David Nyman wrote:
> marc.geddes.domain.name.hidden wrote:
>
> > I did point out in my last post that there appears to be no simple way
> > to make such reductions (between math concepts and classes of specific
> > things). For instance no one has yet succeeded in showing how math
> > concepts such as infinite sets and transfinite sets (which are precise
> > math concepts) could be converted into physical notions. A also
> > pointed to David Deutsch's excellent 'Criteria For Reality':
>
> I fail to see any 'knock-down' character in this argument. Peter says
> that mathematical concepts don't refer to anything 'external', and on
> one level I agree with him. But they are surely derived from the
> contingent characteristics of experience, and AFAICS experience in this
> context reduces to the contents of our brains. So 'infinite sets' is
> just a model (brain material at another level of description) which IMO
> counts as a 'physical notion' unless you start off as an idealist.
If something is "derived from " experience , that does not
mean it is necessarily a "model of" experience. The derivation
might transofrm it into (a concept of ) something which does not
matches expereince.
Unicorns re derived from horses (or rhinos) but do not
exist as such.
> Put
> simply, you can't think mathematical thoughts without using your brain
> to instantiate them -
> and you don't literally have to instantiate an
> 'infinite set' in the extended sense in order to manipulate a model
> with the formal characteristics you impute to this concept.
However, we should not conclude that mathematical entities
exist as ptterns of neural firing. The neural firing
realises the concept, the mathematical entity is what
the concept is "about". The concept is not about neural
firings (so long as what we are conceptualsiing is maths and not
neurology!).
The mathematical entity does not exist "as" a neural pattern. It does
not exist at all. It is what the concept (which *does* exist as a
neural pattern)
is about. But concepts can be about things which don't exist, like
unicorns.
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Received on Wed Sep 13 2006 - 12:50:47 PDT