Results 1 
5 of
5
The Constructed Objectivity of Mathematics and the Cognitive Subject
, 2001
"... Introduction This essay concerns the nature and the foundation of mathematical knowledge, broadly construed. The main idea is that mathematics is a human construction, but a very peculiar one, as it is grounded on forms of "invariance" and "conceptual stability" that single out the mathematical con ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Introduction This essay concerns the nature and the foundation of mathematical knowledge, broadly construed. The main idea is that mathematics is a human construction, but a very peculiar one, as it is grounded on forms of "invariance" and "conceptual stability" that single out the mathematical conceptualization from any other form of knowledge, and give unity to it. Yet, this very conceptualization is deeply rooted in our "acts of experience", as Weyl says, beginning with our presence in the world, first in space and time as living beings, up to the most complex attempts we make by language to give an account of it. I will try to sketch the origin of some key steps in organizing perception and knowledge by "mathematical tools", as mathematics is one of the many practical and conceptual instruments by which we categorize, organise and "give a structure" to the world. It is conceived on the "interface" between us and the world, or, to put it in husserlian terminology, it is "de
Reflections On Formalism And Reductionism In Logic And Computer Science
"... This report contains a preprint (paper 1) and a reprint (paper 2). The first develops some epistemological views which were hinted in the second, in particular by stressing the need of a greater role of geometric insight and images in foundational studies and in approaches to cognition. The second p ..."
Abstract
 Add to MetaCart
This report contains a preprint (paper 1) and a reprint (paper 2). The first develops some epistemological views which were hinted in the second, in particular by stressing the need of a greater role of geometric insight and images in foundational studies and in approaches to cognition. The second paper is the "philosophical" part of a lecture in Type Theory, whose technical sections, omitted here, have been largely subsumed by subsequent publications (see references). The part reprinted below discusses more closely some historical remarks recalled in paper 1. 1. Reflections on formalism and reductionism in Logic and Computer Science (pp. 1  9)
unknown title
, 2009
"... The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning ..."
Abstract
 Add to MetaCart
The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning
unknown title
, 2009
"... The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning ..."
Abstract
 Add to MetaCart
The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning
unknown title
, 2009
"... The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning ..."
Abstract
 Add to MetaCart
The significance of Nathanson’s boss factor in legitimising Aristotle’s particularisation Why we need to revise current interpretations of Cantor’s, Gödel’s, Turing’s and Tarski’s formal reasoning