On 21 Jan 2015, at 07:45, 'Roger' via Everything List wrote:
On Tuesday, January 20, 2015 at 2:49:12 PM UTC-5, Bruno Marchal wrote:
On 19 Jan 2015, at 23:48, 'Roger' via Everything List wrote:
Roger: Even if no mind has yet conceived the the
10^(10^(10^100))th decimal point of pi, the pi proposition and
therefore the process of calculating its 10^(10^(10^100))th decimal
point and being confident that if you do the process that that
number is either 0-9 are all located inside the mind/head. My view
is that whenever we talk about something existing, we have to
specify where and when it exists, that is, in what context or
domain it exists. A thing can exist in one place and not another.
A ball can exist outside the head, and a mental construct labeled
"the concept of a ball" can exist inside the head.
If a ball can exist outside the mind/head, why can't the
10^(10^(10^100))th decimal point of pi exist outside the mind/head?
What property must a thing have to have an independent existence
outside of any mind? (according to your theory?)
Jason
So, if the pi process were carried out inside the mind/head long
enough to figure out the 10^(10^(10^100))th decimal point, that
mental construct for that number (which would be 0-9) would exist
inside the mind/head but not outside the mind/head. So, the mind
is able to reify things (like the 10^(10^(10^100))th decimal point
of pi) so that they exist but so that they only exist inside the
mind/head and not outside the mind/head.
Roger: Just because things can exist outside the mind/head doesn't
mean that a specific thing does occur outside the mind/head. If
the pi proposition and the 10^(10^(10^100))th decimal point of pi
can be shown outside the mind/head or any experimental evidence for
the existence of the pi proposition or the 10^(10^(10^100))th
decimal point of pi existing outside the mind/head, I'd be happy to
accept it. I can see that a circle can exist outside the head, but
I don't see anywhere outside the mind/head, the proposition that if
you divide the circle's circumference by its diameter you get pi.
But that proposition is not in the head of anybody. A body can get a
representation of that proposition in some language (be it LISP or
neural nets, or numbers): that is usually called a sentence, and
*that* is in the head of the machine or the number. The proposition
itself is what is intended by the sentence and the universal machine
in presence. That pi is what you find by dividing the circle's
circumference by the diameter is (true by definition), and that the
sum of the inverse of all squared natural number is true, by a
proposition proved by Euler.
That is true. period. It was true before Euler proved it, and after,
although this is only a metaphor. The number are just not concept to
which time or space attribute can apply.
There is no number, nor proposition, in a brain. You might find
representations of number, and of propositions in the brain, but it
makes no sense to say that a number is in a brain, or on the planet
mars.
Then a brain itself can be described as the representation of a
universal numbers with respect to some other universal numbers.
If you accept Church-Turing thesis, all computations exists in the
elementary arithmetical reality, and in a very special redundant
way, and we are there, and we must explain why the white rabbits are
so rare and why the rabbit hole is so deep. The quantum almost
solves that problem, but to solve the mind-body problem, we must
justify why only the quantum works.
Bruno
Roger: I understand that the sentence, the words and the thought
"divide a circle's circumference by its diameter to get pi" are in
the mind/head.
Yes. even in the mind/head of all universal machine, in the sense of
Turing-Church, which can be defined in arithmetic.
But, what is outside the head is a circle, with a circumference and
a diameter.
This is ambiguous.Are you talkng about the "platonic perfect circle"?
Or about a circle physically realized, like with a pen and a compass?
There is no process outside the mind/head saying that if you
divide the circumference by the diameter, the number 3.14... results.
Yes there is. For each choice of a universal numbers in N, you will
have an infinity of numbers which describes that process, like all
programs simulating Archimedes algorithm to compute Pi. Those programs
and their executions are entirely well defined in arithmetic. Some
quite indirectly, like the programs simulating the milky way, in
string theory, just before Archimedes discovered his algorithm.
That process and the idea of even doing it are inside the mind/head.
But with computationalism everything is inside the mind/ead of the
universal numbers, even the idea that there is something outside the
mind/head of the universal machine.
It will give 3.14 for all physical circles and their circumferences
and diameters outside the head, but the only thing outside the head
is the circle.
The platonic circle? Perhaps.
The process and the idea are inside the mind/head.
There are also in arithmetic, and in the mind/head of all universal
numbers, although they can focus on something else.
The "what you find by dividing..." in your sentence also kind of
implies that an action needs to be taken by the observer.
OK, but the observer is defined by a relative number, or a couple of
universal numbers. We never go outside a tiny fragment of arithmetic,
except for the reasoning on the measure on the computational
histories, where analytical tools are not forbidden at the metalevel.
Keep in mind that I do not assume a physical universe, if only because
I want a non circular explanation of matter and of the physical.
Everett use computationalism to justify the absence of collapse, but
this works only if we can derive the SWE from the measure on *all*
computational "dreams" in arithmetic.
Bruno
That pi is what you find by dividing the circle's circumference by
the diameter is (true by definition), and that the sum of the
inverse of all squared natural number is true, by a proposition
proved by Euler.
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