Godel has a proof of the existence of God that I mentioned on one of my blogs. The idea was really from Anselm and Godel put it into logical form. It depends on God having all positive traits. I tried to reinforce that idea by means of the Compactness Theorem of Godel. This was all in some other blog entry somewhere. Today I just wanted to add that it seems to me that this completeness theorem itself is related to the fact that in differential manifolds we only talk about C^0 or C^ Infinity. The reason is that a manifold M that is C^r itself has a C^r diffeomorphism from M to a manifold that is C^infinity.
[Kelly Ross rightfully noted that existence is a predicate.]
a C^r manifold is a manifold that you can take a derivative r times over the complex field. A C^r manifold has a C^r function to a C^infinity manifold.
[(Compactness Theorem). A set of formulas Γ is satisfiable if and only if every finite subset of Γ is satisfiable.][From the finite to the infinite. Perhaps the simplest use of the Compactness Theorem is to show that if there exist arbitrarily large finite objects of some type, then there must also be an infinite object of this type.] [Mathematical Logic ch. 4 and ch. 9]
This idea is sound. However I prefer to go with the more direct and simpler approach of Saadia Gaon and the חובות לבבות (Obligations of the Heart) and the Rambam of the First Cause, and the fact that there has to be a First Cause because of the problem of the infinite regress, For me that is the simplest and strongest approach, though I think Anselm's one is also good and complementary.
In any case this is related to Kelley Ross in a different way. Here is what he says in his PhD Thesis [Sec III]: "This continues the theory of purposive value by at last addressing the hitherto presupposed polarity of value, although the discussion belong to absolute transcendence because it may be taken to be a general characteristic of positive transcendence (and so characteristic of it as such) and because its meaning seems to be bound up with the meaning of our existence and non-existence."
That is to say in plain English he is considering God as "absolute transcendence" and considers Him to be the One who has positive transcendence. I.e. by means of intention. That is all you can say about this from the standpoint of Kelley Ross. But the connection with Godel and the idea positive traits is certainly tantalizing.
[Kelly Ross rightfully noted that existence is a predicate.]
a C^r manifold is a manifold that you can take a derivative r times over the complex field. A C^r manifold has a C^r function to a C^infinity manifold.
[(Compactness Theorem). A set of formulas Γ is satisfiable if and only if every finite subset of Γ is satisfiable.][From the finite to the infinite. Perhaps the simplest use of the Compactness Theorem is to show that if there exist arbitrarily large finite objects of some type, then there must also be an infinite object of this type.] [Mathematical Logic ch. 4 and ch. 9]
This idea is sound. However I prefer to go with the more direct and simpler approach of Saadia Gaon and the חובות לבבות (Obligations of the Heart) and the Rambam of the First Cause, and the fact that there has to be a First Cause because of the problem of the infinite regress, For me that is the simplest and strongest approach, though I think Anselm's one is also good and complementary.
In any case this is related to Kelley Ross in a different way. Here is what he says in his PhD Thesis [Sec III]: "This continues the theory of purposive value by at last addressing the hitherto presupposed polarity of value, although the discussion belong to absolute transcendence because it may be taken to be a general characteristic of positive transcendence (and so characteristic of it as such) and because its meaning seems to be bound up with the meaning of our existence and non-existence."
That is to say in plain English he is considering God as "absolute transcendence" and considers Him to be the One who has positive transcendence. I.e. by means of intention. That is all you can say about this from the standpoint of Kelley Ross. But the connection with Godel and the idea positive traits is certainly tantalizing.
