The paradox states that this assumption implies the omniscience principle, which asserts that every truth is known.
Essentially, Fitch's paradox asserts that the existence of an unknown truth is unknowable.
The paradox is of concern for verificationist or anti-realist accounts of truth, for which the knowability thesis is very plausible,[1] but the omniscience principle is very implausible.
The paradox appeared as a minor theorem in a 1963 paper by Frederic Fitch, "A Logical Analysis of Some Value Concepts".
Other than the knowability thesis, his proof makes only modest assumptions on the modal nature of knowledge and of possibility.
It resurfaced in 1979 when W. D. Hart wrote that Fitch's proof was an "unjustly neglected logical gem".
Gödel's Theorem proves that in any recursively axiomatized system sufficient to derive mathematics (e.g. Peano Arithmetic), there are statements which are undecidable.