### Abstract

Mathematics used to be portrayed as a deductive science. Stemming from Polya (1954), however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof (Mueller, 1969, p. 295) and which Lakatos examines in Proofs and refutations (Lakatos, 1976). This paper extends the concept of mathematical reasoning along two further dimensions to accommodate thought-experiment.

Original language | English (US) |
---|---|

Pages (from-to) | 489-504 |

Number of pages | 16 |

Journal | Studies in History and Philosophy of Science Part A |

Volume | 37 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2006 |

### Fingerprint

### Keywords

- Informal proof
- Mathematical reasoning
- Thought-experiment

### ASJC Scopus subject areas

- History

### Cite this

**Mathematical reasoning : induction, deduction and beyond.** / Sherry, David M.

Research output: Contribution to journal › Article

*Studies in History and Philosophy of Science Part A*, vol. 37, no. 3, pp. 489-504. https://doi.org/10.1016/j.shpsa.2005.06.012

}

TY - JOUR

T1 - Mathematical reasoning

T2 - induction, deduction and beyond

AU - Sherry, David M

PY - 2006/9

Y1 - 2006/9

N2 - Mathematics used to be portrayed as a deductive science. Stemming from Polya (1954), however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof (Mueller, 1969, p. 295) and which Lakatos examines in Proofs and refutations (Lakatos, 1976). This paper extends the concept of mathematical reasoning along two further dimensions to accommodate thought-experiment.

AB - Mathematics used to be portrayed as a deductive science. Stemming from Polya (1954), however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof (Mueller, 1969, p. 295) and which Lakatos examines in Proofs and refutations (Lakatos, 1976). This paper extends the concept of mathematical reasoning along two further dimensions to accommodate thought-experiment.

KW - Informal proof

KW - Mathematical reasoning

KW - Thought-experiment

UR - http://www.scopus.com/inward/record.url?scp=33747816446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747816446&partnerID=8YFLogxK

U2 - 10.1016/j.shpsa.2005.06.012

DO - 10.1016/j.shpsa.2005.06.012

M3 - Article

AN - SCOPUS:33747816446

VL - 37

SP - 489

EP - 504

JO - Studies in History and Philosophy of Science Part A

JF - Studies in History and Philosophy of Science Part A

SN - 0039-3681

IS - 3

ER -