> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED]]On Behalf Of elephant
> Sent: Tuesday, 27 February 2001 4:20
> To: [EMAIL PROTECTED]
> Subject: Re: MD On materialism....
>
>
> David, I like that alot.
>
> Care to expand?
>
> Zeno said that he could answer the question "are things one or many?", but
> only if someone could explain to him what "one" is.
>
> >Tao gives birth to One.
>
> Hm - does this mean that numerical distinctness is a form that we
> (intellect) give birth to and project upon the continuum? Such
> would be the
> Platonic account.
>
There are TWO expressions of number, one (!) is exact and the other
approximate. This has been around for a while, one of the most recent
findings is:
Spelke,E.S. & Tsivkin,S (2001)"Language and a number: a bilingual training
study" IN Cognition 78, 45-88.
These distinctions are mapped in the above paper to NON-linguistic
representations (even apes can count :-))
The combination of these distinctions through language give us mathematics
as we know it. Analyse the development of such concepts as Cantor's ordinal
transfinite numbers and cardinal transfinite numbers and out pop the same
patterns where ORDINALITY relates to sequence, a particular, repeatable,
START position. To emphasise ordinality you need precision, a concept of
discreteness, of clear 'this' from 'that' as well as 'this' BEFORE/AFTER
'that'.
There is no MAGNITUDE here, each element is seen as following others and of
EQUAL size (or even size is ignored), the 'number' is just a marker of
position.
In ordinality there is a link to metonymy, contiguity, displacement.
In cardinality there is no need for sequence, the emphasis is on magnitude,
on exageration, distortion of a 'one'. This is how Cantor connected set size
in that the members of the set are in no way ordered. From this sort of work
emerged different SIZES of infinity (alephs) with a unique arithematic
compared to the arithematic used to deal with the ordinal transfinites.
In cardinality there is a link to metaphor, to something 'OVER' something
else (higher/lower, bigger/small in size etc) this ties to exageration,
distortion etc.
You can link these distinctions at the neocortical level to the general
characteristics of left (ordinal) and right (cardinal) brains, or zoom-down
to the single neuron and find the same patterns expressed in the axon
(ordinal, frequency modulation, ORDER emphasis) and the synapse/dendrites
(cardinal, amplitude modulation, SIZE emphasis)
Expand these distinctions beyond the individual into cultural development
and the same properties emerge with spiritual emphasis on the explici 'one'
just as there is spirital emphasis on an implicit 'one' (the many are all
linked).
Zeno's question is based on a too 1:1 form of thinking, the brain is 1:many,
when we go LOCAL (particular) so we seek symmetry (1:1), when we go
NON-LOCAL (general) we move to asymmetry (1:many)
In evolution we move from local distinction making in a reactive format to
becoming more proactive. This proactivity results from the derivation of
MAPS based on induction processes (particulars of one individual to
particulars of a SET of individuals). Note how this process (a) speeds up
development through the use of prediction but (2) moves us from direct
experience to the use of metaphor - the MAP. Thus the link of metonymy to
metaphor.
Note that there is a 'zig-zag' process here where metaphors can be taken
literally (localised) and so metaphors formed out of metaphors...
Chris.
------------------
Chris Lofting
websites:
http://www.eisa.net.au/~lofting
http://www.ozemail.com.au/~ddiamond
List Owner: http://www.yahoogroups.com/group/semiosis
> Elephant
>
>
> > From: David Lind <[EMAIL PROTECTED]>
> > Reply-To: [EMAIL PROTECTED]
> > Date: Mon, 26 Feb 2001 16:43:21 +0000
> > To: [EMAIL PROTECTED]
> > Subject: MD On materialism....
> >
> > The Tao gives birth to One.
> > One gives birth to Two.
> > Two gives birth to Three.
> > Three gives birth to all things.
> >
> >> From the Tao Te Ching as translated by Stephen Mitchell
> >
> > Shalom
> >
> > David Lind
> > [EMAIL PROTECTED]
> >
> >
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