Studies in History and Philosophy of Science Part A 44 (1):32-42 (2013)
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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.
The Foundations of Arithmetic.Gottlob Frege - 1884/1950 - Evanston: Ill., Northwestern University Press.
Critique of Pure Reason.Immanuel Kant - 1781/1998 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
View all 89 references / Add more references
Citations of this work BETA
Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method.Carlo Cellucci - 2013 - Dordrecht, Netherland: Springer.
Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
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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