Search results
Results From The WOW.Com Content Network
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.
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.
An oxymoron (plurals: oxymorons and oxymora) is a figure of speech that juxtaposes concepts with opposite meanings within a word or in a phrase that is a self-contradiction. As a rhetorical device, an oxymoron illustrates a point to communicate and reveal a paradox.
The liar paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set theory, respectively. Contradictions are problematic in these theories because they cause the theories to explode —if a contradiction is true, then every proposition is true.
The whole point of Russell's paradox is that the answer "such a set does not exist" means the definition of the notion of set within a given theory is unsatisfactory. Note the difference between the statements "such a set does not exist" and "it is an empty set". It is like the difference between saying "There is no bucket" and saying "The ...
A bootstrap paradox, also known as an information loop, an information paradox, [6] an ontological paradox, [7] or a "predestination paradox" is a paradox of time travel that occurs when any event, such as an action, information, an object, or a person, ultimately causes itself, as a consequence of either retrocausality or time travel. [8] [9 ...
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).