypothetical limiting frequency, fifty percent of them will come up heads.
Now, as far as the last bit goes...
"Propositions are omnitemporally true/false; they feature a time operator such as 'on the 19th October 2009, at 20:00:00 o'clock'."
....that's the tenseless date theory of tensed sentences, and it faces pretty severe difficulties. (Have you ever read Quentin Smith's "Language and Time"? He talks about this there.) If "Priest is now in the room," uttered on October 19th at 8 PM means "Priest (is) in the room on October 19th at 8 PM" (where the (is) is tenseless), "Priest was in the room" uttered on October 19th means "Priest (is) in the room before October 19th at 8 PM" and so on, then you're going to face the following problem. Imagine that as Priest comes into the room, someone asks him what time it is, and he says "it's eight o'clock." Now, for the sake of consistency, Priest's statement has to be translated as "it (is) 8 PM on October 19th at 8 PM", which (unlike "it's eight o'clock") is a tautology.
Of course, even if this objection goes through (and I think it does), that doesn't mean we have to reject the tenseless theory of time and omnitemporal truth-values. It does mean, however, that we have to come up with a better system for tenselessl paraphrasing tensed sentences. I think the token-reflexive view--where "Priest is now in the room" means something like "Priest's being in the room (is) simultaneous with this utterance"--is a much better bet, one that very nicely gets around these sorts of counter-examples. Of course, Smith also has some alleged counter-examples to the token-reflexive view in "Language and Time," but I'm much less bothered by them, because (bringing us full circle) they seem to assume Platonism about unexpressed propositions.
I did not expect such a long post. I'll try to keep my answer short because I don't like this interface for (serious) discussion. I'd rather read up on the things you've mentioned and send you an email or something. :) But then I still have to finish the essay that I am working on, and then there is the one about Begging the Question.
Technically I don't think sentences are omnitemporally true/false. I think that sentences are not true/false at all. I think that it is only propositions that are true/false. When we talk as if a sentence is true/false, I think that that is most plausibly interpreted as saying that the proposition expressed by the sentence is true/false. Likewise with beliefs. When we say that a person has a true/false belief (e.g. in Justified True Belief, JTB), what is really true/false is the proposition believed, not the mental state of believing it. Presuming some mental state theory of beliefs and not some, say, behaviorist theory like Quine's dispositional theory that he mentioned in his co-authored book "The Web of Belief".
I think propositions are omnitemporally true/false.
I suppose these views don't work too well with Priest's views, but I don't know his views in detail. I plan on reading In Contradiction 'soon', but I've got a couple of other books before that to read. :)
I had heard about the frequency analysis/theory before. It seems that I need to read up on that too. (Damn, so many things and so little time!)
No, I have not read Smith's “Language and Time” but I added it to my to read list. I will get around to reading it eventually.
I see the problem with the tautologous statement there. I'll have to think more about that one.
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