Paradox Theory

Tag: mathematics

  • Commentary

    The general liar’s revenge sentence shows that logic is inconsistent even if it is incomplete, based on a hypothetical scenario predicated on the assumption of logic gates. Importantly, the assumption of logic gates as hypothesis suffices to show logic to be inconsistent.

    That being said, when Gödel talks about incompleteness, he is referring to something tantamount to the incompleteness of logic gates.

    Why completeness is preferable:

    1. Proving the proof – asserting that the proof is true is sufficient to prove the proof. Therefore, logic gates are complete. It doesn’t make sense to prove logic incomplete.
    2. Logic gates function – a or b?

  • Sets

    To talk about logic as a distinct object, we need sets. However, I do not know how to go about this, because I do not find how to go about accessing sets to be immediately obvious. I’m tempted to simply use proof by contradiction, which is an attractive option because to do so wouldn’t reduce my theory to triviality, because set theory would structure logic. Can there be a set of “true”?

    Of course, perhaps changing a computational framework into a set-theoretic framework so that the system can comment on itself more readily isn’t what I want to do, because to do so would move away from logic as such.

    Toward set theory – Part 3 of 3

    Earlier: The Predicate

  • The Predicate

    Because the predicate to the formalism is similar to “assume the proof”, it could be asserted that the proof proves itself, obviously.

    I also think Tarski may have commented on the predictate.

    Toward set theory – Part 2 of 3

    Earlier: A Thought

    Later: Sets

  • A Thought

    The predicate of the formalism can be postulated as hypothetical, so the conclusions of the formalism according to that hypothetical could come to bear on that hypothetical.

    Toward set theory – Part 1 of 3

    Later: The Predicate