## Winter 2011 - Topology and Psychoanalysis – From Predicate Logic/Set Theory To Topo-logic/Category Theory

(topology and psychoanalysis)

**Theory of Symbolism Winter 2011 Semester:**

**From Classical Predicate Logic and Set Theory **

**To a Topo-logic and a Theory of Categories.**

**Time:** From 12:00 to 3:00 Saturdays - Begins Jan. 29th / Ends May 28th

**Place:** Santa Monica

**Duration of Seminar:** 5 weeks

**Frequency:** Once per month (Last Saturday of every month).

**Open to those enrolled in the Sclinic, Scholarship Recipients, and Guests (invites from the General Public)**

Our Fall 2010 Seminar began by introducing an analytic theory of the symbol in passing from* A**Theory of Symbolism* in Jone's critique of Jung; we concluded with Lacan's critique of Jones (*In Memory of Ernest Jones*) such that the reference of a symbol, the phallus in question, is revealed to no longer be a positive object (the penis) in a scientific and biological investigation, but its lack and resistance to such an investigation.

Lacan's critique and reconstruction of an analytic theory of the symbol is important because it provides the basis for a critique of the post- and neo-freudians, from Klein to Bion, but opens up a path to the contemporary theories of the symbol in logic and mathematics, most particularly in the work of Pierce, Frege, and the modern category theorists. It is the preponderant problem of reading and writing a symbol of lack that situates both an impossibility of Science and a definition of logic as *'a writing of the real'*.

In our Winter 2011 Seminar we will begin where we left off: by introducing a theory of predicate logic and sets; then showing how their paradoxes and reformulation provides the framework for both the contemporary theory of categories and a topo-logic (or theory of *topoi*). In order to situate *'a writing of the real'*, the seminar will conclude with an introduction to both the completeness and incompleteness theorems of Gödel.

Though our seminar is introductory in its scope and open to the debutant, it is not a vulgarization. We will use the introductory text, *Language, Proof, and Logic *by J. Barwise as a basis from which to pass from a theory of propositions, to predicates, then a theory of sets. By proceeding with the antinomies and paradoxes of such theories, we are led quite naturally to the theory of categories and topoi – which will provide the basis for the Summer 2011 Immersion.

Those attending would profit from buying the book and reading chapters 1-8 on propositional logic. A CD is included in the purchase price of the book that includes exercises that should be attempted.The seminar will assume to some extent this work in propositional logic has been attempted without necessarily having been achieved. This much said, the actual work of the seminar consists in the chapters 9–19 on predicate logic and set theory.

Anyone with questions on the form or content of the course is invited to address the secretary at: *PLACE@Topoi.net*

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