On 05 Sep 2012, at 20:28, Stephen P. King wrote:
On 9/5/2012 9:37 AM, Bruno Marchal wrote:
On 04 Sep 2012, at 17:48, Stephen P. King wrote:
On 9/4/2012 10:55 AM, Bruno Marchal wrote:
On 24 Aug 2012, at 12:04, benjayk wrote:
Strangely you agree
for the 1-p viewpoint. But given that's what you *actually*
live, I don't
see how it makes sense to than proceed that there is a
meaningful 3-p point
of view where this isn't true. This "point of view" is really
just an
abstraction occuring in the 1-p of view.
Yes.
Hi Bruno,
So do you agree that the 3-p point of view is just an
abstraction (a simulation even!) of a 1-p?
This would make the 1p fundamental. This would make vain the search
for explanation of mind, so this does not satisfy me.
Dear Bruno,
In the context of a theoretical framework it does, but that is
not a contradiction of my claim. We are talking about
representations of 1p not the content of the 1p itself. There are
situations when the map is not the territory...
The 1p of the machine have no 3p-representations at all. This follows
simply from Theaetetus definition of knowledge in arithmetic, with
believability played by provability (as we lost Provable("p") -> p),
and restrict the interview on ideally correct machine.
With comp mind is the result of the working of a universal number
relatively to infinities of other universal number, so we need to
start from the numbers (or anything Turing-equivalent).
But you are assuming that numbers can do the "work". I beg to
differ! Number can represent anything but can they do work? No, they
do not "do" anything at all. There is no "action" in numbers. To
represent action we need at least functions to map some object to
some other different object.
You forget that a universal number associate to each number an
"action" mapping number on number.
As I just recall in another post u(i, x) = phi_i(x).
So the 3p can be abstract, but it is not part of the mind, like
"1+1=2" remains true in absence of any thinker.
But does the Truth value have any meaning in a world where it
cannot be known in any way?
Its truth is its meaning. It has nothing to do with being known or not
by an agent.
In logic this is universally accepted for arithmetic, but not for more
powerful theories.
I can only make sense of your claim here if I stipulate that you
think that the truth of a statement is a proxy for the content of
the statement; such that if the statement is "true" then it does not
matter at all what the sentence is. I still do not grasp how you go
from claim that necessitate instantiations of properties such as the
particular property of the sentence "1+1=2" to the truth of the
intention of the sentence.
Good. machines already can know that we can't. Bp -> p is not provable
for arbitrary sentence. With comp, Truth is only a private hope,
somehow.
How is the sentence "#8$<%" not equally true in the absence of any
thinker and have the same meaning as "1+1=2"?
"#8$<%" is a sentence, not a proposition.
When I say that "1+1=2" is true, I mean only that 1 + 1 = 2, not that
the sentence "1+1=2" is true.
So if you want to know if "#8$<%" is true, just tell me if #8$<% or
not. perhaps explain the meaning of it.
You might confuse sentence and proposition. It is obvious that IF
"1+1=2" means that Stephen Paul King is 42 km high, it is plausibly
false, but that would not change the fact that 1 + 1 is equal to 2.
What is making the difference? You seem to be assuming that
there is something above that some how can "see" the truth of
"1+1=2" and know that it is a true sentence and that it is
completely immaterial and "not a thinker". Plato was a bit more
circumspect about assuming such things, I hope!
Just saying that 1+1=2, and that such a fact does not depend on me,
you, or the physical universe. To be communicated, yes, you need a
physical universe, or a human universe, that is some stable sharable
computations with the relevant measure, etc. That's the problem I
explain we have to solve.
It seems to me that this would similar to having a model S that is
part of a theory T such that T would change its beliefs as X -> X'
changes, all while preserving the Bp&p term, p would be a variable
of or in X, X', ... .
A model cannot be a part of a theory. I guess you mean a theory
which is part of the theory, and then I mainly agree with your
sentence.
Does not a true theory require that a model of it exist? Model-
less theories? Are they even possible?
In first order logic:
A theory has a model (but not as a term in itself) iff it is
consistent (that is; does not prove f).
We can build theories which are part of themselves, like we can
make machine which can access any part of their 3p description, by
using the Dx=xx method (or Kleene second recursion theorem).
Sure, but that is a separate issue. The 3p description of a
machine is, in your sentence here, taken from the intentional stance
(or point of view) of another entity (that is not the machine in
question), so that makes it bisimilar to the 1p of a separate
entity. Where is the contradiction to my claim?
Where is the sense?
Bruno
http://iridia.ulb.ac.be/~marchal/
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