Philosophical
Fitch's Paradox of Knowability
If all truths are knowable, then all truths are known
Overview
A logical paradox challenging the thesis that all truths are knowable.
Assume every truth is knowable. Consider some unknown truth P. The statement 'P is true but unknown' is itself true. But it can't be known (knowing it would make P known, contradicting 'unknown'). So some truths are unknowable.