McGee's Counter-Example to Modus Ponens
I heard this mentioned the other day, and had to check it out.
The putative counter-example:
It's election time, 1980. According to the polls, Republican Reagan is in the far lead. Democrat Carter is second, and Republican Anderson is third by some margin. Assess the following argument:
(1) If a Republican wins, then if it's not Reagan who wins, it will be Anderson
(2) A Republican will win
(3) Therefore, if it's not Reagan who wins, it will be Anderson.
The premises are true, and by classic logic they entail the conclusion, but, we ought to reject (3). So it seems to some.
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On seeing this, it took me a while to even see why someone might reject (3). It seemed to me obviously true given the premises. Here is why I failed to feel the pull of the example.
The argument is invalid iff (1) and (2) can be true when (3) is false. And (3) is false iff both Reagan and Anderson lose. So the argument is invalid iff:
(a) If a Republican wins, then if it's not Reagan who wins, it will be Anderson.
(b) A Republican wins.
(c) Reagan loses.
(d) Anderson loses.
These conditions cannot all be true. By hypothesis, Reagan and Anderson cannot both lose but the Republicans win. The argument is valid.
The confusion arises because an argument with necessarily false premises establishes anything whatsoever. "If 2+2=5, then I am the pope" is a valid argument. The premise can't be true and the conclusion false: nevermind that the premise is never true.
The counter-example is just another argument of this kind. The premises can't be true and the conclusion false: nevermind that there is no world in which premise (2) holds and the antecedent of (3) is true.
As we know, necessarily false claims entail anything whatsoever. McGee's counter-example is just one instance of this.
(I understand McGee's aims were not to undermine the logicians sense of modus ponens, but the claim that modus ponens was the conditional used in natural language. This is fine, although if I am right, then this is just a local instance of the known truth that material conditionals allow for irrelevant entailment.)
Diagnosis
I'm not sure you've quite diagnosed the pull of the counterexample correctly. The problem, I would think, is that the natural way to read (3) makes it straightforwardly false (since it is possible, even if false, that a Democrat win, it is possible for Reagan and Anderson both not to win); your response is right but it requires continually making qualifications like this on (3): "given the premises", "on the hypothesis", etc. Thus (3) cannot be detached from the premises at all; it is only true if (2) is true, and, it would seem, you can only read it as true by treating (3) as conveying the same meaning as (1). That is, whenever you clarify the meaning of (3) so that it is not obviously false, you just treat it as a less perspicuous restatement of (1). So the problem is that either the argument is invalid or (3) is really, when properly understood, just a restatement of (1). Thus either the argument is invalid or it is not modus ponens at all. (This conclusion can be avoided, and the argument recognized as modus ponens, if we allow for conditionals that are not material conditionals; since the problem arises by treating all conditionals, including that which expresses the meaning of the conclusion, as material conditionals.)
Not a material conditional
I think you've misinterpreted the argument.
You write: "(3) is false iff both Reagan and Anderson lose."
But that is not what (3) claims at all. It is not a material conditional, but a (non-truth-functional) ordinary English conditional.
(In that case, I think it may be related to the puzzle discussed here.)
Thanks to both of you for
Thanks to both of you for the replies; I'll give this some more thought and perhaps come back to it sometime.
Alex