From: D. F. Siemens, Jr. <dfsiemensjr@juno.com>

Date: Tue Jun 21 2005 - 19:37:49 EDT

Date: Tue Jun 21 2005 - 19:37:49 EDT

On Mon, 20 Jun 2005 20:32:36 -0500 "Glenn Morton"

<glennmorton@entouch.net> writes:

*> Thanks, David, I was hoping to elicit something from you.
*

*>
*

*> > -----Original Message-----
*

*> > From: D. F. Siemens, Jr. [mailto:dfsiemensjr@juno.com]
*

*> > Sent: Monday, June 20, 2005 5:55 PM
*

*> >
*

*> > I'm breaking this up and considering just the one part in my
*

*> response. in
*

*> > order to avoid building up a massive file. This considers just the
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*> matter
*

*> > of math. I noted logic in a separate post.
*

*> >
*

*> > What follows in Glenn's post seems to me to take us out of math
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*> into
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*> > physical theory. I want to stick to math. First, contemporary
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*> number
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*> > theory begins with the null class, which contains nothing, and
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*> goes on
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*> > from there. I guess this could be viewed as constructing the whole
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*> out of
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*> > nothing, but I rather think that there has to be a class in order
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*> to
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*> > construct other classes, not to mention mathematicians to do the
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*> > constructing. But a mathematical class is an abstraction, whether
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*> null or
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*> > containing members. There are concrete classes, like the class of
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*> all
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*> > Thomas Jefferson's descendants, recently perceived to be larger
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*> than
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*> > earlier admitted. Note that the number that applies, yet unknown,
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*> is a
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*> > class which is clearly different from the persons living, dead,
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*> and yet
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*> > to be born, making up the physical class.
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*> >
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*> > What can I construct out of numbers? out of points, lines, plane
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*> figures,
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*> > solids, hypersolids? alephs and omegas? Nothing! A scientists uses
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*> the
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*> > various mathematical constructs to formulate theories that
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*> describe
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*> > aspects of the universe, ideally.
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*>
*

*> If I understand your point here, you don't think that the universe
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*> can come
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*> out of mathematics--I get this from the question and from the
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*> obvious
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*> mention that one has to have mathematicians to do math. What can I
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*> construct
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*> out of numbers?....Nothing!. It sounds like you are an
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*> inventionalist where
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*> it comes to math. I would respond that you don't need
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*> mathematicians to do
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*> math at all. Monkeys, do math, if you include counting as a subset
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*> of math.
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*> They can count
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*>
*

http://www.sciam.com/print_version.cfm?articleID=00091022-CB1F-12A0-895D8

341

*> 4B7FFE87
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*>
*

*>
*

http://www.highbeam.com/library/doc0.asp?docid=1G1:53280914&refid=ink_tpt

d_m

*> ag&skeyword=&teaser=
*

*>
*

*> Human baseball players when chasing a ball do a form of complicated
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*> internal
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*> calculus to put their hand where the ball will be. Chimpanzees,
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*> when
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*> hunting monkeys, have been observed to calculate where the monkey
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*> will be
*

*> and go there. That is a form of math. So, math is not something that
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*> exists
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*> only because mathematicians exist.
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*>
*

First, whether math is invented or discovered, it properly has to be

proved. Essentially, without theorems there is no math. Matching items,

whether with marks, which seems to go back the furthest, or numerals,

which may be a one, two many, or indefinitely large sequence, is hardly

coming up with something that can PRODUCE something, as number theory

does. I note also that, while there are a limited number of kinds of

number built on the natural numbers, there are an infinite number of

modular numbers, complicated with ordinals and cardinals, infinities, and

I know not what else. But none of these are concrete enough to produce a

universe, though they work very well at describing it.

I do not consider your illustration of chimps matching past with current

items, or pursuing monkeys, as genuine math. Pursuit, or hitting a

baseball, is not a matter of mathematical calculation. I recall something

about pursuit, though I cannot connect it to content, that indicated that

the path taken was something like an arc from an ellipse. It did not

resember a hypotenuse, which would be the shortest intercept. While it is

true that the merging paths of ball and bat can be computed, no one

computes that rapidly. Indeed, it has been noted that good pianists

playing a run have to move their fingers faster than they can be

controlled by the brain, and so must be reflex in nature.

*> The point with both the math and logic part of that essay were that
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*> math and
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*> logic had to exist at the very beginning. If it came out of nothing
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*> (and
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*> nothing lacks an ability to store such information) one has a
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*> problem.
*

*>
*

*> Biochemical systems are mathematical information processing
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*> machines. They
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*> have internal clocks (another form of math before mathematicians).
*

*> The laws
*

*> of gravity are also mathematical in nature. So math seems to
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*> pre-exist
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*> mathematicians.
*

*>
*

If I take this seriously, the orbits of all the planets and the

revolutions of all celestial bodies are mathematics, so independent of

mind unless there exist a deity that has a mind. I hold that you are

confusing the possibility of description with construction.

*> >But who confuses E=mc^2 with any part
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*> > of the word she lives in? Everybody but a few folks who have an ax
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*> to
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*> > produce /ex nihilo/ in order to grind it separate description
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*> from
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*> > construction. There are various spots where /creatio ex nihilo/
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*> is
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*> > tacitly called upon without acknowledgement of the Creator.
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*>
*

*> Actually physicists discussing the origin of the universe start with
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*> the
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*> mathematical laws in order to derive the creation of the universe.
*

*> So, I
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*> would suggest that at least that class of people "confuse" the laws
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*> that
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*> lead to E=mc^2 with the existence of the world in which they live,
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*> as well
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*> as the mathematicians who are Platonists.
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*>
*

Again, this confuses the description of the construction with the

construction itself. If there is the kind of confusion you claim, than it

is necessary to disabuse the nuts or isolate them from the thinking

community. If there are mathematicians who are truly Platonists, their

world is a pathetic reflection of the perfect reality, which just is.

*> Concerning the last sentence, calling upon creation ex nihilo
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*> without
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*> tacitly calling upon a creator is done all the time, but I can't see
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*> what
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*> ontological importance you place on such an activity. From your
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*> logic
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*> portion,
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*>
*

*> I would presume that you think one can't derive the universe from
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*> mathematics because it too should be a category mistake. However,
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*> that may
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*> support my case in that physical theory almost always starts
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*> discussion of
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*> the creation with mathematics already in existence?
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*>
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*> Given that some suggest that mathematics is built on the structure
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*> of our
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*> brains and has no more reality than the self delusion of seeing
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*> patterns in
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*> snow on the TV (which actually happens).
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*>
*

However, I have not found any postmodern individual who really believes

this kind of nonsense. What they insist on is that everyone's view but

theirs is without rational foundation.

*> From your Logic reply:
*

*>
*

*> >While it is true that bits have physical exemplification, I see
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*> this as
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*> >essentially analogous to geometry's essential pieces. A point A and
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*> line
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*> >AB have the same area and the same volume, 0. But the diagram drawn
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*> to
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*> >represent these entities has a finite area and a finite volume,
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*> whihc is
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*> >ignored. A polygon ABCDE has an area, but the volume is
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*> theoretically
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*> >still 0. The physical exemplification of the bit is concrete, but
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*> the
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*> >intent of the bit is purely abstract.
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*>
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*> Given the deep connection between information and entropy, I would
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*> beg to
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*> differ that information is purely abstract. When you compute on a
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*> computer
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*> and store everything in memory, no entropy is created, the
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*> universe's
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*> entropy remains constant. But, when you destroy the information,
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*> that is
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*> when entropy rises. Entropy is lost information and if entropy is
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*> physical
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*> then so is information.
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*>
*

This is pure physicalism. Any information encoded in matter involves

considerations of entropy. But note that a common argument against spirit

involves the impossibility of interaction between spirit and matter

because of the conservation of energy. You can claim that God cannot lose

information, eliminating the increase in entropy from that source. But I

consider that the Christian faith involves more than God and opt to be on

the side of the angels.

*> >
*

*> >There is a further problem, the assumption that logic is strictly
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*> >digital. But none of Aristotle's three calculi are digital. They
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*> cannot
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*> >be translated into contemporary calculi. Further, "true" is not a
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*> bit,
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*> >though it can be represented as a bit in some metalanguages. But
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*> this
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*> >gets us into some high-powered abstractions.
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*> >
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*>
*

*> I really don't want to defend Zeilinger's idea but it was one that
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*> needed to
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*> be included because somehow, the universe acquired logic and the
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*> universe
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*> acquired math--even before the existence of logic. Zeilinger's
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*> hypothesis
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*> would have to be considered.
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*>
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*> >Most formalized logics involve two values, which can be represented
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*> by 1
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*> >and 0--true/false for statements, valid/invalid for arguments. But
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*> then
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*> >there is the little problem of wffs, which are totally content
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*> dependent.
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*> >An extension of this notion leads to fuzzy and multi-valued logics,
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*> which
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*> >clearly are not amenable to encapsulation in bits. Related problems
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*> have
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*> >been discussed for the language available in familiar logics. The
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*> classic
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*> >term is "bald," which does not allow a sort into two bins. the
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*> >requirement for valid arguments.
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*> >
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*> >Finally, logic is abstract, but the universe is concrete. Perhaps
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*> one can
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*> >construct a weird version of Berkeley's idealism out of nothing
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*> but
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*> >logic, but I doubt it. Even the bishop required God as the source
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*> of all
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*> >impressions. To state the problem differently, to try to construct
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*> the
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*> >universe out of bits is to make a gross category mistake.
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*>
*

*> Logic is also fuzzy as you noted. You are referring only to the
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*> classical
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*> type of logic where one has true/false. Fuzzy logic the truth values
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*> vary
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*> from 0 to 1. And quantum logic is even fuzzier. Due to
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*> superposition, a
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*> quantum computer can represent 4 or more numbers simultaneously.
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*> So just
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*> because formalized logic is limited, it doesn't necessarily mean
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*> that
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*> quantum logic is subject to the same limitations.
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*>
*

Are you confusing the information with the embodiment? Are my thoughts

the electrons circulating through the CPU and connected chips? Are they

the images formed on the monitor? We can consider words to be informtion,

but it seems better to consider them the bearers of information, which

has to be realized when the reader or hearer constructs thoughts. The

process of communication is fairly efficient, but not foolproof. Though

we often speak of the intermediate steps as information, it is better to

view it as something in mind.

*> Do I think the universe comes out of logic? No, but the idea may not
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*> be as
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*> big a category mistake as you think. We don't know why the universe
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*> is
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*> 'concrete' if we don't know why the universe exists, because to
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*> exist is to
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*> somehow be concrete.
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*>
*

This may be, but if logic is concrete, it's going to set between the ears

for, in all our demonstrable activity, that's where logical

considerations take place. If you have to spell out the origin of logic,

you're necessarily circular, and if you try to carry logic too far, you

run into Goedel. I want neither.

Received on Tue Jun 21 19:44:10 2005

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