What that properly means is that to deny it is a contradiction, because it must be assumed to deny it.
In other words, you can't say "The truth is, there is no truth." Which is what Graham Priest is doing.
1 is an interesting observation, but has no bearing on the facts of the case: he is a fraud.
3: You should be ashamed to make a statement like this in an intellectual conversation. If you feel the need to bolster your argument with an unsubstantiated character attack like this, you must not feel that your argument is sound.
No offense, but I'd flag your comment for #3, except it's not worth wasting moderators' time on.
The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true.
No, they are nonsense. Nothing that claims that something can be true and false can be logically rigorous. To be logically rigorous means to be logical---and to be logical means to obey the law of non-contradiction.
Anyway, it's at least gross negligence for the author to write an article like this and then not explicitly declare that these ideas are nonsensical.
I think I have made my point, I don't want to continue the discussion, though I will be interested to read any further follow-ups.
the point is not to argue against how people define logic, or anything as arbitrary or seemingly self-defeating as that.
the point is to provide a functional logic in the face of the liar's paradox and the like. regardless of the motivations of individual philosophers, the work itself posits as motivations actual technical problems. the technical problems generally arise from self-reference, but (as you can see with varieties of incompleteness proofs as well) you don't need outright self-reference to get the truth of a statement resting on its negation.
yell all you want about rigor, the onus is on you to use conventional logic to resolve these tensions. again, i personally think that proponents of many-valued logic are misguided in their large scale view of truth functional representation (and i probably think the same of you!). however, i respect that they seek to defend it by solving problems rather than saying "hurr, 'this is a lie' just doesn't mean anything at all. and oh yeah, language is compositional, truth is correspondence, and i'll hear nothing saying otherwise!"
2) The LNC is an axiom it doesnt "hold", its either built into what you mean by identity or it isnt. Either way there is no non-circular "hold"ing.
3) Im sure the notions of truth, falsity and consistency are far too technical here for the lay person to get a serious grasp of but i'd be careful of rationalizing your own ignorance by projecting stupidity onto others.