[FOM] Mathematician in the street
Aatu.Koskensilta at uta.fi
Sat Aug 29 05:50:52 EDT 2009
Quoting Bill Taylor <W.Taylor at math.canterbury.ac.nz>:
> Much in the same way that there is really only one concept of
> "effective computability", or of "a universal machine", or of
> Chaitin's constant; but that the particular implementation of it
> may seem quite different according to the technical substrate,
> which is essentialy unimportant, as they all lead to "the same thing".
How is there really only once concept of Chaitin's constant? The
"halting probability" depends in a quite extreme way on the details of
the coding chosen. A theorem of Solovay illustrates this: there's a
coding on which ZFC can't determine a single digit of Omega.
Your general point, that there are in mathematics -- and elsewhere --
many ways of defining and developing essentially a single concept,
that much we find in a typical treatment is just scaffolding of no
intrinsic significance, and so on, is of course unobjectionable.
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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