What is at stake on this point is a crucial feature of any foundationalist position – that is, a position that relies on basic first principles, such as the existence of truth, and not merely on pragmatic effectiveness. Any such position relies in its logic on the difference between demonstrative and dialectical argument – that is, between arguments from first principles and arguments to first principles. (I take the distinction from a short and helpful discussion on pp. 88-9 of Alasdair MacIntyre’s Three Rival Versions of Moral Inquiry.) This distinction is what that the young Socrates at first fails to grasp in Plato’s Parmenides: because Zeno’s arguments show the flaws in others’ positions, Socrates sees them only as sophistry rather than as what they are, namely dialectical arguments knocking down others’ premises in order to establish the truth of Parmenides’s view. The young Socrates knows only demonstrative argument, and not dialectical argument. In an anti-foundationalist position like Ni’s (or Richard Rorty’s), where there are no first principles, there is the opposite: only dialectical argument, and no demonstrative.

The point: One cannot deduce conclusions from first principles (demonstrative argument) with someone who does not share those principles. Rather, one must argue from the assumptions and principles of one’s interlocutor, in order to show that the interlocutor’s position is flawed and one’s own is preferable (dialectical argument). Only by doing so can one arrive at anything like a foundationalist position in the first place. No foundationalist that I am aware of has ever tried to argue otherwise. Even Descartes doesn’t begin his argument with cogito ergo sum; rather, he begins both the Meditations and the Discourse with everyday commonsense knowledge and why it isn’t good enough. The first principles – the existence of truth or self – are first only logically; they do not come first chronologically, in argument or in human development. And the question on which a foundationalist position stands or falls is whether the foundationalist can show his interlocutor’s position to be flawed enough that it merits abandoning in favour of one more like his own. In the case at hand, I believe that I have done this – argued why a position based entirely on pragmatic effectiveness will fail on the grounds of pragmatic effectiveness.

I tried to do the same in my arguments against postmodernism. It does little good to argue that postmodernism is false or contradicts itself, and therefore fails on my terms. It is far more important to argue that postmodernism’s performative effects are neutral or worse, so that it fails on its own terms.

Dialetheism is easy to mock. Indeed, the first I’d heard of it, and the only time I’d heard of it before skholiast’s post, was in two of Ryan Lake’s Chaospet comics that made fun of it. Lake’s comics note apparent problems with dialetheism: if nothing is bad about contradictions, as Priest suggests, then doesn’t that basically allow one to say anything at all? Doesn’t one then just immediately solve every hard problem without having to think about it, by saying (as Lake’s character Nester does) that “the mind both is and is not the brain”?

Priest’s article tries at length to refute the view he calls “explosion.” Explosion is a view usually taken for granted in contemporary formal logic, although (so he claims) not held by Aristotle, that any statement at all follows logically from a contradiction. (While the article itself is behind a pay wall, Priest makes many of the same points in a Stanford Encyclopedia article on the topic.) We are not bound to accept all contradictions, he argues, if we merely accept some; and most of the unfortunate logical consequences we associate with contradiction derive from accepting all contradiction.

I haven’t had the time yet to dive into the details of Priest’s argument and examine whether he’s adequately convincing. Instead, let me assume for present purposes that in the details of his argument he is basically right. What then would his being right imply? Far less, I suspect, than he claims: certainly not that nothing about contradictions is bad.

For as it turns out, Priest himself accepts that there’s usually something wrong with contradictions. In the fourth section of his article he tells us that contradictions are “a priori improbable”; most contradictions in fact turn out to be false. So “inconsistency is a rational black mark,” and “[i]f we have views that are inconsistent we are probably incorrect.” (424) In giving examples of potentially true contradictions, Priest looks primarily at paradoxes, especially the liar paradox (statements such as “This statement is false”) but also the kind of paradoxes associated with Zeno of Elea. Priest claims that the easiest way to understand the liar paradox is to say that the statement “This statement is false” is both true and false. The only reason to reject such a claim is that it is a contradiction; a dialetheist can resolve the paradox by affirming that contradiction. But Priest is quite ready to say that “we do not deal with these kinds of situations very often.”

This isn’t to say that Priest’s dialetheism is insignificant. It’s led me to reinterpret key Madhyamaka Buddhist figures, from Nāgārjuna up to Śāntideva himself. I’ve noted, in my dissertation and elsewhere, that these thinkers see a normative force in non-contradiction: to identify a claim as a contradiction, other things being equal, is to say that something’s wrong with it. But other things are not always equal, and I think it’s fair to say that Nāgārjuna and Śāntideva do not accept a law of non-contradiction in anything like the sense Aristotle intended. I’m not convinced by their views of logic, but I think Priest has pointed me to something important in the way they work. And if it were to be the case that the Madhyamakas are indeed correct, then Priest’s view might turn out to be more significant than he himself is ready to claim.