A paradox is a statement that, despite apparently valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion. A paradox involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, are not yet resolved.
Examples outside logic include the ship of Theseus from philosophy (questioning whether a ship repaired over time by replacing each and all of its wooden parts, one at a time, would remain the same ship). Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.In common usage, the word "paradox" often refers to statements that may be both true and false i.e. ironic or unexpected, such as "the paradox that standing is more tiring than walking".
Not similar or congruent; not matching or fitting in.
Of two numbers, with respect to a third, such that their difference can not be divided by it without a remainder.
"20 and 25 are incongruous with respect to 4."
Not congruous; reciprocally disagreeing; not capable of harmonizing or readily assimilating; inharmonious; inappropriate; unsuitable; not fitting; inconsistent; improper; as, an incongruous remark; incongruous behavior, action, dress, etc.
Of the nature of a paradox.
Inclined to paradoxes, or to tenets or notions contrary to received opinions.
lacking in harmony or compatibility or appropriateness;
"a plan incongruous with reason"
"a joke that was incongruous with polite conversation"
seemingly contradictory but nonetheless possibly true;
"it is paradoxical that standing is more tiring than walking"
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