Signifier and Letter in Set Theory and Logic
(set)

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From L'être et l'événement to Letter and Signifier


Instructor R. T. Groome

PART I. A Psychoanalytic Reading of Being and Event by A. Badiou

1- Preliminary Argument
2- The Undefined Matheme: From Stenography To Abbreviation Symbol
3- From Undefined Matheme To Undefined Set
4- The Undefined Set: The Repetition Of One As 'Being and Event'
5- Informal Construction of the Matheme as both Signifier-Letter
6- Synoptic View On A Theory Of The Signifier As Collection
7- Synoptic View On A Theory of the Signifier as Anti-Philosophy
8- Introductory Exercises
9- Structure Refused: Badiou's conception of an ordered pair.
10- From Politics in the Discourse of Philosophy To Science in the Discourse of Psychoanalysis

Part II: A Psychoanalytic Construction Of A Theory Of Sets As Abbreviation In A Model

1- The Paradox of Russell and Cantor
2- Zermelo and Russell resolutions: stratification and types.
3- Fraenkel's extension of Zermelo: the replacement principle
4- The Critique of Scholem: Definition and Models of Sets
5- Two Types of Selection: The Principle Of Choice And Forcing.

ABSTRACT OF COURSE

The course proceeds into two times: the first part is a critique of the notion of set and matheme as it is proposed in Badiou's L'être et L'événement. In putting forward this critique I will be at the same time putting forward a more just reading of set in terms of a theory of collections and signifiers in the manner of Lacan. In order to facilitate our introduction it is presented in ordinary language throughout Part I. In Part II, we will present a properly formal and structural investigation.


PART I-

1- Preliminary Argument

Since Lacan, psychoanalysts have become interested in set theory, topology, and knot theory as a new and rigorous way of constructing a practice and theory. In reconstituting the field of the clinic and its didactic in this way, analysts are discovering numerous intersections with fields of rationality that had previously been viewed as mere problems of technique or philosophy.

One such intersection began in France quite some time ago, when the French philosopher, Alain Badiou, began an ambitious project of reworking classical questions of philosophy – Why is there something rather than nothing at all? – in the fields of set theory and logic. One could show that Badiou's project in the field of philosophy is not a chance encounter with the psychoanalytic project elaborated by Lacan: both men have proposed that the future of any possible progress in psychoanalysis and philosophy lies in an effective (Wirklichkeit) and material reworking through mathematics and logic.
My aim here is not to justify this intersection of fields, nor to describe summarily their procedures, but instead to underline by what odd turn of events such an intersection open up foundational problems, rather than constituting a new or a radical departure in the domain of psychoanalysis or philosophy. Assuming it resolved that philosophy and psychoanalysis have different foundations and fields of application, the question remains of how a work in set theory and logic differs once constructed according to the suppositions of their respective fields. Yet, if one follows the current publications on psychoanalysis and philosophy there is the tendency to amalgamate Lacan and Badiou, while relegating this 'odd turn of events' to the fashionable non-sense of 'French philosophy.

Thus, before introducing our set theoretical constructions in Part II, we must take a few precautions in Part I to disentangle the amalgamations and journalistic trends . My main preoccupation is not, however, one of making distinctions between oeuvres or disciplines, such a reading would remain infinite in its detail, rather my fundamental question is centered on what authorizes us today, in the field of psychoanalysis, to consider as essential a work in topology, set theory, and logic?

Rather than respond directly, perhaps it would be better, given the time and limits of this article, to use the current amalgamation and read Lacan and Badiou together, in order to crack one nut, with two stones.

To begin to respond, it will suffice to begin with Badiou's celebrated Being And Event (L'être et L'événement; LEE) [1]. Our first goal will be to determine with precision the reference to 'set' and 'matheme' theory in the general economy of LEE. To Badiou claims, we are reading a philosophical treatise on the one and multiple on whose basis it is possible to make the assertion that "ontology=mathematics". What is perhaps different in the way I will approach his text, is that outside of these preliminary comments, I will not be interested in either the philosophical or political goals he sets for his method, only what is constructible from the material provided from the text itself. This narrows down the field quite a bit and, no doubt, some may charge that the author has modified his methodology and themes since the publication of Logiques du Mondes. But this is precisely what I am seeking to avoid: a continual deferral of construction where it is possible to keep claiming one is "introducing" something or has changed their position with regard to a future text. My reading of the set theoretical propositions in LEE can not be exhaustive, but my economization of focus on the effective dimensions of LEE will not be hindered by such deferrals. For the claims that are being made in LEE are explicit and important enough to warrant more than a cursory look at their literal and set theoretical methods. Indeed, Badiou has proposed to call the set theoretical formulas in LEE "mathemes of the real" . It is our task in Part I, to introduce what is at stake in the use of these terms.

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