Whitedragon wrote:Stones in the spirit realm do not make sense, because they would have to be ethereal. It is like asking can something be a gas and a solid at the same time, or the famous question; “can the Lord create a square circle?”
I agree with you that stones in the spirit realm do not make sense. However, an omnipotent deity could still create ethereal stones that are in the spirit world. Otherwise, it would not be omnipotent. In fact, omnipotence contains the ability to make possible the impossible and even the nonsensical. Therefore, God is capable of making a square circle, since he would be restricted by the laws of geometry and thereby not omnipotent if he couldn't.
Whitedragon wrote:To get back to infinities, some infinities are larger than others, but then they are not actual infinities.
Just to clarify terminology: when you say "actual infinity", you mean "true infinity", right? I'm asking because "actual infinity" is usually contrasted with "potential infinity" and taken to mean an actual, completed infinite totality (see Wikipedia). This includes transfinite sets, which are not truly infinite according to your (and my, see nest paragraph) understanding of true infinity.
Now back to the subject. I also agree with you that those infinities which are larger than one another (e.g. the transfinite numbers) are not truly infinite because, although they have different mathematical properties from natural and real numbers, they are definite entities that obey definite laws and can be subjected to logical analysis. Georg Cantor, the discoverer of transfinite numbers, would probably agree, too.
Whitedragon wrote:True infinity cannot be larger than another, since it is not a number to begin with.
That is an interesting and important realization which I agree with, too. We should add that true infinity is also not equal to itself or unequal to itself or in any other way comparable with itself, for that matter, because it is not a number and not a definite entity altogether and self-comparability is a trait of definite objects like numbers.
Whitedragon wrote:If we hold that the Lords power is infinite
That is included in the "definition" of omnipotence and the implicit premise of the omnipotence paradox that God is omnipotent.
Whitedragon wrote:certainly it would not be a countable one, but true infinity.
Of course it would be truly infinite. (But note that there are uncountable cardinals, which are not truly infinite nonetheless.)
I still think that
ChanceIsChange wrote:(strength of God) = ∞ ≤ ∞ = (weight of stone) (so God cannot lift the stone) and (strength of God) = ∞ > ∞ = (weight of stone) (so God can lift the stone) can be true simultaneously
is essentially a paraphrasing of
Whitedragon wrote:The Lord can create a stone that is so big that he cannot lift it, but he can always lift it
expressed and clarified with more symbols. For me, the rest of your first post on this topic, including your statement that infinity could be unequal to infinity, also seems to support my opinion that I had previously paraphrased your solution and added Felix' realization that logic only applies to definite terms to justify it. Am I correct, or had I misunderstood you?
Now, however, you seem to have changed your opinion, and I prefer your new opinion to your old one as well. Originally, we essentially tried to resolve the omnipotence paradox by exploiting some properties of a semi-infinity (e.g. being greater and less than itself at the same time). Now, however, you argue that true infinity is actually beyond being greater than itself, and we have extended this to true infinity's transcendence of self-comparability above. Applied to the concrete paradox, I would say that means that, because both God's power and the stone's weight are truly infinite, it is not meaningful to say that one is greater than the other and that it is therefore also not meaningful to say that God can lift the stone or that he cannot lift it, finally freeing us from (almost) all remnants of logical constraints (hopefully).
Whitedragon wrote:would mean you would have to create
Isn't it true that God is free from all necessities because he is omnipotent?
Whitedragon wrote:which is not possible
Isn't it true that God can make the impossible possible because he is omnipotent?
Whitedragon wrote:if infinity is not a number we cannot say, something is larger than infinity; it is like asking what is longer than an eternity.
It would appear to be as you say. On the other hand, that would make infinity seem to be some pinnacle, a maximum, a typical phenomenon we encounter in the world of the strictly finite. For example, the finite set {1, 2, 3, 4} has a maximum. The countably infinite set of all natural numbers already contains no maximum, and it is a far way from being truly infinite. I prefer the following stance: it is false to say that there is an element of the set {1, 2, 3, 4} which is greater than 4, but it is meaningless to say that something is greater than true infinity.
Whitedragon wrote:Lastly, since true infinity has no end, to creating something of infinite weight would mean you would have to create a universe or place that can hold it with a “larger” infinity, which is not possible.
Concerning the creation of something with truly infinite weight, it appears to me that saying that such an object has to be included in an even larger universe is applying logic to the truly infinite, which is not valid as we saw in previous posts.
Whitedragon wrote:Perhaps it comes down to the state of being, what is the being of infinity? Perhaps we can ask, can the Lord duplicate his essence, and with safety, we can say yes. We can talk of more than one thing in mathematics that is truly infinite and employ that same infinity in various calculations; but we cannot change the nature of infinity itself, if that makes sense.
If true infinity has being (I personally agree with Felix that the truly infinite does not be, but that opinion is not rigid), then the essential question may indeed concern the nature of the being of true infinity. However, I do not understand what exactly you intend to say. Could you please clarify what you mean?