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Toggle Logic subsection. 1.1 Self–reference. 1.2 Vagueness. 2 Mathematics. ... Paradox of free choice: Disjunction introduction poses a problem for modal inferences
[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 .
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter property is an inclusive logic.
As the best known of the paradoxes, and most formally simple, the paradox of entailment makes the best introduction. In natural language, an instance of the paradox of entailment arises: It is raining. And It is not raining. Therefore George Washington is made of rakes.
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
Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despite our sensory experiences, reality is singular and unchanging. The paradoxes famously challenge the notions of plurality (the existence of many things), motion, space, and time by suggesting they lead to logical contradictions.
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.