Paradox Theory

Category: The Paradox of the Liar

  • Plain Explanation

    “Both this sentence is false and this sentence is false or is this sentence is false.”

    The statement above systematizes the liar’s revenge sentence to the hypothetical solution to the liar sentence. Filling out the corresponding truth tables would state that if the revenge statement were true, it would be either false or equal to the liar sentence; if the revenge sentence were false, the revenge statement would be true; and if the revenge sentence were equal to the liars sentence, it would be true. The liar sentence was established to be not true in the initial characterization of the liar sentence.

    In the case of incompleteness, filling out the corresponding truth table shows that the follow-up “revenge statement” to the traditional antimony of the liar would set the revenge statement equal to true if it were incomplete, true if it were false, and either incomplete or false if it were true. That incompleteness differed from truth was established in the solution to the traditional liar paradox in the first step.

  • Regarding the Translation of the Formalism to Formal Symbolic Logic

    It is easy to imagine that a statement could be evaluated as true or false in formal symbolic logic. Therefore, the statement evaluated as true or false, in formal symbolic logic, could be itself. From there, it is easy to translate the whole formalism to formal symbolic logic – “both a statement that evaluates itself as false and a statement that evaluates iself as a statement that evaluates itself as false or false”.

    Of course, this translation doesn’t rebut answers such as Tarski’s, that language can’t define its own truth predicate, for example. But, classical logic per se ineluctably incurs a paradox.

  • Slightly Clearer Phrasing

    Both:

    Subpoint A: that subpoint A is false

    and

    Subpoint B: that subpoint B is equal to subpoint A or false

    Update 6/12/2026 – Explanation

  • Modern Phrasing

    I’m using the following phrasing for the natural language formalism:

    Both this sentence is false and this sentence is false or is this sentence is false

    Update 6/12/2026 – Explanation

  • Formal Symbolic Language Translation


    A translation from the natural language formalism into a formal symbolic language is easily and readily imaginable, and can be asserted.

  • Natural Language Phrasing

    I am incapable of evaluating the Boolean algebra phrasing of the formalism for rectitude. In lieu, a natural language phrasing of the paradox would proceed as follows:

    This sentence is false or is “this sentence is false”.

    Update – I went back to my original phrasing, as of 6/11/2026

  • Correcting a Major Error

    I just noticed that my formula is redundant. It should read:

    Assume Boolean algebra:

    x=((x=0) ∨ (x=(x=(x=0))))

    It corresponds to the sentence “This sentence is false or ‘this sentence is false’ “

    Update – I went back to my original phrasing, as of 6/11/2026

  • Updated Formalism

    Assume boolean algebra.

    ((x=(x=0)) ∧ (x=((x=0) ∨ (x=(x=(x=0))))))

    Update 6/13/2026 –

    Explanation: this is an attempt to formalize the liar’s sentence + liar’s revenge sentence in boolean algebra; I am far from certain I did so correctly.

  • In Vacuo

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

  • Identity Property Continued

    Because the formalism is the theory of everything, it is the only solution to itself. The only solution to the theory of everything is the theory of everything. Any hypothetical solution to the theory of everything other than the theory of everything wouldn’t solve. The formalism is the theory of everything because it is a fully general logic. This fully general logic can have itself as its only possible solution. That is to say, specifically, the formalism can have only the formalism as its solution; because of the formalism’s generality, no other equation is equal to the formalism. The truth of the formalism indicates that the formalism is equal to itself.