Friday, September 02, 2005


Other interesting ECAP sessions included a talk by David Liggins (PhD Sheffield, shortly to take up a year of Analysis-funded research in Cambridge), fearlessly delivered at 9.30am on the first morning of the conference, entitled Naturalism and Nominalism. David suggested (without endorsing) a new way for nominalists about mathematics to accommodate the fact that mathematical theories seem committed to mathematical objects. They could accept that mathematicians utter lots of sentences which express propositions that entail such commitment, but deny that this means they are committed to theories which contain those propositions. When a sentence of this kind is utterered by mathematicians, on the proposed view, what thereby gets put into the mathematician's theory is not the proposition p expressed by the sentence but some other proposition (David suggested some proposition concerning the provability of p from certain axioms). I'd be interested to hear more about what reasons we could have for thinking that what gets put into the theory is a different proposition from the one expressed, as opposed to thinking that a different proposition was being expressed from the one you might have expected.

I should also mention that I was pleasantly surprised to find myself in a Philosophy of Maths talk later on in the same stream where the women in the room outnumbered the men by five to one. This was unprecedented in my experience!

That afternoon I went to a paper on measures of coherence (of the kind Coherentists would seem to need in order to assess how justified our beliefs are), written jointly by Luca Moretti and Ken Akiba and presented by Moretti. One point that came up here was whether logically equivalent sets of sentences were always equally coherent. The speaker thought so, but I was sceptical. Suppose that P in fact entails Q. Then the set {P, Q, P entails Q} is logically equivalent to {P, Q}, but you might reasonably think it was more coherent.

More paper reports to follow soon, I expect!

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