London Ed comments:
I also note a confusion that has been running through this discussion, about the meaning of ‘contradiction’. I do not mean to appeal to etymology or authority, but it’s important we agree on what we mean by it. On my understanding, a contradiction is not ‘the tallest girl in the class is 18’ and ‘the cleverest girl in the class is not 18’, even when the tallest girl is also the cleverest. Someone could easily believe both, without being irrational. The point of the Kripke puzzle is that Pierre seems to end up with an irrational belief. So it’s essential, as Kripke specifies, that he must correctly understand all the terms in both utterances, and that both utterances are logically contradictory, as in ‘Susan is 18’ and ‘Susan is not 18’.
Do we agree?
Well, let's see. The Maverick method enjoins the exposure of any inconsistent polyads that may be lurking in the vicinity. Sure enough, there is one:
An Inconsistent Triad
a. The tallest girl in the class is the cleverest girl in the class.
b. The tallest girl in the class is 18.
c. The cleverest girl in the class is not 18.
This trio is logically inconsistent in the sense that it is not logically possible that all three propositions be true. But if we consider only the second two limbs, there is no logical inconsistency: it is possible that (b) and (c) both be true. And so someone, Tom for example, who believes that (b) and also believes that (c) cannot be convicted of irrationality, at least not on this score. For all Tom knows -- assuming that he does not know that (a) -- they could both be true: it is epistemically possible that both be true. This is the case even if in fact (a) is true. But we can say more: it is metaphysically possible that both be true. For (a), if true, is contingently true, which implies that it is is possible that it be false.
By contrast, if Tom entertains together, in the synthetic unity of one consciousness, the propositions expressed by 'Susan is 18 years old' and 'Susan is not 18 years old,' and if Tom is rational, then he will see that the two propositions are logical contradictories of each other, and it will not be epistemically possible for him that both be true. If he nonetheless accepts both, then we have a good reason to convict him of being irrational, in this instance at least.
Given the truth of (a), (b) and (c) cannot both be true and cannot both be false. This suggests that the pair consisting of (b) and (c) is a pair of logical contradictories. But then we would have to say that the contradictoriness of the pair rests on a contingent presupposition, namely, the truth of (a). London Ed will presumably reject this. I expect he would say that the logical contradictoriness of a pair of propositions cannot rest on any contingent presupposition, or on any presupposition at all. Thus
d. Susan is 18
e. Susan is not 18
form a contradictory pair the contradictoriness of which rests on their internal logical form -- Fa, ~Fa -- and not on anything external to the propositions in question.
So what should we say? If Tom believes both (b) and (c), does he have contradictory beliefs? Or not?
The London answer is No! The belief-contents are not formally contradictory even though, given the truth of (a), the contents are such that they cannot both be true and cannot both be false. And because the belief-contents are not formally contradictory, the beliefs themselves -- where a belief involves both an occurrent or dispositional state of a person and a belief-content towards which the person takes up a propositional attitude -- are in no theoretically useful sense logically contradictory.
The Phoenix answer suggestion is that, because we are dealing with the beliefs of a concrete believer embedded in the actual world, there is sense to the notion that Tom's beliefs are contradictory in the sense that their contents are logically contradictory given the actual-world truth of (a). After all, if Susan is the tallest and cleverest girl, and the beliefs in question are irreducibly de re, then Tom believes, of Susan, that she is both 18 and not 18, even if Tom can gain epistemic access to her only via definition descriptions. That belief is de re, irreducibly, is entailed by (SUB), to which Kripke apparently subscribes:
SUB: Proper names are everywhere intersubstitutable salva veritate.
A Second Question
If, at the same time, Peter believes that Paderewski is musical and Peter believes that Paderewski is not musical, does it follow that Peter believes that (Paderewski is musical and Paderewski is not musical)? Could this conceivably be a non sequitur? Compare the following modal principle:
MP: If possibly p and possibly ~p, it does not follow that possibly (p & ~p).
For example, I am now seated, so it is possible that I now be seated; but it is also possible that I now not be seated, where all three occurrences/tokens of 'now' rigidly designate the same time. But surely it doesn't follow that it is possible that (I am now seated and I am now not seated). Is it perhaps conceivable that
BP: If it is believed by S that p and it is believed by S that ~p, it does not follow that it is believed by S that (p & ~p)?
Has anybody ever discussed this suggestion, even if only to dismiss it?