If every truth could be known, then every truth already is

In 1963, logician Frederic Fitch proved that if every truth is in principle knowable, then every truth must already be known — collapsing the gap between 'knowable' and 'known.' Since plainly not everything true is known, the proof undermines any theory that assumes all truths are knowable.

— Frederic Fitch, A Logical Analysis of Some Value Concepts — Journal of Symbolic Logic, 1963