On 30 Jul 2010, at 17:03, Jason Resch wrote:
On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker
<meeke...@dslextreme.com> wrote:
On 7/29/2010 10:25 PM, Jason Resch wrote:
On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda <her...@acm.org> wrote:
Numbers exist not in any physical sense but in the same sense that
any
idea exists - they exist in the sense that minds exist that believe
logical propositions about them. They exist because minds believe
logical propositions about them. They are defined and distinguished
by
the logical propositions that minds believe about them.
There are three worlds: the physical world of elementary particles,
the
mental world of minds, and the imaginary world of ideas. They are
linked, somehow, by logical relationships, and the apparent flow of
time
in the mental world causes/is caused by changes in these
relationships.
I wouldn't be surprised if the "laws" of physics are changing,
slowly,
incrementally, right under our noses. In fact, I would be delighted,
because it would explain many things.
The existence of numbers can explain the existence of the physical
universe but the converse is not true, the existence of the
physical world can't explain the existence of numbers.
William S. Cooper wrote a book to show the contrary. Why should I
credence your bald assertion?
I should have elaborated more. The existence of mathematical
objects (not just numbers, but all self-consistent structures in
math) would imply the existence of the universe (if you believe the
universe is not in itself a contradiction).
... and if you believe that the universe can be accounted for by a
some consistent mathematical structure. Which is an open problem.
Assuming mechanism, physical universes have no real existence at all,
except as first person sharable experience by machines (mathematical
digital machines).
It would also clearly lead to Bruno's universal dovetailer, as all
possible Turing machines would exist.
... together with their executions.
Regarding the book you mentioned, I found a few books by William S.
Cooper on amazon. What is the title of the book you are referring
to? Does it show that math doesn't imply the existence of the
physical universe, or that the physical universe is what makes math
real? Most mathematicians believe math is something explored and
discovered than something invented, if true, and both math and the
physical universe have objective existence, it is a better theory,
by Ockham's razor, that math exists and the physical universe is a
consequence. I do understand that the existence of the physical
universe leads to minds, and the minds lead to the existence of
ideas of math, but consider that both are objectively real, how does
the universe's existence lead to the objective existence of math,
when math is infinite and the physical universe is finite? (at least
the observable universe).
Also, Cooper's book just address the question of the origin of man's
beliefs in numbers. I don't think Cooper tries to understand the
origin of natural numbers.
Actually, we can explain that numbers cannot be justified by anything
simpler than numbers. That is why it is a good starting point.
I doubt your statement that a physical universes can explain mind.
Unless you take "physical" in a very large sense. The kind of mind a
physical universe can explain cannot locate himself in a physical
universe. This comes from the fact that the identity thesis (mind-
brain, or mind/piece-of-matter) breaks down once we assume we can
survive a 'physical' digital brain substitution.
We can ascribe a mind (first person) to a body (third person), but if
that body is turing emulable, then a mind cannot ascribe a body to
itself. It can ascribe an infinity of bodies only, weighted by
diverging computational histories generating the relevant states of
that body, below the substitution level. This can be said confirmed by
quantum mechanics, where our bodies are given by all the Heisenberg-
uncertainty variant of it.
I agree roughly with the rest of your remarks (and so don't comment
them).
Bruno
Belief in the existence of numbers also helps explain the
unreasonable effectiveness of math, and the fine tuning of the
universe to support life.
If numbers are derived from biology and physics that also explains
their effectiveness. Whether the universe if fine-tuned is very
doubtful (see Vic Stengers new book on the subject) but even if it
is I don't see how the existence of numbers explains it.
Vic Stenger's argument is that fine-tuning is flawed because it
assumes life such as ours. But even assuming a much more general
definition of life, which requires minimally reproduction,
competition over finite resources, and a relatively stable
environment for many billions of generations what percentage of
universes would support this? Does Stenger show that life is common
across the set of possible mathematical structures?
The existence of all mathematical structures + the anthropic
principal implies observers finding themselves in an apparently fine-
tuned universe. Whereas if one only believes in the physical
universe it is a mystery, best answered by the idea that all
possible universes exist, and going that far, you might simply say
you believe in the objective reality of math (the science of all
possible structures).
I think it is a smaller leap to believe properties of mathematical
objects exist than to believe this large and complex universe
exists (when the former implies the latter).
Even small numbers are bigger than our physical universe. There
are an infinite number of statements one could make about the
number 3,
Actually not on any nomological reading of "could".
If 3 exists, but we don't know everything about it, how can 3 be a
human idea? There are things left to be discovered about that
number and things no mind in this physical universe will ever know
about it, do you think our knowledge or lack of knowledge about it
somehow affects 3's identity? What if in a different branch of the
multiverse a different set of facts about 3 is learned, would you
say there are different types of 3's which exist in different
branches? I think this would lead to the idea that there is a
different 3 in every persons mind, which changes constantly, and
only exists when a person is thinking about it. However the fact
that different minds, or different civilizations can come to know
the same things about it implies otherwise.
some true and some false, but more statements exist than could ever
be enumerated by any machine or mind in this universe. Each of
these properties of 3 shapes its essence, but if some of them are
not accessible or knowable to us in this universe it implies if 3
must exist outside and beyond this universe. Can 3 really be
considered a human invention or idea when it has never been fully
comprehended by any person?
On the contrary, I'd say numbers and other logical constructs can be
more (but not completely) comprehended than the elements of physical
models. That's why explaining other things in terms of numbers is
attractive.
Can anything in physics determine the multiples of 3 between N and N
+ 9, where N is 7 ↑ ↑ ↑ ↑ ↑ 100 (Using Knuth's up arrow
notation)? Would you say N doesn't exist because it is too large to
for anyone to know? Or does it only exist now that I thought about
it and wrote it down? Despite that I know very little about that
number. If it doesn't exist, it implies 3 has a finite number of
multiples, which seems strange. Does that mean different numbers
have different numbers of multiples, either depending on what is
thought up or what is small enough to express in the universe? I am
interested in how the approach that numbers/math are only ideas
handles such questions.
Jason
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