# Philosophy of mathematics: Making a fresh start

@article{Cellucci2013PhilosophyOM, title={Philosophy of mathematics: Making a fresh start}, author={Carlo Cellucci}, journal={Studies in History and Philosophy of Science}, year={2013}, volume={44}, pages={32-42} }

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… Expand

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#### References

SHOWING 1-10 OF 112 REFERENCES

The Applicability of Mathematics as a Scientific and a Logical Problem

- Philosophy
- 2010

This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is… Expand

Mathematics. A Science of Patterns?

- Philosophy, Computer Science
- Synthese
- 2004

It is shown that it is possible to construct a realist philosophy of mathematics which commits one neither to dream the dreams of Platonism nor to reduce the word 'realism' to mere noise. Expand

Some proposals for reviving the philosophy of mathematics

- Mathematics
- 1979

By “philosophy of mathematics” I mean the working philosophy of the professional mathematician, the philosophical attitude toward his work that is assumed by the researcher, teacher, or user of… Expand

Top-Down and Bottom-Up Philosophy of Mathematics

- Sociology
- 2013

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice.… Expand

Mathematics-- the music of reason

- Mathematics
- 1992

Introduction.- Mathematics and Mathematicians.- The Nature of Mathematical Problems.- Objects and Methods in Classical Mathematics.- Appendix.- Some Problems of Classical Mathematics.- Appendix.- New… Expand

Grundlagen der Mathematik

- Nature
- 1935

AbstractTHAT the foundations of mathematics are A important is a proposition which will find few opponents, for the science of mathematics is commonly regarded as man's securest intellectual… Expand

Visualization, Explanation and Reasoning Styles in Mathematics

- Computer Science, Mathematics
- 2005

This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of… Expand

Science and Method

- Computer Science
- 1914

One of the main mathematicians of his age, Poincare here deals with a variety of issues of methodology: the selection of facts for study; the calculation of errors; and the use of statistical methods… Expand

What is Mathematics, Really?

- 1997

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon,… Expand

HISTORICAL BACKGROUND, PRINCIPLES AND METHODS OF INTUITIONISM

- Mathematics, Philosophy
- 1975

Publisher Summary This chapter discusses the historical background, principles, and methods of intuitionism. The historical development of the mental mechanism of mathematical thought is naturally… Expand