TY - JOUR
PY - 2015
SN - 1887-3987
N1 - 1887-3987
T2 - PNA
VL - 9
IS - 3
TI - Generalizing is necessary or even unavoidable
UR - http://www.pna.es/Numeros2/pdf/Otte2015PNA9(3)Generalizing.pdf
PB - Grupo FQM
DA - 2002/09/01
KW - Complementarity
KW - Genetic epistemology
KW - Mathematical cognition
AU - Otte, Miguel F.
AU - Mendonça, Tânia M.
AU - de Barros, Luiz
SP - 143-164
LA - English
AD - Universidade Bandeirantes de São Paulo
M3 - Research paper
AB - The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a pattern. Algebra or modern axiomatic come to mind, as examples. However, strictly formalistic mathematics did not pay sufficient attention to the fact that modern axiomatic theories require a complementary element, in terms of intended applications or models, not to end up in a merely formal game.
ER -