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The surprise examination and Bottle Imp paradox use similar logic. Self–reference. These paradoxes, ... [10] Stapp's ironical paradox: ...
[10] [11] Others, such as Curry's paradox, cannot be easily resolved by making foundational changes in a logical system. [12] Examples outside logic include the ship of Theseus from philosophy, a paradox that questions whether a ship repaired over time by replacing each and all of its wooden parts one at a time would remain the same ship. [13]
It should only contain pages that are Logical paradoxes or lists of Logical paradoxes, as well as subcategories containing those things (themselves set categories). Topics about Logical paradoxes in general should be placed in relevant topic categories .
With the epsilon-delta definition of limit, Weierstrass and Cauchy developed a rigorous formulation of the logic and calculus involved. These works resolved the mathematics involving infinite processes. [35] [36] Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems.
A paradox arising from the assumption that if a statement is true, then it is possible to know that it is true, leading to contradictions in certain epistemic frameworks. knower's paradox A paradox related to self-reference and epistemic logic, typically involving a statement that claims its own unprovability or unknowability. Kreisel-Putnam logic
Formal logic has shown itself extremely useful in formalizing argumentation, philosophical reasoning, and mathematics. The discrepancy between material implication and the general conception of conditionals however is a topic of intense investigation: whether it is an inadequacy in formal logic, an ambiguity of ordinary language , or as ...
The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic. The paradox is named after the logician Haskell Curry, who wrote about it in 1942. [1] It has also been called Löb's paradox after Martin Hugo Löb, [2] due to its relationship to Löb's theorem.
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.