Professor Neil Tennant
Friday, October 2, 2020 - 3:30pm*
"Natural Deduction for Pasigraphs"
Set theory is often set out with an austerely primitive vocabulary. But set theorists and ordinary mathematicians making use of set-theoretic ideas employ a host of already familiar-looking defined expressions in ‘informally rigorous’ set theory, such as the familiar ones for ‘is a subset of’ and ‘the power set of’.
These defined expressions are called pasigraphs. They can be names, function signs, or predicates. They live at a level of easy conceptual grasp. They are the bread-and-butter of ordinary mathematical discourse, especially in set theory itself.
Pasigraphs are indispensable for communicating in a conveniently condensed fashion what would otherwise be extremely cumbrously expressed set-theoretical thoughts. The ‘atomicizing inferentialist’ seeks to frame rules of introduction and elimination for these defined expressions, so that they can be understood as being employed as ‘local primitives’ in mathematical discourse of the normal explicit texture. We need to get to grips with pasigraphs directly. Using rules furnished specifically for pasigraphs enables one to be uniform and thorough in regimenting informally rigorous set-theoretical proofs as formal, logical proofs.
We shall illustrate natural deduction methods for pasigraphs in set theory; but the methods are completely general. They apply to all branches of mathematics. We shall also explain some self-imposed methodological constraints on the overall project.
Professor Justin D'Arms
Friday, November 13, 2020 - 3:30pm*
Professor Tristram McPherson & Professor David Plunkett
December 4, 2020 - 3:30pm*
The past twenty years have witnessed an extraordinary revival of interest in metanormative non-naturalism. Despite this interest, it is still unclear how to understand the distinctive metaphysical commitments of this view. In this paper, we first explain why the task of carefully formulating non-naturalism’s metaphysical commitments is both challenging and a crucial task for the non-naturalist. We then examine recently influential ground-theoretic discussions of how to understand the non-naturalists’s metaphysical commitments, offered by Gideon Rosen, Stephanie Leary, and Selim Berker. We argue that each of these accounts overgeneralizes in implausible ways. We argue that this is not simply an artifact of the specific proposals. Rather, it is a predictable consequence of attempts to formulate non-naturalism in terms of grounding. We conclude by suggesting a more promising alternative, and drawing some general methodological lessons.
Graduate Student Workshop
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Minorities and Philosophy (MAP)
MAP is an inclusive group that considers issues pertaining to the status of minorities in philosophy. Philosophy faculty, graduate students, and undergraduate majors are welcome to attend.
Society for the History of Modern Philosophy (SHMP)
The Society for the History of Modern Philosophy organizes a number of events that facilitate learning about philosophy during the modern period. Currently there are three different groups associated with the society:
1) Reading group: currently reading women philosophers from the early modern period
2) Workshop: venue for graduate students and faculty to present work on the history of modern philosophy
3) Latin reading group: focusing on philosophical latin from the 16th and 17th centuries
Society for Mathematical Logic and Foundational Studies (SMLFS)
The Society for Mathematical Logic and Foundational Studies seeks to create a forum for dialogue on the subject of Mathematical Logic and Foundations, and to collaborate with people from all disciplines interested in such matters. SMLFS is primarily a reading group, but also invites speakers annually. The group is open to all interested participants.
Consilience: The CCBS Student Organization Reading Group
The CCBS Student Organization is an interdisciplinary reading group for undergraduate and graduate students with an interest in scientific approaches to mental and physical phonomena. Anyone interested in scientific cognition, mind, psychology, agency, etc. should feel encouraged to come! For more information, please visit CCBS Facebook page.