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<!doctype html>     <html class="no-js" lang="en"> <head> <meta charset="utf-8"> <title>SFE: Paradox</title> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <meta name="description" content="Welcome to the fourth edition of The Encyclopedia of Science Fiction." /> <meta name="keywords" content="" /> <meta name="viewport" content="width=device-width,initial-scale=1">  <script> window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)};ga.l=+new Date; ga("create", "UA-24275979-1", "auto"); ga("send", "pageview"); </script> <script async src="https://www.google-analytics.com/analytics.js"></script>  <link rel="icon" href="favicon.ico" type="image/x-icon"> <link rel="shortcut icon" href="favicon.ico" type="image/x-icon"> <link rel="apple-touch-icon" href="apple-touch-icon.png"> <link rel="stylesheet" href="/static/css/style.css?v=1"> <link rel="stylesheet" href="/static/css/media-queries.css"> <link rel="stylesheet" href="/css/cookie.css"> <script src="/static/js/libs/modernizr-2.0.6.min.js"></script> <style media="screen" type="text/css"> ::-moz-selection { background: navy !important; 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} }) </script> </div> </form> </fieldset> <article class="entryArticle content STeditorial"> <header class="entryHeader icon-theme"> <h1 class="entryTitle">Paradox </h1> </header><p class='tagLine'>Entry updated 9 May 2022. Tagged: Theme.</p><div class="browsingBtns"> <span> <input class="button PNI previous" type="button" onclick="window.location.href='/next.php?id=p&entry=paradox'" value="Prev" /> </span> <span> <input class="button PNI next" type="button" onclick="window.location.href='/next.php?&entry=paradox'" value="Next" /> </span> <span> <input class="button PNI incoming" type="button" onclick="window.location.href='/incoming.php?entry=paradox'" value="About This Entry" title="What links to the entry; contributor initials explained; how to cite; other information" /> </span> </div> <p>A logical contradiction or seeming contradiction. The most famous in sf are the many forms of <a href="/entry/time_paradoxes">Time Paradox</a> and the so-called <a href="/entry/fermi_paradox">Fermi Paradox</a> concerning our continuing lack of expected (according to certain arguments) <a href="/entry/first_contact">First Contact</a> with <a href="/entry/aliens">Aliens</a>. Also frequently cited is the "twins paradox" of <a href="/entry/relativity">Relativity</a>.</p> <p>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 <a href="/entry/computers">Computers</a>, as in Gordon R <a href="/entry/dickson_gordon_r">Dickson</a>'s "The Monkey Wrench" (August 1951 <a href="/entry/asf">Astounding</a>) – which cites Epimenides – and many other stories, to the point of <a href="/entry/cliches">Cliché</a>. They are also useful to bewilder not-so-bright <a href="/entry/aliens">Aliens</a>, as in Eric Frank <a href="/entry/russell_eric_frank">Russell</a>'s "Diabologic" (March 1955 <a href="/entry/asf">Astounding</a>). However, seeming quibbles may have profound implications. The impossibility of excluding self-referential statements from formal mathematical logic (despite efforts by Bertrand <a href="/entry/russell_bertrand">Russell</a> and others) was a major crux of twentieth-century <a href="/entry/mathematics">Mathematics</a>, encapsulated in Gödel's Theorem and most lucidly explained in <i>Gödel, Escher, Bach: An Eternal Golden Braid</i> (<b>1979</b>) by Douglas <a href="/entry/hofstadter_douglas">Hofstadter</a>. This book also incorporates and expands on Lewis <a href="/entry/carroll_lewis">Carroll</a>'s paralogical fantasia "What the Tortoise Said to Achilles" (April 1895 <i>Mind</i> #4), which rings the changes on the paradoxes of infinity and motion proposed by Zeno of Elea (<i>circa</i> 490 BCE-<i>circa</i> 430 BCE) – the race between Achilles and the Tortoise being perhaps the most famous – to argue the impossibility of logical deduction. Zeno had pretended to argue the impossibility of an arrow's flight from A to B because first half the distance must be covered, then half the remaining distance, and so on in an infinite sequence of steps that apparently never reaches the goal; the problem was resolved by the mathematical insight that the infinite series in question has a finite sum and may be traversed in finite time.</p> <p>The racing rivals in the Achilles and Tortoise <a href="/entry/thought_experiment">Thought Experiment</a> are often replaced by the more familiar figures of the Tortoise and Hare from Aesop's fable, as in Tom <a href="/entry/stoppard_tom">Stoppard</a>'s <i>Jumpers</i> (first performed 2 February 1972; <b>1972</b> chap), where Zeno's paradoxes are tragicomically illustrated with an actual arrow, hare and tortoise. Terry <a href="/entry/pratchett_terry">Pratchett</a>'s <b>Discworld</b> analogues of Greek philosophers adopt a similarly practical attitude in <i>Pyramids</i> (<b>1989</b>), setting up an Axiom Testing Station where Zeno's sophistical argument that an arrow in flight can never reach its destination is checked by experiment, with unwilling tortoises as the targets.</p> <p>In Jorge Luis <a href="/entry/borges_jorge_luis">Borges</a>'s <i>Tlön, Uqbar, Orbis Tertius</i> (May 1940 <i>Sur</i>; trans James E Irby <b>1983</b> chap), the alien philosophy of the imagined world Tlön is highlighted by its equivalent of a Zeno sophistry, which to us seems a trivial anecdote. Several coins are lost and later found: surely these are the same coins? This proves to be a shockingly heretical paradox in a culture that denies materialism and sees blasphemy in "attributing the divine category of <i>being</i> to some ordinary coins" (from Alastair Reid's translation).</p> <p>Gödel's Theorem itself, a highly technical <i>reductio ad absurdum</i> demonstration of the incompleteness or inconsistency of any formal mathematical system sufficiently rich to support ordinary arithmetic, is often invoked in an incantatory fashion as "proving" the unknowability of the universe or the future – for example, in Samuel R <a href="/entry/delany_samuel_r">Delany</a>'s <i>The Einstein Intersection</i> (<b>1967</b>; 1 chapter restored <b>1968</b>). [DRL]</p> <p><b>see also:</b> <a href="/entry/information_theory">Information Theory</a>.</p> <p><b>previous versions of this entry</b></p> <ul><li><a href='https://web.archive.org/web/*/http://www.sf-encyclopedia.com/entry/paradox' target='_blank'>Internet Archive</a></li></ul><br /><br /></article></div> <div class="sideBarsWrapper"> <div class="sideBarsColsWrapper clearfix"> <div class="column sideBar12 clearfix"> <div class="columnForm"><aside id="blogFeed" class="widget"> <div class="content STeditorial clearfix"> <h2>Recently visited entries<span style="background:url(/images/thingSFE2.png) !important"></span></h2><ul style='width: 50%; float: left;'> </ul> <p align=center style="float:right; padding-top:20px; padding-bottom:20px;">ISSN 3049-7612<br /> <a href="/facts.php?id=logo"> <img src="/images/VitMan.gif" width=150 height=150 title="Click for larger version of this SFE logo"></a><br /> <b><a href="/donate.php"><img src="/images/Paypal-Donate.gif" WIDTH="92" HEIGHT="26" BORDER="0" /></a><br /><a href="/">Home/Welcome page</a></b></p><div style="margin-bottom:10px;"></div></div> </aside><aside id="blogFeed" class="widget"> <div class="content STeditorial clearfix"> <h2><i>SFE</i> Special Features<span></span></h2><p style="margin-top: 10px;"><input type="button" value="What’s New" style="width: 150px !important;" class="button primary" onclick="window.location.href='/whatsnew.php'">  Latest entries; 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