[FOM] Identity of isomorphic structures
Bas Spitters
b.a.w.spitters at gmail.com
Tue Apr 8 04:24:32 EDT 2014
Dear Martin,
You may be close to answering your own question. The *identification*
by the logarithm is important.
Homotopy type theory provides a precise calculus for transporting
types/structures defined over the multiplicative group to the additive
group.
Bas
On Mon, Apr 7, 2014 at 9:48 PM, Martin Davis <martin at eipye.com> wrote:
> 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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