The Unity of G

Last time I wrote about this, I demonstrated the existence of a kind of non-contingent being on which all other contingent being was contingent, what is traditionally called "God" in most religions (sometimes, as in Taoism "The King of Heaven"). What I did not attempt at that time was the Moral Character or Unity of God leaving at least two avenues wide-open possibilities:

a) that G is morally decrepit or indifferent (e.g. the God of Spinoza)
b) That G is multiple-beings (e.g. the God of the Hindus or ancient greeks)

In this note I want to address (b) that G must be unique.

The argument takes the form of a reductio absurdum of the opposing possibility viz:

There are many things that satisfy the predicate "is non-contingent being upon which all other contingent beings are contingent".

At first glance this seems possible and even likely - why should all contingent things have exactly the one single explanation? There are many kinds of contingent things, why shouldn't there be many kinds of non-contingent things that cause them?

For this we need first an argument for the unity of other kinds of abstract objects, just to show -what it is- to be a unified non-concrete object. For instance, the number "1".

Obviously the number 1 has many different names and properties - it is known as "uno" in spanish, and the result of "3-2" in base-10 decimal arithmetic. It is the identity element for a monoid (under the standard interpretation), etc. We say of these different descriptions that they describe "the same thing" because we think that, for instance, uno = 3 - 2 = the identity field of a monoid = 1.

That is, we think they describe the same thing. Now, for those of you who didn't know that 1 is the identity monoid, this can come as a surprise when you learn it as most people do effectively in 3rd grade nowadays. Nevertheless, it is. If it were not, then there would be some other number which also was a multiplicative identity element on the natural numbers, but since it can be demonstrated that no other element on the natural numbers could be that (since any x 1 will yield a different result than 1 * x and it will not be x for all elements of N which you could prove by induction.)

Thus, we know that there is a proof that 1 = the identity element for multiplication. Any language in which standard mathematics is described that has a multiplication operator and has an identity element in it will have 1 and it will be that element and there will be a proof of that matter. 

Thus it is possible for there to be unique abstract objects with different properties and names, that is, ways of describing them or accessing them, which nevertheless refer to exactly one thing - the same thing. Let us call these things "abstract objects" and we will differentiate them from "abstract properties" on the basis that abstract objects can have properties and share them with other objects (both abstract and non-abstract) whereas abstract properties can be descriptions or properties of other objects (while themselves being objects) AND have properties and alternative descriptions.

So to the particulars - we defined G as 

An object upon which all contingent objects are contingent and which is not itself contingent.

So there is a property, according to us "being the contingency on which all contingent things are based, but not itself being contingent" (call it "O", the "God property" if you will).

And we supposed that there may be a group of things with that property D = (G1, G2, G3, ...) such that Ax:D (Ox) (D is the set of "deities").

Let P be the property "is contingent" and PG1x (where 1 is a subscript) be the property "being contingent on G1", and PG2x be the property "being contingent on G2".

Suppose Ex PG1x && PG2x && G1 G2 (our basic assumption).

That is, x is contingent on G1 and x is contingent on G2 and G1 is not G2.

Here's where our problem arises, by definition above, G1 is sufficient for x (since G1 is the sufficient condition for all contingent beings) and necessary for x (since without G1 no other contingent being is possible). 

If G1 is sufficient and necessary for x and G2 is sufficient and necessary for x but not identical, then there arises the possibility that G2 & !G1 & x (since G2 is supposedly sufficient for x). But obviously there is a contradiction if Nec(!G1 -> !x) & G1 & x.

Hence if G1 is actually sufficient and necessary for the x in question (and that x is the totality of contingent beings) then G2 if it is also sufficient and necessary must be identical with G1.

As a result, there must be only one being which is sufficient and necessary for the existence of all contingent beings (even if this being is in-itself "multiple" - that is has multiple aspects) - the whole of it must be exactly one thing.

There is a further question, namely, what is the "structure" or "character" of the thing - is it simple or complex, good or evil, etc. This will be the topic of a proof to follow.

ALOHA!