[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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