March 01, 2007

Context of Evaluating Counterfactuals

If we call a tail 'a leg', then how many legs would a horse have? It would still have four. The concepts we use to evaluate the question are our actual concepts, even if the truth of the antecedent (at a closest world w) involves (at w) a revision of our actual concepts. A principle is suggested:

(*) when we evaluate the truth of a counterfactual, the concepts employed (in drawing a path in a close world w from the antecedent to the consequent) are determined by the context of evaluation and not by the semantic facts at w.
An analogous principle is this (paraphrased from Jenkins in the comments thread to the last post):
(**) when we evaluate the truth of a counterfactual about logical principles, the logic employed (in drawing a path from the antecedent to the consequent) is determined by the context of evaluation and not by the logical facts at the relevantly close worlds.
The idea is that the logic we use to evaluate the truth of a counterfactual is our default logic (ex hypothesi, classical logic), even if the truth of the antecedent (at close worlds) requires an alternative to our default logic. (*) and (**) would seem to stand or fall together.

However, (*) is not unrestrictedly true. Consider:
(1) If 'one' meant two, then 'one plus one' would mean two plus two.
If the concepts of evaluation are held fixed, then we should insist that the consequent (i.e. 'one plus one' means two plus two) is false in the closest worlds where the antecedent is true. And so, we should insist that (1) is false. But, (1) is prima facie true. Therefore, (*) is prima facie false as a general principle.

We should then expect that (**) likewise fails as a general principle. It had better fail. Otherwise we cannot engage non-vacuously, when we consider what (logical) principles would be the case if others were not. The reason we can in fact engage non-vacuously about such matters is this. When we evaluate counterfactuals about logical principles, the logic at the closest worlds is relevant to---indeed, is essential for---a proper evaluation of the consequent.


Anonymous said...

I don't see why the truth of (1) conflicts with the truth of (*). I think the concept one is not expressed in the consequent of (1) -- 'one' occurs in quotation marks.

Compare your initial example about tails and legs. The analogous claim to (1) would be NOT

If 'leg' meant tail then a horse would have four legs

which is false, BUT

If 'leg' meant tail then 'leg of a horse' would mean tail of a horse (and would apply to only one part of a horse, rather than four).

Am I missing something?

Best, Stephan

Julien said...


I'm not sure about your analogy with the meaning of numerals. One thing is to see what happens in worlds at which our linguistic expressions have different meanings. Quite another thing is to see what happens in worlds at which some logical principles fail. Or so one might argue.

Anyway, I share your intuition that ¬LEM □→ DNE should be false, not true. Still, I'm not entirely clear about the issue yet, and I wonder whether this is a correct intuition or not.

What about counterfactuals whose antecedents is, say, 2+2=5? Should we say that, in these worlds, anything follows? If we go this way (the standard way, I suppose), we would end up evaluating these counterfactuals wrt to *our* logical principles, which however may be different from the ones holding at the worlds at which 2+2=5 happens to be true. The problem, now, is that, if we prescind from our logical principles (say, classical logic), we have no clue about what would be true if 2+2=5 happened to be true. So, it seems, one has to make a choice as to which is the logic with respect to which a counterfactual is to be evaluated.

Of course, this logic need not be classical. Priest and Williamson may evaluate counterfactuals whose antecedent is 2+2=5 in different ways.

Yet, it seems that would both evaluate these counterfactuals using the logic they think is the correct one.

If this is correct, then Carrie is right: ¬LEM □→ DNE represents no counterexample to Williamson's contention that counterpossibles with impossible antecedents are trivially true.