## Sunday, July 5, 2009

### Graham Priest's Theory Of Change

In In Contradiction, Graham Priest argues that all moments of change are necessarily contradictory. What follows is a quick, rough paraphrase of his argument.

Consider any object O changing from being in state S to being in state not-S. For example, imagine that Mark gets very drunk and accidentally smashes his friend Ben's nice glass ash tray. At the moment when it changes from being intact to being broken (i.e. not-intact), is it:

(a) Intact?
(b) Not-intact?
(c) Neither intact nor not-intact?
(d) Both intact and not-intact?

If the answer is (a), then we're not talking about the moment of change, but some moment before the change. If the answer is (b), then we're not talking about the moment but some moment after the change. If the answer is (c), then by double negation that entails (d) in any case. Hence, at the moment of change, it must be both intact and not-intact. Priest thinks this "contradiction theory of change" puts him in a line of thought about change attributable to historical figures like Heraclitus, Zeno, Hegel and Engels. He also extends the thought to accommodate the common intuition that "time flows" as one moment changes into the next, that process being as contradictory as all moments of change.

Now, I'm inclined to view this as a neat little reductio proof against the very idea that there are or could be such things as "moments of change." Change doesn't occur *at moments,* it occurs among moments. That is to say, to say that O goes from being S to being not-S is just to say that at Time T1 it's S and at Time T2 it's not-S, and that's all. To say that an object changes over time, is simply to say that its properties vary across time. (In fact, since I'm a perdurantist about persistence over time, I'd sharpen this by saying that to say that an object changes over time is simply to say that there are differences in the relevant respect among its temporal parts.) Priest is of course aware of this alternative theory of change, which he attributes to Russell and calls the "cinematic" theory of change. The barb here is that this wouldn't be real "change" at all, but a series of static states succeeding each other, like still frames being projected in rapid succession to create the illusion of motion.

Of course, in arguing for the Russellian theory of change against a non-dialetheist partisan of "moments of change," we could just respond to this barb by deriving the contradiction from the notion of moments of change and that would be that. In the rock-paper-scissors rules of standard metaphysical argumentation, inconsistency-avoidance beats vague lingering intuitions every time. In this case, of course, we can't respond that way without begging the question against Priest, so let's see if we can't do better.

The first interesting thing to point out is that Priest, with his talk of time flowing and moments changing into one another, would seem to be deeply committed to the A-Theory of Time, according to which there's an ontologically privileged present moment, and if its not the only moment that exists (as the extreme form of the A-Theory has it), then at the very least, there are real "MacTaggart properties" of pastness, presentness and futurity out there in the world. The alternative B-Theory of Time has it that there are no such properties, no stance-independent fact of the matter about what "the present moment" is, and that words like "now" are just indexicals like "here." It's tellingly relevant that Priest expresses his theory of change with a paraconsistent tense logic, with pastness and futurity operators, and that tense logics have historically been associated with A-Theorists like Prior. It's not clear that from the perspective of the B-Theory, a tense logic with pastness and futurity operators would make any more sense than, say, a "height logic" with tallness and shortness operators, and for about the same reason. Moreover, if the B-Theory is right, and time is just like space, then the varying time slices of objects had better be "static," at least in the sense that all of time equally exists "all the time."

Priest's first problem, then, is that it's awfully hard to reconcile the A-Theory with Einstein's Special Theory of Relativity. As Putnam and others have argued very nicely, without absolute simultaneity, it's hard to make sense of the idea that there could be a fact of the matter about what "the present moment" is. After all, one of the things that seems to be intuitively true about presentness is that if Event A is part of "the present," and Event B is simultaneous with Event A, then Event B is part of the present as well. The problem is that, if simultaneity is relative to reference frames, then A and B could be simultaneous with each other (but not with Event C) according to one reference frame, and B and C could be simultaneous with each other (but not A) according to a different one, and we can keep iterating that principle about simultaneity and presentness until....well, you see where this is going.

So that's Problem #1. Priest's theory of change seems to fly in the face of our best current science. The obvious snarky response to this is that, as a dialetheist, the logical space for Priest would include embracing a contradiction about the Special Theory of Relativity, but this would miss the point. Just because contradictions are, according to the dialetheist, logically possible, doesn't mean that any particular contradiction is particularly plausible, and it seems safe to say that, as far as making Priest's form of dialetheism more plausible and attracting new followers to it, embracing a contradiction about the STR would not be a particularly good move.

This observation leads direction to Problem #2.

A central component of Priest's project of trying to carve out a plausible dialetheism is something called the "classical re-capture." The idea is this. If dialetheism is correct, then some rules of classical logic, like Disjunctive Syllogism, aren't universally truth-preserving. DS is the rule that, given (P v Q) and ~P, we can conclude Q. The problem is that if dialetheism is right, then there could be a situation where P and ~P are both true, but Q is (just) false. In that scenario, since P is true, by the law of disjunction-addition, (P v Q) must true as well, so we have a counter-example to DS.

While this has the happy result of showing that, if dialetheism is true, the explosion proof is invalid (since it relies on DS), it has the unhappy result of rendering invalid a rule that we use all the time in everyday, garden-variety reasoning and which intuitively seems like an obviously correct inference. ("Ryan is either downstairs playing Guitar Hero or in his room sleeping, since those are the only things he ever does. He's not playing Guitar Hero, so he must be sleeping.") Priest accommodates this by saying that, although given the existence of true contradictions, and hence counter-examples to DS, it's not deductively valid, it's at least a probabilistically reliable inference. To get this off the ground, he argues that the statistical frequency of true contradictions is very low, and so, all else being equal, the epistemic probability of any particular contradiction being true is correspondingly low. Hence, classical rules that rely on the assumption that there are no true contradictions still have probablistic force.

So far, so good. But if all moments of change involve true contradictions, then it starts to look like the rate of true contradictions isn't nearly as low as one would think if one thought the only true contradictions involved abstract issues like Liar sentences and naive set theory. Every time we say of an object O that it's in state S when it is in fact at that moment in the process of changing into being in state not-S, we've said something that's both true and false. So it looks to me like, in claiming that change involves contradiction, Priest is playing with fire and putting his "classical re-capture" is serious danger of burning down.

That's Problem #2. Problem #3 is the simplest one. Let's say Priest is right and mere variation of properties that objects have among moments in time wouldn't be real change but merely a succession of static states. Moreover, let's say that on the basis of his intuition that real change exists, there are indeed these strange contradictory moments of change. Now, to adapt a popular argument against mathematical Platonism to this argument, imagine that suddenly, these moments of change stopped happening. (Say, God willed that real change would no longer exist, but that everything else would stay the same.) Ash trays would still go from being intact to being broken, your hair in the shower would still go from being dry to being wet, etc., etc., etc., but there would no longer be contradictory transitional moments. If that happened, how would we ever know? And what difference would it make to anything else? Would people who (in our world) share Priest's intuitions about change not have them? If not, why on earth should we let those intuitions settle this, given that it's much simpler and more cautious to postulate that the observed states of any given object O being (just) S or (just) not-S are the only states there are?

Rafal Urbaniak said...

Interesting. I'm wondering how damaging objection #2 really is.

(This will be a bit handwavy) Suppose I make a distinction between contexts which essentially involve change and contexts which don't do that.

Presumably, in the moment when the ash tray changes from being intact to being broken, even if we buy into the claim that it's both intact and not-intact, I can't argue:

(i) The ash tray is intact.
(ii) Either the ash tray is intact, or I'm a pink elephant.
(iii) The ash tray is not-intact.
(iv) Therefore, I'm a pink elephant.

Now, take the example you used:

"Ryan is either downstairs playing Guitar Hero or in his room sleeping, since those are the only things he ever does. He's not playing Guitar Hero, so he must be sleeping."

If the possibility of change should be taken into account, things get tricky - if Ryan is actually stopping to play Guitar Hero, he is simultaneously playing and not playing it, and DS becomes suspicious.

But this is not what is usually meant, when we use those arguments: we sort of interpret things statically.

This suggests the following strategy: for arguments that involve change, the number of contradictions is pretty high, and thus DS is not reliable when we reason about changing objects if we admit they both are and aren't in certain states. For contexts where we interpret things "more statically", the number of contradictions is pretty low, and hence, when we reason in such contexts we have some reasons to accept DS.

Of course, details of this distinction should be worked out, but I'm wondering if a Priestian cannot take this way out. How do you think?

Deleet said...

I think you did a pretty good job with that argument. I have the same "doubts" (?) about objection #2 as the above poster has.

-

Also I'm wondering what sense it makes to say that some percentage of an infinite set is e.g. even.

Consider the set of integers:
{1,2,3,4,5,6,7,8,9,...}

The percentage of even and odd numbers "should" be 0.5, But how do we calculate this? We cannot do it the normal way: n/m where n is the item in question and m is the total amount. E.g. red bikes when I have 1 red bike and 10 bikes total: n/m=1/10. This doesn't work with two infinites: infinite/infinite=infinite (?).

But I suppose there is a solution for this. I haven't learned math about infinites.

Ben said...

Rafal and Deleet,

Excellent point about #2, worth following up in its own post. Stay tuned!