Friday, February 22, 2019

Grounding of universals and partial grounding

It is common to claim that:

  1. The fact that everything is F is partially grounded in the fact that a1 is F and in the fact that a2 is F and so on, for all the objects ai in the world.

But this can’t be right if partial grounds are parts of full grounds. For suppose you live in a world with only two objects, a and b, which are both sapient. Then everything is sapient, and by (1) it follows that:

  1. The fact that everything is sapient is partially grounded in a being sapient and in b being sapient.

But suppose partial grounds are parts of full grounds. The facts that a is sapient and b is sapient are not a full ground of the fact that everything is sapient, because the full grounds of a fact entail that fact, and a being sapient and b being sapient doesn’t entail that everything is sapient (since it’s possible for a to be sapient and b to be sapient and yet for there to exist a c that is not).

So we need to be able to add something to the two particular sapience facts to get full grounds. The most obvious thing to add is:

  1. Everything is a or b.

Clearly fact (3) together with the facts that a is sapient and b is sapient will entail that everything is sapient.

But applying (1) to (3), we get:

  1. Fact (3) is partially grounded in the facts that a is a or b and that b is a or b.

But, once again, if partial grounds are parts of full grounds, then we need a fact to add to the two facts on the right hand side of the grounding relation in (4) such that together these facts will entail (3). But the obvious candidate to add is:

  1. Everything is a or b.

And that yields circularity.

So it seems that either we should reject the particular-grounds-universal principle (1) or we should reject the principle that partial grounds are parts of full grounds.

Here is a reason for the latter move. Maybe we should say that God’s creating me is partially grounded in God. But that’s merely a partial grounding, since God’s existence doesn’t entail that God created me. And it seems that the only good candidate for a further fact to be added to the grounds so as to entail that God created me would be my existence. (One might try to add the fact that God willed that I exist. But by divine simplicity, that fact has to be partly constituted by my existence or the like.) But my existence is grounded in God’s creating me, so that would be viciously circular.

9 comments:

Walter Van den Acker said...

Alex

Why doesn't God existence entail that God created you?

Rob K said...

Here is a reason to reject universal-particular grounding: that God knows everything is not even partially grounded in the fact that God knows p, for each p. Consider, in particular, a contingently true p. God's omniscience is, given simplicity, identical to God's nature, and God's nature can't be partially grounded in a particular fact.

Alexander R Pruss said...

Walter:

Because God didn't have to create me.

Rob:

Nice!

Alexander R Pruss said...

Rob:

On reflection I don't know that the fact that God knows everything is identical to God's omniscience. The fact that God knows everything is GROUNDED in God's omniscience. But that's compatible with it having other grounds, and maybe even partial grounds, as well (such as God's knowing that there are horses).

Strictly speaking, I think divine omniscience goes beyond God's knowing all truths. It includes, for instance, God's understanding everything, and I don't know that understanding supervenes on knowing all true propositions.

Walter Van den Acker said...

Alex

How do you know that God didn't have to create you?

Unknown said...

Another route would be to deny the entailment principle, according to which the grounds entail the grounded. That would allow us to maintain both partial grounding of universals in their instances, as well as that partial groundings are parts of full grounds. [a is sapient] and [b is sapient] fully ground [everything is sapient], even though in the world where [c is not sapient], they don't. The entailment principle has been questioned on independent grounds, so maybe that's the way to go...

Alexander R Pruss said...

Justin:

One could, but I take that principle to be an analytic consequence of the notion of full grounding. The full grounds are all one needs for what is being grounded.

Alexander R Pruss said...

Walter:

I seem to be contingent.

Walter Van den Acker said...

Alex

That's probably because God did not create you.