Michael D. Resnik Noûs, Vol. 15, No. 4, Special Issue on Philosophy of Mathematics. (Nov., 1981), pp. 529-550. and Michael D. Resnik Noûs, Vol. 16, No. 1, 1982 A. P. A. Western Division Meetings. (Mar., 1982), pp. 95-105.

The two papers provide a detailed structuralist account. We'll also look at the paper by Charles Parsons, which will be available in the Philosophy Department Office (213 Social Sciences) and at WhatAbstractObjectsAre. On infinite ordinals, we'll read some excerpts from my book, Understanding the Infinite. This is not exactly the published version, though it is close, and I'll remove the link after the semester.

Thr links may not work, since you need authorized access to JSTOR to use them. JSTOR is available to U of A students, and so, if the links don't work, go to http://www.jstor.org and do a search.

ResnikandShapiroOnStructuralism

I plan to discuss how both these noted structuralists address ontology in their respective version of structuralism. I will only comment on Resnik’s article “Mathematics as A Science of Patterns: Ontology and Reference” and a chapter on structures in Shpario’s book, Philosophy of Mathematics.

-- JacobCaton? - 25 Apr 2005

In the Routledge Encyclopedia, reference is made to how Poincare's recurrence theorem contributed to the advancement of chaos theory. I posit then that we make chaos theory a focus. I'm intrigued by how something incorporating the notions of aperiodicty and unpredicatiabiltiy can have applications to math in the sense of how it is the study of patterns. Perhaps we can emerge with new questions that cause us to think differently about the ideas we have already covered in the philosophy of math as well as the behavior of math overall in nature - and we can begin with how Poincare provided the groundwork. If this is found to be without interest to the group, I propose a more lofty and noble subject matter: determining the mathematical underpinnings of how psychics don't exist because Las Vegas does.

-- CarlKlaus? - 18 Feb 2005

(1) I'd love to do some discussions about transcendental numbers and the various stages of infinity, and the philosophical history leading up to their discovery and their use in higher level math.

(2) It'd also be cool (yes, 'cool') to have at least a one-session discussion on the birth of the concept of an "effective procedure" and conceivable nonconstructive procedures. Perhaps it'd be best to tie it into Carnap's The Logical Syntax of Language.

-- SethTurtle? - 09 Mar 2005

Multiply-valued logics Look at papers I presented at Arché --EdHopkins 21 March 2005

So far,