You keep claiming expert opinions, but you do not provide citations or references nor do you bring your experts to defend their positions.Speakpigeon wrote: ↑Sun Mar 03, 2019 12:14 pmYet another expert opinion:Logik wrote: ↑Sat Feb 23, 2019 1:25 pm The law of identity is the cornerstone of Arostotelian/Classical logic.
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.So, whatever you infer from the correspondance you may like but no one should feel compelled to accept it as true.According to the Curry-Howard correspondance, a computer programme is analogous to a proof in intuitionistic logic, not classical logic.What programs implement is fundamentally constructive. The correspondance is only an analogy and in fact we already know that it should break down at some point.
Oh, what a disappointment!
What do you call that fallacy again? APPEAL TO AUTHORITY.
I am an expert. I am defending my position. I called my peers. They said your experts are wrong.
Classical logic is one giant false dichotomy. Propositions are either true or false. 1 or 0.
Computer science rejects that notion. Propositions are either true, false or UNDECIDABLE.
There are some claims that are true.
There are some claims that are false.
There are some claim whose truth or false-value CANNOT BE DECIDED.
The law of identity is one such example.
From identity follows that: for all x in Z+: x = x
The set of positive integers is infinite but countable
Suppose that the axiom of identity is true then it follows: ∞ = ∞ => true.Z is a subset of the set of all rational numbers Q, in turn a subset of the real numbers R. Like the natural numbers, Z is countably infinite.
But from computational complexity theory we KNOW that the identity "∞ = ∞" is NOT DECIDABLE.
It is called the halting problem. https://en.wikipedia.org/wiki/Halting_problem
for ALL x: x = x => Undecidable
for SOME x: x = x => True
It SHOULD break down? This is a violation of the is-ought gap.
It SHOULD break down, BUT IT DOESN'T!