Friday, December 21, 2012

Goedelian ontological argument

I just posted a PDF of my "A Goedelian ontological argument improved even more" article. The article came out in an anthology by Fr. Szatkowski. Unfortunately it contains an error (which doesn't affect the main philosophical points): see my May 14, 2016 comment below.


  1. Hi Alex,

    Oppy (2009) argues that your reasons for F2 (on each of the 'positive property' interpretations) are also reasons for Oppy's premise 2 (p. 355). But then, following Oppy's reasoning, there is a much simpler path to C3. Indeed, so much simpler that it perhaps begs the question against atheism. What do you think?


  2. It's been a while, but I remember not being convinced that the reasons were as strong for Oppy's 2 as for my F2.

  3. Hello Mr. Pruss. I have been diligently following your work on the ontological argument and am almost convinced of the soundness of something like Godel's proof moving me quite close to a confessed theism. Your three papers on it as well as the many blog posts here have been very helpful. However what is extremely vexing is how when the concept of positivity is applied to truth it leads to a formal contradiction/paradox which is quite interesting/disturbing. The whole thing is outlined within this paper written by Gregor Damschen of Martin Luther University of Halle-Wittenberg entitled "QUESTIONING GÖDEL’S ONTOLOGICAL PROOF:
    IS TRUTH POSITIVE?" ( If you could comment on this and how it applies to the soundness of these Godel like ontological arguments it would be much obliged as I know much talk is focused on the concept of positivity, i.e. what exactly are the repercussions for the arguments, such as does it refute it or is it just a interesting/trivial consequences, or does truth not play into the argument as truth itself isn't some sort of great making property, or that when analyzing truth it inevitably leads to paradoxes. This has been much bothering me and am not exactly sure what these arguments entail to. Much thanks in advance!

  4. Sorry to post again but I forgot to mention that I think the major problem this article engenders is against the truth of the unity of perfections as axiom two leads to a contradiction when led to the truth values of the perfection statements. I am not sure if this is what its getting at but the contradiction seems to render perfection talk contradictory. I am not sure what this amounts to or how it can be rebutted but a more competent person here may be able to help me see how to move around this problem. Thanks again and apologizes for the double post. Best wishes -ashmen

    1. On my version of the arguments, there is no Axiom 2. In other words a property P can be such that neither P nor non-P is positive.

  5. This is the most powerful ontological argument in the literature at the moment, thank you very much Dr. Pruss. Have you seen any replies to this paper?

  6. I think I've seen something but I can't remember where.

  7. Dr. Pruss, thank you for your recent lecture on Leibniz at our Franciscan University of Steubenville, we very much enjoyed it. Do you think Leibniz's ontological argument (improvement of Descarte's version) is a strong argument or that Goedel's is much better and should be preferred?

  8. Joshua,

    The relevant bit of 17th century intellectual history goes like this:
    1. Mersenne realizes that if God doesn't exist, God can't exist. This makes it possible to run an ontological argument of the form: God possibly exists, so God exists. (Though that's not quite how Mersenne argues.)
    2. Descartes's ontological argument ignores Mersenne's insight.
    3. Leibniz (apparently) independently rediscovers Mersenne's insight, and realizes that all that's needed is to show that God possibly exists. He says that there is a presumption in favor of possibility, and also says that he has a worked-out argument for the possibility of God's existing. It's not clear where that worked-out argument is to be found in his writings, but it seems to be based on the idea that fundamental positive qualities can't have non-trivial logical relationships, and that God has all fundamental positive qualities.

    There are technical problems with Leibniz's argument that relate to how the fundamental positive properties relate to necessary existence. I do not know how to solve these technical problems in a way that makes the argument plausible, and I do not know whether Leibniz was aware of these problems.

    That said, the *presumption of possibility* argument seems to have a fair amount of plausibility.

  9. Pruss: It seems to me that Leibniz (like Descartes) thought "exists necessarily if at all" is an obvious perfection. A supremely perfect being could not be contingent, since a being that was otherwise identical to such a contingently "supreme" being, but existed necessarily, would clearly be greater.

    I would add that, given a causal account of modality, any contingent being would be caused by a greater being, which means that a supreme being cannot be contingent.

    As for possibility, Leibniz's argument seems to hinge on compatibility. Robert Maydole reconstructs it something like this:

    1) All perfections are compatible.
    2) Every essential property of a supremely perfect being is a perfection.
    3) Therefore a supremely perfect being's essential properties are all compatible (1,2).
    4) If the essential properties of something are all compatible, then it is possible that it exists.
    5) Therefore, it is possible that a supremely perfect being exists (3,4).

    (2)-(4) seem self-evident, but (1) is not; so, Maydole explains: Leibniz gave justification on the grounds that a perfection should be a "simple quality which is positive and absolute". Then, for two perfections to be INcompatible, Leibniz says they must be necessarily incompatible, and necessary truths must be either self-evident or demonstrable. Well, it isn't self-evident that any two perfections are incompatible. And for it to be demonstrable, Leibniz says that either the two perfections are negations of each other or else some part of one is incompatible with the other. But, since perfections are always positive and simple, neither of those options is available. Therefore, all perfections are compatible, and (5) follows smoothly.

    This seems pretty solid to me, if a bit far removed from the layman to which one might be trying to evangelize.

    I think it's much easier to just say "God is by definition the ultimate being... such a being would have all power, knowledge, goodness, etc, which can possibly be had... and such a being wouldn't depend on anyone or anything for its own existence. Now, if something doesn't exist, it's either because it's impossible (entails a contradiction and is therefore actually just gibberish) or because the conditions for it to exist haven't been met (yet). So, since this being HAS NO conditions required for its existence, it follows that, unless you can show me some contradiction in the properties, you should believe that it exists.

    In other words, even granting that these properties don't logically rule each other out, grants the actual existence of the thing.

    This is leaving out some steps, but it's been effective in the past. The best a debator can usually do at that point is to try to show that the properties are in fact incompatible (stone paradox, absolute freedom can't cohere with absolute knowledge of the future, etc).

  10. The posted article contains an error. I say in it that F1&F2 is equivalent to F1*&F2*. This is false. (F1&F2 says nothing about negative properties that are not explicit negations of positive ones.) Fortunately, F1*&F2* implies F1&F2 (or so I think) and that's all that's needed for the negativity-based ontological argument.