Friday, August 17, 2012

An Aristotelian argument from a necessary being to a necessary concrete being

Suppose that none of the participants in World War II had ever existed. Then it would have been impossible for World War II to occur. Why? Because World War II's existence is solely grounded in the existence, activities, properties and relations of the participants, and

  1. If an entity x's existence is solely grounded in the existence, activities, properties and/or relations of the Fs, then it is impossible for x to exist without at least one of the Fs existing.
Now add this Aristotelian axiom:
  1. If x is abstract, then x's existence is solely grounded in the existence, activities, properties and/or relations of concreta.
Finally, add this:
  1. Every being is either concrete or abstract.
  2. There exists a necessary being.
  3. There is a world where no one of the contingent concrete beings of our world exists.
One might try to give the number three as an example of a necessary being to support (4).

Now, let N be the necessary being of (4). If N is essentially concrete, we get to conclude that there is a concrete necessary being. If N is essentially abstract, then N is grounded in the existence, activities, properties and/or relations of concreta. If some concreta are necessary, we conclude that there is a concrete necessary being. So suppose all concreta are contingent. Then the beings that N is grounded in don't exist at the world mentioned in (5), which violates the conjunction of (1), (2) and the necessity and abstractness of N. So, no matter what, it follows from (1)-(5) that:

  1. There is a necessary concrete being.

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7 comments:

  1. AlexAugust 17, 2012 at 1:12 PM

    Hi Alex P.,

    I've enjoyed your recent posts on grounding; many thanks for the invitation to comment!

    Here's a quick reply to the argument: I imagine that an Aristotelian who accepts (2) would likely reject (1). Suppose that F is a property had only by things that contingently exist (say, being a frog). And suppose that the xs are all the frogs that actually exist. Then I imagine the Aristotelian would want to say that the existence of F is grounded in facts about the xs, and yet would also want to say that there could have been frogs (and thus, F could have existed) even if some of the xs hadn't existed. Assuming that F is abstract, this would be a view on which (2) is true and (1) is false.

    Alex S.

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  2. AlexAugust 17, 2012 at 1:18 PM

    Slight correction. What I should have wrote is the following:

    "Then I imagine the Aristotelian would want to say that the existence of F is grounded in facts about the xs, and yet would also want to say that there could have been frogs (and thus, F could have existed) even if none of the xs had existed."

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  3. Alexander R PrussAugust 18, 2012 at 9:07 AM

    So, the existence of F is grounded in the xs, but the possibility of the existence of F is grounded in (whatever grounds) the possibility of the xs. That sounds very plausible, but it doesn't seem to get one the necessary existence of F. It gets one F existing in the worlds where the xs do, and F being possible in the worlds where the xs are possible.

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  4. AlexAugust 18, 2012 at 2:50 PM

    But suppose I'm correct that the Aristotelian will want to accept (2) while rejecting (1). Let N be the necessarily existing being of (4), and let w be the possible world of (5). Given the falsity of (1), nothing prevents it from being the case that at w, the existence of N is grounded in facts about concreta--just not by concreta that exist at our world. So given the falsity of (1), (2)-(5) must be supplemented in order to derive the existence of a necessarily existing concrete being (e.g., a premise entailing that there are worlds empty of all concreta). But as it stands, that conclusion isn't derivable from (2)-(5) alone, given the falsity of (1). That's the kind of response I had in mind.

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  5. Alexander R PrussAugust 18, 2012 at 3:25 PM

    Ah, I see.

    But the Aristotelian also wants to ground the possible in the actual.

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  6. AlexAugust 19, 2012 at 12:55 PM

    But that's compatible with the view I've sketched, as far as I can tell. The existence of N is grounded in facts about actually existing concreta. The necessary existence of N is grounded in whatever grounds the fact that there is a plurality of possible worlds such that N exists at each one of them (assuming that grounding is transitive). And presumably, the Aristotelian will say that this fact, like every other fact about the nature and existence of possible worlds, is grounded in facts about actually existing concreta. But I might be missing something--where were you sensing a conflict, exactly?

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  7. Alexander R PrussAugust 20, 2012 at 9:00 AM

    So this is just a method for denying the "essentiality of origins" kind of intuition behind (1), I see.

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