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.