Kant's Schematism and the Foundations of Mathematics

Klaus Frovin Jørgensen

Kant's Schematism and the Foundations of Mathematics

Bidragets oversatte titel: Kants skematisme og matematikkens grundlag

Klaus Frovin Jørgensen

Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling

Abstract

Denne afhandling handler om skematisme, som er en teori, der påbegyndes af I. Kant. Kant var aldrig helt præcis med hensyn til, hvad han forstod under denne teori. Baseret p{\aa} Kants teoretiske v{\ae}rker giver jeg en fortolkning af de vigtigste dele af Kants skematisme, og jeg viser, hvorledes skematisme giver anledning til en nyfortolkning af Kants erkendelsesteori ved at lade begrebet v{\ae}re det centrale begreb. S{\aa}ledes viser jeg, hvorledes m{\ae}rkv{\ae}rdige passager i f.eks.\ den f{\o}rste {\it Kritik} kan g{\o}res forst{\aa}elige, n{\aa}r Kants teori om skemaerne tages alvorligt. Jeg viser ligeledes, hvordan vi p{\aa} baggrund af skemaerne f{\aa}r karakteriseret Kants begreb om `objekt', hvilket leder frem til en analyse af matematikkens ontologi og erkendelsesteori. Kant s{\aa} sig selv som en filosof i kontakt med videnskaberne. Det var videnskaberne han s{\o}gte at fundere med sin erkendelsesteori. Jeg viser, hvorledes han desv{\ae}rre var tidsligt et stykke bagefter med hensyn til matematikken. Dette f{\o}rte ham til at formulere sin noget rigide teori ang{\aa}ende den {\it entydige} og {\it endelige} karakterisering af anskuelsen og forstanden. Jeg viser, at f{\ae}nomener i matematikken, som den s{\aa} ud p{\aa} Kants tid, burde have f{\aa}et Kant til at forholde sig mere kritisk i forhold til netop sin formulering af anskuelse, forstand og fornuft. Endelig viser jeg, hvorledes D.\ Hilbert faktisk giver en generalisation af Kants filosofi. Denne generalisation giver anledning til formuleringen af en generel ramme, der kan fungere som grundlag for en forst{\aa}else af matematikkens erkendelsesteori og ontologi.

Bidragets oversatte titel	Kants skematisme og matematikkens grundlag
Originalsprog	Engelsk

Udgivelsessted	Roskilde University
Forlag	Roskilde Universitet
Status	Udgivet - 2005

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title = "Kant's Schematism and the Foundations of Mathematics",

abstract = "The theory of schematism was initiated by I. Kant, who, however, was never precise with respect to what he understood under this theory. I give---based on the theoretical works of Kant---an interpretation of the most important aspects of Kant's theory of schematism. In doing this I show how schematism can form a point of departure for a reinterpretation of Kant's theory of knowledge. This can be done by letting the concept of schema be the central concept. I show how strange passages in, say, the first Critique are in fact understandable, when one takes schematism serious. Likewise, I show how we---on the background of schematism---get a characterization of Kant's concept of 'object'. This takes me to an analysis of the ontology and epistemology of mathematics. Kant understood himself as a philosopher in contact with science. It was science which he wanted to provide a foundation for. I show that, contrary to Kant's own intentions, he was not up-to-date on mathematics. And in fact, it was because of this that it was possible for him to formulate his rather rigid theory concerning the unique characterizations of intuition and understanding. I show how phenomena in the mathematics of the time of Kant should have had an effect on him. He should have remained more critical towards his formulation and demarcation of intuition, understanding and reason. Finally I show how D. Hilbert in fact gives the necessary generalization of Kant's philosophy. This generalization provides us with a general frame work, which functions as a foundation for an understanding of the epistemology and ontology of mathematics.",

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