The Laws of Logic

Informal description and formal notation of the laws of dialectical thought.

The Law of Identity

Something $(x)$ is what it is.

$\forall x, x = x$

or in set theory:

$\emptyset \cup X = X = X \cap U$

something between nothing $\emptyset$ and everything $U$.

Note that this does not exclude nothing and everything as sets (a type of identity).

The Law of Non-Contradiction

Something (x) is not what it is not.

$\forall x, x \neq \neg x$

The Law of Excluded Middle

Any proposition $(p)$ is either true or false, not something in the middle or neither.

$p \oplus \neg p$