id: 05913269
dt: j
an: 2011d.00463
au: Hersh, Reuben
ti: Mathematical intuition (Poincaré, Polya, Dewey).
so: Mont. Math. Enthus. 8, No. 1-2, 35-50 (2011).
py: 2011
pu: Information Age Publishing (IAP), Charlotte, NC; Department of Mathematical
Sciences, The University of Montana, Missoula, MT
la: EN
cc: E40 D20
ut: intuition; induction; pragmatism; approximation; convergence; limits,
knowledge
ci:
li:
ab: Summary: Practical calculation of the limit of a sequence often violates
the definition of convergence to a limit as taught in calculus.
Together with examples from Euler, Polya and Poincare, this fact shows
that in mathematics, as in science and in everyday life, we are often
obligated to use knowledge that is derived, not rigorously or
deductively, but simply by making the best use of available information
‒ plausible reasoning. The “philosophy of mathematical practice"
fits into the general framework of “warranted assertibility", the
pragmatist view of the logic of inquiry developed by John Dewey.
rv: