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According to Wikipedia, a paradox is:

a statement that, despite apparently sound 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.

My question is, do paradoxes necessarily require a successful explanation in order to be considered a paradox? In other words, is there such a thing as an unexplained paradox? Or that would be called a puzzle, a problem, or a mystery? I am particularly interested in paradoxes in science.

Notice that there are of course a multitude of problems in science that have not been resolved, but they do not necessarily have to be paradoxes in the sense defined above.

  • When Zeno proposed his paradoxes they were "unexplained", and arguably still are (to everybody's satisfaction), same with the Olbers' paradox. Loschmidt's and Zermelo's paradoxes still reflect thorny issues about entropy and the arrow of time. But yes, there is a tendency to label paradoxes without at least a tentative explanation "problems", e.g. the current fine-tuning problems in cosmology. – Conifold Sep 20 '17 at 20:43
  • I would say that there is no such thing as an inexplicable paradox, but as individual thinkers we may discover many that we cannot explain. They may be called problems, puzzles, riddles, mysteries and antinomies. A study of them is usually very rewarding since they reveal problems with our axioms. – PeterJ Sep 21 '17 at 10:02
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    It's not science, but, if you accept Godel's Incompleteness Theorem, mathematics, an entirely invented system of symbolic manipulation (which has some real world uses), is incomplete: there are statements S such that neither S nor "not S" can be proven, and we have no way of knowing all of these statements. Paradoxes like this (and related paradoxes found in computer science), if you accept that they are paradoxes, are not only unexplained, but unexplainable. – barrycarter Sep 21 '17 at 17:05
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A paradox is a result that seems self-contradictory or logically unacceptable to the layman. Usually it can be explained by experts. A self-contradictory or logically unacceptable result that cannot be explained in a sufficient way is called an antinomy.

There are many paradoxes. A comprehensive list of paradoxes is supplied here by Wikipedia.

Note that opinions about classification of results are often differing. In particular modern set theory shows plenty of paradoxical results which by many are called antinomies. The antinomies of Cantor's naive set theory are generally acknowledged as such. For an overview see chapter III of the source book on transfinity.

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