Mathematical thought and its objects
نویسنده
چکیده
Matematikaren filosofia izan da Charles Parsonsen ikerketa-gaia urte askotan. Harvard Unibertsitateko Edgar Pierce Professor of Philosophy emeritua izanik, jarraitzen du lanean, azken liburu honek erakusten duen moduan. Egia da kapitulu gehienak aurrez publikatutakoak direla baina, Parsonsek berak dioen moduan, guztiak daude berrikusiak, berrituak edo garatuak. Denbora luzez espero izan den liburua da eta bere matematikari buruzko azken ikuspegia ez ote den susmoa daukat, bere irakasle nagusiei eginiko erreferentzia dela eta: B. Dreven, W.V. Quine eta Hao Wang. Matematikaren filosofiari buruzko liburua da, noski, baina bereziki matematikaren ontologia eta epistemologiari buruzkoa: zein diren objektu matematikoak eta nola den posible horien ezagutza. Estrukturalista da Parsons eta ikuspegi horretatik aztertzen ditu objektu matematikoak eta beren existentzia. Parsonsek defendatuko duen teoria nominalismotik urrun dago, hau da, objektu matematikoen existentziaren ukaziotik urrun dago, baina baita ere platonismotik, ez baitu objektu transzendenterik onartzen. Beretzat existentzia, beti, estruktura edo egitura batekiko ematen da eta, ondorioz, objektu matematikoen izaera horrelakoa da: egitura batekiko erlatiboa. Parsonsen bigarren ardatz teorikoa intuizionismoa da. Intuizioa da objektu abstraktuetara heltzeko bidea. Ikusiko dugunez, intuizio horrek ez digu zenbakiak eraikitzen uzten, ez baitugu horien intuiziorik, ez baitira oinarrizko objektuak.
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