Fitch’s Paradox of Knowability
Updated 2026-09-10
INTRODUCTION
English translation pending.
CORE DEFINITION
Fitch's paradox of knowability, also called the knowability paradox or the Church-Fitch paradox, targets any theory committed to the thesis that all truths are knowable: from this seemingly modest thesis it appears to follow that all truths are already known, landing antirealism in difficulty. It was proved by Frederic Fitch and remains central to debates about truth.
SCAFFOLDING EFFECT
Reduce cognitive load
- Test knowability: run a formal derivation on slogans such as every truth can be known to expose their hidden cost. - Spot self-reference traps: watch for self-defeat when knowledge is written into the content known. - Map the escape routes: compare restricting the principle, changing the logic, and abandoning the thesis.
Anchor fast decisions
Suppose there is a truth p that has not yet been known. Then the conjunction that p and that p is not known is itself true, and by the knowability thesis that conjunction is knowable; but knowing it would involve knowing that p, contradicting the second conjunct. So the existence of unknown truths is ruled out.
MINIMUM ACTION
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Source support: Explicit
- plato.stanford.eduhttps://plato.stanford.edu/entries/fitch-paradox/verified
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