Sunday, 6 June 2021

Dialetheism and Transition States

I've been thinking recently about an argument given by Graham Priest for the view that, when you're on your way out of a room, there's a point in time at which you're both in the room and not in the room. 

For those who believe in true contradictions (dialethias) already because of Liar-like phenomena, whether or not this kind of example also exist may not seem like such an urgent issue. But if, like me, you are drawn to a gappy rather than a glutty response to Liar-like paradoxes, this sort of argument becomes more important, since it may take you from not believing in true contradictions to believing in them.

Priest's argument appears on p. 415 of his 'What is So Bad About Contradictions?' and is discussed in Section 3.4. of the SEP article on dialetheism. From the latter:

Transition states: when I exit the room, I am inside the room at one time, and outside of it at another. Given the continuity of motion, there must be a precise instant in time, call it t, at which I leave the room. Am I inside the room or outside at time t? Four answers are available: (a) I am inside; (b) I am outside; (c) I am both; and (d) I am neither. There is a strong intuition that (a) and (b) are ruled out by symmetry considerations: choosing either would be completely arbitrary. (This intuition is not at all unique to dialetheists: see the article on boundaries in general.) As for (d): if I am neither inside not outside the room, then I am not inside and not-not inside; therefore, I am either inside and not inside (option (c)), or not inside and not-not inside (which follows from option (d)); in both cases, a dialetheic situation. Or so it has been argued. For a recent description of inconsistent boundaries using formal mereology, see Weber and Cotnoir 2015.

I will now outline what I think we should say in response. 

The appeal to 'symmetry considerations' is where the trouble is in this argument. Let us assume for a moment that there are no true contradictions and see what we can say that is consistent with that commonsense view. On pain of contradiction, the notion of being 'inside' a room is not both true of me and false of me in this case. Now, we can grant that any notion of being 'inside' which is true of me in this case is in a sense biased in favour of insideness, and any notion of being 'inside' which is false of me in this case is biased against insideness. But probably, our normal notion of 'inside' as applied to rooms is just not determinate here; our linguistic behaviour doesn't make it the case that we are using the inside-biased notion rather than the outside-biased notion, nor does it make the opposite the case. But if we need to, we can just pick one of these notions, and everything will be OK as long as this is understood by speakers and hearers.

To me, this seems highly plausible. And it lets us maintain that there are no true contradictions. Let's grant Priest that it's bad philosophy to just reject outright the idea that there might be true contradictions. But if we haven't already adopted dialetheism, which is a pretty radical view, then other things equal, we should look for less drastic ways to make sense of examples like this. And that's what I've sketched above.

Thursday, 15 April 2021

Forthcoming in Philosophical Studies: A Simple Theory of Rigidity


After wrestling inconclusively with this topic a couple of years ago on this blog, I came to a much clearer view about rigidity, which I set forth in this paper:

A Simple Theory of Rigidity

The notion of rigidity looms large in philosophy of language, but is beset by difficulties. This paper proposes a simple theory of rigidity, according to which an expression has a world-relative semantic property rigidly when it has that property at, or with respect to, all worlds. Just as names, and certain descriptions like The square root of 4, rigidly designate their referents, so too are necessary truths rigidly true, and so too does cat rigidly have only animals in its extension. After spelling out the theory, I argue that it enables us to avoid the headaches that attend the misbegotten desire to have a simple rigid/non-rigid distinction that applies to expressions, giving us a simple solution to the problem of generalizing the notion of rigidity beyond singular terms.