De la matemática clásica a la matemática moderna: Hilbert y el esquematismo kantiano

  title={De la matem{\'a}tica cl{\'a}sica a la matem{\'a}tica moderna: Hilbert y el esquematismo kantiano},
  author={Carlos Torres Alcaraz},
  • C. Alcaraz
  • Published 1 September 2016
  • Mathematics, Philosophy
This essay examines the manner in which Hilbert worked out his first formalism in his investigations on the foundations of geometry. To elu- cidate these views, Hilbert's position is compared with that of Kant, who set forth a constructive notion of "geometrical objects" which endured in the Phi- losophy of mathematics for a long time. In the first part, the author explores the way in which Kant explains the notion of proof in classical geometry and clarifies how his account relates to his… Expand
(Geometry, Formalism and Intuition: David Hilbert and the formal Axiomatic Method (1891-1905))
The paper presents and analyzes a set of unpublished notes for lecture courses on geometry, which David Hilbert gave between 1891 and 1905. it will be argued


Kant on space, empirical realism and the foundations of geometry
One of the first reviews (Garve-Feder, 1782) of the Critique of Pure Reason described Kant’s system as a form of idealism of a piece with that of Berkeley. Kant (Letter to Garve, August 7, 1783) wasExpand
Kant’s Theory of Geometry
Since the important work of early twentieth century philosophers of geometry like Russell and Carnap, Schlick and Reichenbach, Kant’s theory of geometry has not looked very attractive. After theirExpand
Kant's philosophy of mathematics : modern essays
Preface. Introduction: Mathematics in Kant's Critique of Pure Reason C.J. Posy. Part I: Classic Papers of the 1960's and 1970's. Kant on the Mathematical Method J. Hintikka. Kant's Philosophy ofExpand
David Hilbert and his mathematical work
A great master of mathematics passed away when David Hilbert died in Gottingen on February the 14th, 1943, at the age of eighty-one. In retrospect it seems to us that the era of mathematics uponExpand
Philosophy of mathematics : selected readings
Preface to the second edition Introduction Part I. The Foundations of Mathematics: 1. The logicist foundations of mathematics Rudolf Carnap 2. The intuitionist foundations of mathematics ArendExpand
Intuitionism and formalism
Publisher Summary This chapter discusses the intuitionism and formalism. In Kant, one find an old form of intuitionism almost completely abandoned in which time and space are taken to be the forms ofExpand
David Hilbert 1862-1943
  • H. Weyl
  • History
  • Obituary Notices of Fellows of the Royal Society
  • 1944
David Hilbert, upon whom the world looked during the last decades as the greatest of the living mathematicians, died in Gottingen, Germany, on 14 February 1943. At the age of eighty-one he succumbedExpand
An introduction to the history of mathematics
Before the 17th Century. Part I: Cultural Connections: The Hunters of the Savanna (The Stone Age). Numeral Systems. Part II: Cultural Connections: The Agricultural Revolution (The Cradles ofExpand
Gauss and Non-Euclidean Geometry
It becomes clear that a mathematician persuaded of the truth of non-Euclidean geometry and seeking to convince others is almost driven to start by looking for, or creating, non-EuclideanExpand
Kant’s Philosophy of Arithmetic
The interest and influence of Kant’s philosophy as a whole have certainly been great enough so that this by itself would be enough to make Kant’s philosophy of arithmetic of interest to historicalExpand