On 11/2/2012 12:49 PM, Bruno Marchal wrote:
On 01 Nov 2012, at 21:33, Stephen P. King wrote:
On 11/1/2012 11:36 AM, Bruno Marchal wrote:
On 01 Nov 2012, at 00:35, Stephen P. King wrote:
On 10/31/2012 9:39 AM, Roger Clough wrote:
1) Yes, numbers float in a sea of universal mind (the One).
2) Here's a thought. If the universe acts like a gigantic
homunculus, with the supreme monad or One as its mind,
then could there be a solipsism to our universe such that
other multiverse versions of oiur universe could not access
(the mind of) ours ? Would this be a problem for multiverse
theories ?
Roger Clough,[email protected] 10/31/2012
Dear Roger,
I think that this idea is exactly wrong. The idea that "numbers
float in a sea of universal mind (the One)" makes the explanation
an infinite regress.
Replace the One by arithmetical truth, and the infinite regress
disappear.
Dear Bruno,
Only if arithmetic truth is theory independent,
Gödel + Tarski => Arithmetical Truth is so independent of any
effective theory that no such theory can get it. mathematical logic,
and math, cannot have any meaning without arithmetical truth being
independent of theories.
Dear Bruno,
"Truth is Independence of theories" cannot mean that truth is a
meaningful value in the primitive ontological level. The relation 'Gödel
+ Tarski => Arithmetical Truth' cannot even exist as a meaningful
expression because there is no differentiation of expression at the
ontologically primitive level. The same argument that disallows for the
existence of a self-aware Universal mind applies. Let me step through a
crude sketch of the argument here.
A Universal
<http://oxforddictionaries.com/definition/english/universal> collection
of facts is such that there is no facts that is not included, it must
cover all possible worlds (ala Kripke), it must be Complete.
The universal set of all facts is not a self-consistent set as
there exists facts in one world that are inconsistent with facts in some
other possible world.
A mind is such that its facts are mutually consistent or else it is
insane or non-self-aware.
A self-aware mind must have some knowledge of facts concerning its
existence or else it is not self-aware.
A universal
<http://oxforddictionaries.com/definition/english/universal> mind must
"know all facts of all possible worlds" or else it would not be universal.
A Universal mind is thus either insane (inconsistent) or non-self-aware.
but that ruins your result! It truth is theory independent then it is
impossible for us to be able to know of it.
That is mathematical solipsism.
I know! My point is that comp implies the singular existence of a
mind (universal number that is the sum of all other universal numbers)
that is incapable of knowing what it is as there is nothing within its
preview that is it not. It is a Universal Mind
It is obviously false.
We disagree.
Theories are lantern on little pieces of the truth, which does not
depend on the theory, even if the lantern can bring shadows, and also
hid some other piece of truth.
You insist on the concept of truth as a Platonic Object with innate
properties. I disagree with this concept as I see it as incoherent.
All this makes sense only because such truth does not depend on us and
on our theories.
No, that is an incoherent statement as it pretends to be meaningful
in the absence of any means to evaluate its meaningfulness. In the
absence of a means to determine some property, it is incoherent and
sometimes inconsistent to claim that the property has some particular
value and the absence of all other possible values. This is like
claiming to know exactly what is in a black box that cannot ever be
opened or even located.
All knowledge is 'theory laden' - as David Deutsch explains well.
They reappear *in* arithmetical truth, but have fixed points (some
provably, some non provably). No problem.
Maybe you might write up an explanation of how arithmetic truth is
independent of any ability to prove it.
Gödel's proof explains this very well. The idea that truth = proof is
intuitionism, and technically, it changes nothing for arithmetic (only
for analysis).
Wrong. Gödel's proof does not prove that truth has a particular
value independent of the means to know that value. Gödel's proof tells
is that theories what (as individuals) include Arithmetic will contain
statements that cannot be evaluated by those theories as individuals. We
can build infinite towers of theories that allow evaluation of the truth
of statments, but int he absence of those towers, there is no such thing
as definiteness for truths.
--
Onward!
Stephen
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