Fitch's paradox of knowability  

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Kunstformen der Natur (1904) by Ernst Haeckel
Kunstformen der Natur (1904) by Ernst Haeckel

Fitch's paradox of knowability is one of the fundamental puzzles of epistemic logic, proposed by Frederic Fitch in 1963.

Given that some truths are merely unknown, Fitch's knowability paradox asserts the existence of other truths that are unknowable. The paradox thus contradicts the widely accepted knowability thesis, which states that any truth is, in principle, knowable.


Essentially, Fitch's paradox asserts that the existence of an unknown truth is unknowable. It thus concludes that it is impossible for all truths to be knowable unless all truths are known.

An old children's riddle illustrates Fitch's paradox: "What was the tallest mountain in the world before Mount Everest was discovered?" The answer is "Mount Everest", because despite everyone's ignorance of the fact, Mount Everest was the tallest mountain in the world. Thus, prior to the mountain's discovery, the following statement was perfectly true:

An undiscovered mountain that will later be named "Mount Everest" is the tallest mountain in the world.

However, according to the paradox, it was never possible for anyone to have known that statement to be true because such knowledge invalidates the "undiscovered" part of the statement.

The paradox applies to many types of statements, including ones about undiscovered scientific principles, information about the future, and secrets yet to be revealed. If the truth of a statement is unknown, it is impossible to know whether a statement about its unknown truth is itself true. Thus, some true statements are unknowable, i.e. not all truths are knowable.

Unless indicated otherwise, the text in this article is either based on Wikipedia article "Fitch's paradox of knowability" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

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