Suspicion on Consciousness as an Immanent Derivative

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The category of the subject (like that of the object) has no place in an immanent world. There can be no transcendent, subjective essence. What, then, is the ontological status of a body and its attendant instance of consciousness? In what would it exist? Sanford Kwinter (conjuncted here) here offers:

It would exist precisely in the ever-shifting pattern of mixtures or composites: both internal ones – the body as a site marked and traversed by forces that converge upon it in continuous variation; and external ones – the capacity of any individuated substance to combine and recombine with other bodies or elements (ensembles), both influencing their actions and undergoing influence by them. The ‘subject’ … is but a synthetic unit falling at the midpoint or interface of two more fundamental systems of articulation: the first composed of the fluctuating microscopic relations and mixtures of which the subject is made up, the second of the macro-blocs of relations or ensembles into which it enters. The image produced at the interface of these two systems – that which replaces, yet is too often mistaken for, subjective essence – may in turn have its own individuality characterized with a certain rigor. For each mixture at this level introduces into the bloc a certain number of defining capacities that determine both what the ‘subject’ is capable of bringing to pass outside of itself and what it is capable of receiving (undergoing) in terms of effects.

This description is sufficient to explain the immanent nature of the subjective bloc as something entirely embedded in and conditioned by its surroundings. What it does not offer – and what is not offered in any detail in the entirety of the work – is an in-depth account of what, exactly, these “defining capacities” are. To be sure, it would be unfair to demand a complete description of these capacities. Kwinter himself has elsewhere referred to the states of the nervous system as “magically complex”. Regardless of the specificity with which these capacities can presently be defined, we must nonetheless agree that it is at this interface, as he calls it, at this location where so many systems are densely overlaid, that consciousness is produced. We may be convinced that this consciousness, this apparent internal space of thought, is derived entirely from immanent conditions and can only be granted the ontological status of an effect, but this effect still manages to produce certain difficulties when attempting to define modes of behavior appropriate to an immanent world.

There is a palpable suspicion of the role of consciousness throughout Kwinter’s work, at least insofar as it is equated with some kind of internal, subjective space. (In one text he optimistically awaits the day when this space will “be left utterly in shreds.”) The basis of this suspicion is multiple and obvious. Among the capacities of consciousness is the ability to attribute to itself the (false) image of a stable and transcendent essence. The workings of consciousness are precisely what allow the subjective bloc to orient itself in a sequence of time, separating itself from an absolute experience of the moment. It is within consciousness that limiting and arbitrary moral categories seem to most stubbornly lodge themselves. (To be sure this is the location of all critical thought.) And, above all, consciousness may serve as the repository for conditioned behaviors which believe themselves to be free of external determination. Consciousness, in short, contains within itself an enormous number of limiting factors which would retard the production of novelty. Insofar as it appears to possess the capacity for self-determination, this capacity would seem most productively applied by turning on itself – that is, precisely by making the choice not to make conscious decisions and instead to permit oneself to be seized by extra-subjective forces.

Category Theory of a Sketch. Thought of the Day 50.0

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If a sketch can be thought of as an abstract concept, a model of a sketch is not so much an interpretation of a sketch, but a concrete or particular instantiation or realization of it. It is tempting to adopt a Kantian terminology here and say that a sketch is an abstract concept, a functor between a sketch and a category C a schema and the models of a sketch the constructions in the “intuition” of the concept.

The schema is not unique since a sketch can be realized in many different categories by many different functors. What varies from one category to the other is not the basic structure of the realizations, but the types of morphisms of the underlying category, e.g., arbitrary functions, continuous maps, etc. Thus, even though a sketch captures essential structural ingredients, others are given by the “environment” in which this structure will be realized, which can be thought of as being itself another structure. Hence, the “meaning” of some concepts cannot be uniquely given by a sketch, which is not to say that it cannot be given in a structuralist fashion.

We now distinguish the group as a structure, given by the sketch for the theory of groups, from the structure of groups, given by a category of groups, that is the category of models of the sketch for groups in a given category, be it Set or another category, e.g., the category of topological spaces with continuous maps. In the latter case, the structure is given by the exactness properties of the category, e.g., Cartesian closed, etc. This is an important improvement over the traditional framework in which one was unable to say whether we should talk about the structure common to all groups, usually taken to be given by the group axioms, or the structure generated by “all” groups. Indeed, one can now ask in a precise manner whether a category C of structures, e.g., the category of (small) groups, is sketchable, that is, whether there exists a sketch S such that Mod(S, Set) is equivalent as a category to C.

There is another category associated to a sketch, namely the theory of that sketch. The theory of a sketch S, denoted by Th(S), is in a sense “freely” constructed from S : the arrows of the underlying graph are freely composed and the diagrams are imposed as equations, and so are the cones and the cocones. Th(S) is in fact a model of S in the previous sense with the following universal property: for any other model M of S in a category C there is a unique functor F: Th(S) → C such that FU = M, where U: S → Th(S). Thus, for instance, the theory of groups is a category with a group object, the generic group, “freely” constructed from the sketch for groups. It is in a way the “universal” group in the sense that any other group in any category can be constructed from it. This is possible since it contains all possible arrows, i.e., all definable operations, obtained in a purely internal or abstract manner. It is debatable whether this category should be called the theory of the sketch. But that may be more a matter of terminology than anything else, since it is clear that the “free” category called the theory is there to stay in one way or another.