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*
(*Zoom info to follow)
Graduate Student Workshop
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Minorities and Philosophy (MAP)
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