Heis, Jeremy (Author)
It is now commonly accepted that any adequate history of late nineteenth and early twentieth century philosophy--and thus of the origins of analytic philosophy--must take seriously the role of Neo-Kantianism and Kant interpretation in the period. This dissertation is a contribution to our understanding of this interesting but poorly understood stage in the history of philosophy. Kant's theory of the concepts, postulates, and proofs of geometry was informed by philosophical reflection on diagram-based geometry in the Greek synthetic tradition. However, even before the widespread acceptance of non-Euclidean geometry, the projective revolution in nineteenth century geometry eliminated diagrams from proofs and introduced "ideal" elements that could not be given a straightforward interpretation in empirical space. A Kantian like the very early Russell felt forced to regard the ideal elements as convenient fictions. The Marburg Neo-Kantians--the philosophical school that included Ernst Cassirer (1874-1945)--thought that philosophy, as "transcendental logic," needed to take the results of established pure mathematics as a "fact," not a fiction. Cassirer therefore updates Kant by rejecting the "Transcendental Aesthetic" and by using elements in Richard Dedekind's foundations of arithmetic to rework Kant's idea that the geometrical method is the "construction of concepts." He further argues that geometry is "synthetic" because it progresses when mathematicians introduce new structures (like the complex projective plane) that are not contained in the old structures, but unify them under a new point- of-view. This new "Kantian" theory of modern mathematics, Cassirer argues, is inconsistent with the traditional theory of concept formation by abstraction. Drawing on earlier Neo-Kantian interpretations, Cassirer argues that Kant's theory of concepts as rules undermines the traditional theory of concept formation, and he gives a "transcendental" defense of the new logic of Frege and Russell. (In an appendix, I discuss the contemporaneous accounts of concept formation in Gottlob Frege and Hermann Lotze.)
...MoreDescription Cited in Diss. Abstr. Int. A 69/01 (2008). Pub. no. AAT 3300571.
Article
Heis, Jeremy;
(2011)
Ernst Cassirer's Neo-Kantian Philosophy of Geometry
(/isis/citation/CBB001035116/)
Article
Brenner, Anastasios;
(2014)
La réception du logicisme en France en réaction à la controverse Poincaré-Russell
(/isis/citation/CBB001551988/)
Chapter
Farzad Mahootian;
(2020)
Kant, Cassirer, and the Idea of Chemical Element
(/isis/citation/CBB657452257/)
Article
Francesca Biagioli;
(2020)
Ernst Cassirer's transcendental account of mathematical reasoning
(/isis/citation/CBB961648354/)
Book
William Boos;
Florence S. Boos;
(2018)
Metamathematics and the Philosophical Tradition
(/isis/citation/CBB060593902/)
Article
Domski, Mary;
(2013)
Kant and Newton on the a priori Necessity of Geometry
(/isis/citation/CBB001320266/)
Thesis
Doyle, Bret J. Lalumia;
(2006)
The Logic of Descartes' Scientific Method in the “Rules,” “Geometry,” and “Optics”
(/isis/citation/CBB001561645/)
Book
Paolo Zellini;
(1999)
Gnomon. Una indagine sul numero
(/isis/citation/CBB253354203/)
Book
Paolo Zellini;
(2010)
Numero e logos
(/isis/citation/CBB843348217/)
Book
Flood, Raymond;
Rice, Adrian;
Wilson, Robin;
(2011)
Mathematics in Victorian Britain
(/isis/citation/CBB001221196/)
Article
Moretti, Alessio;
(2014)
Was Lewis Carroll an Amazing Oppositional Geometer?
(/isis/citation/CBB001550610/)
Article
Tolleya, Clinton;
(2012)
Bolzano and Kant on the Nature of Logic
(/isis/citation/CBB001210999/)
Article
Novy, Luboš;
(2008)
Les relations entre la logique et la mathématique dans l'oeuvre de Bernard Bolzano
(/isis/citation/CBB001021148/)
Article
Günther Eder;
(2021)
Frege on intuition and objecthood in projective geometry
(/isis/citation/CBB221284966/)
Article
Giovanelli, Marco;
(2008)
Kant, Helmholtz, Riemann und der Ursprung der geometrischen Axiome
(/isis/citation/CBB001034987/)
Book
Vinci, Thomas C.;
(2015)
Space, Geometry, and Kant's Transcendental Deduction of the Categories
(/isis/citation/CBB001500573/)
Article
Giovanelli, Marco;
(2010)
Urbild und Abbild: Leibniz, Kant und Hausdorff über das Raumproblem
(/isis/citation/CBB001230056/)
Book
Elena Anne Corie Marchisotto;
Francisco Rodriguez-Consuegra;
James T. Smith;
(2021)
The Legacy of Mario Pieri in Foundations and Philosophy of Mathematics
(/isis/citation/CBB763111584/)
Article
Zammito, John;
(2006)
Teleology Then and Now: The Question of Kant's Relevance for Contemporary Controversies over Function in Biology
(/isis/citation/CBB000770751/)
Book
Alberto Cogliati;
(2024)
La geometria non euclidea. Una breve storia dall’antichità a Poincaré
(/isis/citation/CBB276091257/)
Be the first to comment!