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.
My point is that a number is not a capable of being an
Then I can stop reading as you need to assume the numbers (or anything
Turing equivalent) to get them.
So it is OK to assume that which I seek to explain?
*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. In the absence of some common media, even if
it is generated by sheaves of computations, there simply is no way to
understand anything. You must accept non-well foundedness for your
result to work, but you seem fixated against that.
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 believe that the totality of what exists is eternal, having
no beginning and no end. What we infer from our observations of Hubble
expansion is just an effect that follows, ultimately, from our finiteness.
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.
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 to reason, but this
does not make the principle something external and independent of us.
This is a red herring, Bruno. It is not addressing my claim at all. 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
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.
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