[FOM] 31st Novembertagung 2020
Timothy Y. Chow
tchow at math.princeton.edu
Thu Apr 23 13:24:26 EDT 2020
Joe Shipman wrote:
> > On the other hand, some philosophers also argue that the axiomatic
> > view on mathematics may be harmful in that it omits fundamental
> > aspects of mathematical practice and idealizes mathematical reasoning
> > in an unfaithful way.
>
> Which philosophers? I'm interested in any references you have on this
> topic.
Depending on what exactly is meant by "the axiomatic view on mathematics"
(and also on who counts as a "philosopher"!), Reuben Hersh might be an
example. In his essay, "How Mathematicians Convince Each Other, or `The
Kingdom of Math is Within You,'" Hersh writes (among many other things):
One may use formal proof as a "model" of mathematicians' proof, but
mathematicians' proof is not formal proof. Our starting point is
established mathematics, not some postulated axioms, and our reasoning
is "semantic", based on the properties of mathematical entities, rather
than "syntactic", based on properties of formal sentences.
Note particularly his claim that "Our starting point is ... not some
postulated axioms."
Tim
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