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Showing posts from September, 2009

The "Modal argument" paper is forthcoming

A paper we wrote with Agnieszka Rostalska (I very roughly outlined an early version here ) is forthcoming in Philo . A rather final draft of the paper is available online here . The paper is devoted to the clarification and criticism of Swinburne's modal argument for the existence of the soul. Before I paste the abstract and acknowledgments below, one more remark. When giving this paper at various places, one sort of reactions encountered came from people with good background in logic, but no previous experience with philosophy whatsoever. The reaction boils down to a rather blind stare and comments like "who cares about arguments for the existence of the soul?" or "Why is anyone doing this stuff?". The answers are simple. "Philosophers." to the first question. "Because it's more interesting than using complex mathematical tools to solve problems that only two to three people in the world care about." to the second one. I prefer to use

Trends in Philosophy of Mathematics (day 3, talk 1)

On the third day the schedule was a bit more complicated, we had to choose between one of two parallel sessions. The choice was difficult, so I will be unable to comment on some of really interesting talks that I was unable to attend. If I don’t talk about a certain talk it’s because I was unable to make it to it because the alternative talk was more related to what I’m working on. For now, the first talk of the day. Assadian: Crispin Wright and his Hero Wright, defending the epistemic accessibility of prima facie impredicative Hume’s Principle tells a story of a fictional character (named Hero) who initially knows second-order logic and possesses a bunch of sortal concepts referring to concrete objects, but doesn’t understand the concept of number. Wright then argues that the Hero can process in stages in order to gain the understanding of the concept of natural numbers. Stage 1 - The Hero introduces HP for the initial domain that he possesses a grasp of. Stage 2 - T he Hero now und

Live from Trends in Logic VII (day 2)

Today we had four quite exciting talks. The first one, given by Oystein Linnebo (Bristol) was devoted to A Partial Defense of Frege's Basic Law V . Oystein started off with the intuitions that there is some pressure to accept Frege's BLV (which says that extensions of two concepts are identical iff exactly the same objects fall under that concept). After criticizing the limitation-of-size approach to restricted versions of the comprehension principle, he went modal-and-iterative about BLV. That is, BLV was used to capture how new sets are formed at new stages using the objects already existing in previous stages, and modal operators were thrown in to express the intuition that we're talking about the possible ways our set-formation process can go. This gives a fairly intuitive criterion for a plurality determining a set: it has to have the same elements across possible worlds. Proof-theoretically, once you take S4.2 as the underlying modal logic, throw in some trans-world

Live from Trends in Logic VII

It's the first day of Trends in Logic VII , aka Trends in the Philosophy of Mathematics . So far, we're past an opening, an opening leture by Ryszard Wójcicki, and a splendid conference dinner. Ryszard Wójcicki, an excellent "hardcore" logician known for his work on consequence operations and Polish-style meta-theory of propositional calculi, has recently decided to think about more philosophical issues. He was talking about Two sources of mathematical truth. The main gist was that the key "source" of mathematical truth was "conceptual realities" (the other source being empirical domains). Alas, I didn't quite get what being a source of truth is, how conceptual realities are supposed to be different from mathematical structures, what their ontological status is, and why they're supposed to exist. Having said that, it was interesting to hear a real "hardcore" researcher say what he thinks about the philosophical status of his ow