Nice try but there are too many out there who have actually read all or at least a fair portion of wha I have challenged you to read. Really, I’m not being facitious, start with " Elements of Christian Philosophy, " esp. chaps 7 & 8. It’s for your own good. Linus2ndTranslation: Linusthe2nd cannot refute my argument with real philosophy, and so he is now telling me to read a book that he doesn’t understand himself; a book that even refutes his own position.
Passing the buck will not make your argument true or even probable.
I always love it when people start arguing against their own position, makes it much easier for me. The point is: is a set an abstraction or not. if it is, there is no real difference between a set containing God and God. If it isn’t, then there is a real difference but it also means that even the empty set is not nothing.What do you mean by saying that, “in mathematics, there are actual infinities?” Mathematics is abstract, and abstract is the opposite of actual. In mathematics, we actually deal with infinities, I’ll grant you that. But those infinities are as abstract as any of the values we assign to numbers. That is why, in mathematics, we can deal equally well with rational or irrational, positive or negative, real or imaginary. There is no real square root of negative one, but mathematically, i makes just as much sense as -1 or 1. That is because in mathematics, everything is abstract. So in mathematics, there are infinities, and, mathematics is useful in describing the world, even though in the world there are no actual infinities.
The proper question is, is mathematics useful in describing the world, and can its use be extended to the territory in which we now find ourselves? I submit that, certainly it can. I see no reason to assume that there is some limit to the use we can make of our power of abstraction that is manifest in mathematics. Can we usefully apply the theory of sets, and the generation of the natural numbers as sets from 0, to the possible worlds scenarios? Is it, in fact, legitimate to assign G = 1 and wG = 2? That is the question; that would be the basis of your objection.
And I think, as least insofar as my understanding goes, it is legitimate. It seems intuitively sound. If you maintain that it is not legitimate, then please, give a demonstration of why, if you would. Thanks!
And, by the way, the empty set, the null set, {} is precisely == 0. It is Nothing, by definition.
Ah, but Linux you keep making the same error. You are confusing two very different realities, the eternal realm of God and the finite, contingent, limited, created realm of the universe. The realm of the eternal God is absolutely other than and outside of the realm of the universe. God created the finite universe out of nothing ( not even virtual particles - we have discussed this before ). Nor did he create it " out of " his own esse.Existence is absolutely other than the essence of created things. It is the essence of created things that differentiates between God and creation. Esse has nothing to do with it. Esse is that which actualises potential essences, and thus esse has to exist absolutely as actually distinct before we can rationally speak of actualising potential. God is the esse of created things, but he is not the essence of created things, and therefore it is not pantheism. Nothing you say is going to change that fact.
That’s kind of a weird thing to say, I wonder what contribution that statement actually makes to your argument. Certainly, I am not arguing against my own position. It puzzles me why you would perceive that, but as you just made the statement and dropped it, I guess I will concentrate instead on actually making my own argument and refuting yours. Maybe you should concentrate on the same? Just a thought.I always love it when people start arguing against their own position, makes it much easier for me.
OK, help me here. You SEEM to be saying the following:The point is: is a set an abstraction or not. if it is, there is no real difference between a set containing God and God. If it isn’t, then there is a real difference but it also means that even the empty set is not nothing.
Either way, your criticism of my argument is irrelevant.
I have never claimed that numbers are useless or ignorable, but either you stay in your fantasy world and treat sets and numbers as abstractions, or you treat them as real. What you are doing is conflating the two concepts.That’s kind of a weird thing to say, I wonder what contribution that statement actually makes to your argument. Certainly, I am not arguing against my own position. It puzzles me why you would perceive that, but as you just made the statement and dropped it, I guess I will concentrate instead on actually making my own argument and refuting yours. Maybe you should concentrate on the same? Just a thought.
OK, help me here. You SEEM to be saying the following:
A. A set is an abstraction, and therefore sets can comfortably be dismissed as not holding any possible isomorphism with reality.
- My criticism of your argument is irrelevant because both of the following lines of thought lead to that conclusion.
B. A set is not an abstraction, and therefore {} =/= 0.
1.A. My criticism of your argument (to wit, G = 1, wG = 2, 1 =/= 2) is irrelevant because it is impossible to use numbers to describe reality at all, because numbers are abstractions.
1.B. My criticism of your argument ( G = {{}}, wG = {{{}}}, {{}} =/= {{{}}} ) is irrelevant because ( {} =/= {} ).
That is what I could discern from your statements. I’ll offer a brief criticism of each. For 1.A., the problem is that numbers, despite your dismissal of them as abstract and therefore useless or ignorable, are actually quite useful, and can easily be put to good use describing reality. Anyone in the world familiar with numbers knows this. I surmise that you know it, and are pulling my leg with this “there is no real difference” garbage. But fun is fun, let’s get down to serious discussion, if we may. For 1.B., it is not in fact the case that {} =/= {} nor that 0 =/= 0. In reality, the null set is zero, {} == 0. Even if you were to dismiss all numbers as useless, the fact remains that in our fantasy world where our calculations have consequences, {} == 0.
They are really abstractions. Their reality is in their existence as abstractions. We then use these mental abstractions to guide our actions in physical reality.I have never claimed that numbers are useless or ignorable, but either you stay in your fantasy world and treat sets and numbers as abstractions, or you treat them as real. What you are doing is conflating the two concepts.
Or what relevance any of this has to metaphysics ? Linus2ndAs a matter of set theory, it is not true that {G} = { {}, G } except for the trivial case of G = {}. Nor is it true that elements and subsets are the same thing.
However, I can’t see the relevance of any of this to set theory.
None of this has any sort of relevance to my argument.They are really abstractions. Their reality is in their existence as abstractions. We then use these mental abstractions to guide our actions in physical reality.
Now in philosophy or theology, which is what we are doing here, a similar principle applies, except that philosophical concepts and theological concepts are abstract similarly to numbers, so the possibility of correlation is actually more direct. As an atheist, you might personally hold that there is no reality to correspond to any of our theological concepts, but you can’t assume that in an argument, unless you’ve actually proved it.
Given, then, the possibility that God is real and that there is some possible world prior to God’s creating of anything, we can certainly represent that possible world, as you’ve already done, as wG, and God as G. My contention is simply that wG =/= G, or {G} =/= G. I used a symbol earlier that I failed to define, to wit, ’ {- '. I was trying to make an ‘E’ symbolically, to denote the function, “is an element of.” So that,
2 {- {1, 2, 3}.
Thus, G {- {G}. God is an element or subset of the set that contains only Him and nothing else. There is, in abstract mathematical reality, another subset of that set, namely 0 or {}, the null set. That is one thing we mean when we specify, “and nothing else.” Thus, {G} == { {}, G }. The set containing God alone has the cardinality 2. It correlates exactly to the number 2. It is constructed identically to the number 2.
What we have here is either an identity or an isomorphism. If we take literally the phrase, in Scripture, “God is One,” then we can assert a direct identity between God and 1, or God and {0}, and thus the set {God} or {G} or wG is identical to 2, or {0, 1}, or { {}, G }.
If we do not take that phrase literally, then there is not identity, but there is still isomorphism, and that is all that is necessary for the math and thus the philosophy to be sound. If you want to debunk this, you’ll have to show either why it is not legitimate to draw the isomorphism between possible worlds and mathematical sets, or between God and 1, or, that it is not legitimate to derive the natural numbers according to the schema referenced, but that is already pretty widely accepted among mathematicians, I think.
Because there is no other explanation. Thomas demonstrated that the God of Christianity exists. By Faith we know that the material, limited, contingent universe came into existence, whereas there was no prior existent substance or being ( including the being of God ) from which it sprung. In other words, we know by an act of Faith, strictly and absolutely, that God created this universe out of nothing. How he created it, is also a mystery as has been pointed out before ( see some of my posts above ). Thomas explained how it was necessary, that is logically necessary and ontologically necessary, but neither he nor anyone else could, can, or ever will be able to explain " how. "If you don’t know how God created the universe, then why should they accept God as the cause?