There's a difference, surely, between defining the actual thing and defining a mere concept of that thing?
The phrase "defining the actual thing" seems difficult and ambiguous to me. One spin that we might give it is to say that we are defining a concept and also saying that the concept refers to something, that it has a real existing referrant. We define a concept "Queen of England" and say that the elderly woman in Buckingham Palace is what corresponds to the concept. Compare that to defining our concept of "Sherlock Holmes", which doesn't possess an existing referrant.
There are all kinds of philosophical difficulties associated with this. (I'm going to be returning to the bookstore this morning to purchase a very good but exceedingly expensive textbook on the theory of reference, that covers Frege's logical foundations, Russell's theory of descriptions, Kripke's rigid designators and Grice's innovative take on things.)
When we talk about God, even if we presuppose a particular description for reasons of our adherence to religious tradition or whatnot, as Jan seemingly does (it's supposedly what all "scripture" is about!), the question still remains whether 'God' is like 'Queen of England' or like 'Sherlock Holmes'. We still don't know whether 'God' has an existing referrant. That's the whole issue between the theist and the atheist. The atheist doesn't deny the existence of the word 'God' or even the definitions that various people have given it. Atheists deny that it actually refers to any existing being.
While the onus should surely be on those wishing to prove the existence of God, this is clearly not going to happen with the current main proponent, so surely we can arrive at a definition of the concept of God without accepting or assuming that the thing actually exists.
Such a definition, in my view, can not assert anything other than the characteristics sufficient for us to identify it unambiguously when the evidence arises. As such, defining it along the lines of "cause of all" is not acceptable as, since we are not there to witness the original causation (if indeed one took place) and thus can not prove that characteristic true, it is not a characteristic of God that can be used to identify Him.
Have human beings
created an initial 'definition of God' for themselves out of their own imaginations and then set off searching for anything that corresponds to it? Or are the 'definitions of God' actually supposed to be informative, factual
descriptions of a really existing God? If we say 'God is X', (1) have we learned something about the nature of God (that God really is X), or (2) merely created our own requirement about what anything has to satisfy in order to be called 'God'?
There are obvious theological difficulties with (2). But (1) begs precisely the questions that are at issue between the theist and the atheist.
Describing God, actually learning about the nature and essence of God,
presupposes that God exists, that human beings can somehow contact God and that information about God's nature and essence can pass from God to man. Sure, the Bible, Quran and Gita assume something like that, but is it true? And if we are defining our concept of God not from reciting tradition but from what is actually discovered about God, initial reference to God can't be established by use of a Russell-style definite description. It would seemingly have to be established
ostensibly, by pointing at God in effect: 'I don't have a clue what
that is, but let's call it 'God' and learn more about it.' I think that's the approach that most of the religious traditions take. Man encounters God (on a mountaintop, in a chariot or wherever) and God communicates. One seemingly believes that or one doesn't.
Of course there's the additional complication that many monotheistic theological traditions, both in the West and in the East, would question how much human beings can know about God's essence. God is supposed to be transcendent, beyond human conceptualization entirely. Mankind can know God's actions in this world, but can't really know God as God actually is. If that's so, then the whole project of defining 'God' would seem to be doomed to failure.
So I'm inclined to think that all of this talk about defining 'God' is deeply complicated, perhaps a bit of a red-herring and ultimately a bit circular.