Philosophy of mathematics: Making a fresh start


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Abstract
The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the effectiveness of mathematics in natural science
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DOI 10.1016/j.shpsa.2012.09.002
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References found in this work BETA

Elusive Knowledge.David K. Lewis - 1996 - Australasian Journal of Philosophy 74 (4):549 – 567.
Critique of Pure Reason.Immanuel Kant - 1991 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
The Extended Mind.Richard Menary (ed.) - 2010 - MIT Press.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.

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Citations of this work BETA

Rethinking Knowledge.Carlo Cellucci - 2015 - Metaphilosophy 46 (2):213-234.
Rethinking Philosophy.Carlo Cellucci - 2014 - Philosophia 42 (2):271-288.
Mathematics Dealing with 'Hypothetical States of Things'.Jessica Carter - 2014 - Philosophia Mathematica 22 (2):209-230.

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