Truth Eliminability Sorting Algorithm (Example)

KFG

• S ∈ C → (T(⟨S⟩) ↔ S)
  • More precisely: S ∈ C → (T(⟨S⟩) → S) and S ∈ C → (S → T(⟨S⟩)) from which S ∈ C → (T(⟨S⟩) ↔ S) derives.
  • Since: ((P → (Q → R)) ∧ (P → (R → Q))) → (P → (R ↔ Q)) is a Theorem of Classical Logic.
  • Is of the form: P → (Q → P) (Weakening) or Type Restriction: (∀S∈C)(T(⟨S⟩) ↔ S).
  • Observe that if you think T-Scheme is Analytic (necessarily True) then it also follows from Weakening that S ∈ C → (T(⟨S⟩) ↔ S) also is.
    • Since by the Truth Table semantics for a Material Conditional, an Implication cannot be False if its Consequent is True.
      • Specifically: S ∈ C → (T(⟨S⟩) ↔ S) has the following Truth Assignments:
      • True, True for Truth Eliminable Sentences
      • False, True for Truth Tellers
      • And False, False for Truth Opaque Sentences
      • With optional extensions to harmonize some Interpretations per Definition 6.5 Truth Normalization.
    • That fact makes it very difficult to resist the proposal if you accept the Analyticity of T-Scheme (which nearly everyone does).
  • It satisifies Tarski's Undefinability Theorem for the Truth Predicate.
  • Blocks McGee's T-Intro step.
  • Bacon's 2015 SRT quite plausibly doesn't hold since S ∈ C isn't Diagonalizable.
  • S must be a Sentence and not a Name blocking Diagonalization.
  • One can only Diagonalize into a Number Theoretic Function (such as a Name Forming Operator per Gödel).
• The Truth Eliminability Sorting Algorithm determines where S ∈ C (or not).
• Requires of a Truth Assertion (Truth Predication) that the content can be presented without a Truth Predicate.
• E.g. - "What they said was True." ("All the sentences they spoke about are True.")
• And those are: "It's sunny today.", "It's hot today.", ...
• Note that an explicit assertion of Truth isn't present in any of those Sentences.
• Yet all content is preserved losslessly.
• Doesn't require that any Sentence receive a specific Truth Value (e.g. - that a Truth Opaque Sentence be Untrue).
• So, Standard Revenge Paradox-Style Sentences do no damage here since they require Entailment to Untruth.
• Why the clause S ∈ C?
• We're in Peano or Robinson Arithmetic after all (per Gödel) which is Second Order Logic (per Quine).
• Set Theory is a dependency and Set Theoretic Sentences are in the theory.

Debug Logging:

(Check the console for runtime/execution time logging.)

Cleared to be run through T-Scheme:

Denied entry to T-Scheme:

(They still receive Truth Values)