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 |
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Keywords
- Informal proof
- Mathematical reasoning
- Thought-experiment
ASJC Scopus subject areas
- History
Cite this
Mathematical reasoning : induction, deduction and beyond. / Sherry, David M.
In: Studies in History and Philosophy of Science Part A, Vol. 37, No. 3, 09.2006, p. 489-504.Research output: Contribution to journal › Article
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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 -