Monday, 2 November 2015
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!
Monday, 28 September 2015
Monday, 7 September 2015
(This post can be safely classified as an instance of shameless self-promotion, but here we go anyway...) Last week Stephen Read and I delivered the full manuscript of the forthcoming Cambridge Companion to Medieval Logic to Cambridge University Press. We still need to go through the whole production process (including indexing), but at this point it is safe to assume the volume will appear somewhere in 2016. We've been working on this volume for nearly 3 years, and so we are suitably thrilled to be nearing completion!
Many people asked me about the Table of Contents for the volume, and so I figured I might as well make it public -- now that we know there will not be any changes to chapters and/or contributors. Here it is:
The event is open to the public.
Wednesday, 26 August 2015
Friday, 21 August 2015
(Cross-posted in NewAPPS)
There is a Bloomsbury Philosophical Methodology Reader in the making, being edited by Joachim Horvath (Cologne). Joachim asked me to edit the section on formal methods, which will contain four papers: Tarski's 'On the concept of following logically', excerpts from Carnap's Logical Foundations of Probability, Hansson's 2000 'Formalization in philosophy', and a commissioned new piece by Michael Titelbaum focusing in particular (though not exclusively) on Bayesian epistemology. It will also contain a brief introduction to the topic by me, which I will post in two installments. Here is part I: comments welcome!
Tuesday, 18 August 2015
Thus, in the first two chapters of Rigor and Structure, Burgess asks two questions: What is mathematical rigor? Why did mathematicians strive so hard to achieve it throughout the period just described? To answer the first question, Burgess turns initially to the pronouncements of mathematicians themselves, but he finds little that is precise enough to satisfy a philosopher there. So he turns next to Aristotle and, looking to the Posterior Analytics, extracts the following suggestion:
Mathematical rigor requires that:
- ''every new proposition must be deduced from previously established propositions'';
- ''every new notion must be defined in terms of previously explained notions'';
- there are primitive notions from which the chain of definitions begins;
- there are primitive postulates from which the chain of deductions begins;
- ''the meaning of the primitives and the truth of the postulates must be evident''.
Monday, 27 July 2015
For those who haven't yet come across these, I have two new initiatives relating to women in logic to advertise:
- Women in Logic group on Facebook: "A group for women in Logic, philosophical, mathematical or computational. or any other kind of formal logic that you care about." Membership is not restricted to women.
- Female Professors of Logic, an editable google spreadsheet. One outcome of this will be to give a list of people who should have wikipedia pages if they don't already.
Please share widely and contribute as you can.
© 2015 Sara L. Uckelman
Tuesday, 21 July 2015
- Interlocutor 1 commits to A (either prompted by a question from interlocutor 2, or spontaneously), which corresponds to assuming the initial hypothesis.
- Interlocutor 2 leads the initial hypothesis to absurdity, typically by relying on additional discursive commitments of 1 (which may be elicited by 2 through questions).
- Interlocutor 2 concludes ~A.
Monday, 20 July 2015
Funded by the Canadian Journal of Philosophy, the University of Wisconsin, and a gift from Rodney J. Blackman.