On 02 Nov 2012, at 21:19, Stephen P. King wrote:
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
Roger Clough,rclo...@verizon.net 10/31/2012
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
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.
"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 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 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-
You are to much precise in a too much fuzzy theory.
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.
Then all your references to Boolean algebra becomes nonsensical.
Sometimes I can make sense of what you say, but then you add some
assertion which put so much confusion that I think I was projecting
sense on a sentence which was comp-meaningfully serendipitously.
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
I don't consider truth as an object. The numbers can be considered as
the (only) object. truth concerns only the propositions about those
objects and the derivative notions.
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.
That is arithmetical realism. A statement like Church thesis and comp
makes no sense at all without it.
I have never heard about someone not believing in arithmetical
realism. It is really basic. To pretend that arithmetical realism is
false already needs arithmetical realism.
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.
In math this is called (mathematical) solipsism.
This is like claiming to know exactly what is in a black box that
cannot ever be opened or even located.
Not at all. (Arithmetical) Truth on the contrary is beyond the
knowledge of any machine.
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 did not prove that, but everyone believe this, and Gödel's proof
illustrates this very clearly.
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.
Then why did you mention the non standard model of PA? Such notion
assumes you can give sense to the standard model, which makes definite
the notion of Arithmetical Truth, and the application of boolean logic
on the whole of arithmetical truth.
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