numbers don't exist outside of God

lupac

I want to start with Anselm’s Ontological argument which roughly goes:

The Greatest Conceivable Being (GCB) exists in the understanding.
It’s better to exist in reality than only in understanding.
If the GCB exists only in the understanding and not in reality, then there could be a being greater than the GCB. (1,2)
There can’t be a being greater than the GCB
The GCB can’t exist only in understanding. (3, 4 MT)
Therefore, the GCB exists in reality. (1,5)

Anselm takes God to be the GCB, and I think this is a valid conclusion, but I think the idea of the GCB can be pushed a little to help solve some other philosophical/theological issues for example, are there things outside of God which were not created/did not need to be created? Some say that without God numbers would continue to exist, or if God had chosen not to create the universe numbers would still exist. I think this idea is contrary to the common supposition that God is the GCB because I can easily conceive of a being that could exist outside of numbers, abstract ideas, shapes, and that could create those very things. Furthermore, if the GCB couldn’t (or didn’t) create numbers then we have to contend with the idea that numbers possess properties not given to them by the GCB. Numbers, therefore, would not be beholden to the power or control of the GCB in which case the GCB would not be all powerful.

I’m getting at two different arguments here; the first looks something like:

Either God is the GCB, or there is another GCB
If God is the GCB, then he could create everything from nothing
God could not create numbers
God is not the GCB (2,3 MT)
There is another GCB (1,4 DS)

Of course, if there is something greater than God that ‘something’ deserves to be thought of as God. I take the conclusion of this argument to mean that God truly is the GCB and did create numbers. I’m expecting most objections to come from premise 1, people may object by claiming that even the GCB couldn’t create numbers. I sympathize, it is supremely difficult in our post-number-creation age to imagine an existence without numbers, but I would point them to my second argument, which is an attempt to show that the GCB could not exist “contemporaneously” with numbers.

The GCB is all powerful if and only if the GCB is in control of all things
If there are things that the GCB didn’t create then they don’t have control over them
Numbers exist without the need of creation by the GCB
There is something over which the GCB has no control (2,3 MT)
Therefore, the GCB is not all-powerful (1,4)

I can, of course, conceive of a GCB that is all powerful and created numbers and so we need not worry about the impotence of a GCB.

Some notes, (1) in this argument I used God and GCB interchangeably at most points, the exception being in argument two where ‘God” refers to the being that could not have created numbers. (2) In the second and third arguments, I assume that God (the GCB) exists based upon the ontological argument. Please, I’ve poured too much time into this argument and would love for it to be ripped to shreds. I’d love to hear your ideas and objections. thanks

SophistiCat

I can, of course, conceive of a GCB that is all powerful and created numbers and so we need not worry about the impotence of a GCB. — lupac

Speaking of impotence... Using a parallel argument we conclude that god created masturbation and masturbation cannot exist outside of God. So indeed, we need not worry about the impotence of a GCB!

Devans99

Numbers are concepts in our minds, they are not real so they cannot be created. The fact that God can't create something that cannot be created takes nothing away from his Omnipotence.

Sam26

First, the ontological argument doesn't work for a variety of reasons. One is that you can't infer the existence of something based on a concept or concepts. If that was true you could infer the existence of all kinds of things. There is no good argument for the existence of God.

Second, granting that there is a religious God, it's possible that abstract objects like number are just part of the mind of God, as Devans suggested. They along with a myriad of other abstract ideas, objects, and properties could just be part of what God knows. In other words, they would not be within the realm of the creatables. Think of it this way, if God is omniscient, or even if there is a being that possessed omniscience, that would mean that that being knows all that can be known (simple definition), as such it would know, presumably, the number system. However, if numbers are creatable things, then what you're saying is that an omniscient being, prior to the existence of the number 2, didn't know there was such a number. It doesn't make sense.

The other problem that Devans alluded to is that religious people, at least some, think that if numbers and other abstract ideas don't fall under God's power, then somehow this takes away from God's omnipotence. However, that's just a problem of understanding what omnipotence entails or means.

Jeremiah

The Greatest Conceivable Being (GCB) exists in the understanding. — lupac

The GCB limited by human understanding would not be that great, it would be full of human flaws and limits.

Jeremiah

Couldn't the GCB by human understanding conceive of a even greater conceivable being? Than that being could conceive of even a greater being, and so on to infinity. Meaning that a GCB is could not possibility exist.

Jeremiah

I think we can show that there is no such thing as a greatest conceivable being.

Greatest is a ranked gradation so let's say that there is a ranked scale of greatest beings.

My statement is that there is no greatest conceivable being (GCB).

However, let's suppose there is a GCB and we'll call it B. Then B > b where b is other beings. Now let G = B+1 where G is a being equal to B plus one more rank. Then G > B; however, B is the GCB, so we have have a contradiction which shows there is no GCB.

Devans99

↪Jeremiah

But the GCB would be the GCB from the top rank so you can't do G = B + 1 because there is no B + 1.

Jeremiah

↪Devans99

Your ranks of greatness would simply be integers.

1,2,3,4,..., n

There is no greatest integer and there is no GCB.

Devans99

The GCB would be at rank 1 by definition of the GCB surely?

Jeremiah

↪Devans99

You are talking about an ordinal scale, where objects or events are distinguished from one another on the basis of the relative amount of some characteristic they posses. Or ranking, the idea that things can be lined up from least to greatest.

DingoJones

↪Jeremiah

I don’t think your equation makes sense. The nature of B precludes the part of your equation that is “B+1”, the “B” in “B+1” could not have been “B” (the B that is the GCB) if you can add to it. It wouldnt be B (GCB).

Jeremiah

↪DingoJones

It is a common example found in text books of the proof that there is no greatest integer. So, what do you think, is there a greatest integer?

Jeremiah

↪Devans99

↪DingoJones

Think of the greatest integer you can and we'll call this the greatest conceivable integer (GCI). Post that number here and I'll show you one greater by adding a one.

Devans99

There should be a finite number of ranks (actual infinity is impossible) and the GCB belongs to the top rank.

Jeremiah

↪Devans99

OK your GCB can be at the top rank, and my will be at your top rank plus one more rank. Dang, another contradiction.

DingoJones

↪Jeremiah

You arent really talking about a number here, I think you are misapplying the math. GCB cannot be represented by an infinite set, by definition the GCB exists at the very top. It can never be added too as you have done, so your equation doesnt make sense.
I think what you are really arguing is that the GCB is possible in the first place?

Jeremiah

↪DingoJones

Then don't think of it as an infinite set, think of it as your finite set plus one. Honesty, I don't think you even understand what infinity represents. If GCB is your top rank then mine will always be GCB+1 more rank.

Jeremiah

Btw, religious groups have been warring and killing each other over who has the GCB for thousands of years. Christianity, Islam and Jaduism are prime examples of GCB+1 at work.

LD Saunders

Jermiah: That is part of the basic standard proof for there being no greatest natural number, and one can extend it to integers, real numbers as well, but what does that proof have to do with whether one can conceive of a greatest being? Nothing. It only pertains to numbers, and numbers that can be ordered on a number line, and I think that was DingoJones's point. I may consider woman X as the prettiest woman ever, or who ever could exist, and that would not be refuted by someone coming along and saying, we can prove there is no largest integer by adding one to an assumed largest integer. The math proof has nothing to do with assessing non-quantitative issues.

DingoJones

Then don't think of it as an infinite set, think of it as your finite set plus one. Honesty, I don't think you even understand what infinity represents. If GCB is your top rank then mine will always be GCB+1 more rank. — Jeremiah

Its not a finite set if you can always add one more. Again, you are misapplying your math principal here. This isnt about the numbers, it is about the nature of GCB. As part of its definition (the GCB), you cannot add 1 to it, or .01 or so and so integer...or anything at all. It is a being which cannot be added to, a being that which nothing greater can exist. Adding 1 is making it greater. You yourself in your own equation used the > symbol, demonstrating very clearly you do not understand what GCB means.

Jeremiah

↪DingoJones

It is a logical proof.

A simple version of a proof by contradiction, the plus one simply represents one thing is greater than the other, and the original statement is shown true because supposing the negation leads to a contradiction. So this contradiction that you are hung up on, that there can't be a GCB and a something greater than GCB is exactly what proves there that there is no GCB, as supposing that there is a GCB leads to a contradiction.

You arguing the existence of this contraction only makes me more right. You are proving my position, without even realizing it, as the more you hammer on this contradiction the more it validates my simple proof.

Whatever GCB you can think of I can think of one greater, therefore there is no GCB, because supposing there is one leads to a contradiction.

DingoJones

↪Jeremiah

You do not understand what is meant by GCB. You should read Anslems argument, he goes into more detail than the summary in the OP.

Jeremiah

↪DingoJones

I think you are making that blank statement because you are unable to follow me.

DingoJones

↪Jeremiah

Ok, fair enough.

Devans99

I think you are making that blank statement because you are unable to follow me — Jeremiah

He was trying to correct you. As was LD Saunders and myself.

Jeremiah

↪Devans99

@LD Saunders doesn't even know what a basic fact is.

But go and prove your position, post the details of the GCB and I will show you some flaws in it. You will never be able to conceive of this supposed GCB.

Jeremiah

Can anyone here actually conceive of this supposed GCB? Anyone at all?

Jeremiah

If it is called the Greatest Conceivable Being, then you should be able to conceive of it, right?

So don't be shy, religion has been trying to do it for thousands of years and they still suck at it, so what do you have to lose.

Jeremiah

No matter what you think up, or try to put in thought, mine will always be greater, because that is the door the OP left wide open.

lupac

↪Jeremiah

I'm not convinced that your equation shows a contradiction in the idea of the GCB.
I can think of a being that is omnipotent. I can conceive of a being that is omniscient. I can conceive of a being that is omnipresent and even omnibenevolent. I can conceive of a being that is all these things, and I think it shouldn't take too much imagination for you to as well. Let's forget talking about whether this being exists or not for now.

If I'm following your logic correctly, you're saying that even if you could conceive of my GCB you would just conceive of a GCB+1. This makes sense on paper, but the reality is you have not added anything to the GCB.

If you conceived of a table that was the Greatest Conceivable Table it might have properties like "it can support any weight," "it always has enough space for any number of people," and "it keeps the food at exactly the right temperature." This would be the GCT. I could object to your idea of the GCT by saying that, in addition, my GCT also has "the finest grain wood in the world" because I'm adding to the properties of the GCT. I cannot, however, say that my GCT is Jeremiah's GCT+1. That doesn't make sense. I haven't added anything to the GCT.

Eventually, we would get to a place with the GCT where no more properties or characteristics could be added to make it meaningfully greater, and that would truly be the GCT. You could still say that your GCT+1 is still greater, but that doesn't actually mean anything.

numbers don't exist outside of God

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