On 01 Nov 2012, at 22:50, Stephen P. King wrote:
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?
Too much ambiguous. Even staying in comp I can answer "yes" and "no".
Yes, because my human thinking is locally supported by physical events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.
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.
Truth is free floating, and theories lived through truth, they are
truth floating, even when false.
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.
Our knowing as nothing to do with truth. If an asteroid would have
destroy Earth before the Oresme bishop dicovered that the harmonic
series diverge, she would have still diverge, despite no humans would
know it.
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.
To claim, no. To be true is independent of the claim of the apes.
You must accept non-well foundedness for your result to work, but
you seem fixated against that.
1004.
Pfft. Nice custom made quip.
You are often escaping answers by inappropriate mathematical
precision, which meaning contradicts your mathematical super-
relativism. It is really 1004+contradiction.
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.
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.
Mathematical solipsism.
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?
Come on, you say that you can escape the consequence of comp, you have
to find the flaw, or to be more cautious in your judgment.
There is no one statement I made on this list which I have not
published before, and there have been a lot of peer-review (especially
that many philosophers hate that work, but they try to defend the
philosophy curriculum against a possible invasion of science: that is
usual and normal).
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.
It is not a loop. It is more like a recurring abyss, like the
Mandelbrot set.
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.
You are the one saying that truth is limited to the means of knowing!!!
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.
Ambiguous. trivially true with comp as the reasoning of all entities
belongs to the (tiny part of) arithmetical reality.
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.
I read this. yes. I don't see relevant at all.
I do appreciate his linking of intention and intension, but it is a
bit trivial in the comp theory.
Bruno
http://iridia.ulb.ac.be/~marchal/
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