Mathfest Invited AddressLogic in the Integers
Speaker: Yale Weiss
co-Director of the Saul Kripke Center
City University of New York, The Graduate Center
Friday, August 5, 2022
5:00 - 6:30 pm
Location: Salon I
Reception and Guest Lecture
Since at least 1679, logicians have been interested in arithmetical interpretations of formal systems of logic, that is, in ways of interpreting given logics in natural arithmetical structures (or, identifying logics over such given structures). Thus, for example, Leibniz developed interpretations of the syllogistic in the divisibility lattice (N,|) and, more recently, logicians have investigated the tense logic of (Z,<). In this talk, I will survey some of these results, both historical and contemporary, with a special focus on (N,|) and non-classical logics exactly characterizable therein. Emphasis will be given both to philosophically suggestive features of arithmetical structures and to how certain metalogical results logicians have been independently interested in can be given elegant new proofs by exploiting elementary properties of the numbers.Slides: pdf
Contributed Paper Session
Logic and Intuition in Everyday Mathematics
Friday, August 5, 2022
Many of us likely believe--and teach--that the role of proof is essential to the practice of pure mathematics. However, history is full of examples that suggest intuition may also play a meaningful role in the development of mathematical knowledge. Furthermore, computers can now supply (or at least verify) many of the logical steps in a mathematical proof, and even generate mathematical conjectures. This raises the question: what roles do logic and intuition play in mathematics? Is logic largely a scheme for demonstrating rigor and "correctness" after intuition has led us to a proposition that we believe to be correct? Or is logic more of an essential companion, informing our intuition and the very way think about our subject matter? This contributed paper session welcomes submissions reflecting on the relative roles of logic and intuition in mathematics, based on the contributor's historical/philosophical scholarship or lived experience as a working mathematician.
|1:00 p.m. - 1:15 p.m.||Chris Oehrlein||Re-Imagining Theorem-and-Proof in a Guided-Inquiry Geometry Course for Future K-8 Teachers|
|1:20 p.m. - 1:35 p.m.||Benjamin Gaines||Related Rates and Right Triangles: Developing Intuition in a Calculus Course|
|1:40 p.m. - 1:55 p.m.||Raul Rojas-Gonzalez||Developing Mathematical Intuition with a History of Math Course|
|2:00 p.m. - 2:15 p.m.||Paul Christian Dawkins||Some Ways of Reasoning Productive for the Logic of Mathematical Reasoning|
|Kyeong Hah Roh|
|2:20 p.m. - 2:35 p.m.||Rick Sommer||Logic, Intuition, and Infinity|
|2:40 p.m. - 2:55 p.m.||Rahmat Rashid||Defining Abstraction|
Organizers: Jason Douma, University of Sioux Falls, firstname.lastname@example.org
Tom Morley, Georgia Institute of Technology, Morley@math.gatech.edu
January 4-7, 2023
AMS Special Session
Current Directions in the Philosophy of Mathematics
This session, organized by POMSIGMAA, plays off on our very successful MAA Invited Paper Session at JMM 2012, when JMM was last held in Boston. At that session, taking advantage of the large number of philosophers of mathematics in the Boston area, we had six well-known mathematicians/ philosophers of mathematics share their work. Three of them have agreed to a return engagement, and we have invited several other philosophers of mathematics in the area as well. But an AMS Special Session differs a bit from an MAA Invited Paper Session in that we can have speakers beyond those initially invited. So we encourage anyone who has done some recent work related to the philosophy of mathematics to propose a talk for our session. These should be non-technical talks, aimed at a general mathematical audience (for technical work in foundations, there are ASL sessions, for example) but all topics in the philosophy of mathematics (including philosophical aspects of foundations) are welcome.
Abstracts are due by September 13 (and the meeting organizers are completely strict on this deadline). To submit a proposal, go to https://www.jointmathematicsmeetings.org/meetings/national/jmm2023/2270_abs-submit. Abstracts (not including title) are limited to 2000 characters. The submission process is rather long, but most of it is fairly routine. The first step, though, is to create an AMS web account. It's free, and you don't have to be an AMS member to create one. Once you've created this account, you can start the submission process. To actually submit an abstract, go to https://meetings.ams.org/math/jmm2023/cfp.cgi. At the bottom of that page, click on "BEGIN A SUBMISSION" That brings you to the Session Selection page; scroll down to AMS Special Session on Current Directions in the Philosophy of Mathematics I and choose that. This brings you to the Subject page; for most proposals for our session, choose (at the very bottom) "104 Wider Issues", then (once you click "save"), to the right of that it lists "Subject Level 2", choose "104A: Mathematics and other fields", and to the right of that, Subject Level 3, choose "104A28Mathematics and philosophy ". Once all that has been saved, you go to the things you'd expect: author, title, abstract.
POM SIGMAA held both a Contributed Paper Session and hosted an invited talk by Nicolas Fillion at the Online Virtual Joint Math Meetings, April 6-9, 2022. Follow those links to find the list of talks, abstracts, and in some cases, slides.