Life Is Non-Boolean

George Boole (1815-1864) invented what we now call Boolean logic, which effectively assumes that all propositions are classifiable as either “true” or “false”, with no gradations of evidence or undecided cases. This provided the basis for formally defining logical operators in terms of how they transform what are called truth values, which are just the Boolean values of “true” and “false”. The use of so-called truth tables to define logical operators by cases is characteristic of what is today called “classical” logic.

Though it certainly has its uses in technical contexts, this kind of approach has been criticized as tacitly presupposing what has been called logical omniscience or the assumption of a closed world. For example, in computer science Boolean data types are used to represent things that are stipulated to have one of exactly two values. Then if we can rule out one, we can simply assume the other. This creates a closed world. “Omniscience” is implied by this kind of assumption.

The great developer of mathematical logic Gottlob Frege (1848-1925), at least at one point in his career, went so far as to argue that there are really only two distinct logical propositions: “true” and “false”. Depending one’s point of view, what I call real-world meanings are either reduced to nothing by this or are irrelevant to it.

From the point of view of “constructive” logic, on the other hand, there are infinitely many distinct propositions, distinguishable by the combination of what they presuppose and what they imply. It begins to be possible to reconstruct real-world meanings within logic instead of only outside of it.

In real life there are countless distinctions that are relevant and meaningful, and countless things that we simply don’t know. (See also Logic for People.)

Substance Also Subject

Hegel’s many references to Aristotle should help to clarify the Hegelian claim that “Substance is also Subject”. In particular, Aristotle’s own thesis of the identity of thought with the thing thought is relevant, as is his dialectical development of the different senses of ousia (“substance”) in the Metaphysics.

A thought for Aristotle is identical with its content. It just is a discursively articulable meaning, not a psychological event. What we care about in thought is shareable reasoning. Moreover, this shareable reasoning has a fundamentally ethical character.

Thought in this sense is essentially self-standing, and unlike the mental-act sense not dependent in the determination of its meaning on a “thinker” (who optionally instantiates it, and if so is responsible for the occurrence of a related event). This gives a nice double meaning to the autonomy of reason. (What such thoughts do depend on is other such thoughts with which they are inferentially connected.)

The primary locus of Aristotelian intellect is directly in shareable thoughts of this sort and their interconnection, rather than in a sentience that “has” them. Hegel adopts all of this.

Concepts in a unity of apperception are forms to be approached discursively, not mental representations or intentional acts. They are more like custom rules for material inference. The redoubling implied in apperception, like that of the Aristotelian “said of” relation, hints at the recursive structure of inferential articulation. The Hegelian Absolute, or “the” Concept, just nominalizes such an inferential coherence of concepts.

Thus, “Substance is also Subject” has nothing to do with attributing some kind of sentience to objects, or to the world. Rather, it is the claim that Substance properly understood (in the Aristotelian conceptual sense of “what it was to have been” a thing, rather than in the naive sense of a real-world object, or of a substrate of a real-world object, that Aristotle starts with but then discards) is already the right sort of thing to be able to play the functional role of a transcendental subject. A “Subject” for Hegel just is a concept or commitment, or a constellation of concepts and commitments. (See also Subject and Substance, Again; Substance and Subject.)

Consistent with this general approach, I consider the direct locus of the subject-function to be in things like Brandomian commitments and Kantian syntheses. The subject-function is also indirectly attributable to “self-conscious individuals” by metonymy or inheritance, and to empirical persons by a further metonymy or inheritance. (See also Subject; Substance; Aristotelian Dialectic; Brandom and Kant; Rational/Talking Animal; Second Nature.)