Lectures
Upcoming Lectures
Information about upcoming lectures will be made available in due course.
Past Lectures
December 8, 2011
Hanoch Ben-Yami (Budapest)
April 1, 2011
- 14 Gower Street, McFetridge Room
- 10.00 - 12.00 Ignasi Jané, "Attempt at a faithful interpretation of set theory" (Part II)
- 1.00 - 3.00 José Ferreirós, "Questioning the scope of logical theory: on first- and second-order quantification" (Part II)
- 14 Gower Street, McFetridge Room. Since space is limited, those who wish to attend should register before March 28 by emailing Salvatore Florio.
- 11.00 - 1.00 Ignasi Jané, "Attempt at a faithful interpretation of set theory" (Part I)
- Abstract. I will present Cantor's views about transfinite ordinal numbers, contrasting the original generating approach in Grundlagen with the abstraction view that he held afterwards. Then I will turn to Cantor's late proposal regarding the distinction between sets and inconsistent multiplicities, namely, that all the elements of a set coexist, but the objects in an inconsistent multiplicity cannot all exist together. This attempted explanation is worthless in the realist setting that Cantor countenanced when he proposed it, but, I claim, makes perfect sense (at least as it applies to multiplicities of ordinal numbers) in the early generating context. The problem is that it is unclear that number generation can be made sense of. That is what I will first attempt to do in order to develop the iterative conception of sets based on the generated ordinals. This will involve a discussion of how to understand the power set operation. My aim is to sketch an interpretation of set theory which (1) is faithful to set theory as it is developed by set theorists, with classical first-order logic as underlying logic, (2) is epistemologically sound, allowing, in particular, to see why the axioms are accepted, and (3) offers a clear explanation of the distinction between sets and proper classes.
- 3.00 - 5.00 José Ferreirós, "Questioning the scope of logical theory: on first- and second-order quantification" (Part I)
- Abstract. The two lectures will mainly revolve around the topics discussed in my paper 'The road to modern logic - an interpretation' (BSL, 2001), which deals with the philosophy of logic. At the center of interest will be the traditional, vexing question of how to delimit the logical constants - a question which, in my view, arises already with first-order logic. Reference will be made at several points to historical developments in logic during the 20th century. The discussion should help clarify several arguments that have been offered apropos SOL, in particular those questioning the admissibility (qua logic) of the "standard" semantics of higher-order logic.
- Main Building, Malet Street, Room 532
- 2.00 - 4.00 Harvey Friedman,“Simple Comprehension Axioms”
- Abstract. We show how the formal idea of a simple comprehension axiom (and axiom scheme) generates, exactly, various fragments of ZFC including ZF with weakened foundation. These kinds of results suggest a formal explanation for our adoption of the usual axiom systems, that provides an alternative to the traditional realist explanation. We conjecture that all of the main formal systems of f.o.m. are exactly generated by simple syntactic principles, including extensions of ZFC via basic large cardinal hypotheses.
- Main Building, Malet Street, Room 532
- 2.00 - 4.00 Harvey Friedman,“First, Second, and Higher Order Logic and Set Theory”
- Abstract. We survey the basic formulations and results concerning first, second, and higher order logic, and first, second, and higher order set theories, and their relationships. We will touch on some unexpected normal forms for existential third order sentences.
March 31, 2011
November 5, 2010