Criticisms of Dialetheism
On example that's been cited as, supposedly, a crushing blow against dialethism is:
"A Critique of Dialetheism" (with Greg Littmann), The Law of Non-Contradiction: New Philosophical Essays, edited by Graham Priest, J.C. Beall and Bradley Armour-Garb, Oxford University Press 2005.
A reply to this on the Facebook group 'Analytic Philosophy':
" It's a good article, Jason. I don't agree, at all, that there's any similarity between Hegel's unfortunate take on the dialectic and dialetheism - apart from them both being seen as radical.
Littmann and Simmons make two points about dialethism. The second, that you can construct sentences that are not classifiable as either true, false, or true and false is a good point - not a point against dialethiesm, though, it's a point showing that more work needs to be done. This is certainly true. Dialetheism has a long way to go before it's mainstream.
Their first point is more of a misunderstanding. They're concerned, rightly, about assertion and denial - seeing them as necessary parts of dialethiesm. In fact they think that that's the problem with dialetheism, that it requires these.
It does not. Littmann and Simmons seem surprised that logic works in the same way in dialetheism, but, of course it does, it's the same logic, just without the unnecessary extra axiom.
The points Priest makes about asserting or denying statements are not part of logic, not even part of dialetheism - they're part of the explanation, or interpretation of dialetheism. Attacking them is no more attacking the logic than attacking Schroedinger's cat is attacking quantum mechanics. The story, or parable, or explanation, is not the same as the thing itself.
All dialethism says is that, as I said earlier. If you have two sets, one T and one F, that contain statements based on their truth value, then you have to consider the intersection. That's it, really. Arguing that the only way to deal with the intersection is to exclude it with an axiom has the benefit of appealing to the historical usefulness of just that approach - but it is no argument for it being the only approach.
Littmann and Simmons second argument is based on them establishing that there are statements that are in T and in T ⋂ F, but not in F itself. What they're actually saying is that there are two reasons for something being in the set T - one is that it is a statement that follows from the axioms and rules of logic, the other that it is ~F.
That's an important, and useful, insight, that should help develop dialetheism further. Indeed it should help logic generally. It's interesting that you can have a statement S s.t.:
- S ∈ T
- S ∈ T ⋂ F
- S ∉ F
This is because, as I say either:
- If a ∈ T, b ∈ T, and @ is valid then a @ b => x => ( x ∈ Tp)
- If ~x ∈ F => ( x ∈ Tn)
The mistake is the assumption that T = Tp = Tn - clearly it usually does, but Littman & Simmons have, essentially, shown that we could restate the first set as:
- S ∈ Tp
- S ∈ Tn ⋂ F
- S ∉ F