[FOM] Identity of isomorphic structures
W.Taylor at math.canterbury.ac.nz
W.Taylor at math.canterbury.ac.nz
Mon Apr 7 20:43:26 EDT 2014
There is also the matter of automorphisms, which might not even exist
under this view!
- Bill Taylor
Quoting Martin Davis <martin at eipye.com>:
> Steve Awodey's provocative and interesting article "Structuralism,
> Invariance, and Univalence" in the February 2014 issue of Philosophica
> Mathematica discusses the proposal to regard isomorphic structures as
> identical. (This proposition is a consequence of an even more widely
> embracing proposed axiom.) Examples are given of situations in which
> mathematicians routinely "identify" two isomorphic structures with one
> another, such as identifying the Cauchy-sequence-of-rationals real numbers
> with the Dedkind-cuts-in-rationals real numbers.
>
> I would be interested to learn what proponents of this view would say about
> the well-known isomorphism between the group of positive real numbers under
> multiplication and the group of all real numbers under addition. Note that
> in this case it's the isomorphic mapping itself that is important: it
> underlies the use of logarithms in computation that had such a significant
> role before modern computers.
>
> Martin
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