A cosmological argument from simple existential facts

There are loads of different cosmological arguments out there and hopefully someday I’ll be able to write blog posts about some of them. Right now, however, I want to share an interesting version I came up with, thanks to an argument from Alexander Pruss: define a “simple existential fact” to be a true proposition reporting simply the existence or non-existence of a specific being[1,2]. So U doesn’t exist, where U is any specific unicorn and Roland exists, where Roland is me, are simple existential facts of the actual world. Now, let K be the conjunction of all simple existential facts of the actual world that don’t involve necessary beings. So, K only reports the existence or non-existence of beings which possibly fail to exist.

Now assume that possibly, K has an explanation. From this it follows that a necessary being exists. We now show this: Let α denote the actual world[3]. Since possibly, K has an explanation, there is some possible world w, in which K is true and there is some fact q that explains K. Since K involves existential facts, q must involve the causal activity of some being that exists in w[4], call it N. Now either N exists in α or it doesn’t. Assume it doesn’t. Then N doesn’t exist is a conjunct of K. Since K is true at w, it follows that N doesn’t exist in w. But this is a contradiction. Therefore, N exists in α. Is N necessary? Well, assume N isn’t necessary. Then N exists is a conjunct of K, and in w, N explains its own existence. But surely, nothing contingent can explain its own existence. So N is a necessarily existent being.

What’s really nice about this argument is that it doesn’t assume S5 or even the Brouwer axiom. Furthermore, even though I think the Principle of Sufficient Reason is true, to say that K has an explanation doesn’t commit one to the full-blown PSR. In fact, to say that possibly, K has an explanation doesn’t even entail that K actually has an explanation: while N could explain K, N needn’t actually explain K.

Notes

  1. “Specific” has a specific meaning here: rigidly designated. A rigid designator always refers to the same entity and is different from a definite description which changes depending on the current state of affairs. For example, “the president of the United States” is a definite description, whereas “Richard Nixon” is a rigid designator (of course, if there were more than one Richard Nixon we could be talking about, then some more specificity would be needed).
  2. I wonder if I couldn’t simplify this even further by saying “a specific being or class of beings” where class could be something like “unicorns”?
  3. That is, α is the rigid designator for this possible world.
  4. This was discussed very briefly here. It doesn’t seem possible to explain the existence of contingent beings “conceptually”.

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