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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 14, 2012 3:32 PM
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On Fri, Sep 14, 2012 at 12:46 PM, kirby urner <kirby.urner@gmail.com> wrote:
> A lot of believers don't self style as uber-logical and would not
> follow you in your claim that belief in God entails God believing in
> real numbers or creating in advance every board game, like Monopoly.

I said "a standard belief" - not any belief.

I have been saying "know" - not "create".

One can create something already known by another.

You dumped on the belief in an omniscient being (the belief in a being who already knows of anything we could create and this covers our objects of thought and much knows of much else) as a stupid fiction, implying that people who believe in such a being are stupid knuckle-draggers and whatever.

I could be wrong, but:

I believe that the vast majority of the many billions of everyday people in this world that profess belief in God (Christian, Muslim, Hindu, Buddhist, pantheists and non-pantheists alike, doesn't matter) hold to the belief that this God they believe in is Supreme Divinity and is infinite, and is Logos of some sort, meaning that in some way it is or has or is the ground of Mind and is or has or is the ground of Thought. What I'm trying to say is, in the language of how I believe everyday people would say it, is that I believe that the many billions of everyday people in this world who believe in God believe in an infinite God that is capable of having knowledge and has infinite knowledge and has infinite thought and that this means omniscience at least as they would understand that term - all-knowing or whatever. They would I believe say that the infinite God they believe in, being over and beyond all of possibly infinite time and space, most certainly already knows of those things that finite beings could know or create.

I ask you this question: Why do you feel the need to insult this belief?

> It doesn't make me an atheist to think poor deluded creatures such as
> yourself and myself, barely able to think at all, let alone logically,
> are unable to share coherently about the content of a mind we can't
> fathom.

Then why do you so surely proclaim (with insulting language against any negating belief) that this mind cannot possibly already know of whatever we could possibly know or create?

If such a mind does know such, then how is that not some form of mathematical realism (you know, it exists outside the human mind as an object of thought of a non-human mind)?

> By the way, what does Satan know (in a "standard belief in God" you
> often find lesser deities -- a kind of polytheism)? Does Satan know
> about the real numbers in advance, or just God in your model? Or does
> Satan only find out about these things after the fact, by watching
> over humans' shoulders? Just curious.

Well, if God is at the level of the class of all sets, superior to all transfinite ordinal and cardinal numbers, then an open mind would see that that allows for the possibility that some created beings could be infinite and not just finite.

>> 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

> Some sort of mathematical realism is acceptable to me.

Great. Let's remember this.

>> "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.

> This is a somewhat empirical claim that you're making, falsifiable and
> therefore testable. I can start polling standard believers and asking
> them if they think God knew about

Would you be surprised if they said that sure, since the God they believe in is all-knowing - as in knowing all of every event of time and space even if it is all infinite? Would you be surprised if they told you that they didn't think that the God they believe in is trapped inside of the time or space that God created? (Ask them that one, too, whether think that God created time and space as well as ask them whether they think God is trapped in time or space.)

To make this point mathematical:

Enter normal numbers, disjunctive numbers (if a number is the former then it is the latter), and lexicons.



"A number that is disjunctive to every base is called absolutely disjunctive or is said to be a lexicon (Calude and Zamfirescu, 1999). A lexicon contains all writings, which have been or will be ever written, in any possible language.... The set of absolutely disjunctive reals (lexicons) is a residual (Calude and Zamfirescu, 1999)."

This means that any infinite being that knows what is encoded in a lexicon knows all writings, which have been or will be ever written, in any possible language.

Now extend this idea to whatever degree possible to every possible event in all space and all time in every possible universe, encoded in sequence.

Now, technically speaking this may not be what it means to be omniscient, but....

> I'm sorry if God has to know all this garbage plus even more garbage
> that hasn't been invented yet. You'd think humans knowing it would be
> sufficient i.e. why a redundant universe in which everything has to
> exist twice, once in the mind of man and a second time in the mind of
> God.

You forgot the minds of aliens and angels and whatever else.

Maybe it ain't redundant - maybe sharing knowledge is a good and even morally good idea.

> I was thinking something similar. Now that I've shown how repeated
> addition is quite competent to model two irrationals coupling and
> begetting a child irrational,

It depends now on what you mean by "model" - are we now abandoning the part of the definition of repeated addition that requires that we are computing the product?

Enter the set of all non-computable real numbers, specifically the set of all non-computable irrationals (the computable reals are all the rationals, all the algebraic irrationals, and some of the non-algebraic irrationals), exactly that set of all irrationals that makes the set of all reals uncountable.

You cannot compute the non-computable with repeated addition or anything else.

That is, you cannot compute almost all irrationals with repeated addition or anything else.

That is, you cannot compute almost all reals with repeated addition or anything else.

That is, this is a proof of the falsity of the repeated addition crowd claim that repeated addition is what real number multiplications *is*.

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