## Tuesday, March 22, 2022

### The spectrum of values

Let’s do some rough and ready thinking about the spectrum of possible values of objects on a classical theistic view.

1. God has his value essentially.

2. Necessarily, God is more valuable than everything other than God.

3. Necessarily, everything that exists exists by participation in the good God and hence has positive value.

The spectrum of possible values thus has an upper bound: God’s value. Moreover, it follows from (2) that God is infinitely many times more valuable than anything else. For consider some object x other than God, and imagine a world (perhaps a multiverse) where x is duplicated some number n of times. By (2), God will be more valuable than the duplicates of x, and hence God is more than n times valuable than x. Since n is arbitrary, it follows that God is infinitely many times more valuable than x.

Thus, our spectrum of values has God at the top, then an infinite gap, and below that possible creatures.

What does the lower end of the spectrum of possible values of objects look like? Well, by (3), all the values are positive. So the lower end of the spectrum lies above zero. I suspect that it asymptotically approaches zero. For consider an object x and now imagine an object y which has exactly one essential causal power, that of producing x with a probability of 1/2. Intuitively, y has something like half the value of x. So it is plausible that the lower end of the spectrum of possible values approaches zero but does not reach it.

But now suppose that y has only an infinitesimal probability of producing x (imagine y has an internal spinner and it produces x whenever that spinner lands exactly at ninety degrees). Then x seems like it would be infinitely more valuable than y. If this is right, then for every value in the spectrum, there is a value that is infinitely many times smaller than it.

The spectrum of values has a top (God) but no bottom. For any value on the spectrum of values, there is a value infinitely many times smaller than it. And for any value on the spectrum of values other than God, there is a value infinitely many times greater than it.

There is thus a very natural sense in which everything is relatively infinite in value: everything is infinitely many times more valuable than something else. But only God is absolutely infinite in value: God is infinitely many times more valuable than everything else.

Incommensurability complicates things, though.

#### 1 comment:

Wesley C. said...

I wonder though how God's infinity here relates to higher infinities in math - specifically large cardinal axioms. We already know the infinity of the reals is bigger than the infinity of the naturals, and that by powersetting there are infinitely many ascending aleph sets above the reals, and even that many large cardinal axioms are much greater than all the infinite alephs as well. Now if there is a ceiling to the large cardinal axiom hierarchy, would God be the thing equal to or above it in terms of inifnity? And if there isn't a ceiling and there are infinitely many LCA's, each larger than the one before, then how does God's infinity "compare" to the infinity of those LCA's?

Since God is the ultimate reality who grounds the Principle of Non-contradiction and is more certain and unshakeable than anything else, but also isn't any one thing in particular due to not having definitional limits like creatures with essences, it seems one could say God's infinity is uniquely absolute in not being mathematical, and being the one unified ground of all the others. What do you think?