Infinity Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! ===Early Greek=== The earliest recorded idea of infinity in Greece may be that of [[Anaximander]] (c.β610 β c.β546 BC) a [[Pre-Socratic philosophy|pre-Socratic]] Greek philosopher. He used the word ''[[apeiron]]'', which means "unbounded", "indefinite", and perhaps can be translated as "infinite".<ref name=":1" /><ref>{{harvnb|Wallace|2004|p=44}}</ref> [[Aristotle]] (350 BC) distinguished ''potential infinity'' from ''[[actual infinity]]'', which he regarded as impossible due to the various paradoxes it seemed to produce.<ref>{{cite book |author=Aristotle |url=http://classics.mit.edu/Aristotle/physics.3.iii.html |translator-last1=Hardie|translator-first1=R. P. |translator-last2=Gaye|translator-first2=R. K. |at=Book 3, Chapters 5β8|title=Physics|publisher=The Internet Classics Archive}}</ref> It has been argued that, in line with this view, the [[Hellenistic]] Greeks had a "horror of the infinite"<ref>{{cite book |author=Goodman |first=Nicolas D. |title=Constructive Mathematics |chapter=Reflections on Bishop's philosophy of mathematics |year=1981 |editor1-last=Richman |editor1-first=F. |series=Lecture Notes in Mathematics |publisher=Springer |volume=873|pages=135β145 |doi=10.1007/BFb0090732 |isbn=978-3-540-10850-4 }}</ref><ref>Maor, p. 3</ref> which would, for example, explain why [[Euclid]] (c. 300 BC) did not say that there are an infinity of primes but rather "Prime numbers are more than any assigned multitude of prime numbers."<ref>{{Cite journal |last=Sarton |first=George |date=March 1928 |title=''The Thirteen Books of Euclid's Elements''. Thomas L. Heath, Heiberg |url=https://www.journals.uchicago.edu/doi/10.1086/346308 |journal=Isis |volume=10 |issue=1 |pages=60β62 |doi=10.1086/346308 |issn=0021-1753 |via=The University of Chicago Press Journals}}</ref> It has also been maintained, that, in proving the [[infinitude of the prime numbers]], Euclid "was the first to overcome the horror of the infinite".<ref>{{Cite book |last=Hutten |first=Ernest Hirschlaff |url=https://archive.org/details/originsofscience0000hutt_n9u7 |title=The origins of science; an inquiry into the foundations of Western thought |date=1962 |publisher=London, Allen and Unwin |others=Internet Archive |isbn=978-0-04-946007-2 |pages=1β241 |language=en |access-date=2020-01-09}}</ref> There is a similar controversy concerning Euclid's [[parallel postulate]], sometimes translated: {{blockquote|If a straight line falling across two [other] straight lines makes internal angles on the same side [of itself whose sum is] less than two right angles, then the two [other] straight lines, being produced to infinity, meet on that side [of the original straight line] that the [sum of the internal angles] is less than two right angles.<ref>{{cite book|author=Euclid |orig-year=c. 300 BC|translator-last1=Fitzpatrick |translator-first1=Richard |title=Euclid's Elements of Geometry |url=http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf|year=2008 |isbn=978-0-6151-7984-1 |page=6 (Book I, Postulate 5)|publisher=Lulu.com }}</ref>}} Other translators, however, prefer the translation "the two straight lines, if produced indefinitely ...",<ref>{{cite book|last1=Heath|first1=Sir Thomas Little|last2=Heiberg|first2=Johan Ludvig|author-link1=Thomas Heath (classicist)|title=The Thirteen Books of Euclid's Elements|volume=v. 1|publisher=The University Press|year=1908|url=https://books.google.com/books?id=dkk6AQAAMAAJ&q=right+angles+infinite&pg=PR8|page=212}}</ref> thus avoiding the implication that Euclid was comfortable with the notion of infinity. Finally, it has been maintained that a reflection on infinity, far from eliciting a "horror of the infinite", underlay all of early Greek philosophy and that Aristotle's "potential infinity" is an aberration from the general trend of this period.<ref>{{cite book|last=Drozdek|first=Adam|title=''In the Beginning Was the'' Apeiron'': Infinity in Greek Philosophy''|year=2008|isbn=978-3-515-09258-6|publisher=Franz Steiner Verlag|location=Stuttgart, Germany}} </ref> Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page