## Monday, January 5, 2015

### Subtraction and divine simplicity

There has been recent interest in subtraction arguments for the thesis that possibly there is nothing concrete. These arguments tend to be based on the thesis that there cannot be a concrete object such that subtracting it necessitates adding something to the world. Here is a much weaker subtraction principle:

1. There is no concrete contingent object o such that there could be a concrete object o* with the property that necessarily o* exists if and only if o does not exist.
This is weaker in several ways than the standard subtraction principle. It only extends to actual objects o. It is restricted to contingent objects. And it rules out only the possibility that there is a single possible concrete o* that, necessarily, exists if and only if o does not.

Now, suppose that divine believings are objects distinct from God. Believings seem to be concrete objects. Let o be God's believing that there are horses and o* be God's believing that there are no horses. Without divine simplicity, o and o* will be distinct from God, and presumably necessarily o* will exist if and only if o does not (since God is necessarily existent and essentially omniscient). But that would violate (1).

So it seems that we shouldn't suppose divine believings to be objects distinct from God. Thus, either divine believings aren't objects, or they are identical with God. In either case, we have divine simplicity with respect to divine believings.

Unknown said...

Dr. Pruss,

Believings seem to be concrete objects.

I don't understand this part of your argument. Wouldn't believings be abstract?

Unknown said...

*That is, in the sense that some philosophers of math think mathematical objects are abstract objects, rather than Aristotle's abstract.

Mark Rogers said...

Hey Dr. Pruss,
Thanks for the post. Does principle (B) not tell us that o and o' can possibly co-exist in some w'?

Here is principle (B):

(B) ∀w∀x[x exists in w ⟶ ∃w*{~(x exists in w*) ⟶ ∀y(y exists in w* & y exists in w)}].

So if God could have conflicting beliefs, which I doubt, they could only be actualized in an impossible world.

Thanks for the post.

Alexander R Pruss said...

I don't understand why (B) is plausible?

Mark Rogers said...

Hi, Dr. Pruss!
I do not think your example is a true subtraction argument. According to Gonzalo Rodriguez-Pereyra A3' is like a room with a door. When a belief (o) is subtracted then all parts of that belief are removed as well as all that is implied by that belief. Now while any finite number of beliefs could possibly come in while the door is opened and subtraction occurs no parts of (o) or anything implied by (o) could enter. Your example seems to me to imply that o and o' are already in the room so you are not adding o' to the room such that the non-existence of o implies the addition o' to the room.

Alexander R Pruss said...

I don't understand, I'm afraid.

Mark Rogers said...

Hey Dr. Pruss!
I had two things in mind. First, I thought that o implied o' as the belief (horses) implies the belief not(not horses) and so both o and o' would be subtracted as o was subtracted, including all parts of o and all that o implies.  But more importantly it seems to me that God's perfect knowledge would include all His beliefs so subtracting the belief (horses) does not necessarily add the belief (not horses) as it would already exist "in the room from the beginning"  if it is indeed one of God's beliefs.