Re: The Physics of the Platonic Realm
- From: Des <descartesnewts@xxxxxxxxx>
- Date: Sat, 04 Aug 2007 16:08:03 -0700
On Aug 5, 4:28 am, Uncle Al <Uncle...@xxxxxxxxxxxxx> wrote:
Des wrote:
Many scientists hold to the platonic view
[snip]
1) Plato's "Cave" is crap. It isn't even good literature.
2) Lying idiot.
--
Uncle Alhttp://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/lajos.htm#a2
Stupid genius, read Penose stuff about it to
be briefted (He has IQ as high as you):
Penrose said:
"I have briefly described the three main streams of
present-day mathematical philosophy: formalism,
Platonism, and intuitionism. I have made no secret of
the fact that my sympathies lie strongly with the
Platonistic view that mathematical truth is absolute,
external, and eternal, and not based on man-made
criteria; and that mathematical objects have a
timeless existence of their own, not dependent on
human society nor on particular physical objects. I
have tried to make my case for this view in this
section , in the previous section, and at the end of
Chapter 3. I hope that the reader is prepared to go
most of the way with me on this. It will be important
for a good deal of what we shall encounter later."
[....]
(Penrose continues)
"PLATONISM OR INTUITIONISM?
I have pointed out two opposing schools of
mathematical philosophy, siding strongly with the
Platonist rather than the formalist view. I have
actually been rather simplistic in my distinctions.
There are many refinements of viewpoint that can be
made. For example, one can argue under the heading of
'Platonism' whether the objects of mathematical
thought have any kind of actual "existence' or whether
it is just the concept of mathematical 'truth' which
is absolute. I have not chosen to make an issue of
such distinctions here. In my own mind, the
absoluteness of mathematical truth and the Platonic
existence of mathematical concepts are essentially
the same thing. The 'existence' that must be
attributed to the Mandelbrot set, for example, is a
feature of its 'absolute' nature. Whether a point of
the Argand plane does, or does not, belong to the
Mandelbrot set is an absolute question, independent
of which mathematician, or which computer, is
examining it. It Is the Mandelbrot set's
'mathematician-independence' that gives it its
Platonic existence. Moreover, its finest details lie
beyond what is accessible to us by use of computers.
Those devices can yield only approximations to a
structure that has a deep er and
computer-independent' existence of its own. I do
appreciate, however, that there can be many other
viewpoints that are reasonable to hold on this
question. We need not worry too much about these
distinctions here."
[....]
(Penrose continues)
"Is mathematics invention or discovery? When
mathematicians come upon their results are they just
producing elaborate mental constructions which have
no actual reality, but whose power and elegance is
sufficient simply to fool even their inventors into
believing that these mere mental constructions are
'real'? Or are mathematicians really uncovering
truths which are, in fact, already 'there'- truths
whose existence is quite independent of the
mathematicians' activities? I think that, by now, it
must be quit e clear to the reader that I am an
adherent of the second, rather than the first, view,
at least with regard to such structures as complex
numbers and the Mandelbrot set.
Yet the matter is perhaps not quite so
straightforward as this. As I have said, there are
things in mathematics for which the term 'discovery'
is indeed much more appropriate than 'Invention',
such as the examples just cited. These are the cases
where much more comes out of the structure than is
put into it in the first place."
[....]
(Penrose continues)
"Having made these points, however, I cannot help
feeling that, with mathematics, the case for
believing in some kind of etherial, eternal existence,
at least for the more profound mathematical
concepts, is a good deal stronger than in those
other cases. There is a compelling uniqueness and
universality in such mathematical ideas which
seems to be of quite a different order from that
which one could expect In the arts or engineering.
The view that mathematical concepts could
exist in such a timeless, etherial sense was
put forward in ancient times (c. 360 Bc)
by the great Greek philosopher Plato. Consequently,
this view is frequently referred to as mathematical
Platonism. It will have considerable importance for us
later."
.
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