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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