Peter;
I try to keep out from the ongoing discussions lately
(no succes to report) but sometimes I get carried
away. I will barge in with 2 remarks into your text
below
John M
--- 1Z <peterdjones.domain.name.hidden> wrote:
>
>
> 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, ...
JM:
Neural firing can refer to 'concept' if you have
either
1.) topically (conceptually) marked neurons (like: the
1,000 for my poppylove, 2000 for your nosebleeding) -
or
2.) distinguished type firings related to topical,
within those even ceptually characterised electrical
(or else - still unknown?) variations - and/or
3.) there is a topical/conceptual homunculus (organ?)
registering the 'meaning' of each firing of THOSE
topically marked and distinguished neurons.
Otherwise the 'firing' is a physiological process,
well measurable in its electrical behavior, but
conceptually meaningless as far as we know today. The
area of the brain where a certain activity is causing
physiological activity is not 'generating' ideas. No
indication so far to the generation of such mental
authoritative thinking in any bunch of neurons. It is
well assumed by the 'neurons only' crowd as a belief.
(In congruence with your continuing statement on
math).
>
>... 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.
JM:
Could you describe the 'neural pattern' meaning a
unicorn? (or simply: a corn?)
John M
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Received on Wed Sep 13 2006 - 15:40:12 PDT