Architectonics: Logic and Metaphysics

Logic affects metaphysics#

It is often overlooked that the architectonic construction of logic drastically affects metaphysics, and induces tension that may lead to failure in metaphysics. I'll briefly illustrate how this works. (This really needs to be explicated and refined, but here I'm just trying to give a sketch.)

Example: Aristotelian logic#

The edifice of Aristotelian logic is organized according to several architectonic principles:

• Subject-predicate structure: a truth-bearer is always a sentence composed of a subject and a predicate.
• Affirmation and denial: affirmation and denial are given equal footing. A premise in a syllogism is always a sentence affirming or denying something of something. A conclusion, will always be either an affirmation or a denial.
• Quantification: affirmations and denials are themselves always either universal or particular.

Subject-predicate structure leads to a kind of metaphysics that treats existence/being as an act. Existence is not "there is something", but "something exists". But this is in tension with affirmation and denial: If what is ‘exists’, does what is not ‘not exist’? How can we talk meaningfully about what is not? If truth reflects what is, then is falsity about what is not?

In fact there's a further internal tension in Aristotle's logic: syllogism doesn't respect the syntactic principle of subject-predicate composition of sentences. In a syllogism, a term can be a subject in a premise, but a predicate in another premise. Thus we call Aristotle's logic term logic. Term logic is - in tension with subject-predicate logic - a logic about things in the world, since term logic allows conversion (transposition of subject and predicate) and hence allow empty terms (given all A are B, then some B are A, but what if there is no any A?), which leads to problem if it is treated as something that is not about things in the world.

Quantification leads to the sharp distinction between universal and particular, which further extends to the sharp distinction between abstract and concrete, in metaphysics. Especially since Aristotle's logic is at the same time term logic and subject-predicate logic, it is at the same time syntactical and "thingy" (semantic), the phenomenal and the noumenal are heavily confused when metaphysics is based upon Arostotelian logic.