Repression of non-objectivism?

Since we cannot know what God is, but only what He is not, we must consider ways in which He is not rather than the ways in which He is. --Summa Theologiae, I, Pt. 1, Qu. 3, introd.

 The truths that we confess concerning God fall under two modes. Some things true of God are beyond all the competence of human reason, as that God is Three and One. Other things there are to which even human reason can attain, as the existence and unity of God, which philosophers have proved to a demonstration under the guidance of the light of natural reason. That there are points of absolute intelligibility in God altogether beyond the compass of human reason, most manifestly appears. For since the leading principle of all knowledge of any given subject-matter is an understanding of the thing's innermost being, or substance -- according to the doctrine of the Philosopher, that the essence is the principle of demonstration -- it follows that the mode of our knowledge of the substance must be the mode of knowledge of whatever we know about the substance. Hence if the human understanding comprehends the substance of anything, as of a stone or triangle, none of the points of intelligibility about that thing will exceed the capacity of human reason. But this is not our case with regard to God. The human understanding cannot go so far of its natural power as to grasp His substance, since under the conditions of the present life the knowledge of our understanding commences with sense; and therefore objects beyond sense cannot be grasped by human understanding except so far as knowledge is gathered of them through the senses. But things of sense cannot lead our understanding to read in them the essence of the Divine Substance, inasmuch as they are effects inadequate to the power that caused them. Nevertheless our understanding is thereby led to some knowledge of God, namely, of His existence and of other attributes that must necessarily be attributed to the First Cause. There are, therefore, some points of intelligibility in God, accessible to human reason, and other points that altogether transcend the power of human reason. 

The point is that I agree with you, GWL that we can rationally defend assertions that we cannot prove.

Two things need be, in order for an argument to be sound:

1) valid inferences (ie. validity)
2) true premises (ie. reality)

Godel's argument is unsound ...

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive

This definition smuggles in a conception of God (what Rand calls a Stolen Concept). If the argument was about a "zero" or a "negative", then it would read ...

"x is negative-like iff x has as essential properties those and only those properties which are positive"

... showing the inherent problem of just placing a "word" into the phrase "x is _____-like iff x has ... properties which are positive".

The philosophical underhandedness engaged in (by Godel) is in failing to differentiate the definiendum (in this case, God) from all other known entities.

You see, GWL, THAT is the ultimate purpose of a definition. It's what definitions are "needed" for (for keeping straight what it is that we are talking about -- from all the other known things that we "might" be talking about).

It is philosophically underhanded to define something by nonessentials (ie. by attempting to define, while failing to differentiate).

I did not misunderstand. And, if you were more careful, you should not have even thought that I would (had you been thinking more straight, about what it is that I've been saying to you). Considering the "privation" proposition that I have already offered from Aquinas, you should KNOW that I understand the difference between substantiality ("being largely but not wholly that which is specified") and privation ("lack of what is needed for existence").

Your error is considering bounds as imperfection.... it eliminates context, which, actually, eliminates reality.....

Unextended substance? THIS is what I speak of, GWL, when I speak of the incomprehensibility of God. Tell me, GWL, in 20 lines or less, what "unextended substance" is.

Socrates: Take a look round, then, and see that none of the uninitiated are listening. Now by the uninitiated I mean: the people who believe in nothing but what they can grasp in their hands, and who will not allow that action or generation or anything invisible can have real existence.

Theaetetus: Yes, indeed, Socrates, they are very hard and impenetrable men.

Socrates: Yes, my boy, outer barbarians.

"Immaterial"...certainly the precise word to describe arbitrary assertions about the "supernatural" -- whatever that is.