Paradox Theory

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  • Reflexivity Continued

    The translation of the paradox into a format that can be evaluated by the paradox-read-as-logic circuit would perhaps be “both true and false”. From there, filling in the truth tables of the solution “both true and false” would mimic that evaluation.

    Reflexivity – Part 3 of 3

    Earlier: Reflexivity Continued

  • Reflexivity Continued

    If the paradox is treated as a logic circuit, that logic circuit could evaluate a hypothetical input, perhaps a sequence of ones and zeros. Of course, translating the paradox, or perhaps trinary logic, into an input that could be parsed by a logic circuit remains unfinished.

    Reflexivity – Part 2 of 3

    Earlier: Reflexivity

    Later: Reflexivity Continued

  • Reflexivity

    I would think that the formalism expressed as logic-circuit could evaluate itself.

    Reflexivity – Part 1 of 3

    Later: Reflexivity Continued

  • Considerations

    Any attempt to disprove the formalism would be redressed via generality.

    Properties on solid footing:

    1. Identity – the logic gates are equal to themselves times one.
    2. Generality – any alternative solution to the formalism than itself isn’t a solution to the formalism.
    3. Algorithmic – any departure from the formalism would forsake both identity, because a departure from the formalism wouldn’t be equal to the formalism, and generality, because a departure from the formalism wouldn’t be a solution to the formalism.
    4. Paradoxical – the formalism is both true and false.

    Miscellania:

    1. Regarding reflexivity – what if logic’s description of itself were incomplete?
    2. Regarding truth – what if logic were both incomplete and inconsistent? However, the identity property is suggestive of the truth of the formalism, because it would be equal to itself. Additionally, generality proves that logic is inconsistent, even if logic were incomplete.

    Update 6/12/2026

    Regarding the algorithmic property, a boolean algebra circuit is an algorithm.

    The five properties – Part 5 of 5

    Earlier: Updated Properties

  • In Vacuo

    I think it is important to focus on the formalism per se.

  • 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?

  • Updated Properties

    In light of careful consideration of my work, I’ve decided to update some of the properties:

    1. Identity: plug-in – logic is logical. Reflexivity connotes that logic describes itself.
    2. Reflexivity: I assert that the logic gates function because logic is true. This idea is not well-developed, but I think that the notion that logic gates work because the proof proves itself will be shown. Also, for these reasons, logic will describe itself.
    3. Truth – that the proof proves itself connotes trinary logic is true.

    The five properties – Part 4 of 5

    Earlier: Why the properties

    Later: Considerations

  • 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