Tartu Pluralism Day #2

OK, it’s a short day here today – thankfully, since I’m knackered after Day #1 – with two talks. Last night we dined at an Italian Restaurant, and I learned more about Roger Swyneshed from Stephen Read, than I ever expected to learn. Talks today are:

• Peter Pagin, on Universalist and Actualist Consequence. Peter connected his work with Kathrin Glüer on relational modality and the semantics of names with considerations concerning the difference between universal validity (truth in all possible worlds whatsoever) and actualist validity (truth in all candidate actual worlds – down the diagonal in a 2D semantics, for example). He indicated that his looks like our distinction, both should count as validity notions which ought to be endorsed. Peter wondered whether this was a problem, and whether there’s a conflict between endorsing universalist validity and actualist validity.

This is a good question: I think that this is a good case where being a pluralist makes sense: if we think of validity as classifying deduction steps into those that are valid and those that aren’t, then actualist and universalist validity notions have their place. Take the step from p to actually p. This is OK in one obvious sense (we’d make a mistake to assert p and deny actually p), and bad in another (that step doesn’t work if we are under a counterfactual assumption – we grant that not p, and then consider what would have happened were p the case – we can’t infer from that to actually p).

More must be done, of course, on what it is to endorse the logic, and to say why we might like to have both of these criteria in our toolkit. I think we do want both, and I don’t think that arguing abou which of these is the ‘deductive validity’ is fruitful.

The next talk is

• Johan van Benthem, for whom Logical Pluralism Meets Logical Dynamics. Johan kicked off by addressing the issue of what logic is, noting that proof, definition and computation, which are equally important. Logical systems are neat–they do all these things. In the talk, rich with different ideas, the focus was on the dynamic treatment of logic, of proof and deduction. The thought is simple, but the consequences are rich: thinking of announcements as acts in which the space of possibilities is narrowed down, we can think of the argument from A, B, C to D as valid when after announcing A, B, and C (in that order), the announcement that D would be redundant. The neat thing here is that Knower-paradoxical announcements (p but you don’t know that p) have interesting logical properties such that announcing them twice has a different effect than announcing them once. There are clearly different notions of information processing and deduction in play here, and as always, Johan’s work is rich with ideas and consequences for many people to work out.

I’m very glad that the paper this talk was based on will be appearing in the AJL, with commentaries by others, too. So hopefully, that will bring the dynamic epistemic approach into conversation with other traditions.

Then after lunch, we’re off to the lake.