- Original Message -
From: Lennart Nilsson [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Sunday, June 15, 2003 9:14 AM
Subject: Something for Platonists
Here is something from David Deutsch for Platonists to contemplate...I
think
LN
We see around us a computable universe; that is
Lennart Nilsson
Here is something from David Deutsch for Platonists to
contemplate...I think
LN
We see around us a computable universe; that is to say, of all
possible mathematical objects and relationships, only an
infinitesimal
proportion are ever instantiated in the relationships of
Speaking as a devout Platonist I see nothing much to contemplate
in Deutsch's statement! Whether the Universe is computable, as
he states without argument, or the computable subrealm of the
mathematical world coincides with the physical, which he
believes for unstated reasons, is of no concern to
Joao wrote:
Speaking as a devout Platonist ...
About 7 years ago I realized there was
a severe contradiction resident in modern
concepts of Being.
Godel's Incompleteness Theorems have
established a condition-of-knowledge which seem
to challenge if not negate Platonic thought.
I'd like to
Dear Joao,
Is this the statement of a person that bases their belief in faith or
reason?
Sincerly,
Stephen
- Original Message -
From: Joao Leao [EMAIL PROTECTED]
To: Lennart Nilsson [EMAIL PROTECTED]
Cc: Everything List [EMAIL PROTECTED]
Sent: Monday, June 16, 2003 11:18 AM
Dear Stephen,
Given that, were it not for Plato the question you ask me would
not make sense and could not probably be formulated, I should
not have to answer it.
If that is what you driving at: Mathematical Realism or Platonism is
not a religion, but a conviction which most working
Joao Leao wrote:
James N Rose wrote:
Joao wrote:
Speaking as a devout Platonist ...
About 7 years ago I realized there was
a severe contradiction resident in modern
concepts of Being.
Godel's Incompleteness Theorems have
established a condition-of-knowledge which seem
Gödel's incompleteness theorems have and justly should be judged/interpreted
purely on the merits of the arguments themselves, not the author's
subjective(prejudiced?) interpretation, no?
He was as much a victim(beneficiary?) of his discoveries as was anyone...
CMR
--enter gratuitous quotation
CMR wrote:
Gödel's incompleteness theorems have and justly should be judged/interpreted
purely on the merits of the arguments themselves, not the author's
subjective(prejudiced?) interpretation, no?
He was as much a victim(beneficiary?) of his discoveries as was anyone...
Precisely! The
Joao Leao wrote:
CMR wrote:
Gödel's incompleteness theorems have and justly should be
judged/interpreted
purely on the merits of the arguments themselves, not the author's
subjective(prejudiced?) interpretation, no?
He was as much a victim(beneficiary?) of his discoveries as was
anyone...
Jesse Mazer writes:
Yes, a Platonist can feel as certain of the statement the axioms of Peano
arithmetic will never lead to a contradiction as he is of 1+1=2, based on
the model he has of what the axioms mean in terms of arithmetic. It's hard
to see how non-Platonist could justify the same
James N Rose wrote:
You have glossed over the issue I was establishing.
I am sorry if I did. That was not my intention. I still
think you are mixing platonic apples with not so
platonic oranges, but let us see if I can make out
what you are saying.
Godel pretty well specified a disconnect
The answer is that an incomplete arithmetic axiom system could presumably
by consistent, but who cares? If it is incomplete there will be true statements
that it cannot prove and we are back to the platonist position! The alternative
of an inconsistent system that is complete may actually be more
From: Hal Finney [EMAIL PROTECTED]
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
Subject: Re: Fw: Something for Platonists]
Date: Mon, 16 Jun 2003 10:46:56 -0700
Jesse Mazer writes:
Yes, a Platonist can feel as certain of the statement the axioms of
Peano
arithmetic will never lead to a
Joao,
:-) of course Plato wasn't aware of QM,
but, he was also unaware of the importance
that -mechanism- -real communication involvements-
are resident in any information relation situation,
as would be that which connects the Ideal and Real
and gives validation/meaning to any correspondences
James N Rose wrote:
Joao,
:-) of course Plato wasn't aware of QM,
but, he was also unaware of the importance
that -mechanism- -real communication involvements-
are resident in any information relation situation,
as would be that which connects the Ideal and Real
and gives
Jesse Mazer wrote:
From: Hal Finney [EMAIL PROTECTED]
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
Subject: Re: Fw: Something for Platonists]
Date: Mon, 16 Jun 2003 10:46:56 -0700
Jesse Mazer writes:
Yes, a Platonist can feel as certain of the statement the axioms of
Peano
arithmetic
Joao Leao wrote:
James N Rose wrote:
Joao,
:-) of course Plato wasn't aware of QM,
but, he was also unaware of the importance
that -mechanism- -real communication involvements-
are resident in any information relation situation,
as would be that which connects the Ideal and
James N Rose wrote:
Joao Leao wrote:
James N Rose wrote:
Joao,
:-) of course Plato wasn't aware of QM,
but, he was also unaware of the importance
that -mechanism- -real communication involvements-
are resident in any information relation situation,
as would be that
Joao Leao wrote:
James N Rose wrote:
Joao Leao wrote:
James N Rose wrote:
Joao,
:-) of course Plato wasn't aware of QM,
but, he was also unaware of the importance
that -mechanism- -real communication involvements-
are resident in any information relation
Joao Leao wrote:
Jesse Mazer wrote:
As I think Bruno Marchal mentioned in a recent post, mathematicians use
the
word model differently than physicists or other scientists. But again,
I'm
not sure if model theory even makes sense if you drop all Platonic
assumptions about math.
You are
Jesse Mazer wrote:
Joao Leao wrote:
Jesse Mazer wrote:
As I think Bruno Marchal mentioned in a recent post, mathematicians use
the
word model differently than physicists or other scientists. But again,
I'm
not sure if model theory even makes sense if you drop all Platonic
Joao Leao wrote:
James N Rose wrote:
If there are no qualia but there are universals --
which cannot be identified except via qualia --
something is awry.
Why so? Why can universals only be identified
via qualia if they are, by definition, what
is not reducible to qualia !!!
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