Tuesday, February 25, 2014

An Aristotelian argument for a necessary concrete being

All of the quantifications in the following are to be understood tenselessly. Consider these premises:

  1. If y is an entity grounded solely in the xs and maybe their token relationships, then it is impossible that y exist while none of the xs exist.
  2. All y is an abstract being, then there are concrete xs such that y is grounded solely in the xs and maybe their token relationships.
  3. There is a possible world in which none of the actual world's concrete contingent beings exist.
  4. There is a necessarily existing abstract being.
Alright, then:
  1. Suppose there are no necessary concrete beings. (For reductio)
  2. Let y be a necessarily existing abstract being. (4)
  3. Let the xs be concrete entities such that y is grouned solely in the xs and maybe their relationships. (2 and 6)
  4. The x are contingent. (5 and 7)
  5. Possibly none of the xs exist. (3 and 8)
  6. Possibly y does not exist. (1,7 and 9)
  7. y does and does not necessarily exist. (5 and 10). Which is a contradiction.
  8. So, by reductio, there is a necessary concrete being.

Premise 2 is a basic assumption of Aristotelianism. Premise 1 is more problematic. Note, however, that it is very plausible that this computer could not have existed had none of its discrete parts (CPU, screen, etc.) existed (i.e., ever existed, since the quantifications are tenseless). An object can have its parts get gradually replaced, but by essentiality of origins it must at least start off out of some of the stuff it started out of. And so it must have at least some of its constituents (at some time) in any world where it exists.

Further, premise 1 follows from the thought that when y is grounded solely in the xs and maybe their token relationships, then there is nothing more to the being of y than the being of the xs and maybe their relationships. But the token relationships of the xs couldn't exist if the xs never existed.

Premise 3 is very plausible. It must, of course, be distinguished from the much more controversial claim that there could be no contingent beings. Premise 3 is, on its own, compatible with the thesis that necessarily something contingent or other exists, as long as there aren't any contingent things that necessarily exist.

If premise 3 is the sticking point, but S5 is granted, an alternate argument can be given. Very plausibly, there is a possible world w containing a concrete being c with the property that all the concrete beings of w modally depend on w, i.e., they couldn't exist without c. (For instance, maybe they are solely grounded in c and its properties, or maybe c is a common part of them all, or maybe there is nothing but c.) Then running our argument in that world we conclude that c is a necessary being in w, and, by S5, actually.


Michael Rabenberg said...

I'm probably just misunderstanding (1), but might this be a problem for it?

Suppose the only concrete beings at world W1 are a couple of cows. Plausibly, the universal animalness is wholly grounded at W1 in the cows there. But suppose at world W2 the only concrete beings are a couple of pigs. Plausibly, the universal animalness is wholly grounded at W2 in the pigs there. But then it follows that there is a thing--the universal animalness--that exists and is grounded in a set of things S in one world but that also exists in another world at which none of the members of S exists.

Alexander R Pruss said...

Nice illustration. The lesson of (1) here is that animality cannot be grounded in animals and in nothing else.

What could the something else be? Well, Aristotle does say that the form of the house exists in the mind of the builder. And while he may not be a realist about forms of houses, it does open up the idea, taken up by Aquinas, that there are two ways a form can be concretely grounded: it can be grounded in an instance but also it can be grounded in a mind.

So the reasonable conclusion is that animality is grounded in a necessary being's mind.

Derrick said...

Your argument for (1) seems to be comparing apples to oranges. Aristotelians don't think that universals are COMPOSED by their instances. Universals (in part) compose their instances. So, it's unclear how the essentiality of origins stuff is supposed to help.

Alexander R Pruss said...

If universals compose particulars, then it seems that universals are explanatorily prior to particulars.