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Re: Anselm's proof
Posted By: gremlinn, on host 24.25.220.173
Date: Thursday, October 18, 2001, at 17:32:15
In Reply To: Re: God and Universe posted by Darien on Thursday, October 18, 2001, at 07:47:37:

> > And it had better not be anything as absurdly flawed as the Ontological Proof.
>
> What? You didn't like the Ontological proof? You're just saying that because you're jealous of St. Anselm's grammatical... litheness. :-} Personally, I think Anselm was one of my favourite theologians to study. The ontological proof is very simple from a philosophical standpoint, and yet, it's amazingly hard to wrap one's brain around, simply because of Anselm's amazing grammar. To wit:
>
> "For if that greater than which cannot be thought can be thought of as not existing, then that greater than which cannot be thought is not that greater than which cannot be thought, which does not make sense."
>

True, I don't like having to wade through his writing the way it is. But I've seen his arguments summarized into a form I could readily understand (and, interestingly enough, as the subject of a mathematics seminar).

Basically, if I recall correctly after several years have passed, the argument is:

1. A being, regardless of its other properties, might either exist or not exist.

[Comment: "Being" is not to be construed necessarily as a living thing, but rather in the most general terms of a noun -- basically anything which can be referred to as "that". A problem: if a being does not exist, can it even be attributed any other properties whatsoever?]

2. A being which, regardless of its other properties, does in fact exist, is greater than it would be if it did not exist.

[Comment: OK, out of nowhere he asserts that existence is a property which adds to a being's greatness. Now I looked up "great" in the dictionary, and I'm not sure which, if any, of the definitions Anselm was referring to. Since he didn't give a precise definition (and neither did the professor who gave the lecture I attended), I suppose that either (1) Anselm defined "greatness" in great detail in a previous writing which I did not read, or (2) he was deliberately being vague. If it's (2), this would probably be enough for me to consider the entire proof invalid past step 1. In any case, I'll assume that "greatness" is a transitive property, i.e., if X is greater than Y and Y is greater than Z, then necessarily X is greater than Z.]

3. One can conceive of that which nothing greater could exist or be conceived of. (Call this hypothetical being A, and let B denote the conceptualization of A. Anselm is arguing that B necessarily exists.)

[Comments:
(1) There are only finitely many distinct things of which one can conceive (at least, it seems reasonable to assert such), so it follows that for *any* definition of greatness which ranks beings by a partial ordering, there will be at *least* one for which nothing greater could be conceived, possibly more if any two beings are comparable (oooh, and what about if two beings tie for greatest?) I don't think this is what Anselm meant, though.

(2) More likely, Anselm meant that without entirely conceiving of this being's nature(for I'm sure he'd say that one can not fully understand the nature of God), one can conceive of it to the extent of understanding that nothing greater could exist. Well then, by analogy let us consider the greatest possible integer. We can try to conceive of an integer which has the property expressed as "there is no integer which is greater", but we immediately come to an absurdity when we realize that no such integer could exist. How do we know we are not in the same situation, especially without knowing Anselm's definition of "greater"? For this reason, I find step 3 to be provisionally invalid as well.]

4. Combining steps 2 and 3, it follows that A, the being for which nothing greater could be conceived to exist, must also exist.

[Comment: Well sure, the meat of everything has already been accomplished by step 3. This step is fairly clear and valid as a single extension from the previous steps.]

I think Anselm goes on to prove that being A, also denoted as God, has other properties which we common ascribe to it, including being "creative, rational, omnipotent, merciful, unchangeable, just, eternal..." (from the page at http://www.fordham.edu/halsall/source/anselm.html), but I haven't read further than this basic argument.

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