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Topic: Re: Non-Euclidean Arithmetic
Replies: 5   Last Post: Sep 15, 2012 9:30 AM

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Paul A. Tanner III

Posts: 5,920
Registered: 12/6/04
Re: Non-Euclidean Arithmetic
Posted: Sep 13, 2012 10:36 PM
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On Thu, Sep 13, 2012 at 7:54 PM, kirby urner <> wrote:
> On Thu, Sep 13, 2012 at 12:39 PM, Paul Tanner <> wrote:
> << snip >>

>> I avoided the term "God" - a being as we all know according to many
>> who believe in various types of scholastic theologies knows our
>> futures and any and all futures of any and all universes, but maybe it
>> seems I should have not to make my point.
>> My point is that the idea that a thing does not exist unless and until
>> it exists in the mind of some human being is clearly and unavoidably a
>> rejection of that philosophy of mathematics called mathematical
>> realism as well as a rejection of major forms of theism.

> So? What's wrong with clearly and unavoidably rejecting some specific
> philosophy such as "mathematical realism", an infantile philosophy of
> little repute, believed in by lesser minds through the ages?

Well, since as I pointed out, since a standard belief in God implies a belief in some sort of mathematical realism, denigrating any and all mathematical realism as "an infantile philosophy of little repute, believed in by lesser minds through the ages" implies denigrating a standard belief in God as "an infantile philosophy of little repute, believed in by lesser minds through the ages."

Just making sure that you know that you are insulting most people through what seems to be your militant atheism.

Note: I am not arguing nor I am going to argue against atheism, even your evident militant kind. Just know that are you insulting most people.

> I think
> it my civic duty to cast aspersions on these inferior memes trafficked
> in by the purveyors of ignorance.

More dumping on a standard belief in God, I see.

>> If you wish to dump on the belief that mathematical objects can have
>> some sort of existence outside of the human mind and promote that they
>> cannot have some sort of existence outside of the human mind, then OK,
>> but note that in doing so you are dumping on many people's belief in
>> God, since many people's notion of God is that anything we could
>> possibly "invent" or "discover" (or even our futures or any future of
>> any universe in any multiverse) is already known to this God. Perhaps
>> then you could be more respectful of the beliefs of those who believe
>> differently than you.

> I'm sure if they need to bolster their beliefs, they can do so on
> their own without my assistance. The mangled "philosophy" you present
> is so unbelievable on the face of it that I wouldn't no where to
> begin.


It's mangled only in the mind of perhaps some militant atheists.

I'm only pointing out the obvious, which is that a standard belief in God implies some sort of mathematical realism.

If you deny this obvious fact, then perhaps you could explain how the former does not imply the latter, and so perhaps you could explain how this denigrating of mathematical realism is not denigrating a standard belief in God.

> I do speak of "math objects" though and agree that institutionalized
> ways of thinking transcend any one individual's thinking. There's a
> "zeitgeists" aspect to ideas, which is another way of saying "the
> whole is more than the sum of the parts".

>> No, mathematical realism does not imply the existence of such a God,
>> but the existence of such a God does imply mathematical realism, and
>> so negating mathematical realism yields negating the existence of such
>> a God. (Notice I said "such a God" since I'm allowing for the
>> possibility that some might believe in an ignorant God.)

> It's very possible to believe in God and yet to think human beings and
> their pathetic "real numbers" are not godly in any way.

Hello? Mathematical realism is simply the notion that mathematical objects exist outside the human mind. Period. That means that if the standard belief in God holds, which includes the notion of God as Logos (literally, Logic), that any thought of any created being already is known by the Creator - and this holds in theism as well as pantheism, then some sort of mathematical realism holds. I just don't see why you don't see that if the God of scholastic theology of all the major religions exists, then some sort of mathematical realism holds. The operative word is "outside" or "beyond" the human mind. If such a God of scholastic theology is in any way "outside" or "beyond" the human mind, then some sort of mathematical realism holds. I repeat: I just don't see why you don't see this.

And before you start to make even more mistakes as to what so many people actually belief about what they worship, why don't you ask people who actually believe in an infinite God whether they think that this infinite God they worship is so dumb that this infinite God has never thought of irrational numbers - or is capable only of thinking of natural numbers or whatever.

And "pathetic "real numbers""?

Boy, it seems that since I've utterly destroyed your position on the merits, your "argument" has become nothing but throwing whatever insults you can think of towards what you so clearly hate.

> In humans, you're dealing with an inferior life form of less than
> average intelligence (as ETs go) who have indulged in a kind of brain
> rot we today call "mathematics".

This is true evidently only in the mind of some militant, bitter atheists.

> It's nothing to be proud of, and if
> we were more faithful, better people, we would have a much more
> adequate mathematics than we do today.

Why don't you show us what this "much more adequate mathematics" would be?

> I'd say that's closer to my thinking than mindless obeisance to one
> particular lineage of human ancestor and their one particular "cruft
> wagon" (aka "dogma cart" aka "belief system").

I think someone needs to speak for himself on this "mindless obeisance" stuff and his evident worship of Wittgenstein.

> Of browbeating people into believing just the right stuff to make
> advances in that stuff, is par for the course. It's what we do.
> Mostly, that's what we call "education" (a brainwashing in the local
> belief system).

So brainwashing is what you think of what you do to kids?

>> OK, but make that "repeated addition repeatedly redefined" while
>> recalling that scaling has no problem and requires no redefinition
>> from day one.

> I never did any redefining.

This is not true. You need to stick to the truth. And so we see that what I'm doing is necessary: Some of those who push the repeated addition agenda so while refusing to be up front about what they do.

In the naturals, repeated addition, is directly using the two given factors such that one of them repeatedly an addend under addition and the number of times it is such an addend is the other factor.

In non-integer rational number multiplication (a/b)(c/d) such that each factor is not an integer, we *cannot* do this above, and so we *must* redefine the algorithm, what we do - we *must* first break up one of the factors such that we obtain two new factors, one of the factors being the numerator of the broken up fraction, a[(c/(bd)), and only then can we talk of repeated addition of a given factor, this one being the one other than that former numerator in question.

In irrational number multiplication ab such that each factor is an irrational, repeated addition breaks down completely in terms of being able to preserve the original function a,b -> f(a,b), and we *must* redefine things so much that we now must replace it with some sort of approximation, a,b -> *approximately* f(a,b).

> You kept saying, "oh, but that's a redefinition". But it's never
> clear in these discussions how or why it is you have any authority to
> tell me what's a definition and what's a redefinition.

After the naturals, it's all a redefinition of what is done in the naturals, since recall that this is about math education and the progression from the naturals through the rationals to the reals and then Algebra I and beyond almost all of it based on the reals.

>>> Thanks to my learning about multiplication as repeated
>>> addition with whole numbers, and then with fractions, this
>>> extending to real numbers is not conceptually a problem.

>> With repeated redefinition of "repeated addition" you have gotten to
>> the point of giving up what the function actually is, which is a,b ->
>> f(a,b) - you have redefined things so much that we now just have a,b
>> - -> *approximately* f(a,b).

> Approximation is not a new idea. It was there from the beginning,
> with estimation, which Devlin is not against.

Not so, since again, this is about math education and the progression through the number systems in question.

>>> When the teacher sides with Devlin and tries to censor my
>>> thoughts, take away my repeated addition model, I fight
>>> back, as it helps me and I see no reason to surrender this
>>> tool

>> Keep it all you want. Just be up front about the fact that you have to
>> redefine things every step of the way and then get to the point where
>> you even have to replace what the function actually is, which is a,b
>> - -> f(a,b), with a,b -> *approximately* f(a,b).

> I have to redefine things *for you*.

No, again, since this is about math education, you have to redefine things for the students as they progress through the number systems in question.

>> [In reply to what some of the greatest mathematicians in history have
>> done on the topics of the infinite and the continuum, Kirby writes:]

>>> "They" -- you're sound so awed by authority.
> Mathematicians are not universal in their assessment of one another's
> work. The laity tends to be uniformly awed, but once you start
> reading the history, you find that they squabble. Kronecker thought
> Cantor was just silly, indulging in a kind of insanity and calling it
> math. People jumped on that bandwagon though.

And Kronecker as a denier was judged by history to be on this issue a crank.

Yes, even a great mind can be a crank on some issue.

Throughout history, many great minds' accomplishments were denied at the time by sometimes even other otherwise great minds, and these deniers all were in the end judged by history to be at least on those issues cranks.

It's too bad that you are throwing your lot in with the denying cranks of history.

I see a double standard: You deny and/or denigrate the math you dislike, math based on that which is not computable (almost all real numbers) and infinity and continua, but you turn around and have a problem with what you perceive others to be doing, which is the same to math you like, math based on that which is computable and finitude and the discrete.

(I say "perceive" because I don't think anyone is actually denying and/or denigrating the math in question you like. No, I'm not doing that. I'm just pointing out the limitations it has with respect to the math you don't like, math based on that which is not computable (almost all real numbers) and infinity and continua.)

> The proof God does not exist is that existence is precisely that
> imperfection which makes one less than eternal. If God exists, then
> He's not really God, as "existence" is a big step down from exalted.
> Mere existence is too lowly for a true deity. If God exists, we
> should pity Him as a poor slob.

I know, I know, there is all this that the term "existence" is not the proper term to use, and all that. This is why existentialist philosopher Paul Tillich phrased things the way he did, used the type of language he did, when speaking of God.

But still, we all know what is meant when it's said that God exists or does not exist. And so given that, I say that it's OK to use the easier to use "exist" language.

But if you want to be dogmatic about it, then that's you.

> You make the same mistake a lot of beginners make: they think for
> something to have meaning, there must be some "existing object" that
> is that meaning.

No - I don't make that mistake, not at all.

It's all based on one's personal ontological beliefs. If I was an atheist, then of course it is not the case that there must be some "existing object" in question and all that. As one who is not, that there is the "existing object" in question already there - in the mind of what I believe "exists" - is merely a natural consequence of my belief in such a one who has such a mind.

That is, you get it backwards: I do not say that there must be some "existing object" for there to be meaning. I say instead that since I believe that God "exists" and that this God has certain attributes with respect to knowing, then the "existing object" in question is already there in the mind of what I believe "exists". The latter is different than the former.

Message was edited by: Paul A. Tanner III

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