numbers don't exist outside of God
I want to start with Anselm’s Ontological argument which roughly goes:
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:
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.
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
- 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
Comments (39)
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!
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.
The GCB limited by human understanding would not be that great, it would be full of human flaws and limits.
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.
Your ranks of greatness would simply be integers.
1,2,3,4,..., n
There is no greatest integer and there is no GCB.
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.
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).
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?
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.
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?
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.
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.
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.
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.
I think you are making that blank statement because you are unable to follow me.
Ok, fair enough.
He was trying to correct you. As was LD Saunders and myself.
@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.
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.
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.
All three of those traits have fallen under heavy criticism over the ages. They cause logical and moral conflicts and are far from being characteristics of a "greatest" conceivable being. I think a conceptual being which does not possess any of those traits is a vastly superior concept, as it is a far more practical conceptual form.
GCB +1
So it looks like it is good on paper and in practice.
I do not quite understand what you mean here, but it seems like you are saying that the Greatest Being you can conceive of would NOT be omnipotent, or omniscient, or omnipresent. That seems to beg the question of what makes that being 'great'?
Simply because you can conceive of a Being that is not omnipotent, omnipresent, and omniscient and label that being "the Greatest being" means nothing unless the Being conceived has some intrinsic qualities that make it, by definition, 'great'. There seems to be objective, great-making factors that the Greatest Conceivable Being must have, or else we should revise our concept to be a Being that has those great-making traits. For example, let us say that lifting objects is a great-making trait. Everyone agrees that to be great, you must be able to lift an object. If I say, "the greatest possible being can lift a car over his/head" and you say, "the greatest possible being can lift a skyscraper over his/head" clearly the being you have conceived of is greater than mine. However, the concept of the GCB+1 ends because, eventually, it becomes clear that truly the greatest conceivable being must be able to move any object, and so we can all agree that unless the being we are conceiving of can move any object, it is not the Greatest Conceivable Being.
If you object to the idea that power, presence, knowledge, and goodness are 'great making' qualities, I am curious as to what you believe makes one thing better than another. But, as it seems obvious that there are great making qualities that people can agree on, we must the ascribe the Greatest Conceivable Being to possess those qualities to the qualities' greatest extent, and so there can be no GCB+1, as the GCB is then objective.
You are just now realizing this? The moment you read the word "greatest" you should realized that was an entirely subjective gradation.
The omni traits carry a slew of inconsistencies and conflicts, for a conceptual being to have a rational form, that humans can actually convince, it is far better just to forget about them.
Quoting Ben Hancock
So can your GCB make an object so big it can't lift it? Your entire argument is logically flawed, so your purposed GCB being is deeply flawed. Thus by limiting my conceptual being my GCB > your GCB, as with removing the omni traits it becomes more logically congruent.
Omni traits make for horrible conceptual beings.
I was mostly giving an example about how objective greatness exists, and mentioned nothing about God creating, but it seems that creation is also a great making property as you have so perceptively noted. The 'rock so heavy God can't lift it' is very easily solved by having a clear definition of what omnipotence is. The classic argument goes something like this:
1. Either God can create a stone so heavy that he cannot lift it or he cannot create it.
2. If God cannot the stone, he is not omnipotent
3. If God can create the stone, he is not omnipotent
4. Therefore, God is not omnipotent
I'm assuming that this argument serves as proof thatQuoting Jeremiah
Really, the problem here is just a misunderstanding of what omnipotence is. It would seem that God being omnipotent means He, by definition of being omnipotent, cannot fail. It would seem then, that God cannot create the stone not because he is limited in capacity, but because He is limited by the nature of being omnipotent. It seems at this point we are splitting hairs over definitional truths, but it is important to highlight that a GCB+1 who gains anything by being able to fail, is in no way greater than God described above. Even if you object to God being omnipotent in that scenario, it seems that a God who cannot fail then has some sort of great making property.
The basic point that people have been attempting to establish is that the 'Greatest' is objective. I am curious what you mean when you say Quoting Jeremiah As it seems quite simple that any trait you identify, there is some maximization of that trait that makes greatest objective?
Quoting Ben Hancock
So you are going to decide the limits of an all-powerful being? Really? That is some ego you have, but OK. So what you are saying here, is that humans have the power to limit and define the power of an all-powerful being. Which makes humans more powerful and thus humans are now GCB+1.