Talks and Workshops

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June, the month when academics migrate (I'm posting this blog from Bergen, in Norway, when I've been invited to give a seminar on the foundations of the philosophy of information).

The invited talk I gave in Siena made me realise (thanks to Claudio Pizzi!), that we might have some Quinean doubts about second order logic and modal logics in general, but we actually lack a theory of second order probability, let alone a philosophical justification for it. This is odd (sorry for the pun). Imagine: if you have a fair coin, the probability (P) that, when tossed, it will turn out to be head (h) is 0.5, obviously. So P(h) = 1/2 or 0.5. But what is the probability of this probability, i.e. P(P(h))? Does it even make sense to ask the question? If you think it does not, consider the following case: what is the probability (P1) that Othello (o) knows (K) the probability (P2) that Desdemona (d) might be unfaithful (U)? That is: P1(KoP2(Ua))?
Some people think that the two Ps are not referring to the same concept of probability, some others that P1 really modifies the epistemic operator K not P2... but the jury is still out.

The talk I gave in Ferrara was actually about a joint work with Marcello D'Agostino. Marcello is a sophisticated logician, and has invited me to join our forces to crack the so-called scandal of deduction (so-called by Hintikka). The point is simple. According to our standard theory of information and its semantic extension, the less likely a proposition is, the more informative it becomes. It makes sense rather easily if you think in terms of possible worlds (PW) and their exclusions. "The train leaves in the morning" excludes more PW than "the train leaves tomorrow", so it is more informative, but so is "the train leaves between 10 and 11 am" and so forth. This inverse relation between infomativeness and probability is classic, reasonable and intuitive but causes two problems:
a) what I defined as Bar-Hillel-Carnap Paradox: at one extreme, contradictions, which exclude all PW (i.e. they are impossible) are the most informative propositions. Unpleasant. Luckily,I solved this problem in a paper in Minds and Machines were I showed that we need to make the concept of information semantically stronger, so that it encapsulates truth. In a nutshell, if we do, contradictions fail to be informative because they are false.
b) the scandal of deduction: at the other extreme, tautologies and logical truths do not exclude any PW (i.e. their possibility = 1) so they convey zero information. But then so does logic and mathematics as a whole. Unpalatable.
Marcello and I are working now on (b). Thanks to Marcello's brilliant idea (no anticipation, but stay tuned) we might have cracked this too... it seems that travelling opens one's mind, if one can meet the right people 8)

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