Monday, 26 October 2015
Another instance of some shameless self-promotion... Here is a podcast with an interview with me by the ever-wonderful Peter Adamson -- the host of the fabulous podcast series History of Philosophy without any Gaps -- on Latin medieval logic, more specifically the senses in which medieval logic can (or cannot) be said to be formal -- both according to contemporary notions of formality and medieval ones. Hope some of you will enjoy it!
Saturday, 17 October 2015
Back in January, I posted some reflections on what fictional languages can tell us about what meaning can and cannot be, here and here. Those thoughts eventually became a paper jointly written with one of my students, Phoebe Chan, which is forthcoming in Res Philosophica next April, "Against Truth-Conditional Theories of Meaning: Three Lessons from the Language(s) of Fiction".
For those who are interested in these topics, I gave a talk based on this paper at the Durham Arts & Humanities Society last Thursday evening. The talk was recorded, and is available to listen to on Soundcloud, for a few months at least.
© Sara L. Uckelman, 2015.
Wednesday, 14 October 2015
Monday, 12 October 2015
Friday, 9 October 2015
Thursday, 8 October 2015
Wednesday, 7 October 2015
This is the third installment of my series of posts on the beauty, function, and explanation in mathematical proofs (Part I is here; Part II is here). In this post I start drawing connections (later to be discussed in more detail) between beauty and explanatoriness.
We acknowledge a theorem's beauty when we see how the theorem "fits" in its place, how it sheds light around itself, like a Lichtung, a clearing in the woods. We say that a proof is beautiful when such a proof finally gives away the secret of the theorem, when it leads us to perceive the actual, not the logical inevitability of the statement that is being proved. (Rota 1997, 182).
- · Serious: connected to other mathematical ideas
- · General: idea used in proofs of different kinds
- · Deep: pertaining to deeper ‘strata’ of mathematical ideas
- · Unexpected: argument takes a surprising form
- · Inevitable: there is no escape from the conclusion
- · Economical (simple): no complications of detail, one line of attack
Tuesday, 6 October 2015
Monday, 5 October 2015
I am currently working on a paper provisionally entitled 'Beauty, function, and explanation in mathematical proofs', and so this week I will post what I have so far as a series of blog posts. Here I start with a discussion on the current literature on the presumed beauty of some mathematical proofs. As always, comments very welcome!