All of Mathematics is inconsistent. Turing machines are consistent

2 points

7 years ago

There is a conflation between identity and equality in Classical logic, but a distinction between these concepts on a Turing machine.

IDENTITY means unique memory address. EQUALITY means contents-of-memory address.

The error in Mathematics is precisely the conflation of identity and value. Or in terms of a physics conception. Mistaking the space-time coordinates with that which occupies them.

In the real world A = A is allowed to be false (when interpreted as identity) because the two "A"s exist at different space-time coordinates. And so what does it mean for TWO individual things to be "equal" are they entangled or what?

Classical logic overloads "=" to mean both identity and equality. That's why it's inconsistent. Classical logic doesn't have UUIDs - computers do. Memory addresses.

   for all x: x = x  => Undefined, Complexity: O(1) to O(∞)
   for all x: id(x) = id(x) => True, Complexity: O(1)   
   for all x: id(x) = x => False, Complexity: O(1)

Further. ALL operators are supposed to do actual, physical work. The energy spent on deriving the correct result of x = x is the proof-of-work.

If x is an infinite-byte object then comparing it to itself should take infinite time e.g machine will not halt, whereas determining its identity is O(1)

Solution to Symbol-grounding problem. ( https://en.wikipedia.org/wiki/Symbol_grounding_problem)

Q.E.D

λ-calculus ⇔ λ-calculus ⇔ λ-calculus ⇔ λ-calculus ⇔ λ-calculus ⊇ Mathematics

Feedback welcome.

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