Editing Rationalism (section)

===Rationalist philosophy in Western antiquity===
[[File:Pythagoras with tablet of ratios.jpg|thumb|Detail of Pythagoras with a tablet of ratios, numbers sacred to the Pythagoreans, from ''[[The School of Athens]]'' by [[Raphael]]. [[Vatican Palace]], [[Vatican City]]]]
Although rationalism in its modern form post-dates antiquity, philosophers from this time laid down the foundations of rationalism. In particular, the understanding that we may be aware of knowledge available only through the use of rational thought.{{Citation needed|date=April 2018}}

====Pythagoras (570–495 BCE)====
{{Main|Pythagoras}}
Pythagoras was one of the first Western philosophers to stress rationalist insight.<ref name="Epistemological rationalism in modern philosophies">{{Cite web|url=https://www.britannica.com/topic/rationalism|title=rationalism &#124; Definition, Types, History, Examples, & Descartes|website=Encyclopædia Britannica|date=28 May 2023|access-date=14 May 2021|archive-date=18 May 2015|archive-url=https://web.archive.org/web/20150518105808/https://www.britannica.com/EBchecked/topic/492034/rationalism|url-status=live}}</ref> He is often revered as a great [[mathematician]], [[mysticism|mystic]] and [[scientist]], but he is best known for the [[Pythagorean theorem]], which bears his name, and for discovering the mathematical relationship between the length of strings on lute and the pitches of the notes. Pythagoras "believed these harmonies reflected the ultimate nature of reality. He summed up the implied metaphysical rationalism in the words 'All is number'. It is probable that he had caught the rationalist's vision, later seen by [[Galileo Galilei|Galileo]] (1564–1642), of a world governed throughout by mathematically formulable laws".<ref name="Epistemological rationalism in ancient philosophies">{{Cite web|url=https://www.britannica.com/topic/rationalism|title=rationalism &#124; Definition, Types, History, Examples, & Descartes &#124; Britannica|website=www.britannica.com|date=28 May 2023|access-date=14 May 2021|archive-date=18 May 2015|archive-url=https://web.archive.org/web/20150518105808/https://www.britannica.com/EBchecked/topic/492034/rationalism|url-status=live}}</ref> It has been said that he was the first man to call himself a philosopher, or lover of wisdom.<ref>[[Cicero]], ''[[Tusculan Disputations]]'', 5.3.8–9 = [[Heraclides Ponticus]] fr. 88 Wehrli, [[Diogenes Laërtius]] 1.12, 8.8, [[Iamblichus]] ''VP'' 58. Burkert attempted to discredit this ancient tradition, but it has been defended by [[C.J. de Vogel]], ''Pythagoras and Early Pythagoreanism'' (1966), pp. 97–102, and C. Riedweg, ''Pythagoras: His Life, Teaching, And Influence'' (2005), p. 92.</ref>

====Plato (427–347 BCE)====
{{Main|Plato}}
[[File:Plato by Raphael.png|thumb|[[Plato]] in ''[[The School of Athens]]'', by [[Raphael]]]]
Plato held rational insight to a very high standard, as is seen in his works such as [[Meno]] and [[The Republic (Plato)|The Republic]]. He taught on the [[Theory of Forms]] (or the Theory of Ideas)<ref>Modern English textbooks and translations prefer "Theory of Forms" to "Theory of Ideas", but the latter has a long and respected tradition starting with Cicero and continuing in German philosophy until present, and some English philosophers prefer this in English too. See W. D. Ross, Plato's Theory of Ideas (1951) and [http://www.philosophyprofessor.com/philosophies/platos-theory-of-forms.php this]{{webarchive|url=https://web.archive.org/web/20110927061811/http://www.philosophyprofessor.com/philosophies/platos-theory-of-forms.php|date=2011-09-27}} reference site.</ref><ref>The name of this aspect of Plato's thought is not modern and has not been extracted from certain dialogues by modern scholars. The term was used at least as early as [[Diogenes Laërtius]], who called it (Plato's) "Theory of Forms:" {{lang|grc|Πλάτων ἐν τῇ περὶ τῶν ἰδεῶν ὑπολήψει}}...., {{cite encyclopedia |title=Plato |encyclopedia=Lives of Eminent Philosophers |volume=Book III Paragraph 15 |pages=}}</ref><ref>Plato uses many different words for what is traditionally called ''form'' in English translations and ''idea'' in German and Latin translations (Cicero). These include ''idéa'', ''morphē'', ''eîdos'', and ''parádeigma'', but also ''génos'', ''phýsis'', and ''[[Ousia|ousía]]''. He also uses expressions such as ''to x auto'', "the x itself" or ''kath' auto'' "in itself". See Christian Schäfer: ''Idee/Form/Gestalt/Wesen'', in ''Platon-Lexikon'', Darmstadt 2007, p. 157.</ref> which asserts that the highest and most fundamental kind of reality is not the material world of change [[allegory of the cave|known to us through sensation]], but rather the abstract, non-material (but [[Ousia|substantial]]) world of forms (or ideas).<ref>''Forms (usually given a capital F) were properties or essences of things, treated as non-material abstract, but substantial, entities. They were eternal, changeless, supremely real, and independent of ordinary objects that had their being and properties by 'participating' in them.'' [http://www.philosophyprofessor.com/philosophies/platos-theory-of-forms.php Plato's theory of forms (or ideas)] {{webarchive|url=https://web.archive.org/web/20110927061811/http://www.philosophyprofessor.com/philosophies/platos-theory-of-forms.php|date=2011-09-27}}.</ref> For Plato, these forms were accessible only to reason and not to sense.<ref name="Epistemological rationalism in ancient philosophies"/> In fact, it is said that Plato admired reason, especially in [[geometry]], so highly that he had the phrase "Let no one ignorant of geometry enter" inscribed over the door to his academy.<ref>{{cite web|url=http://plato-dialogues.org/faq/faq009.htm|title=Plato FAQ: "Let no one ignorant of geometry enter"|first=Bernard F.|last=Suzanne|website=plato-dialogues.org|access-date=2013-05-22|archive-date=2013-05-19|archive-url=https://web.archive.org/web/20130519153541/http://plato-dialogues.org/faq/faq009.htm|url-status=live}}</ref>

====Aristotle (384–322 BCE)====
{{Main|Aristotle}}
[[Aristotle]]'s main contribution to rationalist thinking was the use of [[Syllogism|syllogistic]] logic and its use in argument. Aristotle defines syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so."<ref>[[Aristotle]], ''Prior Analytics'', 24b18–20.</ref> Despite this very general definition, Aristotle limits himself to categorical syllogisms which consist of three [[categorical proposition]]s in his work ''[[Prior Analytics]]''.<ref>[http://plato.stanford.edu/entries/logic-ancient/#SynSemSen] {{Webarchive|url=https://web.archive.org/web/20180828102117/https://plato.stanford.edu/entries/logic-ancient/#SynSemSen|date=2018-08-28}} Stanford Encyclopedia of Philosophy: ''Ancient Logic'' Aristotle Non-Modal Syllogistic.</ref> These included categorical [[modal logic|modal]] syllogisms.<ref>[http://plato.stanford.edu/entries/logic-ancient/#ModLog] {{Webarchive|url=https://web.archive.org/web/20180828102117/https://plato.stanford.edu/entries/logic-ancient/#ModLog|date=2018-08-28}} Stanford Encyclopedia of Philosophy: ''Ancient Logic'' Aristotle Modal Logic.</ref>