Argument

Paradox

Overview

A paradox is a logically self-contradictory statement or a statement that runs contrary to expectations. 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. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".

In logic, many paradoxes exist that are invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were 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, cannot be easily resolved by making foundational changes in a logical system.

Examples outside logic include the ship of Theseus, 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. 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.

The term paradox is often used to describe a counterintuitive result, which may be termed a veridical paradox.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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3. But this author's humour, which prompts him to paradoxes and makes him seek to contradict others, has made him draw out exaggerated and odious conclusions and expressions, as if everything happened through an absolute necessity. The Bishop of Derry, on the other hand, has aptly observed in the answer to article 35, page 327, that there results only a hypothetical necessity, such as we all grant to events in…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
States what Paradox is; the author is tied to Paradox in the knowledge graph.
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As we see, _N_ is not equal to the _n_th number of _E_, and as _n_ is arbitrary, _N_ does not appertain to _E_ and yet _N_ should belong to this assemblage since we have defined it with a finite number of words. We shall later see that M. Richard has himself given with much sagacity the explanation of his paradox and that this extends, _mutatis mutandis_, to the other like paradoxes. Again, Russell cites another…
Henri Poincaré, The Foundations of Science
States what Paradox is; names Paradox several times.
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This reference to absolute space was not an oversight. I know that the doctrine of the relativity of space at present holds the field both in science and philosophy. But I do not think that its inevitable consequences are understood. When we really face them the paradox of the presentation of the character of space which I have elaborated is greatly mitigated. If there is no absolute position, a point must cease to…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Paradox is; names Paradox twice.
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Paradox

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