[FOM] Formalization Thesis vs Formal nature of mathematics
Vladimir Sazonov
Vladimir.Sazonov at liverpool.ac.uk
Wed Jan 2 20:45:32 EST 2008
Alex Blum wrote
> But more
> importantly, it is not clear that rigour is not the consequence of the
> abstract subject matter of mathematics. It's scientific methodology
> demands it.
For me, abstractness of mathematical objects appears to be consequence
of its rigorous (formal) character. When we separate the form of
mathematical reasoning from its content/intuition (and judge
correctness of this reasoning according to its form, thereby making it
rigorous), this is a very special kind of abstraction. This explains
which way mathematical abstraction differs from the general
philosophical category of abstraction. The process of abstraction
appears in any human activity. Evidently this does not mean that these
activities are of mathematical character. In other words, abstractness
is not the definitive, distinctive attribute of mathematics, whereas
formality (rigour) is.
Vladimir Sazonov
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