You have not explained how God is logically necessary. I already explained how he is not necessary in the chain of events that led to the creation of the universe, i.e. if the universe is temporal.

I see that 3 is a premise, but I don't see how 4 logically follows from the rest. Premise 1 is also suspect, as it is arbitrary. I could just as well say that a god that is omnifryingpan is maximally excellent.

See Voyaging's post for proof that an actual infinity cannot exist in reality (the Kalaam version of the cosmological argument).

God's existence is necessary because it is definitional: If God exists and God is the designer, then God must exist for the world to be designed. Question begging? Perhaps. Regardless, if God exists, He is a necessary being.

If the universe created itself, as you suggested, that means simply that "the universe" is necessary, and for the purposes of our argument you may substitute the term "the universe" for the term "god".

This post was edited by Jp2050 on Oct 12 2012 08:03pm

It must be because maximal greatness is explicitly defined in the argument.

The original ontological argument (Anselm) can be turned into symbolic syntax and proven valid by a computer. And this has been done. The formal argument is as follows.

1. ¬E!ιxφ1 Assumption for reductio
2. ∃y(Gyιxφ1 & Cy) from (1), by Premise 2 and MP
3. Ghιxφ1 & Ch from (2), by EE, ‘h’ arbitrary
4. Ghιxφ1 from (3), by &E
5. ∃y(y = ιxφ1) from (4), by Description Theorem 3
6. Cιxφ1 & ¬∃y(Gyιxφ1 & Cy) from (5), by Description Theorem 2
7. ¬∃y(Gyιxφ1 & Cy) from (6), by &E
8. E!ιxφ1 Reductio (1); (2) vs. (7)
9. E!g from (8), by definition ‘g’

Premises:

Premise 1: Cx & ¬∃y(Gyx & Cy)
In this premise, the expression "Cx" asserts that x is conceivable, and so Premise 1 asserts that there is something which is conceivable and such that there is nothing y which is greater than x and conceivable.



Premise 2: ¬E!ιxφ1 → ∃y(Gyιxφ1 & Cy)
This asserts that if the conceivable thing such that nothing greater is conceivable doesn't exist, then there is something greater than it which is conceivable.

This is necessarily a valid argument, assuming premises 1 and 2 are true. If you know symbolic logic, you can learn the additional defined symbols they used here: http://mally.stanford.edu/cm/ontological-argument/ and see if you accept the premises. If the premises are both true, the validity of the argument is proven and God exists. (God is df ιxφ1 )

The following was an interesting result described in Oppenheimer and Zalta 1991, namely, that if greater than is connected, then if there is something than which none greater can be conceived, then there is a unique thing than which none greater can be conceived. This is capture by Lemma 2:

Lemma 2: ∃xφ1 → ∃!xφ1

The importance of this lemma cannot be overstated, for it validates the introduction of the definite description into Anselm's language. It justifies his use of the expression "the (conceivable) x such that nothing greater is conceivable".

Note the subscripts didn't come out correctly so go to the link above to see the argument properly.

That wasn't proof that actual infinity cannot exist, those were assumptions that actual infinity cannot exist. No one can prove that actual infinity cannot exist.

I could just as well define invisible pink unicorns who serve no purpose as necessary. That doesn't make them so, and, like you said, begs the question.

The universe is obviously necessary considering we know it exists. And no, we cannot substitute the universe for god, they are two distinct modes of existence, and, if they are not distinct, then doing so is only playing a semantics game.

It says in parentheses that 3 is a premise.

1. In an actual infinity, a part is equal to the whole.
2. In reality, a part cannot be equal to a whole.
3. An actual infinity cannot exist. (in reality)

This post was edited by Jp2050 on Oct 12 2012 08:13pm

This:

How does that make sense in the slightest? A single number out of the set of aleph null is still a single number.

This post was edited by AEtheric on Oct 12 2012 08:14pm

Thought experiment:

1. You have a library containing an infinite number of books.
2. The books are ordered such that there is one red book then one black book then one red book and so on.
3. You remove all the red books from the library.
4. The remaining number of books (all black) is still infinite.
5. A part of the library (only the black books) is equal to the whole library.

This post was edited by Jp2050 on Oct 12 2012 08:16pm