1. If the square root of 2 were rational, it could be expressed as n/m, with n, m integers.

2. If the square root of 2 were rational, it couldn't be so expressed.

Intuitively, you might think, 1 looks true and 2 looks false. Why, if they are both trivially true?

The answer that tempts me is that counterfactuals (including counterpossibles) are often used for, and often naturally heard as, expressing claims which are distinct from their literal contents. When we evaluate 1 as true and 2 as false, we are actually evaluating the sort of claim which is often conveyed by sentences like 1 and 2, although it is not what they literally mean. (In the case of 1, it might be something like the claim that any number which is rational can be written as n/m with n, m integers, so in particular this is true of the square root of 2).

A worry that a colleague put to me this morning concerning this view is that we have an intuition that it is wrong even to

*think*things like 2, but stories which focus on the pragmatic communication in conversation of claims distinct from literal content will not capture that intuition.

I wonder whether one might respond that accepting in thought that 2 is true could be a mistake if it relied upon (or amounted to) mistakenly assuming that the non-literal content often conveyed by claims like 2 was true. If one accepted 2 in thought without realizing that it was only true because its antecedent was impossible, one might (e.g.) be making the mistaken assumption that no number which is rational can be expressed as n/m with n, m integers, so in particular this is true of the square root of 2.

It wouldn't be misleading to think 2 was true if one's reason for doing so was that one knew its antecedent to be impossible. But in this case I don't get the intuition that there is anything wrong or mistaken about thinking 2 is true.

## 9 comments:

(1) certainly does seem true for non-trivial reasons. But maybe because lots of theoretical antecedents present no conceivability resistance and so seem perfectly entertainable. For instance (3)

3. If Fermat's last theorem were false then Andrew Wiles wasted his time.

Even after Wile's proof the antecedent in (3) seems perfectly conceivable. And so (3) seems non-trivially true as well. I guess I'm suggesting that it might be just a psychological matter that these seem true in something more than a trivial way.

Thanks Mike - the 'psychological resistance' perspective is an interesting one. But it doesn't seem that we always need to have entertainable antecedents in your sense in order to get the intuition of non-triviality. I don't think I can in that sense entertain the possibility that there is a round square, but still

4. If there were a round square it would be round and square

has the same aura of non-trivial rightness as things like 1 and 3 do.

What is it that underwrites the temptation to think that all these examples are true (even (2))? Lewis defends it in 'Counterfactuals' on the grounds that we have an intuition that if an impossibility were true, then 'anything you like would be true' (p24), but that doesn't seem like a strong enough consideration to outweigh our intuition that there's a relevant difference between (1) and (2). Why not just take these sorts of problems to show that we should abandon the truth of (2) and its relatives (as Wright for one has suggested)?

I don't have any great stake in the debate, but I'd be interested to see what could be said in favour of the semantic treatment of counterfactuals that drives the problem (given I find Lewis' remarks a little unpersuasive).

I guess I'm less sure that the antecedent in (4) is not entertainable, it's just not imaginable. But I can't imagine a 400-sided figure, either. Does (5) seem non-trivially true?

5. If there were something round and not round, then it would be round.

It doesn't to me, and that seems to be because the antecedent contains an explicit contradiction.

We could fuss over "explicit". Say a close-enough-to-explicit contradiction. And so it is more clearly not entertainable. On the other hand (6) seems true and trivial.

6. If there were something round and not round, then it would be round and not round.

Aidan,

You probably won't like my answer as it's really just a way of expanding slightly on Lewis's comment. The intuition I find motivating (very roughly) is something like this. Impossible things are the hardest kind of thing to make true. So if something impossible were going to count as true, truth would have to have become so liberal that everything would count as true. You'd have to lower the bar of truth so far, to get an impossible thing to count as true, that everything else would get over the bar as well. Because (to continue with the metaphor!) everything jumps at least as high as the impossible things do.

Mike,

There might be some interference with our intuitions as to whether 4, 5 and 6 are trivially true: one might take them to be trivially true in another sense to the one we're chasing, namely the sense in which anything of the form: 'If A were true then A would be true' or 'If A&B were true then A would be true' is trivially true (rather than the kind of triviality which has something special to do with their antecedents).

To avoid that sort of worry, let's consider:

7. If something were a horse and not a horse, it would eat hay (because it would be a horse).

Do you get the intuition of non-trivial truth for this sort of claim? (For what it's worth, I do - at least insofar as I get such an intuition for any counterpossible.)

7. If something were a horse and not a horse, it would eat hay (because it would be a horse).

What would the denial of your view be? Suppose I say, "no, it wouldn't be a horse. So it *might not* eat hay". You'll presumably say, "yes, that's right, too". So we've got two substantive and true claims: X would and might not eat hay. Something's gone wrong, no? I mean unless we start altering truth-conditions for "would" and "might" counterfactuals.

Mike,

To deny my view would be to say:

8. It's not the case that (if something were a horse and not a horse it would eat hay).

As for 'might' counterfactuals, I guess if you're thinking of them as interdefinable with 'would' counterfactuals in Lewis's way, then 'If something were a horse and not a horse, it might not eat hay' will come out false provided counterpossible 'would' conditionals are vacuously true. But maybe you think that sounds a little odd - if one thought that all counterpossible 'would' conditionals are true, one might be tempted to say all counterpossible 'might' conditionals are all true too (perhaps on the grounds that would implies might). If so, so much the worse for that kind of interdefinability. If I remember rightly, Lewis thinks the failure of 'would implies might' for vacuous counterfactuals is a counterintuitive bullet we should just bite. But I myself don't have firm views on how 'might' counterfactuals are to be understood, so I'm not particularly committed to either side of this debate.

"You probably won't like my answer as it's really just a way of expanding slightly on Lewis's comment"

No, thanks Carrie, that's useful. I can see that must be the kind of thought Lewis had in mind, but I find your way of putting it far more convincing that the quote above.

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