On 01 Nov 2012, at 01:18, Stephen P. King wrote:
On 10/31/2012 12:45 PM, Bruno Marchal wrote:
On 30 Oct 2012, at 18:39, Stephen P. King wrote:
On 10/30/2012 12:51 PM, Bruno Marchal wrote:
On 30 Oct 2012, at 17:04, meekerdb wrote:
On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their
constructions, not to numbers themselves.
Truth applies to proposition, or sentences representing them
for some machine/numbers. If not, comp does not even makes sense.
So your are agreeing? "Two" has no truth value, but "Two equals
one plus one." does.
Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to
assert that the truth of, say "Two equals one plus one." depend
on some numbers or subject having to discover it, or prove it.
Bruno
http://iridia.ulb.ac.be/~marchal/
Dear Bruno,
My point is that a number is not a capable of being an
ontological primitive
Then I can stop reading as you need to assume the numbers (or
anything Turing equivalent) to get them.
Dear Bruno,
So it is OK to assume that which I seek to explain?
You can't explain the numbers without assuming the numbers. This has
been foreseen by Dedekind, and vert well justified by many theorem in
mathematical logic. Below the number, you are lead to version of
ultrafinitism, which is senseless in the comp theory.
*and* having some particular set of values and meanings.
I just assume
x + 0 = x
x + s(y) = s(x + y)
x *0 = 0
x*s(y) = x*y + x
And hope you understand.
I can understand these symbols because there is at least a way
to physically implement them.
Those notion have nothing to do with "physical implementation".
Implementation and physical will be explained from them. A natural
thing as they are much more complex than the laws above.
In the absence of some common media, even if it is generated by
sheaves of computations, there simply is no way to understand
anything.
Why ?
You must accept non-well foundedness for your result to work, but
you seem fixated against that.
1004.
A statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to have the same meaning because there are multiple and
separable entities that can have the agreement on the truth value.
In the absence of the ability to judge a statement independently
of any particular entity capable of "understanding" the statement,
there is no meaning to the concept that the statement is true or
false. To insist that a statement has a meaning and is true (or
false) in an ontological condition where no entities capable of
judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments
disallow.
Do you agree that during the five seconds just after the Big Bang
(assuming that theory) there might not have been any possible
observers. But then the Big Bang has no more sense.
No, I don't. Why? Because that concept of "the five seconds just
after the Big Bang" is an assumption of a special case or pleading.
I might as well postulate the existence of Raindow Dash to act as
the entity to whom the Truth of mathematical statements have
absolute meaning. To be frank, I thing that the Big Bang theory, as
usually explained is a steaming pile of rubbish, as it asks us to
believe that the totality of all that exists sprang into being from
Nothing.
I actually agree, by accident, on this. But this is not relevant for
my point. Imagine that we can show that some solution to GR equantion
have universe so poor that life cannot exist in there, would you say
that such universe cannot exist?
I believe that the totality of what exists is eternal, having no
beginning and no end.
I am OK with that. It is close to Platonism. But with comp we can
restrict this to the arithmetical truth (a highly non computable
structure, but still conceivable by universal numbers, relatively).
What we infer from our observations of Hubble expansion is just an
effect that follows, ultimately, from our finiteness.
Including time and space. So we do agree again.
I think Brent is right, and Quentin. You confuse 1+1=2 with human
expression for pointing on that proposition. You obviously needs
human to understand those " "1+1=2" ", but the content of "1+1=2"
has simply no relation at all with the human, or with a physical
universe.
No, none of you have yet to be able to understand my counter-
argument. It is not complicated. We cannot assume to have something
when the means for its existence is not allowed. My claim is that
meaningfulness supervenes on the possibility of interaction of
*many* entities and is independent of any *one* (or some lesser
finite subset) of that Many.
But arithmetical truth is full of entities, even full of galaxies
themselves full of self-aware being. That is a fact. But with comp
(and UDA), those entities are saved from zombieness.
I asked you some time ago if you agree with the use of the excluded
middle in arithmetic. It asserts that for any arithmetical
proposition P, even highly non computably verifiable, you can
accept as new arithmetical truth the proposition asserting that P v
~P. Which intuitive meaning that the proposition is unambiguously
either true, or false, despite you have no idea if it is P or ~P
which is the true one. To accept this means that you accept that
such truth are independent of the means to prove or verify them.
We must us the principle to excluded middle [PEM] to reason, but
this does not make the principle something external and independent
of us.
1) the intuitionist can reason without them.
2) the PEM is a way to assert formally platonism, and I use it only in
arithmetic. And it means that thetruth is independent of our reasons.
This is a red herring, Bruno. It is not addressing my claim at all.
Then you have to try to state it more clearly.
You seem to be stuck on the idea that only one entity can have or
not have some property or power and cannot reason about the
possibility that *many* may be required to solve some problems. A
plurality is not a multiplicity...
This is too vague. I don't see that one one entity can have or not
have some property or power, nor why I can't reason on the possibility
that ยจ*many* might be required (on the contrary, there are many notion
of many playing in comp and the emergence of physics. No clue what you
mean here.
Even intuitionist (who are sort of mathematical solipsist) accept,
for P arithmetical, the proposition
~ ~ (P v ~P), which makes them already realist in the sense used
in comp.
Not relevant. Your intransigence in this debate only reinforces
by suspicion that you are not interested in extending your result so
that its open problem might be solved.
?
Please stop the ad hominem remarks, as they add nothing to the debate.
You are the one who doesn't succeed to make clear your point, despite
my generous willingness to bet there is one hidden in your post.
Bruno
http://iridia.ulb.ac.be/~marchal/
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