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).


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.


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