The Philosophy of Mathematics Association is an affiliated group of the American Philosophical Association and as such is invited to organize sessions in the group program at APA divisional meetings. The PMA has held such a group session at the 2020 Eastern meeting, and is hoping to make philosophy of mathematics symposia a regular component of APA divisional meetings. Please submit your proposal for a 2- or 3-hour symposium on a topic in the philosophy of mathematics by July 30, 2020.
Proposals should be submitted online at https://forms.gle/L99aE6s1GtJWYCMy5
Proposals will be vetted by a joint committee of the PMA and the Association for the Philosophy of Mathematical Practice (APMP), and successful proposals will be scheduled for inclusion at a 2021 APA divisional meeting. A proposal requires:
- names, affiliations, and email addresses of organizer and speaker
- short abstracts (up to 200 words) for the session
- confirmation that organizers and speakers commit to attending the meeting
- whether the session shall be held at the 2021 Central (February 24-27, New Orleans) or Pacific (March 31-April 4, Portland) meeting
During the COVID crisis it is of course not easy to predict whether these meetings will take place, or whether they will take place face-to-face or in some online format. The APA is currently planning to hold in-person meetings in 2021, but is also considering alternative formats. In case the meetings do not take place, PMA and APMP will ensure that the online versions of the symposia are advertised widely.
Mark Steiner, Professor emeritus of Philosophy at Hebrew University in Jerusalem, died April 6, 2020 of complications from COVID-19. He was a leading philosopher of mathematics, who was especially well known for his books The Applicability of Mathematics as a Philosophical Problem (1998, Harvard University Press) and Mathematical Knowledge (1975, Cornell University Press) and his pioneering work on explanation in mathematics.
The PMA held a session in the Group Program at the 2020 Eastern Division Meeting of the American Philosophical Association. The session was organized by Juliette Kennedy, and consisted of a book symposium on John Baldwin’s Model Theory and the Philosophy of Mathematical Practice. The participants were John Baldwin (University of Illinois at Chicago), Timothy Bays (Notre Dame University), Colin McLarty (Case Western) and Scott Weinstein (University of Pennsylvania)..
This book can advance philosopher’s understanding of both structure and mathematicians. As to structure, John gives a great look at current working methods, which differ markedly from the usual philosophic ideas for an obvious reason: Mathematicians ideas cannot just be defended in philosophic debate. They must produce results. And they do. John describes how a lot of these developed and what they achieve. This leads to the point about mathematicians. Philosophy of mathematics, and philosophy of science more generally, too often neglect the raw experience of desperately desiring scientific answers. Mathematical proof is so different from philosophic argument that we sometimes treat mathematical knowledge as something that just follows from the axioms. As if you just identify which axioms are relevant, put them in the right order, and then the answer is in front of you. John shows the living experience of the model theory community seeking, sometimes finding, and always reacting to, new concepts and methods to answer various standing questions. He shows how this goes at stages before anyone knows whether it will work. Philosophy of mathematics can benefit immensely from absorbing these insights. I will say, though, that textbooks and research talks and papers all show mathematicians use model theory, per se, much less often than they use categories and functors to describe structure.
John Baldwin heralds the significance of the “dividing lines” at the very beginning of Model Theory and the Philosophy of Mathematical Practice.
After the paradigm shift there is a systematic search for a finite set of syntactic conditions which divide first order theories into disjoint classes such that models of different theories in the same class have similar mathematical properties. In this framework one can compare different areas of mathematics by checking where theories formalizing them lie in the classification.
For John, the interest of the “syntactic” character of the dividing lines consists primarily in the fact that they are absolute for transitive models of set theory, and in consequence, that many of the central results of contemporary model theory do not rely on theories stronger than ZF. But, a number of the dividing lines, for example, NOP, are syntactic in a more robust sense – they are Π02 properties familiar from combinatorics. We explore whether this aspect of the dividing lines may have any interest from the point of view of the philosophy of mathematical practice. On the one hand, we observe that for every formal system F , there is an NOP theory T , such that T cannot be established to be NOP in F . On the other hand, all “naturally occurring” NOP theories (of which we are aware) can be proven to be NOP in primitive recursive arithmetic. We suggest investigating whether there is a recursively axiomatizable theory T that arises naturally in the course of mathematical practice such that T is NOP, but T is not provably NOP in primitive recursive arithmetic. If not, why? Might this tell us something interesting about mathematical practice? Or about the nature of mathematics itself? If so, might the additional strength required to establish that such a theory is NOP reflect some interesting phenomenon that helps to clarify our understanding of the mathematical topic it formalizes?
Slides of John Baldwin’s Responses.
Mic Detlefsen, founding president of the Philosophy of Mathematics Association, has died. The philosophy of mathematics community deeply mourns his loss.
Call for papers
Robert Thomas, editor of Philosophia Mathematica, writes:
Oxford University Press has given the impression this year that they would not be continuing personal subscriptions to Philosophia Mathematica since in 2018 the journal will be online only, what institutions overwhelmingly want. This decision was in fact made, but it has been reversed and at favorable rates as follows:
|Euro zone||North America||GB & rest of world|
|Unaffiliated||78 euros||99 US dollars||62 pounds|
|ASL members||39 euros||50 US dollars||31 pounds|
CSHPM members, anywhere outside Canada, 50 US dollars, paid to the Canadian Society for History and Philosophy of Mathematics.
Two things to note. Membership in CSHPM is so cheap at 23 US dollars (Cdn$30 in Canada), that it could easily pay to join CSHPM for the sole purpose of saving money on a PM subscription. See www.cshpm.org/join/
Subscriptions by ASL members and others are arranged through OUP:
UK Journals Customer Service, Tel: + 44 (0)1865 353907, Fax: + 44 (0)1865 353485.
USA Journals Customer Service, Tel: + 1 919-677-0977, + 1 800-852-7323 (toll-free in USA and Canada), Fax: + 1 919-677-1714.
12-14 October 2016
Munich Center for Mathematical Philosophy, LMU Munich
In the course of the last century, different general frameworks for the foundations of mathematics have been investigated. The orthodox approach to foundations interprets mathematics in the universe of sets. More recently, however, there have been other developments that call into question the whole method of set theory as a foundational discipline. Category-theoretic methods that focus on structural relationships and structure-preserving mappings between mathematical objects, rather than on the objects themselves, have been in play since the early 1960s. But in the last few years they have found clarification and expression through the development of homotopy type theory. This represents a fascinating development in the philosophy of mathematics, where category-theoretic structural methods are combined with type theory to produce a foundation that accounts for the structural aspects of mathematical practice. We are now at a point where the notion of mathematical structure can be elucidated more clearly and its role in the foundations of mathematics can be explored more fruitfully.
The main objective of the conference is to reevaluate the different perspectives on mathematical structuralism in the foundations of mathematics and in mathematical practice. To do this, the conference will explore the following research questions: Does mathematical structuralism offer a philosophically viable foundation for modern mathematics? What role do key notions such as structural abstraction, invariance, dependence, or structural identity play in the different theories of structuralism? To what degree does mathematical structuralism as a philosophical position describe actual mathematical practice? Does category theory or homotopy type theory provide a fully structural account for mathematics?
- Prof. Steve Awodey (Carnegie Mellon University)
- Dr. Jessica Carter (University of Southern Denmark)
- Prof. Gerhard Heinzmann (Université de Lorraine)
- Prof. Geoffrey Hellman (University of Minnesota)
- Prof. James Ladyman (University of Bristol)
- Prof. Elaine Landry (UC Davis)
- Prof. Hannes Leitgeb (LMU Munich)
- Dr. Mary Leng (University of York)
- Prof. Øystein Linnebo (University of Oslo)
- Prof. Erich Reck (UC Riverside)
Call for Abstracts
We invite the submission of abstracts on topics related to mathematical structuralism for presentation at the conference. Abstracts should include a title, a brief abstract (up to 100 words), and a full abstract (up to 1000 words), blinded for peer review. Authors should send their abstracts (in pdf format), together with their name, institutional affiliation and current position to firstname.lastname@example.org. We will select up to five submissions for presentation at the conference. The conference language is English.
Dates and Deadlines
Submission deadline: 30 June, 2016
Notification of acceptance: 31 July, 2016
Registration deadline: 1 October, 2016
Conference: 12 – 14 October, 2016
For further details on the conference, please visit: http://www.mathematicalstructuralism2016.philosophie.uni-muenchen.de/
The Emergence of Structuralism and Formalism, June 24- 26, 2016
PRAGUE, CZECH REPUBLIC
organized by Catholic Theological Faculty, Charles University and Institute of Philosophy, Czech Academy of Sciences, v.v.i.
The focal question of the workshop is how the nature of mathematics is regarded by representatives of formalism and structuralism. The conference language is English. To submit a proposal, please send a proposal of your paper to email@example.com
Proposals for papers should be prepared for anonymous review. Proposals should include title and abstract of the paper (maximum 500 words).
If you have inquiries about the conference or about the submission process, please write to firstname.lastname@example.org
SUBMISSION DEADLINE: April 30. 2016
Notification of acceptance on May 10. 2016.
The scheduled length of lectures is 30 minutes including approx. 10 minutes for discussion. Selected contributions will be published.
Call for Abstracts
Canadian Society for History and Philosophy of Mathematics Annual Meeting
University of Calgary, May 29-31, 2016
Special Session: Mathematics and Logic in the 19th and 20th Century
Kenneth May Lecturer: Dr. Jamie Tappenden, Department of Philosophy, University of Michigan
The CSHPM will be holding its 2016 Annual Meeting at the University of Calgary in conjunction with the 2016 Congress of the Humanities and Social Sciences. The meeting will be held Sunday through Tuesday, May 29-31, 2016.
Members are invited to present papers on any subject relating to the history of mathematics, its use in the teaching of mathematics, the philosophy of mathematics, or a related topic. Talks in either English or French are welcome.
Please send your title and abstract (200 words or less) in Word or in the body of an email by February 1, 2016 to:
For the Special Session:
Department of Mathematics
University of Wisconsin-Whitewater
Whitewater, WI 53190-1790
For the General Session:
Department of Mathematics & Statistics
University of Maine
Orono, ME 04469
With deep sadness we announce the sudden passing of Aldo Antonelli on October 11. The announcement from the UC Davis Department of Philosophy follows. If you would like to share your memories of Aldo or express your condolences, please do so at the UC Davis website.
Our colleague, friend and collaborator, Aldo Antonelli, passed away suddenly on Sunday, October 11, 2015 while bicycling in Sacramento, California. He is survived by his partner, Elaine Landry, brother David, sons Federico and Riccardo, and their mother Giovanna Fogli.
Aldo Antonelli was a professor of philosophy at the University of California, Davis. An expert in pure and applied logic, his research largely focused on issues in defeasible reasoning and non-monotonic logic. His more recent work in philosophy of logic was concerned with applications of generalized quantifier theory and abstraction principles to the foundations of arithmetic in the more general context of Fregean foundations, as well as making contributions to Frege scholarship.
Together with his partner and colleague, philosopher of mathematics Elaine Landry, Antonelli established philosophy of logic and mathematics as a focal point of scholarship in the Davis department. Antonelli was a member of the Association for Symbolic Logic, the American Philosophical Association, the Philosophy of Mathematics Association, and the Society for Exact Philosophy. He had served as coordinating editor of the Journal of Philosophical Logic and the Review of Symbolic Logic. He taught at Pittsburgh, Yale, Stanford and Michigan State, before joining the University of California, first at Irvine in 1998, and then moving to UC Davis in 2008.
Aldo’s self-description captures his spirit, focus, and sense of humor best:
I grew up in Torino, Italy, where I received my undergraduate education. After a brief stint in corporate R&D, I ended up in Pittsburgh, pursuing a graduate degree at Pitt. I taught here and there around the country for a few years before obtaining my first tenure track job. I then spent ten years at UC Irvine, including two years while on assignment abroad, before coming to Davis. My Erdös number is 4 (Paul Erdös to Joel Spencer to Nuel Belnap to Rich Thomason).
Contributions in Aldo’s memory may be made to a fund in support of graduate students working in logic and philosophy of logic. Please write checks to: UC Davis Foundation, marked “Aldo” and mail to: Chair, Department of Philosophy, One Shields Avenue, Davis CA 95616 USA. You may donate via credit card directly through an Antonelli Memorial Fund Giving page at the UC Davis website.