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This will be a talk at the London Philosophy and the Formal Sciences Seminar on 28 February.
Abstract: I consider inquiry in mathematics and suggest that it supports an account of inquiry as concerned with epistemic improvement. I further argue that two norms of inquiry; that we should regard the questions we inquire into as sound and we should not know their answers, are incorrect (at least for some kinds of inquiry).
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This will be a talk in the NUS Logic Seminar on 21 February 2024.
Abstract: A popular view in the philosophy of set theory is that of potentialism: the position that the set-theoretic universe unfolds as more sets come into existence or become accessible to us. This often gets formalised using modal logic, but there is always a question of how to move to non-modal theories. In this latter regard, a difficult question for the potentialist is to explain how intensional entities (entities individuated by an application condition rather than an extension) behave, and in particular what logic governs them. This talk will discuss some work in progress on this issue. We’ll see how to motivate acceptance of different propositional logics for different flavours of potentialism, and discuss the prospects for proving results about the kinds of first-order theories validated.
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This will be a talk on Monday 11th December in the Center for Philosophy and the Sciences Lunch Forum at Universitetet i Oslo.
Abstract: A recent position in the foundations of mathematics borrows its terminology from physics, namely the Multiverse View. This position states that there is not one universe containing all the sets, but rather many. At first glance, it looks like this view doesn’t share so much with the view in physics beyond somehow involving talk of multiple universes. For a start, the set-theoretic multiverse (realistically understood) is composed of mathematical abstracta, whereas the physical multiverse contains many concreta.
In this talk, I want to explore the extent to which this idea is more than a mere similarity of catchy terminology. In particular, I’ll suggest that an important motivation of each is fine-tuning; the idea that if there was just one universe, then it would be (seemingly without good grounds!) set up with very precise anthropocentric constraints. I’ll use these observations to explore what each view can learn from the other and whether there are common pitfalls to be mindful of.
Neil Barton 