previously: You say the following "I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid." I don't follow why the form of the argument would be altered if one assumes something in the definition?
Tarski wrote: Because it is improper and invalid in deductive form to assume the existence of something as part of it's very definition when the goal is to prove existence.
For example, the following is an improper definition. Just make it clear that it is indeed the logical form at issue, I will state it somewhat symbolically:
Definition (improper): An "H" is defined to be a G that is larger than the first H.
This definition is bad.
However, Definition 1 in the Godel argument makes no such error.
I agree that the def'n you give is logically false. If H =G and G> H, then H can not equal H.
However any statement which defines a word is not logically false just because it assumes existence. Perhaps the entire argument is not sound but the one statement definition alone I don't see as being false if it makes an assumption of a thing existing.
In addition it seems to me that modal logic deals with imaginary possible worlds as well as the world we live in. So effectively, what one can conceive of is assumed to exist within modal logic unless it is a logical contradiction. i.e. a squarecircle.
previously: You also say this "by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument."
Tarski wrote: An ad hominem is not a fallacy if it is legitimate and is argued as part of an argument.
To say "you are incompetent" is not a logical fallacy.
To say "you are incompetent therefore you conclusions are false" is a logical fallacy. I did not commit such a fallacy. JAK claims that I did. That is evidence that he doesn't understand the fallacy.
To say one is incompetent when it has not been established and when it is in lieu of arguing the issues
is a fallacy . If you say "you are incompetent and your conclusions are false" and you have demonstrated that the incompetence is a factor which resulted in wrong/false warrants for a conclusion, it is not a logical fallacy.
I agree with JAK you did commit ad hominem fallacy. You have not demonstrated in my opinion his argument false due to incompetence.