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Paradox of value – Contradiction between utility and price Paradoxes of material implication – logical contradictions centred on the difference between natural language and logic theory Pages displaying wikidata descriptions as a fallback
Faint young Sun paradox: The contradiction between existence of liquid water early in the Earth's history and the expectation that the output of the young Sun would have been insufficient to melt ice on Earth. Olbers' paradox: Why is the night sky dark if there is an infinity of stars, covering every part of the celestial sphere?
This diagram shows the contradictory relationships between categorical propositions in the square of opposition of Aristotelian logic. In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.
The main difference between Russell's and Zermelo's solution to the paradox is that Zermelo modified the axioms of set theory while maintaining a standard logical language, while Russell modified the logical language itself. The language of ZFC, with the help of Thoralf Skolem, turned out to be that of first-order logic. [4]
Oxymorons in the narrow sense are a rhetorical device used deliberately by the speaker and intended to be understood as such by the listener. In a more extended sense, the term "oxymoron" has also been applied to inadvertent or incidental contradictions, as in the case of "dead metaphors" ("barely clothed" or "terribly good").
Trivialism in symbolic logic; Read as "given any proposition, it is a true proposition.". Trivialism is the logical theory that all statements (also known as propositions) are true and, consequently, that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true.
Formally the law of non-contradiction is written as ¬(P ∧ ¬P) and read as "it is not the case that a proposition is both true and false". The law of non-contradiction neither follows nor is implied by the principle of Proof by contradiction. The laws of excluded middle and non-contradiction together mean that exactly one of P and ¬P is true.
That is a contradiction. As with König's paradox, this paradox cannot be formalized in axiomatic set theory because it requires the ability to tell whether a description applies to a particular set (or, equivalently, to tell whether a formula is actually the definition of a single set).