Re: Skolem's Paradox and why is math the way it is?

From: Ross A. Finlayson (raf_at_tiki-lounge.com)
Date: 11/12/04 

Date: 11 Nov 2004 18:47:06 -0800

troubled6man@yahoo.com (J.E.) wrote in message news:<39d6e584.0411111038.737afdaf@posting.google.com>...
> raf@tiki-lounge.com (Ross A. Finlayson) wrote in message news:<3c6b9c1e.0411101834.4b4f06fc@posting.google.com>...
> > troubled6man@yahoo.com (J.E.) wrote in message news:<39d6e584.0411100706.6fbf1e7a@posting.google.com>...
> > > raf@tiki-lounge.com (Ross A. Finlayson) wrote in message news:<3c6b9c1e.0411092307.6bf5fda4@posting.google.com>...
> > > > troubled6man@yahoo.com (J.E.) wrote in message news:<39d6e584.0411091553.70ac985a@posting.google.com>...
> > > > > raf@tiki-lounge.com (Ross A Finlayson) wrote in message news:<200411090734.iA97YJ230806@proapp.mathforum.org>...
> > > > > > On 07 Nov 2004, J.E. wrote:
> [snip]
> > Hi, J.E.,
> >
> > I'm probably ignorant in both ways. Also, I'm ignorant.
> >
> > I try to have a general understanding of mathematical terms that are
> > in current usage, and how they are used, and to some extent their
> > background and surrounding historical arguments and developers. I'm
> > not a polymath. I've posted the titles of mathematical books that I
> > have read to sci.math, and I haven't taken any college math classes
> > since "Calc III." So, I have never taken a graduate level math,
> > physics, or engineering class at university.
> >
> > While that is some level of ignorance, I've "heard of" Clifford
> > algebra and the four-dimensional space-time.
>
> I think I understand what you are saying so far.
>
> > So, I theorize the quantum, subquantum, and superquantum as scalar
> > unity, infinitesimal, and infinity, and turned to sci.math to share my
> > opinion. Words ensue.
>
> And now I'm lost again. I've never seen any evidence for anything
> other than quantum, neither subquantum, nor superquantum mean anything
> to me. Infinity seems vague enough to mean most anything, and for an
> infinetesimal I could probably follow what you meant within the
> confines of a specific example, but I'd have to see and example to
> know (and I'm not asking for one, I'm just telling you that I don't
> understand you). Even scalar unity is something I don't know what you
> mean.
>
> > You can plainly read my mathematical development on sci.math.
> >
> > I am of the opinion that non-Euclidean "geometry" is Euclidean
> > geometry without the parallel postulate, but that it is a superset of
> > Euclidean geometry and not exclusive, ie, the parallel postulate may
> > or may not be so for a given situation, ie, super-Euclidean geometry.
> > Perhaps I am wrong about that.
>
> I've never met someone who believed that, most people I meet consider
> Euclidean geometry a subset of Non-euclidean geometry, not the other
> way around, and the rest think they are exclusive. If you look at the
> Clifford algebra of a N+2 dimensional space, you can find a set of
> simple 3-vectors that are closed under addition, and that when
> multiplied are isomorphic (as an algebra with multiplication and
> addition) to the Clifford algebra of a Euclidean N dimensional space,
> just as one example of Euclidean being a part of Non-euclidean). The
> breakdown of multivectors into k-vectors in obviously different since
> those original 3-vectors are 1-vectors in the other algebra. It's
> really fun to see the example of taking space-time bivector and
> interpreting them as 3-d spatial vectors though, especially if you
> look at the way non-relativist QM is usually taught.
>
> I don't know anything about super-anything, let along super-Euclidean
> geometry.
>
> > In the theory with ubiquitous ordinals, U contains only itself.
>
> Why? Aren't orginals supposed to contain all their predecessors?
>
> > I typed "dual set theory" into Google, and there were no results.
>
> Well it's nice to know that Google doesn't follow me to the beach. I
> thought I had made it clear that that was just based on a few moments
> thoughts while on the beach.
>
> > Paradoxes are not allowed because they are a sign of insufficient
> > knowledge or prevarication. Consider Zeno, with a completed infinity
> > and infinitesimals his situations are not paradoxes, thus a theory of
> > reality, upon which those are modeled, with your completed infinity
> > and infinitesimals is not paradoxical. Russell's set can not be
> > constructed? It is not, although I have a line of argument about it
> > confirming extensions to my logical theory.
>
> Zeno got paradoxes by bad reasoning, I agree. "Russell's set" is
> *not* a set in the sense that it is not the case for for any thing we
> can consistently know whether or not something else is in it,
> specifically we can't consistently know whether or not it is in
> itself. If you have an excluded middle, that's a problem. If you
> have a set of all sets U, AND you have separation that is allowed to
> operate on U, THEN you can DEFINE R:={xeU : ~xex}, and "call" it the
> Russel set. It's the question ReR that is hard to answer, but I don't
> know what you mean by Russell's set "can not be constructed," if you
> have U and R and by definition of U ReU is true, then you have ReR iff
> ~ReR. Are we really talking past each other here?
>
> > About models in set theory, vis-a-vis models of set theory, you want
> > your IF logic to say that with that logic-and-a-half you can operate
> > in your first order logic, I just say to stay in first order logic in
> > the first place.
>
> "First order logic" is vague, most people mean Ordinary FOL, but
> IF-logic is first order in that the only things you need to write it
> down is the elements of the domain of discourse, it *can* be written
> in terms of second order elements, but it is about the combinatorics
> of the first order entities. I'm not sure why anyone would object to
> IF-logic, the ordinary FOL is a subset of it, so it's not a
> restrictive assumption.
>
> Now regarding models, I think different people mean different things
> by that word, so I'd have to know what your meaning is to know what
> you are saying.
>
> And as for "I just say to stay in first order logic in the first
> place," what exactly *is* your objection to IF-logic?
>
> > About the notion of "boring", do you mean that in the sense of dull or
> > drilling? The simple interpretation is dull.
>
> Dull as in repeticious, hence the name I choose of "dual." It doesn't
> really provide anything above and beyond the original set theory,
> unless you figure out how to discuss sets and dual sets together at
> the same time.
>
> > I'm pleased that you're back to a countable theory. It may well be
> > that you can have both, a post-Cantorian set theory just like there is
> > a super-Euclidean geometry.
>
> I thought I was to "no model". And again I don't know anything about
> a super anything.
>
> > About infinity, in one of its many guises, shapes, forms, meanings,
> > interpretations, uses, allusions, and mathematical constructs, it's
> > forced to be in some cases zero, one, or negative one, and I believe
> > i, an orthonormal vector to the unit vector, by its role within
> > logical and mathematical constructs.
>
> I will agree that i is linearly independant from 1 and from a vector,
> and I heard you vague motions towards a big spiral being related to a
> rotation by 90 degrees after having a bunch of undisclosed (by you)
> meaning float in and do some undisclosed (by you) thing, but I haven't
> a clue what you are talking about. P.S. I don't like calling a scalar
> a vector, scalars commute with vectors, and only vectors don't commute
> with each other unless they are colinear, which is really the case of
> commuting scalars again anyway. If that's what you meant by "unit
> vector" then I do take objection, and for the same reason, I don't
> like to call "i" a vector, for the same commutation reasons. Yes in
> 2-d there is a linear mapping between the rotations and the vectors,
> but that generalizes poorly in my opinion, so I find the mapping
> rather useless conceptually. Whereas keeping the rotation 2-vectors
> and scalars separate from vectors goes to n-d just fine.
>
> > That's not always the case: it's infinity, there are lots of meanings,
> > uses, and interpretations of the word that refers to the things. So,
> > yes, please qualify what you say when you mean infinity.
>
> I try to avoid the word because it doesn't seem to be playing fair to
> *use* words whose meanings are always changing. If I used it, I
> apologize, and frankly I was probably trying to talk about something
> you brought up with the word that I didn't know what you meant by it.
>
> > It's not my goal to be unclear, my goal is to find a logical system
> > that supplants contemporary theory because it's better, besides being
> > good. I've already reached the goal of having a logical theory
> > adequate for my own purposes, and in a way portentious for the
> > previous goal, for others. To some extent, the unclear points are
> > that way for a reason, they're complicated or overly simple. That's
> > one reason why I think it is key to examine these plain language
> > statements about logic that are saying many things at once, or nothing
> > at all.
>
> I've had a lot of experience dealing with people being vague, and I'm
> not sure that it's actually helpful to me, so if you are doing it on
> purpose, then ...
>
> > You pose no questions?
>
> yes, I no questions for you.

How about this: i is emplyed as the pseudo-scalar. The spacetime
pseudoscalar alternately commutes and anticommutes.

That's a Lounesto reference.

http://groups.google.com/groups?selm=ntgm5zyfhd6a%40forum.mathforum.com

I'm not intentionally vague to be vague, the problem is that we're
talking about vague things.

No, J.E., I want you to ask me questions. If you have an open
question and I can contribute to it, then I'm in good company.

That dual set theory has some interest. Thanks for bringing that to
the attention of this group.

I turn to Cartan, selecting a page from 1-100, 47: "THE PRODUCT OF
TWO SPINORS AND ITS DECOMPOSITION INTO IRREDUCIBLE PARTS": "The three
monomials E^2_0, E_0 E_1, and E^2_1 a priori form a tensor that is
equivalent to a vector; they are in fact linearly independent
combinations of the components of an isotropic vector, but an
isotropic vector, considered as a tensor, is equivalent to a general
vector."

All hail Elie Cartan.

This is a thread about Skolem, Skolem's "paradox", and why you, J.E.,
make requests of the foundations of mathematics to reflect your theory
of everything.

I'm pleased that you feel a countable model is sufficient for your
theory of reality in terms of concrete mathematical physics. To
paraphrase Ullrich: "Tee hee." Woo-hoo. Woo-hoo's the Bronco. That
should go over well.

I think it's a good idea to have an infinitesimal scalar.
Infinitesimals are located on the real number line very near to zero,
and under some definitions coincidentally.

There might be some interesting results from having infinity be the
square root of negative one. We're talking about infinity here, when
infinity is plus/minus one it is not zero. I think there are a bunch
of projections from a given vector base to another where it might be
finite in the one and then infinitesimal in the next with spin, or to
the "light-like" vector with the particles and the waves.

If you accept a countable theory, where infinite sets are equivalent,
then EF and compositions of EF are still the only functions bijecting
the naturals and reals. Heh, the photon. Is there one photon, or
two? There's only one photon, damnit. Is the average shift of all
emitted and reflected light of all objects throughout all the skies
zero? Consider the local group:

http://www.seds.org/messier/more/local.html

I'm glad to have brought that to your attention. Thanks for that dual
set theory idea and more interpretations of the axiom-free logical
system.

I search for "J.E." and "physics" and Jorge Hirsch tells me a
superconductor is one big atom. It's not, yet it is. People toss
around words like "infinity" and "atom" quite too cavalierly if you
ask me. The superconductor just has some dielectric/diamagnetic
behavior of the atom. That's what he says.

http://physics.ucsd.edu/~jorge/giantatom.html

That reminds me of that wacko Plutonium, except it's lucid and very
concrete, and he claims the universe is one big atom. That's
ridiculous, we've all compared the orbitals of the electron to the
orbits of the solar system. Hirsch says the proton mass is only 2000
times the electron mass, I thought it was many orders of magnitude
more than that.

If space-time is curved, how is it flattened?

You've heard of me. It's nice to hear from you.

Do we speak past each other? No, we appear to be communicating quite
readily.

Do you get my drift? Non-relativist quantum mechanics is usually
taught. I don't even know what that is, and if I did, I'd probably be
nonplussed. I'm arrogant, AND ignorant, because that's funny. Also
it's humorous.

J.E., post-Cantorian set theory is a superset of Cantorian set theory.

And warm regards,

Ross F.

Relevant Pages

  • Re: Skolems Paradox and why is math the way it is?
    ... >> unity, infinitesimal, and infinity, and turned to sci.math to share my ... Even scalar unity is something I don't know what you ... >> in your first order logic, I just say to stay in first order logic in ... make requests of the foundations of mathematics to reflect your theory ...
    (sci.physics)
  • PANORAMARE
    ... concept of infinity is indefensible - 24 messages ... should be a less interesting>>part of mathematics. ... approximation in your immediate neighbourhood. ... centric solar system is overly complicated, ...
    (sci.physics.relativity)
  • Re: Wheres respect? was Re: Corrective interpretation of real numbers
    ... then denial of the actual infinity ... Those wo are using mathematics in physics often complain about allegedly ... He imagined cardinality of standard continuum much ...
    (sci.math)
  • Re: Earth 8??
    ... The problems you're bringing up come from the fact that you're using common English words that have common English meanings that don't apply to transfinite numbers. ... By definition of _infinity_. ... lay speech, philosophy, and pretty much anywhere but pure mathematics. ... This defined mapping puts the positive integers and the even positive integers into a 1:1 correspondence. ...
    (rec.arts.comics.dc.universe)
  • Re: Metaphysics of Potential Infinity
    ... >> My clarification of the distinction does not mean to undermine the ... We are talking about the concept of infinity. ... instance in philosophy of computation, or philosophy of mind, or ... philosophy of mathematics. ...
    (sci.logic)
Loading