Formalizing Self-Reference Paradox using Predicate Logic We begin with the hypothetical assumption that Tarski's 1933 formula ∀ True(x) φ(x) has been defined such that ∀x Tarski:True(x) → Boolean-True. On the basis of this logical premise we formalize the Truth Teller Paradox: "This sentence is true." showing syntactically how selfreference paradox is semantically ungrounded. https://plato.stanford.edu/entries/tarski-truth/#ForCor 1.2 Formal correctness The definition of True should be 'formally correct'. This means that it should be a sentence of the form: For all x, True(x) if and only if φ(x), where True never occurs in φ; or failing this, that the definition should be provably equivalent to a sentence of this form. The equivalence must be provable using axioms of the metalanguage that don't contain True. Definitions of the kind displayed above are usually called explicit, though Tarski in 1933 called them normal. "This sentence is true." Formalized as this predicate logic: ∃x ∈ Propositions ∃P ∈ Properties ∃T ∈ Predicates | (x ↔ P(x)) & (P(x) ↔ T(x)) Simplified as this formula x ↔ hasProperty(x, True(x)) When the above x is plugged into True(x) to be evaluated we get (1) True(hasProperty(x, True(x))) (2) True(hasProperty(x, True(hasProperty(x, True(x))))) (3) True(hasProperty(x, True(hasProperty(x, True(hasProperty(x, True(x))))))) (n) ... On and on to an infinitely recursive depth. Copyright 2016, 2017 by Pete Olcott