{"id":641,"date":"2026-02-28T18:30:39","date_gmt":"2026-02-28T08:30:39","guid":{"rendered":"https:\/\/stevewatson.info\/blog\/?p=641"},"modified":"2026-02-28T18:56:30","modified_gmt":"2026-02-28T08:56:30","slug":"the-divided-line","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2026\/02\/28\/the-divided-line\/","title":{"rendered":"The Divided Line"},"content":{"rendered":"

Plato\u2019s analogy in Republic<\/em> 509d<\/sup>-511e<\/sup> can be summarised as follows.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
Line segments<\/span><\/td>\nA<\/span><\/td>\nB<\/span><\/td>\nC<\/span><\/td>\nD<\/span><\/td>\n<\/tr>\n
Realm<\/span><\/td>\nIntelligible (\u03bd\u03bf\u03b7\u03c4\u03bf\u03c2) (509d<\/sup>)<\/span><\/td>\nVisible (\u03bf\u03c1\u03b1\u03c4\u03bf\u03c2) (509d<\/sup>)<\/span><\/td>\n<\/tr>\n
Objects<\/span><\/td>\nForms (511c<\/sup>) \u2013 considered in their relationship to the Good.<\/span>
\nThe First Principle of things. (511a, b<\/sup>)<\/span>
\nThe unassumed.<\/span><\/td>\n		Forms \u2013 NOT<\/em> considered in their relationship to the Good<\/span><\/p>\n

Assumptions, mathematical postulates. (510c<\/sup>-511b<\/sup>)<\/span><\/td>\n

Living beings, plants, artificial things. (510a, e<\/sup>)<\/span>
\nModels, drawings of geometrical figures (510d, e<\/sup>)<\/span><\/td>\n		\u2018Images\u2019 of objects in C. Shadows, reflections, etc. (510a<\/sup>)<\/span><\/td>\n<\/tr>\n
Operations<\/span><\/td>\na. Derive First Principle from conclusions in B (511a, b<\/sup>)<\/span><\/p>\n

b. From First Principle, draw conclusions for objects in B<\/span><\/td>\n

a. Draw conclusions from assumptions (to be applied to objects of C?)<\/span><\/p>\n

b. Assumptions are taken for granted<\/span><\/p>\n

c. Appeals made to sensibilia (in C)<\/span><\/td>\n

<\/td>\n<\/td>\n<\/tr>\n
Operators<\/span><\/td>\nPhilosophers<\/span><\/td>\nMathematicians and other masters of \u03c4\u03b5\u03c7\u03bd\u03b1\u03b9<\/span><\/td>\n[Scientists]<\/span><\/td>\nSophists, poets, artists<\/span><\/td>\n<\/tr>\n
Mental States<\/span><\/td>\nIntelligence
\n<\/span>(\u03bd\u03bf\u03b7\u03c3\u03b9\u03c2\/\u03bd\u03bf\u03c5\u03c2)<\/span>
\n(Intelligence)<\/span>
\n(511a, b<\/sup>)<\/span><\/td>\n		Thinking<\/span>
\n(\u03b4\u03b9\u03b1\u03bd\u03bf\u03b9\u03b1) (Reason)<\/span>
\n(511a, b, d<\/sup>)<\/span><\/td>\n		Perceptual Assurance<\/span>
\n(\u03c0\u03b9\u03c3\u03c4\u03b9\u03c2)<\/span>
\n(Belief)<\/span>
\n(511d, e<\/sup>)<\/span><\/td>\n		Conjecture<\/span>
\n(\u03b5\u03b9\u03ba\u03b1\u03c3\u03b9\u03b1)<\/span>
\n(Illusion)<\/span>
\n(511d, e<\/sup>)<\/span><\/td>\n<\/tr>\n
Status<\/span><\/td>\nKnowledge (\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b7)<\/span><\/td>\nOpinion (\u03b4\u03bf\u03be\u03b1)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Just as the Line Segments are related A:B::C:D::A+B:C+D wrt length,<\/span>
\nso are the associated Objects related wrt \u2018genuineness\u2019\/\u2019reality\u2019 (\u03b1\u03bb\u03b7\u03b8\u03b5\u03b9\u03b1)<\/span>
\nand the Mental States (\u03c0\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b1) wrt \u2018clarity\u2019 (\u03c3\u03b1\u03c6\u03b7\u03bd\u03b5\u03b9\u03b1)<\/span><\/p>\n

Note that whereas the construction Plato gives actually forces B=C, he makes no reference to that and we must assume that it is irrelevant to the analogy.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Plato\u2019s analogy in Republic 509d-511e can be summarised as follows. Line segments A B C D Realm Intelligible (\u03bd\u03bf\u03b7\u03c4\u03bf\u03c2) (509d) Visible (\u03bf\u03c1\u03b1\u03c4\u03bf\u03c2) (509d) Objects Forms (511c) \u2013 considered in their relationship to the Good. The First Principle of things. (511a, b) The unassumed. Forms \u2013 NOT considered in their relationship to the Good Assumptions, mathematical […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-641","post","type-post","status-publish","format-standard","hentry","category-philosophy"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/comments?post=641"}],"version-history":[{"count":4,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/641\/revisions"}],"predecessor-version":[{"id":645,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/641\/revisions\/645"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}