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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.
Barbershop paradox: The supposition that, "if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved" leads to paradoxical consequences. Not to be confused with the Barber paradox .
From this, Post was able to derive the following definition of inconsistency—without the use of the notion of contradiction: Definition. A system will be said to be inconsistent if it yields the assertion of the unmodified variable p [S in the Newman and Nagel examples].
A temporal paradox, time paradox, or time travel paradox, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future.
Chief among these is that since dialetheism recognizes the liar paradox, an intrinsic contradiction, as being true, it must discard the long-recognized principle of explosion, which asserts that any proposition can be deduced from a contradiction, unless the dialetheist is willing to accept trivialism – the view that all propositions are true ...
(This set is sometimes called "the Russell set".) If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox. In symbols:
[1] [2] Diogenes Laërtius, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees. [3] Modern academics attribute the paradox to Zeno. [1] [2]
A paradox, such as "this sentence is false," can also be considered to be an antinomy; ... This is a manifest contradiction because infinity cannot, by definition, be ...