Quote (AEtheric @ Oct 12 2012 10:13pm)

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.

Quote (AEtheric @ Oct 12 2012 10:13pm)

I could just as well say that a god that is omnifryingpan is maximally excellent.

Quote (Voyaging @ Oct 12 2012 08:16pm)

1 is not a premise. I feel you should understand the language of logic before making false criticisms.




Yes, you could

Quote (AEtheric @ Oct 12 2012 10:18pm)

I don't have to fully know the language of logic to criticize it. We have to accept 1 in order to move on to the next statements. If 1 is not a premise, then what is it?

And you never answered how 4 logically follows from the rest.

Quote (Jp2050 @ Oct 13 2012 02:12am)

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)

Quote (duffman316 @ Oct 12 2012 10:21pm)

i think you're missing the point that "infinity" while treated as a number is not in fact a number

singularities (black holes) exist afaik

Quote (Jp2050 @ Oct 12 2012 08:20pm)

I'll step in for Voyaging here and present his same Kalaam argument in slightly different words:

Premise: Possibly there is a maximally great being. (A being that possesses maximal excellence [omniscience, omnipotence, moral perfection] in every possible world.)
Conclusion: Necessarily there is a maximally great being.

Quote (AEtheric @ Oct 12 2012 10:22pm)

The conclusion does not follow. How is it that since something is possible, that means that it must exist? Unicorns are possible, but does that mean that they exist?

Quote (Jp2050 @ Oct 12 2012 08:24pm)

If a maximally great being is possible, it is necessary, by definition.

The only objection you can raise here is that a maximally great being is not possible.

Quote (Voyaging @ Oct 12 2012 10:07pm)

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.