Computer Validates Anselm’s Proof for God’s Existence

Paul Oppenheimer and Edward Zalta (2011) have used Prover9 to check the validity of Anselm’s ontological argument.  The program not only proved the argument’s validity, but went on to derive a simplified version of the argument containing only one non-logical premise and avoiding many of the metaphysical pitfalls of Anselm’s original formulation.  Their article, A Computationally-Discovered Simplification of the Ontological Argument, appears in the June issue of the Australian Journal of Philosophy.

In plain English, the one non-logical second premise of the simplified argument reads:

If the conceivable thing than which nothing greater is conceivable fails to exist, then something greater than it is conceivable (348).1

[Spoiler Alert] Oppenheimer and Zalta do not claim that this simplified version of the argument is sound.  They think the premise has some prima facie plausibility (ibid.).  Further analysis reveals that the defender of the ontological argument must provide an independent argument to think the premise is true.  Still, they seem to suggest that such an independent argument could be constructed out of their previous work.  They write:

Our 1991 analysis of the argument is still relevant, since it shows how the ontological arguer could justify Anselm’s use of the definite description. The present analysis
shows why the use of the definite description needs independent justification.  Consequently, though the simplified ontological argument is valid, Premise 2 is questionable and to the extent that it lacks independent justification, the simplified argument fails to demonstrate that God exists.  The use of computational techniques in systematic metaphysics has illuminated the relationship between Premise 2 of the ontological argument and the conclusion that God exists (349).

So the argument in plain English would run something like this:

1. Nothing greater is conceivable than the conceivable thing than which nothing greater is conceivable.

2. If the conceivable thing than which nothing greater is conceivable fails to exist, then something greater than it is conceivable.

3.  Therefore, the conceivable thing than which nothing greater is conceivable does not fail to exist.

Premise One does seem to be a priori true.  So, in this formulation, the question of the soundness of the argument really does come down to Premise 2.  All else being equal, is a conceivable thing that exists greater than a conceivable thing that fails to exist?  Kant would say no.  Existence is not a real predicate!  But I don’t remember Kant really giving an argument for this.  All he gives is a weak analogy about thalers, the Prussian currency of his day.  Kant argues that 100 real thalers does not contain a coin more than 100 imagined thalers.  Thus, by analogy, “that God exists” adds nothing to the concept of God.  Now it might be true that 100 imagined thalers have as many coins as 100 real thalers.  But the for the analogy to hold, the question is not with regard to the equality of coins between the two, but which is greater.  So I offer the following prize: if you can prove that 100 imagined dollars are just as great as 100 real dollars, you win 100 imagined dollars.  Once you have submitted the proof just close your eyes and imagine that green-hued Benjamin Franklin with his perturbed expression.  Are you not motivated to win the prize?  Would you prefer that I offer you a real 100 dollar bill for the proof?  Why?

[An Aside] The fact that a computer program was able to refine the ontological argument is quite intriguing to me.  Suppose the singularity occurs, as predicted by some futurists.  What if the resulting super-intelligent machines were able to demonstrate the soundness of the ontological argument?  Would these super-intelligent machines develop religion?

1P. Oppenheimer & E. Zalta. (2011). “A Computationally-Discovered Simplification of the Ontological Argument”. Australasian Journal of Philosophy 89 (2): 333-349.

Posted on August 5, 2011, in Arguments for God and tagged , , , , . Bookmark the permalink. 3 Comments.

  1. I think “greater” is quite an ambiguous term here, and it carries a lot of water in this argument.

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  2. Also, is God “conceivable?” It seems to me that, even if you accept the role “greater” plays in this argument, if your concept of a thing does not capture all of its attributes, then you can’t situate it within this argument (i.e. greater than, lesser than).

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  3. Matthew,

    Thanks for your comments. The term “greater” is difficult to fully define. And without a clear definition in hand, the charge could be leveled that the argument contains an ambiguous term. However, I think Anselm makes a good effort not to use the term in an ambiguous way. He uses “greater” to describe degrees of reality. For example, the painting in intellectu is real for Anselm, but is of a lesser degree of reality than the painting that is both in intellectu and in re. Anselm’s use of the “greater than” relation need only mean at least this much in order for the term to be used univocally throughout this argument.

    Oppenheimer and Zalta also seem to suggest that the “greater than” does not have to have a robust definition for the argument to run:

    Our 1991 paper showed, however, that it suffices for the validity of the ontological argument that the greater than relation be a connected relation and satisfy Premises 1 and 2. Now the present analysis shows that the greater than relation doesn’t even have to be connected or satisfy Premise 1. It simply has to satisfy Premise 2. . . We think it is striking that greater than need have so little content for the ontological argument to be valid (347).

    I think this might address your second concern that more of God’s attributes must be conceivable to be able to know what role “greater” plays in the argument. I would says that “greater” at the very least needs to describe the relationship between in intellectu and in intellectu and in re. Furthermore, one need not fully conceive of something in order to have a well-defined description of it in mind. At the same time, Oppenheimer and Zalta argue that one can infer from Anselm’s definition of God to Descartes’ perfect being, which may imply those other divine-making attributes one traditionally thinks God has. Interestingly enough, they do not think that the inference from Descartes’ definition to Anselm’s would work without additional assumptions (See On the Logic of the Ontological Argument, 1991, pp. 16-17, mally.stanford.edu/ontological.pdf). If they are correct, we have a concept of a perfect being that is greater than a mere concept so long as it exists both in the mind and in reality.

    Best,

    Daniel

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