Lecture
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7.7.2014

Session one: Diagonalization in the Space of Reasons (9:00-12:00)

The notion of "the space of reasons" -- if taken as more than a figure of speech – makes demands on reasons' structure and forms of articulation. And, conversely, how we conceive the structure of reasoning constrains our efforts to conceive the "space" or horizon in which they unfold. In the first session of this seminar, I will be examining, in as distilled and minimalistic a fashion as possible, a certain kind of conflict that happens between the structure of reason -- as articulated in mathematical logics -- and the notion of a "space of reasons", under the aegis of fixed point phenomena and the mode of argumentation these phenomena enable: diagonalization.

It is to diagonal arguments that we owe the most striking antinomies and paradoxes that mathematical logic has discovered. Frequently stemming from our simplest and most intuitively transparent concepts, these paradoxes invite comparison with the Kantian antinomies, and the historically predominant reaction to these discoveries has been overwhelmingly "Kantian" in spirit: restricting the jurisdiction of our discourse, refusing to totalise the universe to which it refers, and opting instead for its stratification. In the margins of mathematical history, however, we can detect other "orientations of thought" (to borrow an expression from Badiou). These include efforts towards a roughly "Hegelian" way of thinking through the paradoxes of diagonalization. At their best, these efforts yield potent criticisms of the "Kantian" orientation in semantics and logic, and trace the outlines what "dialectical logic" might mean today.

The aim of this first session will be to first examine, and then generalize the concept of diagonalization -- so that it might be mobilized, philosophically and somewhat hazardously, outside of mathematics -- and then to do the same for the various "orientations of thought" that have arisen in response to fixed point phenomena and diagonal arguments, so that they might later be recognized and redeployed elsewhere.

Session two: Diagonalization in the Space of Sex (14:00-17:00)

This is what we will try to do in our second session: recognize and redeploy these "orientations of thought" on the terrain of sexual politics. In particular, we will examine the metamorphosis of the concept of sex since the mid-twentieth century, its splitting into the notions of sex and gender, and aspects of the debates that have resulted between different factions of feminism, psychoanalysis, and gender theory. I am interested in seeing whether these metaphorphoses and conflicts can be understood as reactions to a "diagonal" moment in the history of sexuality, and, again, whether it is possible to describe a dialectical orientation towards sex on this basis -- one that might stand as an alternative to the liberal semantics of gender, and the patriarchical fetishization of the "fixed points of sexuation".

The motive for articulating such a "dialectical" position with respect to sex is, primarily, political: the battlefield, here, is the cultural terrain of transsexuality, precariously stationed between a patriarchical ideology that makes a mystical fetish of the transsexual as the fixed point of castration in the shape of The Woman (while conveniently, by and large, ignoring trans men), a liberal ideology of "gender identity" that stratifies and diversifies the semantics of patriarchy in a classical fashion without essentially challenging it, and the radical feminist opponents of both trends, for whom the transsexual is only ever a reflection of the systems that subjugate them. The idea here is that if transsexuals have been ideologically stationed at a site where patriarchical ideology ensnares itself, or encounters its contradictory fixed-points, then perhaps they are also in a good position to advance a dialectical reconfiguration of that ideology, rather than acceed to its liberal stabilization with a new semantics of gender. Formally speaking, my guiding thread in this experiment will pass between Sartre's dialectic of reflection, and the Lacanian mathemes of sexuation, taken together as an informal schema onto which certain mathematical analogies can be mapped.

The notion of "the space of reasons" -- if taken as more than a figure of speech – makes demands on reasons' structure and forms of articulation. And, conversely, how we conceive the structure of reasoning constrains our efforts to conceive the "space" or horizon in which they unfold. In the first session of this seminar, I will be examining, in as distilled and minimalistic a fashion as possible, a certain kind of conflict that happens between the structure of reason -- as articulated in mathematical logics -- and the notion of a "space of reasons", under the aegis of fixed point phenomena and the mode of argumentation these phenomena enable: diagonalization.

It is to diagonal arguments that we owe the most striking antinomies and paradoxes that mathematical logic has discovered. Frequently stemming from our simplest and most intuitively transparent concepts, these paradoxes invite comparison with the Kantian antinomies, and the historically predominant reaction to these discoveries has been overwhelmingly "Kantian" in spirit: restricting the jurisdiction of our discourse, refusing to totalise the universe to which it refers, and opting instead for its stratification. In the margins of mathematical history, however, we can detect other "orientations of thought" (to borrow an expression from Badiou). These include efforts towards a roughly "Hegelian" way of thinking through the paradoxes of diagonalization. At their best, these efforts yield potent criticisms of the "Kantian" orientation in semantics and logic, and trace the outlines what "dialectical logic" might mean today.

The aim of this first session will be to first examine, and then generalize the concept of diagonalization -- so that it might be mobilized, philosophically and somewhat hazardously, outside of mathematics -- and then to do the same for the various "orientations of thought" that have arisen in response to fixed point phenomena and diagonal arguments, so that they might later be recognized and redeployed elsewhere.

Session two: Diagonalization in the Space of Sex (14:00-17:00)

This is what we will try to do in our second session: recognize and redeploy these "orientations of thought" on the terrain of sexual politics. In particular, we will examine the metamorphosis of the concept of sex since the mid-twentieth century, its splitting into the notions of sex and gender, and aspects of the debates that have resulted between different factions of feminism, psychoanalysis, and gender theory. I am interested in seeing whether these metaphorphoses and conflicts can be understood as reactions to a "diagonal" moment in the history of sexuality, and, again, whether it is possible to describe a dialectical orientation towards sex on this basis -- one that might stand as an alternative to the liberal semantics of gender, and the patriarchical fetishization of the "fixed points of sexuation".

The motive for articulating such a "dialectical" position with respect to sex is, primarily, political: the battlefield, here, is the cultural terrain of transsexuality, precariously stationed between a patriarchical ideology that makes a mystical fetish of the transsexual as the fixed point of castration in the shape of The Woman (while conveniently, by and large, ignoring trans men), a liberal ideology of "gender identity" that stratifies and diversifies the semantics of patriarchy in a classical fashion without essentially challenging it, and the radical feminist opponents of both trends, for whom the transsexual is only ever a reflection of the systems that subjugate them. The idea here is that if transsexuals have been ideologically stationed at a site where patriarchical ideology ensnares itself, or encounters its contradictory fixed-points, then perhaps they are also in a good position to advance a dialectical reconfiguration of that ideology, rather than acceed to its liberal stabilization with a new semantics of gender. Formally speaking, my guiding thread in this experiment will pass between Sartre's dialectic of reflection, and the Lacanian mathemes of sexuation, taken together as an informal schema onto which certain mathematical analogies can be mapped.