[This is a standard introduction to all my commentaries on videos.]
When it comes to my commentaries on particular videos, only the content of - or the words within - the video itself will be discussed. That is, the commentary won't be a case of detailed research on the subject discussed or person interviewed (as one would find in an academic paper or even in an in depth article). The reason for this is that I believe that this will help both the readers of the piece and the viewers of the video – even if such readers and viewers aren't exactly newcomers to the subject discussed or the person being interviewed in the video.
Some philosophers (perhaps Graham Priest himself) have argued that dialetheism isn’t a formal logic. Dialetheism, instead, is “a thesis about truth”. One can conclude from this that it must also be at least partly world-based in nature. (Hence the reference to New York in the video.) However, I don’t believe that Graham Priest’s position — or anyone’s position — is entirely world-based.
Here’s another reference to the world from Priest. He cites quantum mechanics. (Incidentally, Priest rejects the idea that the Schrödinger’s cat thought-experiment displays dialetheism-in-concreto, as it were. That is, that the cat is both alive and dead.) Priest’s own example is one of radioactive decay. He states that at the moment of decay, the atom is both integral and nonintegral. (Though couldn’t the atom be neither integral nor nonintegral when it instantaneously and spontaneously decays? Or, alternatively, at that point it may not be an atom at all.)
Priest is also open about his debt to both Hegel and Heidegger. So there’s much philosophy “behind” his logic. Indeed philosophy of a very particular kind.
Pragmatic positions and themes from the philosophy of science also provide some of Priest’s motivations — along with Buddhism.
Graham Priest’s upshot (i.e., in the video, if nowhere else):
i) Arguments to support the law of noncontradiction have failed (have they?).
ii) Therefore let’s accept the conclusion of the Liar Paradox.
i) The Liar paradox hasn’t been solved.
ii) Therefore let’s embrace it and other contradictories (though not all).
Sure, I’m putting Priest’s position simply in the above. (There are “hidden premises” between i) and ii).) His position is informally and ironically put in that this isn’t a claim that Priest would ever put it in this quasi-deductive way. (As if a single premise and a conclusion can be conclusive at all.) Nonetheless, Priest does make similar bald statements in the video above (if not in the informal way I’ve expressed it). Of course in his papers he’ll go into more detail. Yet hidden among Priest’s mass of detail it can still be said that he holds these basic positions.
So, i) and ii) is also to embrace the Liar Paradox. However, there are indeed other reasons for accepting dialetheism.
Anyway, is Priest advising us to accept the arguments which conclude that we must accept the conclusion of the Liar Paradox? Or is he stating (not arguing) that we should simply accept the conclusion - full stop? Priest seems to take the latter position — at least in this video.
Priest may be correct to say that the Humean “evidence” shows us that the logical defences of the law of noncontradiction haven’t worked . But how does that alone show us that we should accept contradictions?
All this is similar to the well-known pessimistic meta-induction which states:
i) All previous scientific theories have been found wanting.
ii) Therefore that must also be true of contemporary scientific theories.
Let’s take an extreme equivalent:
i) All previous attempts to cure cancer have failed.
ii) So let’s stop attempting to cure cancer.
Is Priest’s dialetheic logic about the world (i.e., an ontological position) or is it about what we can — or even should — say about the world? If it’s the former, then Priest could indeed be both in New York and not in New York! If it’s the latter, then it’s simply a logic that can helpfully capture and formulate such things as the inconsistencies in scientific theories. Alternatively, dialetheic logic can advance the pragmatic option of seeing two contradictory positions as true — at least for the time being!
Priest offers us the following possible-worlds symbolisation of his position. He rejects the following negation. Thus:
i) ¬A is true at w iff A is false at w.
ii) ¬A is false at w iff A is true at w.
i) It is not the case that A is true at a world if and only if A is false at that world.
ii) It is not the case that A is false at a world if and only if A is true at that world.