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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 ..."
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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
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
Is Science going through a critical stage?
, 1998
"... The unexpected discoveries at the beginning of the century, particularly thanks to Heisenberg, Bohr, and Gödel, has driven the science to drastic changes, opening new, extraordinary, and infinite research fields. After this, many scientists saw, and still today see, a crisis, with dreadful meaning, ..."
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The unexpected discoveries at the beginning of the century, particularly thanks to Heisenberg, Bohr, and Gödel, has driven the science to drastic changes, opening new, extraordinary, and infinite research fields. After this, many scientists saw, and still today see, a crisis, with dreadful meaning, in the science. However, this crisis is only present in that type of science, driven by determinism, which is strictly linked to the common sense. Originally published in italian: L. Foschini, La Scienza è in crisi?, AEI 83, (1996), 455458. English translation by Ms. Simona Baldoni. Revised by the author. The first half of this century has been one of the most intense period in human history: tragic episodes the two world wars were interwoven with moments of great cultural activity. At the end of the XIX century, the world was still permeated with an extremely determinist spirit, which was the result
EXTENDING CANTOR’S PARADOX A CRITIQUE OF INFINITY AND SELFREFERENCE
, 809
"... Abstract. This paper examines infinity and selfreference from a critique perspective. Starting from an extension of Cantor Paradox that suggests the inconsistency of the actual infinite, the paper makes a short review of the controversial history of infinity and suggests several indicators of its i ..."
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Abstract. This paper examines infinity and selfreference from a critique perspective. Starting from an extension of Cantor Paradox that suggests the inconsistency of the actual infinite, the paper makes a short review of the controversial history of infinity and suggests several indicators of its inconsistency. Semantic selfreference is also examined from the same critique perspective by comparing it with selfreferent sets. The platonic scenario of infinity and selfreference is finally criticized from a biological and neurobiological perspective. 1.
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]. ..."
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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].