Lecture
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3.7.2014

Navigating Reason: Duality, Dialectics, and Speculation

It is pretty much a platitude that, in the attempt to erect certain boundaries of thought, thought extends beyond those boundaries (e.g. Lawvere's construction of the generic structure of Cantor's, Russell's, Tarski's, Godel's arguments). Typically, these have been understood to be "mere pathologies", which engender contradiction and inconsistency that can be excised from thought before thinking even has chance to begin. Logic is supposed to range over all "things"; a kind of semantic transcendence, prior to reasoning (emptied of navigational possibility). Indeed, there are entire sophistical industries for the erection of prophylactic blockages to the horror of the (internally) inconceivable (Kantian nihil ulterius).

This strategy of confinement maintains that logic is based on a notion of Truth, so that the foundation of logic is outside of logic itself in pre-formatted metaphysics. Here, I pursue the idea that we can only recover the constructive role of reasoning by understanding that fundamental inconsistency does not reside at the edges of thought (shores of the island), rather, it ultimately uproots the (classical) bedrock of thinking itself. Indeed, grounding thought upon Truth is simply metaphysical fiat with the supposed formatting of semantics prior to the act of reasoning itself. In this respect, the ultimate (read incredulous) definition of truth is Tarski's: "A is true iff true-A". This essentialised truth is then nested in a hierarchy of metalanguages since truth can not speak of itself in the language in which it resides (injunction: do not speak of truth!).

Instead, we consider thinking and logic to be acts, where "truth is not a minted coin that can be given and pocketed ready-made" (Hegel). This is Hegel's insight: that the content of a concept is not the sort of thing that is containable inside the neat compartmentalisability of truth-conditions or discrete semantics. And, "logic is not a thinking about something which exists independently as a base for our thinking and apart from it" (Hegel). There is an inconsistent ground of concepts which is universal; not excisable; not containable. The imagination is limited in ways that concepts are not.

The picture that we sketch develops an account of logic and reasoning that is grounded in the normative relation of preclusion over assertion and denial in dialogue. With this in place, I show that, rather than ground logic in truth, instead truth can be constructed from the (partial) coherence of inference. I then construct a notion of "paracoherence" (neither completeness nor consistency are assumptions), with a Galois connection between the dual structures of assertions and denials. Paracoherence is a non-equilibrium state, which is the motor of a logic of speculation: an emancipation of thought from within thought itself. Given this, (and contra Kant), we have a generic navigation structure which does not require the absolutisation of any one logical structure.

It is pretty much a platitude that, in the attempt to erect certain boundaries of thought, thought extends beyond those boundaries (e.g. Lawvere's construction of the generic structure of Cantor's, Russell's, Tarski's, Godel's arguments). Typically, these have been understood to be "mere pathologies", which engender contradiction and inconsistency that can be excised from thought before thinking even has chance to begin. Logic is supposed to range over all "things"; a kind of semantic transcendence, prior to reasoning (emptied of navigational possibility). Indeed, there are entire sophistical industries for the erection of prophylactic blockages to the horror of the (internally) inconceivable (Kantian nihil ulterius).

This strategy of confinement maintains that logic is based on a notion of Truth, so that the foundation of logic is outside of logic itself in pre-formatted metaphysics. Here, I pursue the idea that we can only recover the constructive role of reasoning by understanding that fundamental inconsistency does not reside at the edges of thought (shores of the island), rather, it ultimately uproots the (classical) bedrock of thinking itself. Indeed, grounding thought upon Truth is simply metaphysical fiat with the supposed formatting of semantics prior to the act of reasoning itself. In this respect, the ultimate (read incredulous) definition of truth is Tarski's: "A is true iff true-A". This essentialised truth is then nested in a hierarchy of metalanguages since truth can not speak of itself in the language in which it resides (injunction: do not speak of truth!).

Instead, we consider thinking and logic to be acts, where "truth is not a minted coin that can be given and pocketed ready-made" (Hegel). This is Hegel's insight: that the content of a concept is not the sort of thing that is containable inside the neat compartmentalisability of truth-conditions or discrete semantics. And, "logic is not a thinking about something which exists independently as a base for our thinking and apart from it" (Hegel). There is an inconsistent ground of concepts which is universal; not excisable; not containable. The imagination is limited in ways that concepts are not.

The picture that we sketch develops an account of logic and reasoning that is grounded in the normative relation of preclusion over assertion and denial in dialogue. With this in place, I show that, rather than ground logic in truth, instead truth can be constructed from the (partial) coherence of inference. I then construct a notion of "paracoherence" (neither completeness nor consistency are assumptions), with a Galois connection between the dual structures of assertions and denials. Paracoherence is a non-equilibrium state, which is the motor of a logic of speculation: an emancipation of thought from within thought itself. Given this, (and contra Kant), we have a generic navigation structure which does not require the absolutisation of any one logical structure.