Kant's Schematism and the Foundations of Mathematics

Klaus Frovin Jørgensen

    Research output: Book/ReportPh.D. thesisResearch

    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.
    Original languageEnglish
    Place of PublicationRoskilde University
    PublisherRoskilde Universitet
    Publication statusPublished - 2005

    Cite this

    Jørgensen, K. F. (2005). Kant's Schematism and the Foundations of Mathematics. Roskilde University: Roskilde Universitet.
    Jørgensen, Klaus Frovin. / Kant's Schematism and the Foundations of Mathematics. Roskilde University : Roskilde Universitet, 2005.
    @phdthesis{c5709fe0a70111db8e5a000ea68e967b,
    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.",
    author = "J{\o}rgensen, {Klaus Frovin}",
    year = "2005",
    language = "English",
    publisher = "Roskilde Universitet",

    }

    Jørgensen, KF 2005, Kant's Schematism and the Foundations of Mathematics. Roskilde Universitet, Roskilde University.

    Kant's Schematism and the Foundations of Mathematics. / Jørgensen, Klaus Frovin.

    Roskilde University : Roskilde Universitet, 2005.

    Research output: Book/ReportPh.D. thesisResearch

    TY - BOOK

    T1 - Kant's Schematism and the Foundations of Mathematics

    AU - Jørgensen, Klaus Frovin

    PY - 2005

    Y1 - 2005

    N2 - 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.

    AB - 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.

    M3 - Ph.D. thesis

    BT - Kant's Schematism and the Foundations of Mathematics

    PB - Roskilde Universitet

    CY - Roskilde University

    ER -

    Jørgensen KF. Kant's Schematism and the Foundations of Mathematics. Roskilde University: Roskilde Universitet, 2005.