{"id":181017620,"date":"2025-12-08T15:23:33","date_gmt":"2025-12-08T15:23:33","guid":{"rendered":"https:\/\/exphilnerd.com\/index.php\/2025\/12\/08\/les-videre-om-rom-geometri-og-a-priori-kunnskap\/"},"modified":"2025-12-21T18:54:51","modified_gmt":"2025-12-21T17:54:51","slug":"les-videre-om-rom-geometri-og-a-priori-kunnskap","status":"publish","type":"post","link":"https:\/\/exphilnerd.com\/index.php\/2025\/12\/08\/les-videre-om-rom-geometri-og-a-priori-kunnskap\/","title":{"rendered":"Les videre om rom, geometri og a priori kunnskap"},"content":{"rendered":"\n<p>Kapit\u00adtelet \u00abRom og geometri. Hva kan vi vite uten erfar\u00ading?\u00bb i pen\u00adsum innehold\u00ader utdrag fra Immanuel Kants <em>Kri\u00adtikk av den rene for\u00adnuft<\/em> og Albert Ein\u00adsteins tekst \u00abGeometri og erfar\u00ading\u00bb.<\/p>\n\n\n\n<p>Dette kapit\u00adtelet han\u00addler f\u00f8rst og fremst om kunnskapens natur: Hva kan vi vite med sikker\u00adhet uten \u00e5 m\u00e5tte under\u00ads\u00f8ke ver\u00adden empirisk? Kant intro\u00adduser\u00ader dis\u00adtinksjonene mel\u00adlom <em>ana\u00adlytisk<\/em> og <em>syn\u00adtetisk<\/em> kunnskap, og mel\u00adlom <em>a pri\u00adori<\/em> (uavhengig av erfar\u00ading) og <em>a pos\u00adte\u00adri\u00adori<\/em> (avhengig av erfar\u00ading). Hans rev\u00ado\u00adlusjon\u00e6re p\u00e5s\u00adtand er at det finnes <em>syn\u00adtetisk a pri\u00adori<\/em> kunnskap \u2013 dom\u00admer som b\u00e5de er infor\u00adma\u00adtive og n\u00f8d\u00advendi\u00adge uten \u00e5 avhenge av erfar\u00ading. Geome\u00adtrien er hans hov\u00adedek\u00adsem\u00adpel: Den er ikke bare defin\u00adisjon\u00ader (ana\u00adlytisk), men beskriv\u00ader n\u00f8d\u00advendi\u00adge struk\u00adtur\u00ader i rom\u00admet som vi m\u00e5 kjenne <em>f\u00f8r<\/em> all erfar\u00ading for\u00addi rom\u00admet selv er en \u00abren anskuelses\u00adform\u00bb vi p\u00e5leg\u00adger ver\u00adden. Ein\u00adstein utfor\u00addr\u00ader dette: Hans rel\u00ada\u00adtivitet\u00adste\u00adori vis\u00ader at fysikkens geometri fak\u00adtisk er ikke-euk\u00adlidisk og bestemt av materie og ener\u00adgi. Dette reis\u00ader sp\u00f8rsm\u00e5let: Hadde Kant rett i at noe kunnskap er a pri\u00adori n\u00f8d\u00advendig, eller er selv geome\u00adtrien empirisk?<\/p>\n\n\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\">\n\n\n\n<div class=\"wp-block-pms-content-restriction-start\">You must be logged in with an active sub\u00adscrip\u00adtion to view this con\u00adtent. <a href=\"https:\/\/exphilnerd.com\/index.php\/register\/\">Click here to sub\u00adscribe<\/a>.<\/div>\n\n\n\n<p class=\"is-style-text-subtitle is-style-text-subtitle--1\"><em>Kants epis\u00adte\u00admolo\u00adgi i filosofisk sam\u00admen\u00adheng<\/em><\/p>\n\n\n\n<p>For \u00e5 forst\u00e5 Kants rev\u00ado\u00adlusjon m\u00e5 du se den i lys av debat\u00adten mel\u00adlom <em>rasjon\u00adal\u00adis\u00adter<\/em> og <em>empiris\u00adter<\/em> p\u00e5 1600- og 1700-tal\u00adlet.<\/p>\n\n\n\n<p><em>Rasjon\u00adal\u00adis\u00adtene<\/em> \u2013 s\u00e6rlig Descartes, Spin\u00adoza og Leib\u00adniz \u2013 mente at ekte kunnskap m\u00e5 v\u00e6re n\u00f8d\u00advendig og uni\u00adversell, og der\u00adfor ikke kan komme fra de up\u00e5litelige sansene. Descartes fant fun\u00adda\u00admentet i klare og dis\u00adtink\u00adte ideer (som <em>cog\u00adi\u00adto ergo sum<\/em>), mens Leib\u00adniz skilte mel\u00adlom <em>sannhets\u00adbaserte p\u00e5 for\u00adnuft<\/em> (n\u00f8d\u00advendi\u00adge, ana\u00adlytiske) og <em>sannhets\u00adbaserte p\u00e5 fak\u00adta<\/em> (kontin\u00adgente, empiriske). For rasjon\u00adal\u00adis\u00adtene er matem\u00adatikk og geometri par\u00ada\u00addig\u00admer p\u00e5 ekte kunnskap for\u00addi de er a pri\u00adori og n\u00f8d\u00advendi\u00adge.<\/p>\n\n\n\n<p><em>Empiris\u00adtene<\/em> \u2013 Locke, Berke\u00adley og Hume \u2013 insis\u00adterte at all kunnskap m\u00e5 stamme fra erfar\u00ading. Locke avviste med\u00adf\u00f8dte ideer og hevdet at sin\u00adnet ved f\u00f8d\u00adse\u00adlen er en <em>tab\u00adu\u00adla rasa<\/em> (blank tavle). Hume skilte mel\u00adlom <em>id\u00e9sam\u00admen\u00adhenger<\/em> (rela\u00adtions of ideas, som \u201calle ungkar\u00ader er ugifte\u201d \u2013 ana\u00adlytiske sannheter) og <em>fak\u00adtap\u00e5\u00ads\u00adtander<\/em> (mat\u00adters of fact, som \u201csolen stiger opp i mor\u00adgen\u201d \u2013 alltid usikre). Det radikale hos Hume: All sub\u00adstan\u00adsiell kunnskap om ver\u00adden er empirisk og der\u00adfor aldri helt sikker.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/exphilnerd.com\/wp-content\/uploads\/2025\/12\/a5ad1036-1a3f-4d7d-a73b-a009aa8111e6_6094x4936.jpeg\" alt><figcaption class=\"wp-element-caption\">(After a draw\u00ading by) Augus\u00adtus Charles Pug\u00adin, Library of the Roy\u00adal Insti\u00adtu\u00adtion, 1809; Rijksmu\u00adse\u00adum<\/figcaption><\/figure>\n\n\n\n<p> <em>Kants syn\u00adtese<\/em>: Kant fors\u00f8k\u00ader \u00e5 red\u00adde b\u00e5de rasjon\u00adal\u00adistenes n\u00f8d\u00advendighet og empiristenes sub\u00adstan\u00adsielle innhold gjen\u00adnom begrepet <em>syn\u00adtetisk a pri\u00adori<\/em>. Han argu\u00admenter\u00ader at rom\u00admet (og tiden) er <em>tran\u00adscen\u00adden\u00adtale<\/em> betingelser for erfar\u00ading \u2013 ikke egen\u00adskaper ved tin\u00adgene selv, men struk\u00adtur\u00ader v\u00e5rt sinn p\u00e5leg\u00adger sanse\u00adda\u00adta. Geome\u00adtrien beskriv\u00ader denne struk\u00adturen, og er der\u00adfor b\u00e5de infor\u00adma\u00adtiv (syn\u00adtetisk) og n\u00f8d\u00advendig (a pri\u00adori). Dette er verken ren defin\u00adisjon (Leib\u00adniz) eller empirisk gen\u00ader\u00adalis\u00ader\u00ading (Hume), men en tred\u00adje kat\u00ade\u00adgori.<\/p>\n\n\n\n<p>For \u00e5 fordype denne kon\u00adtek\u00adsten, les:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><p><strong>Descartes, <\/strong><em><strong>Med\u00adi\u00adtasjon\u00ader over f\u00f8rste filosofi<\/strong><\/em> \u2013 S\u00e6rlig med\u00adi\u00adtasjon 1\u20132 om fun\u00adda\u00admentet for sikker kunnskap<\/p><\/li>\n\n\n\n<li><p><strong>Hume, <\/strong><em><strong>En under\u00ads\u00f8kelse om den men\u00adneske\u00adlige for\u00adstand<\/strong><\/em>, sek\u00adsjon IV om id\u00e9sam\u00admen\u00adhenger vs. fak\u00adtap\u00e5\u00ads\u00adtander<\/p><\/li>\n\n\n\n<li><p><strong>Leib\u00adniz, <\/strong><em><strong>Mon\u00adadolo\u00adgien<\/strong><\/em><strong> og <\/strong><em><strong>Nye essays om den men\u00adneske\u00adlige for\u00adstand<\/strong><\/em> \u2013 Om sannheter basert p\u00e5 for\u00adnuft vs. fak\u00adta<\/p><\/li>\n\n\n\n<li><p><strong>Paul Guy\u00ader &amp; Allen Wood (red.), <\/strong><em><strong>The Cam\u00adbridge Com\u00adpan\u00adion to Kant<\/strong><\/em> (1992) \u2013 S\u00e6rlig kapitler om Kants epis\u00adte\u00admolo\u00adgi og forhold\u00adet til rasjonalisme\/empirisme<\/p><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<p class=\"is-style-text-subtitle is-style-text-subtitle--2\"><em>Utfor\u00addrin\u00adgen fra ikke-euk\u00adlidisk geometri og rel\u00ada\u00adtivitet\u00adste\u00adori<\/em><\/p>\n\n\n\n<p>P\u00e5 1800-tal\u00adlet oppdaget matem\u00adatikere som Rie\u00admann, Lobachevsky og Bolyai at Euk\u00adlids femte pos\u00adtu\u00adlat (par\u00adal\u00adlel\u00adlak\u00adsiomet) kunne erstattes med alter\u00adna\u00adtive aksiomer, og dermed finnes det <em>kon\u00adsis\u00adtente ikke-euk\u00adlidiske geome\u00adtri\u00ader<\/em>. Dette viste at euk\u00adlidisk geometri ikke er den eneste logisk mulige geome\u00adtrien. Sp\u00f8rsm\u00e5let ble der\u00adfor: Hvilken geometri beskriv\u00ader v\u00e5rt fak\u00adtiske rom?<\/p>\n\n\n\n<p>Ein\u00adstein ga svaret: I generell rel\u00ada\u00adtivitet\u00adste\u00adori er romti\u00adden <em>kroket<\/em> av materie og ener\u00adgi, og geome\u00adtrien er ikke-euk\u00adlidisk (Rie\u00admannsk). Dette under\u00adgraver Kants p\u00e5s\u00adtand om at euk\u00adlidisk geometri er a pri\u00adori n\u00f8d\u00advendig for all mulig erfar\u00ading.<\/p>\n\n\n\n<p><strong>Reichen\u00adbach og de logiske pos\u00adi\u00adtivis\u00adtene<\/strong> trakk en radikal kon\u00adklusjon: Syn\u00adtetisk a pri\u00adori kunnskap eksis\u00adter\u00ader ikke. Geometri er enten:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><p><em>Ana\u00adlytisk<\/em> (ren matem\u00adatikk, defin\u00adisjon\u00ads\u00admes\u00adsig sann men uten empirisk innhold), eller<\/p><\/li>\n\n\n\n<li><p><em>Syn\u00adtetisk a pos\u00adte\u00adri\u00adori<\/em> (fysisk teori som m\u00e5 testes empirisk)<\/p><\/li>\n<\/ul>\n\n\n\n<p><strong>Poin\u00adcar\u00e9<\/strong> utviklet en mel\u00adlom\u00adpo\u00adsisjon: Geometri er en <em>kon\u00adven\u00adsjon<\/em> vi vel\u00adger av prak\u00adtiske grun\u00adner, verken a pri\u00adori n\u00f8d\u00advendig eller rent empirisk.<\/p>\n\n\n\n<p>For dette, les:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><p><strong>Reichen\u00adbach, <\/strong><em><strong>The Phi\u00adlos\u00ado\u00adphy of Space and Time<\/strong><\/em> (1928) \u2013 Klas\u00adsisk analyse av hvor\u00addan rel\u00ada\u00adtivitet\u00adste\u00adori p\u00e5virk\u00ader filosofi<\/p><\/li>\n\n\n\n<li><p><strong>Car\u00adnap, <\/strong><em><strong>Der Raum<\/strong><\/em> (1922) \u2013 Skiller mel\u00adlom for\u00admalt, intu\u00aditivt og fysisk rom<\/p><\/li>\n\n\n\n<li><p><strong>Poin\u00adcar\u00e9, <\/strong><em><strong>Sci\u00adence and Hypoth\u00ade\u00adsis<\/strong><\/em> (1902) \u2013 Kon\u00adven\u00adsjon\u00adal\u00adis\u00adtisk posisjon<\/p><\/li>\n\n\n\n<li><p><strong>Tor\u00adret\u00adti, <\/strong><em><strong>Phi\u00adlos\u00ado\u00adphy of Geom\u00ade\u00adtry from Rie\u00admann to Poin\u00adcar\u00e9<\/strong><\/em> (1978) \u2013 Grundig his\u00adtorisk analyse<\/p><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<p class=\"is-style-text-subtitle is-style-text-subtitle--3\"><em>Neo-kan\u00adtianske forsvar og samtids\u00adfilosofi<\/em><\/p>\n\n\n\n<p>Betyr Ein\u00adsteins oppdagelse at Kants pros\u00adjekt er d\u00f8d? Ikke n\u00f8d\u00advendigvis.<\/p>\n\n\n\n<p><strong>Michael Fried\u00adman<\/strong> argu\u00admenter\u00ader for at Kants poeng kan bevares: Det finnes <em>kon\u00adsti\u00adtu\u00adtive a pri\u00adori prin\u00adsip\u00adper<\/em> som gj\u00f8r viten\u00adskap mulig, men disse kan <em>rev\u00adideres<\/em> his\u00adtorisk n\u00e5r ny empiri krev\u00ader det. New\u00adtons teori\u00ader krevde euk\u00adlidisk geometri som kon\u00adsti\u00adtu\u00adtivt ram\u00admev\u00aderk; Ein\u00adstein erstat\u00adtet dette med Rie\u00admannsk geometri. Poenget er at vi alltid trenger noen a pri\u00adori struk\u00adtur\u00ader for \u00e5 tolke erfar\u00ading, selv om disse ikke er evige.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/exphilnerd.com\/wp-content\/uploads\/2025\/12\/813be8b7-0a46-434f-b8c4-80547b2f89c1_1694x1032.jpeg\" alt><figcaption class=\"wp-element-caption\">Oxyrhynchus papyrus (P.Oxy. I 29) show\u00ading frag\u00adment of Euclid\u2019s Ele\u00adments<\/figcaption><\/figure>\n\n\n\n<p> Samtids\u00adde\u00adbat\u00adten dreier seg om:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><p>Kan vi skille mel\u00adlom kon\u00adsti\u00adtu\u00adtive prin\u00adsip\u00adper og empiriske hypoteser?<\/p><\/li>\n\n\n\n<li><p>Er matem\u00ada\u00adtisk kunnskap a pri\u00adori, eller nat\u00adu\u00adralis\u00adert epis\u00adte\u00admolo\u00adgi?<\/p><\/li>\n\n\n\n<li><p>Hva med andre p\u00e5st\u00e5tte syn\u00adtetiske a pri\u00adori sannheter (kausalitet, logikk)?<\/p><\/li>\n<\/ul>\n\n\n\n<p>For dette, les:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><p><strong>Fried\u00adman, <\/strong><em><strong>Dynam\u00adics of Rea\u00adson<\/strong><\/em> (2001) \u2013 Neo-kan\u00adtian\u00adsk forsvar<\/p><\/li>\n\n\n\n<li><p><strong>Ryck\u00adman, <\/strong><em><strong>The Reign of Rel\u00ada\u00adtiv\u00adi\u00adty<\/strong><\/em> (2005) \u2013 Filosofi og fysikk 1915\u20131925<\/p><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\">\n\n\n\n<p><em><strong>Prim\u00e6rtek\u00adster<\/strong><\/em><strong> <\/strong><\/p>\n\n\n\n<p>Kant, I. (1781\/1787\/1996). Kri\u00adtikk av den rene for\u00adnuft\ufeff (R. Schmidt, Trans.). Oslo: Pax For\u00adlag.<br>Kant, I. (1783\/2003). Pro\u00adle\u00adgom\u00ade\u00adna til enhver frem\u00adtidig metafysikk\ufeff (K. Aarnes, Trans.). Oslo: Vidar\u00adfor\u00adlaget.<br>Ein\u00adstein, A. (1916\/2001). Om den spe\u00adsielle og den generelle rel\u00ada\u00adtivitet\u00adste\u00adori\ufeff (S. Neple, Trans.). Oslo: Solum For\u00adlag.<br><\/p>\n\n\n\n<p><em><strong>His\u00adtorisk kon\u00adtekst \u2013 Rasjon\u00adal\u00adisme og empirisme<\/strong><\/em><\/p>\n\n\n\n<p>Descartes, R. (1641\/1996). Med\u00adi\u00adtasjon\u00ader over f\u00f8rste filosofi\ufeff (E. Storheim, Trans.). Oslo: Pax.<br>Hume, D. (1748\/2004). En under\u00ads\u00f8kelse om den men\u00adneske\u00adlige for\u00adstand\ufeff (A. Sti\u00adgen, Trans.). Oslo: Gylden\u00addal.<br>Leib\u00adniz, G. W. (1714\/1990). Mon\u00adadolo\u00adgien\ufeff (R. Myhre &amp; S. Stenerud, Trans.). Oslo: Pax.<\/p>\n\n\n\n<p><em><br><strong>Ikke-euk\u00adlidisk geometri og rel\u00ada\u00adtivitet\u00adste\u00adori<\/strong><\/em><\/p>\n\n\n\n<p>Rie\u00admann, B. (1854\/1873). \u00dcber die Hypothe\u00adsen, welche der Geome\u00adtrie zu Grunde liegen\ufeff. In <em>Gesam\u00admelte math\u00ade\u00adma\u00adtis\u00adche Werke<\/em>. Leipzig: Teub\u00adn\u00ader.<br>Poin\u00adcar\u00e9, H. (1902\/1952). <em>Sci\u00adence and hypoth\u00ade\u00adsis<\/em>. New York: Dover.<br>Reichen\u00adbach, H. (1928\/1958). <em>The phi\u00adlos\u00ado\u00adphy of space and time<\/em>. New York: Dover.<br>Car\u00adnap, R. (1922). Der Raum: Ein Beitrag zur Wis\u00adsenschaft\u00adslehre\ufeff. Berlin: Reuther &amp; Reichard.<\/p>\n\n\n\n<p><em><br><strong>Samtids\u00adfilosofi<\/strong><\/em><\/p>\n\n\n\n<p>Guy\u00ader, P., &amp; Wood, A. (Eds.). (1992). <em>The Cam\u00adbridge com\u00adpan\u00adion to Kant<\/em>. Cam\u00adbridge: Cam\u00adbridge Uni\u00adver\u00adsi\u00adty Press.<br>Fried\u00adman, M. (2001). <em>Dynam\u00adics of rea\u00adson<\/em>. Stan\u00adford, CA: CSLI Pub\u00adli\u00adca\u00adtions.<br>Tor\u00adret\u00adti, R. (1978). <em>Phi\u00adlos\u00ado\u00adphy of geom\u00ade\u00adtry from Rie\u00admann to Poin\u00adcar\u00e9<\/em>. Dor\u00addrecht: Rei\u00addel.<br>Ryck\u00adman, T. (2005). <em>The reign of rel\u00ada\u00adtiv\u00adi\u00adty: Phi\u00adlos\u00ado\u00adphy in physics 1915\u20131925<\/em>. Oxford: Oxford Uni\u00adver\u00adsi\u00adty Press.<br><br><br><em><strong>Over\u00adsik\u00adt\u00adsar\u00adtik\u00adler<\/strong><\/em><\/p>\n\n\n\n<p>Jani\u00adak, A. (2022). Kant\u2019s views on space and time. In E. N. Zal\u00adta (Ed.), <em>The Stan\u00adford ency\u00adclo\u00adpe\u00addia of phi\u00adlos\u00ado\u00adphy<\/em> (Sum\u00admer 2022 ed.). <a href=\"https:\/\/plato.stanford.edu\/archives\/sum2022\/entries\/kant-spacetime\/\">https:\/\/plato.stanford.edu\/archives\/sum2022\/entries\/kant-spacetime\/<\/a> <br>Han\u00adna, R. (2022). Kant\u2019s the\u00ado\u00adry of judg\u00adment. In E. N. Zal\u00adta (Ed.), <em>The Stan\u00adford ency\u00adclo\u00adpe\u00addia of phi\u00adlos\u00ado\u00adphy<\/em> (Spring 2022 ed.). <a href=\"https:\/\/plato.stanford.edu\/archives\/spr2022\/entries\/kant-judgment\/\">https:\/\/plato.stanford.edu\/archives\/spr2022\/entries\/kant-judgment\/<\/a><br>Gray, J., &amp; Fer\u00adreir\u00f3s, J. (2025). Epis\u00adte\u00admol\u00ado\u00adgy of geom\u00ade\u00adtry. In E. N. Zal\u00adta &amp; U. Nodel\u00adman (Eds.), <em>The Stan\u00adford ency\u00adclo\u00adpe\u00addia of phi\u00adlos\u00ado\u00adphy<\/em> (Win\u00adter 2025 ed.). <a href=\"https:\/\/plato.stanford.edu\/archives\/win2025\/entries\/epistemology-geometry\/\">https:\/\/plato.stanford.edu\/archives\/win2025\/entries\/epistemology-geometry\/<\/a><\/p>\n\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Videre lesning | Rom og geometri. 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