Faculty of Philosophy

Mathematical Logic Seminar

Mathematical Logic Seminar

Prof. Michael Potter

Lent Term 2012: Thursdays at 4.30pm

Philosophy Faculty Common Room

Intended audience

Part II Mathematical Logic and philosophy graduate students.

Arrangements

The first two weeks of term will be visiting speakers. After that, each week's seminar will focus on one or two papers, copies of which will be available in advance. Anyone who attends should be willing, if asked, to do a short summarizing presentation once during the term.

Provisional programme

    Visiting speakers

  1. Juliette Kennedy (Helsinki), Logical pluralism and meaning variance in the set-theoretic context

    Abstract: We examine Quine's dictum "A change in logic is a change of meaning" from the set-theoretic point of view. In particular, we consider various canonical concepts, e.g. the notion of constructibility, under permutations of the underlying logic. We show that the constructible hierarchy does not seem very sensitive to the underlying logic. We suggest this is evidence for the claim that logical pluralism does not necessarily involve meaning variance.

  2. Jouko Väänänen (Helsinki), Second order logic, set theory and foundations of mathematics

    In a metamathematical investigation first order logic and second order logic look very different. The rich model theory of the former is dominated by non-categoricity results going back to Skolem, while the latter is celebrated for its ability to characterize important mathematical structures categorically. I will argue in my talk that the difference is much smaller if first order set theory or second order logic is used foundationally. I will pay special attention to the substance and impact of categoricity results. I will also present some recent results on the model theory of second order logic and will discuss their possible impact.

    3. The iterative conception of set

  3. George Boolos, `The iterative conception of set', J. Phil., 68 (1971) 215-31
  4. Michael Potter, `More thoughts on replacement' (unpublished draft)

    5. First and second order logic

  5. Benacerraf, P. ‘Skolem and the sceptic’, Arist. Soc. Supp. Vol., 59 (1985), 85-115; repr. in S. Shapiro, ed., The Limits of Logic (Aldershot: Dartmouth, 1996)
  6. George Boolos, On second order logic, J. Phil., 72 (1975), 509-27

    7. Gödel's Theorem

  7. Curtis Franks, `The Gödelian inferences', History and Philosophy of Logic 30 (2009) 241-56
  8. Hilary Putnam, `Minds and machines', in his Philosophical Papers, Vol 2 CUP, 1975)

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