Yesterday, at the University of York, Saul Kripke (if you don’t know who he is, you’re on the wrong site) gave a lecture on the foundations of logic. The main point he wished to emphasise, was, for certain logical laws, there can be no way of ‘adopting’ them without first presupposing them. This he called the adoption problem. For example, how does one grasp: for every instance of ‘x’ apply UI… without UI?
Adoption requires adherence. The rule presupposes itself.
This was put brilliantly by Romina Padro, who gave the example (call it S):
- All Animals in the movie Madagascar talk.
- Alex is a lion in the movie.
- Therefore, Alex talks.
Now, if we imagine a person called Harry who did not grasp UI. Well, we can explain the law to him, but still, when he reads the review of Madagascar containing 1. he would not be able to infer 3.
He might say: “but the review doesn’t say whether the lion talks or not.” But the jump from 1. to 3. requires UI… and so does the adoption itself! You need to have the function UI for S1: “apply UI all statements ‘S'” such that S1 requires UI. Otherwise, UI cannot be implemented in all cases fitting the application of UI.
Romina suggested, that this may lead us to consider such ‘basic’ logical laws as foundational. (One member of the audience referenced, as I was thinking myself, possible parallels between this theory and Chomsky’s UG.)
Well, I asked why one, when faced with such a paradox, cannot give up on truth conditions in favour of justification conditions, as allowing Wittgenstein’s arguments against internalisation, Quine’s indeterminacy of translation and Ruth Millikan’s work on teleosemantics: there is no need, nor any feasible way, of cashing-out truth conditions. Why can’t logical laws simply be normative [and not internalised, so as to force UI into behaviour, which, with Humean inversion, implies we follow UI because we say ‘S’ and not the inverse]*?
To this Kripke responded that Quine’s translation problem might be a problem, but that it was specific to translation, and that, there was no need to maximise truth conditions. Rather, what Quine spoke of (in Kripke’s example) was justification conditions and that wait… (he smiled) is this an objection?
I responded no, simply a question. Why can’t the laws be normative, so we have method of turning away from logical paradoxes? (See Wittgenstein vs. Turing.)
Again, he gave a brilliant historical lesson of why Quine’s later arguments are too sweeping, in that they contradict even his own conception of logic in Two Dogmas. His knowledge and rigour is something to behold. Though, I didn’t feel my question was answered, nor do I feel I put it across correctly. Of course, the former accords with the latter, and so it was entirely my fault. Nevertheless, I thought I’d quickly outline what I remembered of the portion of the lecture dedicated to the adoption problem, and the interaction for anybody interested.
*The portion in brackets, I did not ask for brevity, as I thought it was implied, or followed logically. Or rather, I wish I had added it.