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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

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Elusive Knowledge.David K. Lewis - 1996 - Australasian Journal of Philosophy 74 (4):549 – 567.
The Foundations of Arithmetic.Gottlob Frege - 1884/1950 - Evanston: Ill., Northwestern University Press.
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Citations of this work BETA

Rethinking Knowledge.Carlo Cellucci - 2015 - Metaphilosophy 46 (2):213-234.
Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
Rethinking Philosophy.Carlo Cellucci - 2014 - Philosophia 42 (2):271-288.
Necessity of Thought.Cesare Cozzo - 2015 - In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Springer. pp. 101-20.

View all 8 citations / Add more citations

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