Thursday, July 24, 2014

From necessary abstracta to a necessary concrete being

Start with the Aristotelian thought that abstract entities are grounded in concrete ones. Add this principle:

  1. If x is grounded only in the ys, then it is impossible for x exist without at least some of the ys existing.
Consider now a necessarily existing abstract entity, x, that is grounded only in concrete entities. (Some abstract entities may be grounded in other abstract entities, but we want to avoid circularity or regress.) Thus:
  1. x is a necessarily existing abstract entity.
Add this premise:
  1. There is a possible world in which none of the actual world's contingent concrete entities exist.
This isn't the more controversial assumption that there could be a world with no contingent concrete entities. Rather, it is the less controversial assumption that these particular concrete entities that we have in our world could all fail to exist, perhaps replaced by other contingent concrete entities.

If the concrete entities that ground x are all contingent, then we have a violation of the conjunction of (1)-(3), since then all the actual grounders of x could fail to exist and yet x is necessary. So:

  1. There is at least one necessary contingent entity among the entities grounding x.


Heath White said...

Couldn't we get

4+. There is at least one necessary concrete entity among the entities grounding x, sufficient by itself to ground x.

And even

4++. There is at least one necessary concrete entity sufficient to ground all necessarily existing abstract entities.


Alexander R Pruss said...

I don't see how off-hand.

Anonymous said...

Just a few comments.

Looking at your explanation of (3), wouldn't it be better if we re-worded it so we could avoid the necessitism/contingentism debate? This would just mean we reformulate (3) to something like the following:

(3') there is a possible world in which all of the objects in this world either (1) fail to exist or (2) are not concrete.

Thus, the contingentist can accept (1) while the necessitist can accept (2) and so both can accept (3'). Not a big deal, but maybe worth thinking about (in all honesty, I'm not even that sure on what the necessitist *does* believe and so I'm not very confident that he would deny (3) anyway).

As a minor point, I think (4) should have "concrete" instead of "contingent". (Also, what is standard procedure (if there is one) on whether you put a punctuation inside or outside of a quote mark? Neither seems right.)


(5) For any world, w1, there is a world, w2, accessible from it that all of the objects from worlds in the accessibility chain excluding w2 either (a) fail to exist or (b) are not concrete.

If we find (5) plausible or could give an argument for it, then we might be able to get some interesting results. For it seems we could keep accessing worlds until the chain contains every entity that is either (1) contingent or (2) accidentally concrete. Given that, we would find a world that has no entities that are both concrete and contingent. Next, we argue for S5 and thus show that that world is possible.

Depending upon one's evaluation of Occam's razor, we could say that there is one necessary concrete entity. This gives us something like (4+). And if we say that a concrete entity non-derivatively grounds an abstract entity if it immediately grounds it or it derivatively grounds an abstract entity if it derivatively or non-derivatively grounds the abstract entity that grounds it, then we can get something similar to (4++):

(4++*) There is one necessary concrete entity sufficient to ground all necessarily existing abstract entities either derivatively or non-derivatively.

Of course, I'm not sure this would be a particularly strong route due to (5) and the certain interpretation of Occam's razor, but it's something to toy with nonetheless.

Heavenly Philosophy said...

I don't think the existence of abstract objects is compatible with Classical Theism. Consider this argument:

1. God is the cause of everything other than himself. (This was found in your essay in the book Classical Theism edited by Robert Koons and Jonathan Fuqua. You can see the arguments for it there.)

2. God is a concrete object.

3. Anything caused by God is a concrete object.

4. Therefore, everything is a concrete object. (1-3)

5. Nothing can be both a concrete object and an abstract object.

6. Therefore, there are no abstract objects. (4,5)

The only substantive premise is (1), and you admit that this premise is true in the reference I gave. You mention the existence of abstracta in your chapter and state that efforts to restrict this doctrine are mistaken, citing Craig. However, you argue for the existence of abstracta in chapter 7 of Necessary Existence, of which the argument in this blog post is a variant. So, it's hard to see how your view on creation and abstract objects is consistent.

Alexander R Pruss said...

I think your premise (3) is substantial.

Additionally, it probably makes sense to distinguish existence from something like *real* existence. There is the ordinary sense of "is" as in "There is a hole in the road." In the same ontologically innocent sense we might say that there are abstract objects without assuming Platonism. But of course we need a grounding for these abstract objects, just as the hole in the road needs grounding.

Heavenly Philosophy said...

I don't think that an abstract object can enter into causal relations. I don't see how that is possible. Another way you could put the argument is that if there necessarily is an abstract object (one of the premises of the argument in Necessary Existence) then there cannot be a possible world where only God exists. And, that conflicts with classical theism.

In another commment you said 'I think ordinary English sentences like "There is a table in my kitchen" are true. But I don't think tables "really exist". What do I mean by that? Well, think of some other cases: holes, shadows, in-game items, and average plumbers. In each case (though a bit less so in the last case) we talk in ordinary English as if the item really existed.

But if pressed whether reality really includes such entities, I think we are apt to say that of course not. For instance, if shadows really exist, then we have a violation of the principle that nothing moves faster than light (the earth casts a shadow on space-dust; that shadow does one rotation around the sun in a year; thus, at about one light-year away from the sun, the earth's shadow sweeps through space at a speed about six times that of light). If holes really exist, then we will have silly pseudophilosophical questions such as "If there are two holes side-by-side in the road, and the road wears out between them thereby joining them, so that now there is only one hole, have we destroyed the original holes?'

It just seems like you are denying that one has to be ontologically committed to something one quantifies over. I am perfectly happy saying that numbers exist in the same way that Spiderman exists. And of course, in order for Spiderman to "exist," there would need to be concrete really existing objects, like comic books, that form our concept of Spiderman and that the character of Spiderman is based off of.

Are you referring to ontological pluralism in your reply to me instead?

Alexander R Pruss said...

1. Some people define concrete objects as ones that can be causes. That sounds plausible to me. But I don't see why *being caused* makes something concrete.

2. And even if it did, it's not obvious to me that something can't be both concrete and abstract. A paradigm of an abstract object is something that can be instantiated. But why couldn't instantiability coexist with causal powers in one and the same object?

3. Natural language is messy. One can have operators that have the syntactic and logical features of quantifiers but do not have the ontological import of quantifiers. Whether we should call such operators "quantifiers" is a merely verbal question. Depending on the answer to this purely verbal question, we can say that the English "There is" is not a quantifier, or is a quantifier but lacks ontological commitment.

4. From an Aristotelian point of view, one might call some such operators "quantifiers" in an analogical, nonfocal sense. Compare how Aquinas holds that even nonbeing is, in a nonfocal sense.

Heavenly Philosophy said...

Even taking that first point into account, one can construct a new argument against abstracta.

1. Necessarily, God is the cause of everything other than himself.

2. Possibly, there is nothing that is caused by God.

3. Necessarily, God exists.

4. Therefore, possibly, only God exists. (1-3)

5. God is not an abstract object.

6. Therefore, possibly, are no abstract objects. (4,5)

7. If there is an abstract object, then necessarily, there is an abstract object.

8. Therefore, there are no abstract objects. (6,7)

In support of the first two premises, I found this quote from Vatican I:
"If anyone does not confess that the world and all things which are contained in it, both spiritual and material, were produced, according to their whole substance, out of nothing by God; or holds that God did not create by his will free from all necessity, but as necessarily as he necessarily loves himself; or denies that the world was created for the glory of God: let him be anathema."
It does not seem totally plausible to me that "the world and all things which are contained in it" can be restricted to exclude abstracta.

So, it seems like the only premises that can be denied are (5) and (7). You said in your second point that something can be both concrete and abstract, so maybe that is the best route out. Maybe you could say that God is identical to the abstract object of divinity. However, you could still have the number 3 existing because God is three persons, and I don't think God is identical to the number 3. If you deny (7), (6) is already a substantive conclusion, given that you argue against it in Necessary Existence. I've already argued that if one needs abstract objects to talk about numbers, then one needs abstract objects because the Trinity is necessary. I don't know what abstracta would be doing in the actual world if it wasn't necessary that there was an abstract object.

I'm still not sure what you mean in your forth point. I guess you could say abstracta exist in a fictionalist sense. Again, are you referring to ontological pluralism, like numbers existing virtually?