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Hilbert’s Program Then and Now
, 2005
"... Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of Göttingen and els ..."
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Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of Göttingen and elsewhere in the 1920s
VISUALIZATION OF ORDINALS ∗
"... We describe the pictorial representations of infinite ordinals used in teaching set theory, and discuss a possible use in naturalistic foundations of mathematics. 1 ..."
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We describe the pictorial representations of infinite ordinals used in teaching set theory, and discuss a possible use in naturalistic foundations of mathematics. 1
CHAPTER 7 MATHEMATICAL CONCEPTS AND PHYSICAL OBJECTS
"... Abstract. The notions of “construction principles ” is proposed as a complementary notion w.r. to the familiar “proof principles ” of Proof Theory. The aim is to develop a parallel analysis of these principles in Mathematics and Physics: common construction principles, in spite of different proof pr ..."
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Abstract. The notions of “construction principles ” is proposed as a complementary notion w.r. to the familiar “proof principles ” of Proof Theory. The aim is to develop a parallel analysis of these principles in Mathematics and Physics: common construction principles, in spite of different proof principles, justify the effectiveness of Mathematics in Physics. The very “objects ” of these disciplines are grounded on commun genealogies of concepts: there is no trascendence of concepts nor of objects without their contingent and shared constitution. A comparative analysis of Husserl’s and Gödel’s philosophy is hinted, with many references to H. Weyl’s reflections on Mathematics and Physics. Introduction (with F. Bailly) With this text, we will first of all discuss a distinction, internal to mathematics, between “construction principles ” and “proof principles ” (see [Longo, 1999; 2002]). In short, it will be a question of grasping the difference between the construction of mathematical concepts and structures