Results 1 
7 of
7
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 ..."
Abstract

Cited by 7 (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
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
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)
The Constructed Objectivity of Mathematics and the Cognitive Subject 1
"... ÇThe problems of Mathematics are not isolated problems in a vacuum; there pulses in them the life of ideas which realize themselves in concreto through out human endeavours in our historical existence, yet forming an indissoluble whole transcend any particular scienceÈ [Hermann Weyl, 1949]. ..."
Abstract
 Add to MetaCart
ÇThe problems of Mathematics are not isolated problems in a vacuum; there pulses in them the life of ideas which realize themselves in concreto through out human endeavours in our historical existence, yet forming an indissoluble whole transcend any particular scienceÈ [Hermann Weyl, 1949].
Space and Time in the Foundations of Mathematics, or some challenges in the interactions with other sciences 1
"... Summary: Our relation to phenomenal space has been largely disregarded, and with good motivations, in the prevailing foundational analysis of Mathematics. The collapse of Euclidean certitudes, more than a century ago, excluded ‘’geometric judgments’ ’ from certainty and contributed, by this, to isol ..."
Abstract
 Add to MetaCart
Summary: Our relation to phenomenal space has been largely disregarded, and with good motivations, in the prevailing foundational analysis of Mathematics. The collapse of Euclidean certitudes, more than a century ago, excluded ‘’geometric judgments’ ’ from certainty and contributed, by this, to isolate the foundation of Mathematics from other disciplines. After the success of the logical approach, it is time to broaden our foundational tools and reconstruct, also in that respect, the interactions with other sciences. The way space (and time) organize knowledge is a crossdisciplinary issue that will be briefly examined in Mathematical Physics, Computer Science and Biology. This programmatic paper focuses on an epistemological approach to foundations, at the core of which is the analysis of the ‘’knowledge process’’, as a constitutive path from cognitive experiences to mathematical concepts and structures. Contents: