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The reasonable effectiveness of Mathematics and its Cognitive roots
, 2001
"... this paper, Mathematics is viewed as a "three dimensional manifold" grounded on logic, formalisms and invariants of space; we will appreciate by 1 ..."
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this paper, Mathematics is viewed as a "three dimensional manifold" grounded on logic, formalisms and invariants of space; we will appreciate by 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