Patrick Grim’s Cantorian argument and Pruss’s Big Conjunctive Contingent Fact

I was thinking about Patrick Grim’s Cantorian argument against omniscience this week, and it was after I read the exchange between him and Alvin Plantinga (which I admit required too much familiarity with set-theoretic semantics for me to follow with any ease), and while I was reading William Lane Craig’s review of Jordan Howard Sobel’s book Logic and Theism, that I thought perhaps one could use a Cantorian argument against the Leibnizian Cosmological argument as Alexander Pruss articulates it.

Pruss formulates a cosmological argument in this way:

  1. Every contingent fact has an explanation.
  2. There is a contingent fact that includes all other contingent facts.
  3. Therefore, there is an explanation of this fact.
  4. This explanation must involve a necessary being.
  5. This necessary being is God.

Perhaps premise 2 could be called into question, since it seems to require a set of all contingent facts, but there is no such set. I wonder how this could be answered…

[Edit: obviously, that the maximally specific true proposition is contingent, and requires an explanation].


About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
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6 Responses to Patrick Grim’s Cantorian argument and Pruss’s Big Conjunctive Contingent Fact

  1. Marc-André Argentino says:

    I hope you appreciate the fact that I actually can follow and understand this post. I do personally have an issue with the second point, however if a contingent proposition is neither necessarily true nor necessarily false then I can understand where it comes from, though i severally dislike it. Though I find that the jump to point 5 is very “quick” and I wonder if you could expand upon it (slightly playing devil’s advocate for my own personal interest)

    • Well, if you want to see the argument fleshed out (and I do think this argument is sound and beyond rational refutation) then I recommend reading the paper it comes from here:

      The jump to point 5 is neither quick nor facile.

      However, my post was just concerning an objection to premise 2 – if Patrick Grim is right that there is no such thing as the set of all true propositions (as it seems he is) then he is also right about the set of all true contingent propositions not existing. If that is the case, then the argument has to be appropriately modified, but as I say at the end, that can easily be done by arguing that the one maximally specific true proposition, as opposed to the big conjunctive contingent fact, is contingent.

  2. Marc-André Argentino says:

    I feel like i’m short 3-4 phd’s to fully grasp this

    • Well, we can talk about it face to face at the Theology party if you’d like. As I said, I’m convinced that it is a sound argument, and not only in the form that Pruss presents it (I think even Aquinas’ second and third ways are sound and equally compelling).

  3. I do discuss issues related to such worries in my PSR book.

    • I need to give that book a more careful cover-to-cover read this summer. I know there are sections I have skipped on previous readings. It is an excellent book though, and I continue to find it an invaluable resource because ever since becoming Catholic after discovering Aquinas and Copleston I have been adamant about the PSR, and have been confronted with innumerable challenges to it, especially from a friend of mine, Michael Long.

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