nLab being

Idea

According to 道德經 (English translation following Xiao-Gang Wen here):

The nameless nonbeing is the origin of universe;

The named being is the mother of all observed things.

Within nonbeing, we enjoy the mystery of the universe.

Among being, we observe the richness of the world.

Nonbeing and being are two aspects of the same mystery.

From nonbeing to being and from being to nonbeing is the gateway to all understanding.

Rather similarly, according to (Hegel 12) pure being is the opposite of nothing whose unity is pure becoming.

		Dasein
becoming :	nothing	$\;\;\;\dashv$	being	: ceasing

According to the formalization of this proposed by (Lawvere 91), this is described by the adjoint modality

$$(\emptyset \dashv \ast)$$

of the idempotent monad constant on a terminal object $\ast$ and its left adjoint $\emptyset$.

In this interpretation any other adjoint modality of the form $(\Box \dashv \bigcirc)$ characterizes a more “determinate” form of being ( Dasein in the terminology of (Hegel 12)).

A category equipped with such a notion of being is, naturally, called a category of being.

Related concepts

• ontology, metaphysics

• category of being

• Aufhebung

• modality

• beable

• existential quantifier

References

• Hegel, Science of Logic, Volume One: The Objective Logic, Book One, The Doctrine of Being, Chapter 1 Being

• Bill Lawvere, Some Thoughts on the Future of Category Theory (1991)

• Hermann Grassmann, Ausdehnungslehre, 1844

• German Wikipedia, Sein