A = A is True.

In the 2nd half of the 20th century the American mathematician Haskell Curry and logician William Alvin Howard discovered an analogy between logical proofs and working computer programs. This is known as the Curry-Howard correspondence.

Mathematical proofs are working computer programs. https://en.wikipedia.org/wiki/Curry%E2% ... espondence

Therefore, if we can write a working computer program which asserts that A = A is false without producing an error then we have living proof contradicting the founding axiom of Classic/Aristotelian logic.

I hereby reject the law of identity, and give you the law of humanity: A = A is False.

A thing needs not be the same as itself!

Version 1: https://repl.it/repls/SuperficialShimmeringAnimatronics

Update1: I have INTENTIONALLY overridden the meaning of "=" and I am being accused of playing tricks.

You are missing the forrest for the trees. What is important is NOT that I am "cheating". What is important is that I have removed the "foundation" of classical logic and the skyscraper remains standing. The system did not explode ( https://en.wikipedia.org/wiki/Principle_of_explosion ). Because the explosion is contained by Chomsky's hierarchy! https://en.wikipedia.org/wiki/Chomsky_hierarchy

To the point: how can you call something a "LAW" of thought when it it plays no role in the functionality of the system? Computation is the "LAWS OF THOUGHT".

First Order Logic is a massive error! It is complete-but-undecidable. How do you THINK without making decisions?!?

Turing-completeness/equivalence is the bar for "reason": λ-calculus ⇔ λ-calculus ⇔ λ-calculus ⇔ λ-calculus ⇔ λ-calculus ⊇ Type theory ⊇ Mathematics

I will spell this out in English: Turing-completeness guarantees GLOBAL consistency. Type theory allows for the containment of LOCALIZED contradictions thus preventing explosions. This is why intuitionistic logic is vastly superior to any "complete" logic that is NOT Turing-complete.

Consistency paralyzes human thought! We are wildly inconsistent!

Being able to contain LOCAL inconsistencies actually allows for the GLOBAL system to become more and more consistent. This is completely and utterly counter-intuitive to most logicians!

##### EDIT 1 (changelog)

SpeakPigeon has embarked on a crusade to smear my character. So for the sake of transparency (and to let make an even bigger fool of himself) I have revised the code. I have nothing to hide

Version 2: https://repl.it/repls/TintedDefiantInstruction

Observe how the Aristotelian universe dehumanizes John and Jane

#### EDIT 2English: John is human.

Formalism: John = Human

False

English: Jane is human.

Formalism: Jane = Human

False

I am tightening the noose around the Pigeon's neck

Version 3: https://repl.it/repls/StrangeLiquidPolyhedron