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This is the canonical self-referential paradox. Also "Is the answer to this question 'no'?", and "I'm lying." Card paradox: "The next statement is true. The previous statement is false." A variant of the liar paradox in which neither of the sentences employs (direct) self-reference, instead this is a case of circular reference.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. [1] [2] It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, nor would either truly be 13x5 if it were, because what appears to be the hypotenuse is bent. In other words, the "hypotenuse" does not maintain a consistent slope , even though it may appear that way to the human eye.
Paradox – Logically self-contradictory statement; Sophist – Teachers of 5th century BC Greece; Soundness – Term in logic and deductive reasoning; Truth – Being in accord with fact or reality; Validity – Argument whose conclusion must be true if its premises are
In literature, the paradox is an anomalous juxtaposition of incongruous ideas for the sake of striking exposition or unexpected insight. It functions as a method of literary composition and analysis that involves examining apparently contradictory statements and drawing conclusions either to reconcile them or to explain their presence.
The paradox is ultimately based on the principle of formal logic that the statement is true whenever A is false, i.e., any statement follows from a false statement [1] (ex falso quodlibet). What is important to the paradox is that the conditional in classical (and intuitionistic) logic is the material conditional .
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F". The paradox requires only a few apparently-innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything.
The first paradox is probably the most famous, and is similar to the famous paradox of Epimenides the Cretan. The second, third and fourth paradoxes are variants of a single paradox and relate to the problem of what it means to "know" something and the identity of objects involved in an affirmation (compare the masked-man fallacy ).