Meetings 1999-2000
Wednesday, May 3, 2000, 6:00-7:00 Dennes Room, 234 Moses Hall
Chris Pincock (Philosophy, Berkeley)
Carnap's Engagement with Russell: 1921-1928
In recent years a debate has begun concerning the nature of Rudolf Carnap's project in Der Logische Aufbau der Welt (Logical Structure of the World, 1928). Michael Friedman and Alan Richardson have initiated this debate by claiming that the Aufbau is best understood as a work that is firmly grounded in the neo-Kantian philosophy that dominated Germany at the time the book was written. They have made these claims in opposition to what is often termed "the received view" of the Aufbau. The received view, advocated by Quine and Nelson Goodman, sees the Aufbau as an attempt to carry out in detail Russell's proposals for the logical construction of our knowledge of the external world out of sense-data advocated in Russell's 1914 book Our Knowledge of the External World. On the received view, then, Carnap is concerned more with the traditional epistemological problems of the British empiricists. In my paper I argue that both sides of this debate have made serious errors in their interpretation of Russell. Drawing on unpublished correspondence and manuscripts, I argue that Russell exerted a crucial influence on Carnap in the 1920s and that central parts of the Aufbau are best understood in connection with Russell's own writings.
Wednesday, April 5, 2000, 6:00-7:00 Howison Philosophy Library, 305 Moses Hall
Jerrold Katz (Philosophy, Graduate Center, CUNY)
From the Philosophy of Mathematics to the Philosophy of Philosophy (meeting was cancelled due to illness)
The talk will survey a response to Benacerraf's criticism of mathematical realism in my book Realistic Rationalism, then responses to some critics, then an attempt to vindicate the idea of mathematical intuition, and finally a proposal about how a rationalist philosophy of philosophy can be grounded in a realist philosophy of mathematics.
Wednesday, March 1, 2000, 6:00-7:00 Dennes Room, 234 Moses Hall
Richard Tieszen (Philosophy, San Jose State University)
Gödel and the Intuition of Concepts
Gödel has argued that we can cultivate the intuition or 'perception' of abstract concepts in mathematics and logic. His ideas about the intuition of concepts are related to many other themes in his work, and especially to his reflections on the incompleteness theorems. I will describe briefly how Gödel's claims about the intuition of abstract concepts are related to some other themes in his philosophy of mathematics. I will then focus on a central question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that is based on the work of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. This talk is drawn from work-in-progress on Gödel's philosophy of mathematics, some of which has been published recently in the Bulletin of Symbolic Logic 4, 2 (1998), 181-203.
Wednesday, January 26, 2000, 7:00-8:00 Howison Philosophy Library, 305 Moses Hall
Dirk van Dalen (Philosophy, Universiteit Utrecht)
Ideas and notions underlying Brouwer's philosophy and mathematics (Cosponsored by the Department of Philosophy)
Brouwer's mathematical intuitionism is actually part of an overall view of man and the world. He based his views on the objects and methods of mathematics, logic, language, society on the primary sensations and experiences of the individual. There is a mystical flavour to the basic motivation, that dates back to his student years. Unusual as this may seem, it certainly was coherent, and it yielded strong results and methods in mathematics. In particular his mathematical universe contained objects (such as choice sequences) that, in combination with his notion of construction and proof, to establish facts that flatly contradicted classical mathematics., e.g. the continuity of all real functions.
Wednesday, December 8, 1999, 6:00-7:00 Room t.b.a.
Richard Zach (Logic, Berkeley)
Finitistic Consistency Proofs
Wednesday, November 3, 1999, 6:00-7:00 Howison Philosophy Library, 305 Moses Hall
John Etchemendy (Philosophy, Stanford University)
Reflections on Consequence
Wednesday, October 6, 1999, 6:00-7:00 Townsend Center Seminar Room 220 Stephens Hall
Steve Givant (Mathematics, Mills College)
Some unifying threads in Alfred Tarski's work
Alfred Tarski is one of the great figures in the history of logic, along with Aristotle, Gottlob Frege, and Kurt Goedel. His work covers an astonishing range of subjects: set theory, measure theory, topology, geometry, classical and universal algebra, algebraic logic, various branches of formal logic and metamathematics, philosophy, even economics. How did a logician end up working in so many different areas? Were there interconnections in his work that led him from one field to another? What drew him to set theory in the first place, and what drew him away from it a few years later? What sparked his interest in algebra and geometry? How did he become involved in the problem of defining truth? Why did he work so intensively in algebraic logic--a field that does not attract many logicians--and what did this work have to do with his other research? Just why did he go into logic, anyway? This talk will try to answer some of these questions.