Smullyan on the Ontological Argument

Raymond Smullyan is name that is probably familiar to a lot of readers of this blog. In addition to being a mathematician and philosopher, he is known for being a master of using brainteasers and other puzzles to illuminate sometimes deep ideas in logic, especially Godel’s theorems. He is perhaps best known for his knight/knave puzzles. Those are the ones where knights always tell the truth and knaves always lie. Remember those?

Anyway, I’ve recently been browsing through his book 5000 BC and other Philosophical Fantasies. In one section he has a series of short vignettes containing anecdotes, jokes, puzzles and paradoxes. I especially liked this one:

Speaking of proofs of the existence of God, the funniest one I have ever seen was in a term paper handed in by a freshman. “God must exist because he wouldn’t be so mean as to make me believe he exists if he really doesn’t!” Is this argument really so much worse than the ontological proofs of the existence of God provided by Anselm and Descartes, among others?

Well put.


  1. #1 Blake Stacey
    December 29, 2006

    I’ve always liked to reappropriate Anselm’s argument for modern ends. For example, “The perfect Wikipedia article must exist, because it must have among its many excellent attributes the attribute of existence.”

  2. #2 Jonathan Vos Post
    December 29, 2006

    From a sibling to your blog, which linked to an interested paper where the Ontological Argument was found irreparably deficient in a new way:

    Posted by JVP on the
    “Contemporary Discussions of the Ontological Argument”
    thread of the Mixing Memory science blog

    My frustration with the Millican paper was that it stopped right where I expected an interesting analysis of “Kripke’s seminal ‘Naming and Necessity’ (1972) had made possible worlds and the occupants respectable….”
    (p.472 in Mind, p.36 of 40 in the PDF)

    That would also take us back to Vasiliev’s invention of “Imaginary Logic” — which has received recent metamathematical correction of its modern popularizer.

    The treatment of God in terms of imaginary worlds, and/or fictional worlds, has to be done carefully. One can axiomatically and precisely discuss from our Universe #1 with Logic #1 the hypothetical occupants of Universe #2 with Logic #2, or, more subtly,
    Universe #2 with Logic #3 as alleged by someone in Universe #2 with Logic #2 about someone who it is claimed has a different logic. Proper language strips away the common errors of anthropologists and fiction critics alike.

    An ontological argument in the proper Model Theory now becomes axiomatically possible. But, I fear, this has not been done by Kripke or Millican or anyone else I can find.

    Posted by: Jonathan Vos Post | December 10, 2006 03:03

  3. #3 Tyler DiPietro
    December 30, 2006

    A way to satirize the Ontological Argument that mathematicians will appreciate:

    Leibniz’s Ontological Argument: There can only be one being who hates Newton than I do, and that can only be an omnipotent deity. Therefore God exists.

  4. #4 John Wilkins
    December 30, 2006

    Leibniz’s Ontological Argument: The best of all possible arguments for God.

  5. #5 Tyler DiPietro
    December 30, 2006

    For John Wilkins, and elaborated version of Leibniz’s Ontological Argument for the EoG.

    1. I hate Newton’s guts because he stole differential and integral calculus ideas from me, and has hitherto accused me of stealing them from him.

    2. Only an omnipotent being could possibly hate Newton more than I do.

    Corollary to 2: Only an omnipotent being could know more about differential and integral calculus than I hitherto do.

    It hereby follows from 1, 2 and corollary 2 that an omnipotent deity exists.

  6. #6 Dave S.
    December 30, 2006

    “Speaking of proofs of the existence of God, the funniest one I have ever seen was in a term paper handed in by a freshman. �God must exist because he wouldn’t be so mean as to make me believe he exists if he really doesn’t!� Is this argument really so much worse than the ontological proofs of the existence of God provided by Anselm and Descartes, among others?”

    Maybe He’s an omnimalevolent God who torturing that student by making him think He exists when He really doesn’t. A God who can simultaneously exist and not exist…indeed He works in mysterious ways. :)

    To me Smullyan is best known as The Man when it comes to retrograde analysis problems in chess. His books The Chess Mysteries of Sherlock Holmes and The Chess Mysteries of the Arabian Knights are classics.

  7. #7 Craig Pennington
    December 30, 2006

    Smullyan’s Godel’s Incompleteness Theorems (Oxford Logic Guides, No 19) is absolutely the best book I’ve seen on the subject. The man is awesome.

  8. #8 mark
    December 30, 2006

    Like we learned in school, ontology recapitulates pettifoggery.

  9. #9 Jonathan Vos Post
    December 30, 2006

    With all due respect, the Ontological Argument is wrong. However, it is wrong in subtle ways that require careful axiomatic construction of mathematics and metamathematics, metaphysics, and model theory to avoid mere category errors and errors induced by ambiguities in ordinary language. The history of attempted refutations of Ontological Argument is long and complex; a significant literature with many extremely important authors. In a similar way, Fermat’s Last Theorem is a closed book now, but the entire field of Algebraic Number Theory grew up in the peer review of erroneous proofs.

    The Truth is often very hard to come by. It is foolish to merely crack jokes about an earnest and significant attempt to find that Truth, even if the attempt was fatally flawed. We learn, in part, by finding flaws in others’ arguments, and in debugging our own assumptions.

    Ontology and Epistemology may have begun within a Theology that you reject. But the process of adaptive radiation by which new branches of learning diversify into niches opening up due to extinction of rejected theories is one with biological complexity (as this metaphor indicates) and the fascinating thought processes of brilliant men and women, whom we reject at our own peril.

    There are plenty of false argument in motion; see any TV news broadcast, or political speech. But knowing exactly WHY they are wrong is more valuable than knee-jerk dismissal. When, for instqance, a public policy is inherently flawed, the government needs to understand WHY, and have someone put forth a serious proposal for a better policy.

  10. #10 Friend Fruit
    December 30, 2006

    Is this argument really so much worse than the ontological proofs of the existence of God provided by Anselm and Descartes, among others?

    John Lynch actually suggested recently that the fact that Descartes built his proofs on top of the Ontological proof was reason not to dismiss it hastily. I think a better summing up of that is: so much the worse for Descartes.

  11. #11 Jonathan Vos Post
    December 30, 2006

    “Descartes built his proofs on top of the Ontological proof”

    Nonsense. Descartes did Math, Physics, and Philosophy. Some of the Philosophy is now rejected as mere Theology. Some is not. Don’t put all his eggs into one basket. Psychologically tortured soul that he was (severely dysfunctional family structure in his infancy) he was one of the great geniuses of his millennium. Compare to, say, Pascal, who also did Math, Physics, and Philosophy. Or Newton!

    It is folly to reduce the life work of polymaths to a slogan, and then turn the slogan into a joke. If you have no respect for our intellectual predecessors (and superiors) then you cannot learn anything from them.

    Do you want to throw out Cartesian Coordinates?

  12. #12 AJS
    December 30, 2006

    The problem with this argument is simply that it’s utterly bogus. There’s nothing subtle or complicated about that, no need for hand-waving – it’s just that the Ontological Argument is built on a laughably unsound premise.

    It’s far from certain that a perfect being could exist in fact — there might be mutually-conflicting requirements such that it would be impossible to satisfy both. It’s not even necessarily true that a perfect being could count “existence” among its attributes. You haven’t considered that for a perfect being, existing (if it’s even at all possible, but since this is a thought experiment we have to let that slide for now) in an imperfect universe (as Theists invariably assume this to be) might actually harm the inhabitants of that universe. If we further assume that a perfect being wouldn’t wish anybody harm (I don’t think Theists would dispute this), then a perfect being who could do harm merely by existing, would have not to exist.

  13. #13 Friend Fruit
    December 30, 2006

    My apologies for my ambiguous use of the word “proof.”

  14. #14 SmellyTerror
    December 31, 2006

    I strongly suspect that this statement will represent my own unzipping of my ignorance and waggling it around for all to mock, but:

    Anselm defines God as something that exists (God is that than which no greater can be conceived), and then uses that premise to conclude that God exists. How is this worth more than a few seconds consideration before you give it a gigantic “pfff”?

    No really, how? I’m clearly missing something here…

  15. #15 Jonathan Vos Post
    January 1, 2007

    Because, “SmellyTerror”, it is by no means obvious what is really meant by “exists.” That’s one of those things that you’re sure that you understand, until you try to define it. Like “Time.” The branch of Philosophy called “Ontology” is all about perfecting the definition of “exists.”

    Descartes operated in the Augustinian tradition. Augustine is a 4th Century philosopher who infused Christian doctrine with Neoplatonism. An inimitable Catholic theologian, he made agnostic contributions to Western philosophy.

    Augustine argued that skeptics have no basis for claiming to know that there is no knowledge. In a proof for existence similar to one later made famous by Descartes, Augustine wrote: “[Even] If I am mistaken, I am.”

    He is the first Western philosopher to promote what’s now called the Argument by Analogy: there are bodies external to mine that behave as I behave and that appear to be nourished as mine is nourished; hence, by analogy, I am justified in believing that these bodies have a similar mental life to mine.

    Augustine claimed reason to be a uniquely human cognitive capacity (there not being Artificial Intelligence in those days) that comprehends deductive truths and logical necessity.

    Further, regarding both “time” and “exists” — Augustine adopts a subjective view of time, i.e. that time is nothing in reality but exists only in the human mind’s apprehension of reality. He believes that time is not infinite because God “created” it.

    This was also the launch pad for Baruch Spinoza, who had great influence on Einstein.

    As I say, even if you think this is all nonsense, it is historically significant, to many brilliant thinkers.

    The above was partly off the top of my eggnog-addled head, and partly from

  16. #16 David D.G.
    January 1, 2007

    Jonathan Vos Post:

    < < Because, "SmellyTerror", it is by no means obvious what is really meant by "exists." That's one of those things that you're sure that you understand, until you try to define it. Like "Time." The branch of Philosophy called "Ontology" is all about perfecting the definition of "exists." >>

    PLEASE tell me you’re not REALLY attempting to argue about what the definition of “is” is!

    ~David D.G.

  17. #17 David D.G.
    January 1, 2007

    Now THAT was weird! Prior to my own commentary, I had quoted the first paragraph of Jonathan Vos Post’s post, which showed up when I hit Preview, but disappeared when I hit Post! Here is my next attempt to present this:

    Jonathan Vos Post:
    [Because, "SmellyTerror", it is by no means obvious what is really meant by "exists." That's one of those things that you're sure that you understand, until you try to define it. Like "Time." The branch of Philosophy called "Ontology" is all about perfecting the definition of "exists."]

    PLEASE tell me you’re not REALLY attempting to argue about what the definition of “is” is!

    ~David D.G.

  18. #18 Jonathan Vos Post
    January 2, 2007

    David D.G. — depends. Would you vote for me or my wife?

    Actually, it is interesting to see the “logic” and the “philosophy” of U.S. Presidents in action.

    Reagan saying: “Evolution is only a theory” — although he played an evolutionary chimp psychologist in “Bedtime for Bonzo”;

    George W. Bush in his first run for White House calling numbers involved in balancing the budget: “Fuzzy Math.”

    George W. Bush, in debate, being asked who his favorite philosopher was: “Jesus Christ.”

    Clinton on “it depends what the definition of ‘is’ is…” was speaking as a lawyer, not an Ontologist, and it got him disbarred.

    Ther anti-science spewings of the current president are a danger to us all, regardless of party. Can you hear Tom Jefferson and Ben Franklin spinning in their graves?

  19. #19 oz
    January 2, 2007

    i strongly suspect a more detailed philosophical discussion of the topic could be found in smullyan’s 2002 who knows? a study of religious consciousness though i am unable to recite any appropriate quotes from it… sigh. [i had the book very briefly, skimmed it and decided that it was neither playful enough nor serious enough to warrant my time, and returned it with regret...]

  20. #20 Existor
    January 5, 2007

    Hi All

    I don’t have your experience of the literature so I’ve no quotes to quote. But I’d say that existence is a property affirmed by interaction, or observation. Self-perception must therefore be the strongest proof of existence that we have. This could be the starting point for positing a lot of alternatives about the reality of everything we perceive that is not part of our selves (or seems not to be), but you must have read of them all already.
    I think the really intriguing questions surround the nature of time (as you’ve already said), how anything exists, and how this is related to the fact that we are able to be aware of it – this last seems to defy analysis, at least for the time being, suggesting that perception (or mind) is more fundamental than we think.
    Talking about a “perfect” universe is a waste of time because that’s a human value judgement and can only have meaning individually. God is only a human idea, too. I have the following response to your freshman’s argument:
    “If god exists, the essence of god must be built into the fabric of our reality in a fundamental but non-obvious way. Therefore I propose that the essence of god has to be very similar physically to the other fundamental components of our Universe.
    Hence I conclude that god is constrained by the same laws that govern the quantum realm and has a wave function corresponding to a range of probabilities of existence, and so exists not actually but potentially; or that the most that can be said about the existence of god is that the probability of his existence at particular spacetime coordinates could in principle be defined, but since none of these probabilities is ever equal to one, the existence of god is never actually certain.
    OK, you might say, then when god interacts with something the wave function collapses and so at that time he definitely exists. For a normal quantum entity that would be true, yes, but the most essential requirement for being god is that his existence is always certain, ie the probability is always equal to one. If this were so, because god must be everywhere, the Universe would be forced to be deterministic at a fundamental level – and then it wouldn’t be what it is at all. Therefore since god must not interact with the Universe to avoid destroying it, we can only speak of the effective probability of the existence of god, which must of course always equal zero.”
    That’s really just a bit of fun, but I think it’s obvious that “god” needs to be more rigorously defined in relation to the universe we observe in order to have any meaningful discussion about the existence of god. But what we’re really interested in is our origins – and this is primarily why we’re discussing the existence of god. If we could truly understand the nature of time, physical existence, and how this relates to mind, I suspect the idea of god would become obsolete

  21. #21 Existor
    January 22, 2007

    No responses, so I guess that means you all agree, right?
    By induction then, if the effective probability of the existence of god equals zero, it is logical and natural to conclude that god does not exist. QED (almost).
    Now for questions that are perhaps more relevant, as they relate to truly-exisitng phenomena. How does anything exist? What are particles, spacetime and quanta? How is this related to the fact that we can perceive it?

  22. #22 Crandaddy
    June 4, 2009


    My understanding of Anselm is that he held to an essence-first ontology, which means that (for him, at least) existence subsists in essence (or the definitive, “what” aspect of a being).

    Therefore, from establishing the existence in the intellect (i.e. as an essence) of the ultimate great-making essential attribute (namely existing), the existence of “that than which none greater can be conceived” falls out.

    This was later turned on its head by Thomas Aquinas who proposed a radically existence-first metaphysic and subsequently threw out the ontological argument.