A logical contradiction or seeming contradiction. The most famous in sf are the many forms of Time Paradox and the so-called Fermi Paradox concerning our lack of expected (according to certain arguments) First Contact with Aliens. Also frequently cited is the "twins paradox" of Relativity.
Logical paradoxes – like the traditional statement of Epimenides the Cretan that "All Cretans are liars." – are generally regarded as trifling verbal games. They are routinely deployed in sf to immobilize or destroy insufficiently resilient Computers, as in Gordon R Dickson's (August 1951 Astounding) – which cites Epimenides – and many other stories, to the point of Cliché. They are also useful to bewilder not-so-bright Aliens, as in Eric Frank Russell's "Diabologic" (March 1955 Astounding). However, seeming quibbles may have profound implications. The impossibility of excluding self-referential statements from formal mathematical logic (despite efforts by Bertrand Russell and others) was a major crux of twentieth-century Mathematics, encapsulated in Gödel's Theorem and most lucidly explained in Gödel, Escher, Bach: an Eternal Golden Braid (1979) by Douglas Hofstadter. This book also incorporates and expands on Lewis Carroll's paralogical fantasia "What the Tortoise Said to Achilles" (April 1895 Mind #4), which rings the changes on the paradoxes of infinity and motion proposed by Zeno of Elea (circa 490BC-circa 430BC) – the race between Achilles and the Tortoise being the most famous – to argue the impossibility of logical deduction. Terry Pratchett's Discworld versions of Greek philosophers take a practical attitude to all this in Pyramids (1989), setting up an Axiom Testing Station where Zeno's sophistical proof that an arrow in flight can never reach its destination is checked by experiment, with unwilling tortoises as the targets. Gödel's Theorem itself, a highly technical demonstration of the incompleteness of any formal mathematical system, is often invoked in an incantatory fashion as "proving" the unknowability of the universe or the future – for example, in Samuel R Delany's Babel-17 (1966; rev 1969). [DRL]
see also: Information Theory; Thought Experiment.
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