Will Gamester (University of Leeds), "Nothing is True"
Journal of Philosophy, 2023
Have you heard about squircles? A squircle is a shape that is both a square and a circle. How many squircles are there? The obvious (and correct!) answer: none! If a shape was a squircle it would have just one side and also four sides, and that’s impossible.
Have you heard about R-barbers? An R-barber is someone who cuts the hair of all and only the people in their town who do not cut their own hair. How many R-barbers are there? The answer is, again, none. To see this, imagine trying to become an R-barber. The crucial question is: would you cut your own hair? If not, then there is someone in your town who does not cut their own hair (namely, you), whose hair you do not cut. But if you do, then there is someone in your town who cuts their own hair (namely, you), whose hair you do cut. Either way, you’re not an R-barber: R-barbers cut the hair of all and only the people in town who don’t cut their own hair. The only way to be an R-barber is both cut and not cut your own hair, and that’s impossible.
When it comes to squircles and R-barbers, we are all nihilists, in the sense that we think that there is (and, indeed, can be) no such thing.
What is interesting about these cases is a certain characteristic pattern they share. We start with an account of a certain concept: “squircle” or “R-barber”. We then try applying that concept to a particular case, and we see that doing so leads to contradiction. And that leads us to the nihilistic conclusion that there is no such thing. I’m interested in the extent to which we are able to carry this over to more philosophically interesting cases.
One such case concerns truth. A sentence, like ‘grass is green’, is true if and only if what it says is so. ‘Grass is green’ says that grass is green, and grass is in fact green, so that sentence is true. ‘Snow is black’ says that snow is black, and snow is not black, so that sentence is not true. Easy peasy lemon squeezy.
But now consider: THE SENTENCE WRITTEN IN CAPITALS IS NOT TRUE. That sentence says, of itself, that it is not true. So, that sentence is true if and only if it is not true – a contradiction. This is an example of the famous Liar Paradox. Difficult difficult lemon difficult.
Strikingly, the pattern here is very similar pattern to what we had with squircles and R-barbers. We started with an account of truth. We then saw that applying that concept to a particular case led to contradiction. By parity, then, you might think that we should draw the same nihilistic conclusion: just as there is no such thing as a squircle or an R-barber, there is no such thing as a truth.
In fact, almost no one writing on the Liar Paradox goes this way. Instead, they offer revisionary accounts of meaning, truth, or logic in order to try and avoid or live with the contradictory conclusion that the sentence in capitals is both true and not true. This turns out to be incredibly difficult. Many proposed solutions to the Liar are impenetrably complex and independently unjustified, and more often than not just give rise to further paradoxes.
The starting point for my paper, “Nothing is true,” is the observation that these desperate contortions stand in need of justification. None of us hesitates to draw the nihilistic conclusion when it comes to squircles or R-barbers. Why can’t we draw the same conclusion when it comes to truth?
I think there are basically two possible responses to this challenge.
The first is to maintain that the claim that nothing is true is somehow incoherent or otherwise self-defeating. I think most people have this reaction. And you can see why. After all, if you think that nothing is true, then you’re committed to saying:
(1) ‘Snow is white’ is not true.
(2) ‘Snow is not white’ is not true.
(3) ‘The Holocaust was morally wrong’ is not true.
(4) ‘Nothing is true’ is not true.
And we normally think that anyone committed to (1)-(4) is also committed to:
(5) Snow is not white.
(6) It’s not the case that snow is not white.
(7) The Holocaust was not morally wrong.
(8) It’s not the case that nothing is true.
And this is multiply problematic: (5) is just obviously wrong; (5) and (6) contradict each other; (7) is not just obviously wrong but morally heinous; and (8) is the denial of the very theory the nihilist purports to believe.
As I say, this is a very natural reaction. But it rests on a simple mistake. The nihilist about truth is, of course, committed to (1)-(4). But, by the nihilist’s lights, the inference from, say, ‘snow is white’ is not true to snow is not white is not valid. We normally think this is valid because we normally think that, if snow is white, then ‘snow is white’ is true; so, if ‘snow is white’ is not true, that must be because snow is not white. But the nihilist thinks there is no such thing as truth. So, ‘snow is white’ is not true, even if snow is white.
The nihilist about truth is therefore not automatically committed to any of (5)-(8), thankfully. Indeed, besides the claim that nothing is true, the nihilist is not committed to any particular claims about what the world is like. They can agree that snow is white, and that the Holocaust was morally wrong, and any other claim about the world that does not involve the notion of truth.
The other, better response is to maintain that nihilism is coherent, but costly. We deploy the notion of truth all the time. This is so in everyday life, but especially so in philosophy. We analyse meaning in terms of truth-conditions; knowledge in terms of justified, true (and, er, something else) belief; logical validity in terms of necessary truth-preservation. If nothing is true, what becomes of meaning, knowledge, or logic?
I think there’s a good challenge lurking here. But a debate about exactly what kind of role the notion of truth plays for us has been chugging along for a long time now quite independently of the Liar Paradox. Probably the dominant position here (but not my own!) is that truth merely plays an “expressive” role, rather than an explanatory one. One of the key things I argue in the paper is that we can use the notion of truth to play this “expressive” role, even if nothing is true, by treating truth as a useful fiction. If that’s right, and the utility of truth is exhausted by its expressive role, then nihilism is not costly either.
The upshot is that, at least for most philosophers working on truth these days, nihilism should look like a cost-free solution to the Liar Paradox. We have no more need for truth than squircles.
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