On 30 Jul 2010, at 17:03, Jason Resch wrote:

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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 thatanyidea exists - they exist in the sense that minds exist that believe logical propositions about them. They exist because minds believelogical propositions about them. They are defined and distinguishedbythe logical propositions that minds believe about them.There are three worlds: the physical world of elementary particles,themental world of minds, and the imaginary world of ideas. They arelinked, somehow, by logical relationships, and the apparent flow oftimein the mental world causes/is caused by changes in theserelationships.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 physicaluniverse but the converse is not true, the existence of thephysical world can't explain the existence of numbers.William S. Cooper wrote a book to show the contrary. Why should Icredence your bald assertion?I should have elaborated more. The existence of mathematicalobjects (not just numbers, but all self-consistent structures inmath) would imply the existence of the universe (if you believe theuniverse 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 allpossible 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 referringto? Does it show that math doesn't imply the existence of thephysical universe, or that the physical universe is what makes mathreal? Most mathematicians believe math is something explored anddiscovered than something invented, if true, and both math and thephysical universe have objective existence, it is a better theory,by Ockham's razor, that math exists and the physical universe is aconsequence. I do understand that the existence of the physicaluniverse leads to minds, and the minds lead to the existence ofideas of math, but consider that both are objectively real, how doesthe universe's existence lead to the objective existence of math,when math is infinite and the physical universe is finite? (at leastthe 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 theunreasonable effectiveness of math, and the fine tuning of theuniverse to support life.If numbers are derived from biology and physics that also explainstheir effectiveness. Whether the universe if fine-tuned is verydoubtful (see Vic Stengers new book on the subject) but even if itis I don't see how the existence of numbers explains it.Vic Stenger's argument is that fine-tuning is flawed because itassumes life such as ours. But even assuming a much more generaldefinition of life, which requires minimally reproduction,competition over finite resources, and a relatively stableenvironment for many billions of generations what percentage ofuniverses would support this? Does Stenger show that life is commonacross the set of possible mathematical structures?The existence of all mathematical structures + the anthropicprincipal implies observers finding themselves in an apparently fine-tuned universe. Whereas if one only believes in the physicaluniverse it is a mystery, best answered by the idea that allpossible universes exist, and going that far, you might simply sayyou believe in the objective reality of math (the science of allpossible structures).I think it is a smaller leap to believe properties of mathematicalobjects exist than to believe this large and complex universeexists (when the former implies the latter).Even small numbers are bigger than our physical universe. Thereare an infinite number of statements one could make about thenumber 3,Actually not on any nomological reading of "could".If 3 exists, but we don't know everything about it, how can 3 be ahuman idea? There are things left to be discovered about thatnumber and things no mind in this physical universe will ever knowabout it, do you think our knowledge or lack of knowledge about itsomehow affects 3's identity? What if in a different branch of themultiverse a different set of facts about 3 is learned, would yousay there are different types of 3's which exist in differentbranches? I think this would lead to the idea that there is adifferent 3 in every persons mind, which changes constantly, andonly exists when a person is thinking about it. However the factthat different minds, or different civilizations can come to knowthe same things about it implies otherwise.some true and some false, but more statements exist than could everbe enumerated by any machine or mind in this universe. Each ofthese properties of 3 shapes its essence, but if some of them arenot accessible or knowable to us in this universe it implies if 3must exist outside and beyond this universe. Can 3 really beconsidered a human invention or idea when it has never been fullycomprehended by any person?On the contrary, I'd say numbers and other logical constructs can bemore (but not completely) comprehended than the elements of physicalmodels. That's why explaining other things in terms of numbers isattractive.Can anything in physics determine the multiples of 3 between N and N+ 9, where N is 7 ↑ ↑ ↑ ↑ ↑ 100 (Using Knuth's up arrownotation)? Would you say N doesn't exist because it is too large tofor anyone to know? Or does it only exist now that I thought aboutit and wrote it down? Despite that I know very little about thatnumber. If it doesn't exist, it implies 3 has a finite number ofmultiples, which seems strange. Does that mean different numbershave different numbers of multiples, either depending on what isthought up or what is small enough to express in the universe? I aminterested in how the approach that numbers/math are only ideashandles such questions.Jason --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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