On 11/1/2012 12:04 PM, Bruno Marchal wrote:
On 01 Nov 2012, at 01:18, Stephen P. King wrote:
On 10/31/2012 12:45 PM, Bruno Marchal wrote:
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.
Dear Bruno,
I disagree with ultrafinitists, they seem to be the mathematical
equivalent of "flat-earthers'.
*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".
So your thinking about them is not a physical act?
Implementation and physical will be explained from them. A natural
thing as they are much more complex than the laws above.
Numbers are meaningless in the absence of a means to define them.
Theories do not free-float.
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 ?
Because there is not way to know of them otherwise. Unless you can
communicate with me, I have no way of knowing anything about your ideas.
Similarly if there is no physical implementation of a mathematical
statement, there is no meaning to claims to "truth" of such statements.
You must accept non-well foundedness for your result to work, but you
seem fixated against that.
1004.
Pfft. Nice custom made quip.
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
<http://3.bp.blogspot.com/-g3rGLKs9-t0/Tb2OVrEtc2I/AAAAAAAAAGU/3N5mSCci-_8/s1600/9234%2B-%2Bartist-Stinkehund%2Bcloud%2Brainbow_dash.png>
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.
It is very relevant to mine.
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?
If there does not exist a means to "show the solution" there is no
solution.
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).
Well, can we work with that agreement?
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.
Good!
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.
Yes, and bundles of arithmetic statements generate many individual
observers that in turn "interact" (which I model via a combination of
cyclic gossiping on graphs and bisimulations) with each other to define
a common physical world which in turn acts to "implement" the
arithmetic. It is a loop, an eternal cyclical process that never exactly
repeats. It is in this infinite loop that I see your UD.
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.
Yes, but their reasonings are severely limited.
2) the PEM is a way to assert formally platonism, and I use it only in
arithmetic. And it means that the truth is independent of our reasons.
Truth is independent of any particular reasoning, but it is NOT
independent of the reasoning of all entities.
This is a red herring, Bruno. It is not addressing my claim at all.
Then you have to try to state it more clearly.
I am trying. ;-)
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.
OK, I will try again.
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.
Are you familiar with Jaakko Hintikka's ideas? I am using his
concept of game theoretic semantics to derive truth valuations.
--
Onward!
Stephen
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