The equation for the formalism is expressible as a logic circuit, so the ternary logic can be expressed as true, false, and a particular logic circuit expressible as a Boolean algebraic equation, structurally.
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Identity Property Continued
The equation for the formalism is equal to itself because it is a normative equation expressed in Boolean algebra.
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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.
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Why the properties
My explanation for why the properties hold are:
Identity – Plug in – what is logical? Logic.
Reflexivity – if truth is complete, it is recursively enumerable ( to borrow tarskis phrase).
Generality – solutions such as “idiotic”, “inane”,.”non-sensical”, etc. are addressed.
Truth – the formalism equation is accurate.
Algirithmic the formalism in application is an algorithm, with the equation as the rules.
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More Properties
Truth – logic is true
Generality – logic is general (I’m guessing that logic has this property)
Algorithmic – logic is an algorithm (I’m guessing that logic has this property)
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Infinite Language Continued
The assumption of Boolean algebra demands the paradox. However, every possible sequence of ones and zeros isn’t paradoxical. The synthesis of these two truisms will revolutionize logic. Moreover, language will be able to speak the impossible, unlimited from what we thought was every possible sentence.
Note that this phrasing doesn’t necessitate use of Gödel numbers.
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Infinite Language
According to Boolean algebra, the paradox is both real and cannot be mapped to a Gödel number.
A sequence of ones and zeros constitutes a computer program. To assign indices to different sequences of ones and zeros would be possible. Those indices would then be equivalent to Gödel numbers. Those collective Gödel numbers would compose a traditional logical positivist framework. Paradoxes occur outside the limits of that mapping.
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Formalism
Assume true and false.
((x=(x=0)) ∧ (x=((x=0) ∨ (x=(x=(x=0))))))
Update 6/12/2026 –
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.