Synthetic a priori and mathematical account in Kant’s philosophy

Giacomo Maria Virone

Synthetic a Priori and Mathematical Account in Kant’s Philosophy

Collana: «Il Filarete. Pubblicazioni della Facoltà di Lettere e Filosofia dell’Università degli Studi di Milano» - 281
16 x 23,5 cm – pagg. 258 – 2012 – € 37,00
ISBN 978-88-7916-599-0

CONTENTS: Preface — Introduction — FIRST PART. On the nature of mathematics in Kant. A critical comparison with traditional interpretation. I. General logic and transcendental logic: 1. Preliminary questions. First general reflections on the analytic and the synthetic – 2. Why a transcendental logic? – 2.1. Criticism of the non-contradiction principle – 3. Some clarifications of the distinction between the analytic and the synthetic — II. Intuition, concept and synthetic a priori: Kant’s mathematics: 1. Are there «given» synthetic a priori cognitions? – 2. ‘Judgments’ of mathematics and «fundamental propositions of understanding» – 3. Principles of understanding, mathematical constitution of experience and synthetic a priori. On «mathematical» and «dynamical» – 4. On the concept of ‘construction’. The synthetic a priori: logical or epistemological issue? — III. Are space and time forms of intuition or concepts? Logic, geometry and epistemological reasons: 1. The issue of the infinite: logical concerns and geometrical reasons in contemporary criticism – 2. The pure intuition of space: the intelligibility of epistemological reasons – 2.1. Intension and extension of concept. Speaking of the «metaphysical exposition of space» – 2.2. «Actu infinitum non datur a parte rei, sed tantum a parte cogitantis» – 3. Impossibility de jure of an «Aesthetic» without an «Analytic». The unity de facto of concept and intuition – 4. Conclusions — SECOND PART. A heterodox way. The analyticity of mathematical sciences and the meaning of the synthetic a priori. IV. Substantial analyticity of ‘judgments’ of mathematical sciences: 1. Mathematical sciences and their relations with the pure forms of space and time – 1.1. Transcendental schematism and schema of mathematical concepts. The different levels of considering mathematical sciences – 2. Mathematical sciences and synthetic activity of the understanding – 3. Kant through Fries: the particular case of arithmetic — V. T he category of reality: «Anticipations of perception» and intrinsic mathematization of the real: 1. Kant’s concept of experience, the role of mathematics and the nature of space and time. The development of epistemological considerations – 2. Metaphysics and transcendental a priori. Reflections and interpretative suggestions – 3. Is a «general metaphysics» without mathematics possible? – 4. The sense of the infinitude of concepts of space and time. The epistemological validity of the «transcendental dialectic» – 5. Conclusions — Bibliography — Index of names.

Kant’s account of mathematics has been one of the most debated topics in the recent literature. It amounts to a complicated matter Kant bequeathed to philosophy. Since Kant’s time, several philosophers have been trying to disentangle the Kantian claims on the nature of mathematical sciences. The issue of the synthetic a priori is the stumbling block, insofar as it grounds the general structure of Kant’s portrait of human knowledge. Different proposals critics have put forward so far incline to overestimate logical or geometrical reasons in the attempt at fi nding out why Kant considered mathematics and geometry as synthetic a priori sciences. Conversely, this book aims at taking transcendental facets of critical project seriously. An epistemological analysis of the role of the notion of synthetic a priori is the principle clue. The outcome might sound a bit heterodox but aims at giving Kant his due.

Giacomo Maria Virone (Caltanissetta, 1981) studied philosophy at Università degli studi di Milano wherefrom he also obtained his PhD in philosophy. During his research he spent a period at the Department of Logic and Philosophy of Science at University of California, Irvine. He published a paper about Alois Riehl’s realism.

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