So from the real premises we find an immediate counterexample simply by looking around the room. Anything that really exists is greater than Thomas's non-existent God. So all you can conlcude from Tom's argument is that there are some things greater than a non-existent God. But it can be anything that is real - a pet rock, a garden slug, Albert Einstein who discovered relativity, or, yes, Halle Berry - are all greater than Thomas's non-existent God. Or in other words, Tom could rightly conclude that if God exits, he, she, or it is greater than a God that does not.

There are two ways to salvage Tom's argument. One fancy way was derived by Kurt Godel. Kurt was the gentleman who proved predicate logic is complete and consistent and who discovered the famous incompleteness theorems of math and logic. However, to tackle the ontological problem, Kurt had to use a more - quote - "advanced" - unquote - type of logic known as modal logic which includes the concept of possibility and necessity. Although no one seems to dispute that Kurt's manipulation of the symbols is correct (the proof is actually quite short), he needs some extra premises, properties, axioms, concepts, symbols, and transformation rules. And for the hard nosed realist these axioms, rules, and properties are far from being clear and distinct to borrow a phrase from René Descartes. Instead the argument comes off more as a logician's game of reverse engineering to figure out which axioms we need to get the conclusion we want.

A simpler procedure than Kurt's can also be taken. Yes, it requires additional premises and axioms, but they are almost trivial to the point their addition seems to be a case where (as they say in France) nous enculons les mouches.

Briefly, we reason like this. If you assume that the universe is not democratic - that is, no one has equal greatness - then you can rank everybody in order as to how great they art. Then as long as you assume there are, were, and will be a finite number of people, places, and things (including divine beings), there is something or someone in the universe who comes out "greater" than anyone else. So there is a being above which no greater can be conceived. If you think you're conceiving something greater, then you're jack out of luck. Remember, if it doesn't exist, it can't be greater than something that does.

But hold on, there, pardner. We've just proven that as long as no one has equal greatness, the somewhere, someplace, there is a being of which no greater can be conceived. So with one minor, very minor correction to Tom's argument, we've proven, there is indeed something you can call God.

There is, though, a couple of wee, tiny glitches here, First you can say God exits as long was we do the defining. This is in fact a lot like Kurt Godel's proof that there are true statements in number theory that can't be proven. That is, as long as you define number in a certain manner.

But more to the point, Tom's God so defined need not be the stereotypical Big Guy of traditional Judeo-Christian-Islamic theology. God could be some guy with a white beard sitting on a cloud surrounded by harp players, true. But depending on your ranking rules, God might very well be Albert Einstein.

Or who knows? Fiddle with your rules just right, and God could end up being Halle Berry.

Hallelujah!

Or should we say "Halle-lujah!"?

 

References and Bibliography

The Prayers and Meditations of Saint Anslem with the Proslogion, Saint Anselm, Penguin Books (Various Editions). You can, though, find Tom's book on-line (see below).

Formal Logic: Its Scope and Limits, Richard Jeffrey, McGraw-Hill (1981). Richard was a great popularizer of formal logic and an exponent of using truth trees to find validity or non-validity in arguments. With truth trees - which are stick type diagrams - you either show the argument valid or automatically arrive at counterexamples. Truth trees are really slick, and it was fiddling with truth trees that led to finding the counterexamples given above.

Introduction to Logic, Patrick Suppes, Originally published by Van Nordstrom but reprinted by Dover. A classic introduction and includes a lot of formal first order predicate logic with the various techniques. There's nothing about truth trees, though.

Set Theory and Logic, Robert Stoll, Freeman and Company (1963) (Later reprints by Dover). A more advanced treatment of mathematical logic which gets pretty hairy sometimes and ends up with Kurt Godel's and Alonzo Church's theorems on undecidability.

One irritation is this book is it throws in the statement that the union of a set of indexed empty sets is the empty set (which is OK), but that the intersection of the same sets is the universal set - that is, the set that contains everything. For those condemned to self-study, it seems particularly odd that the intersection of a bunch of nothings comes out to be everything, particularly when the union of the same bunch of nothings (and unions of sets contain the set composed of their intersections) is nothing! And then all the book does is say it is up to the readers to "convince themselves" this is true.

What's worse, some authors write that the intersection of indexed empty sets are undefined! But other texts say it's simply defined as being the universal set. What the hey?

I mean, if it's a theorem, prove it; if it's a weird definition or undefined, just say so, or if it's the odd ball reasoning along the lines of three mile submarines - that is, a "trivial" truth (which is ultimately what it is) then demonstrate it.

Convince themselves! Sheesh!

Theory and Problems of Logic, John Eric Nolt, Dennis A. Rohatyn, and Achille C. Varzi, Schaum's Outline Series (1998). This gives a lot of problems to work through starting with simple propositional logic and on through predicate logic and probability. Teaching yourself? Try Schaum's Outlines.

A History of Western Philosophy, Bertrand Russell, Simon and Shuster (1972) (Originally published by George Allen & Unwin, 1946). A broad survey which was drawn from Bertie's lectures when he was living in Malvern, Pennsylvania and lecturing (briefly) at the Barnes Foundation. Not much on Anselm, though, but he goes into more depth in the arguments of Aquinas and Descartes. The book is dated, but is still a good relaxed introduction to the history of western philosophy. But it's big.

Bertie, of course, was the author of the (at the time) controversial essay (also delivered as a lecture) "Why I Am Not a Christian". In the talk he pointed out that although he was not a Christian he probably agreed with Christ more than most people who did think they were Christians. So it makes you think Bertie was quite familiar with American Sunday morning television.

The Case of the Philosopher's Ring, Randall Collins, Crown Publishing (1978). As sad as it is to state, this book is capable of initiating an interest into the serious study of mathematical logic. This was one of the many Sherlock Holmes pastiches that came out in the 1970's following the success of Nicholas Meyer's The Seven Percent Solution. In this book Sherlock Holmes and his trusty sidekick, Dr. John H. Watson, get a telegram from Cambridge University that a great mind is about to be stolen.

Holmes and Watson seek out the writer of the incomprehensible message who turns out to be none other than Bertrand Russell (yes, Sherlock Holmes and Bertrand Russell). In the course of the adventure Holmes meets Bertie, Bertie's mathematical colleague Alfred North Whitehead, their fellow philosophers, George Hardy and Ludwig Wittgenstein, mathematician Srinivasa Ramanujan, all around weirdo Aleister Crowley, economist John Maynard Keynes, and a host of others. Ignoring the various liberties with the facts (the book has Ramanujan dying of constipation in his Cambridge room in 1914 rather than in India in 1920 of what was diagnosed as tuberculosis), the book is a fun read for Sherlock Holmes fans, but beyond that it's literary merit is debatable.

But during the course of the novel, Bertie makes a reference to the famous Russell Paradox. Does the set of sets that do not contain themselves contain itself? You can show that if it does, it doesn't and if it doesn't it does. Clearly a case for further investigation which inevitably can lead the curious to the study of mathematical logic and philosophy in general.

Try and Stop Me, Bennett Cerf, Simon and Schuster (1945). Bennett tells the story of his meeting with Albert on the sidewalks of New York. Bennett is known mostly to the baby boomers as the panelist of "What's My Line", but those who also read books also know him as the co-founder of Random House and the man who was responsible for getting James Joyce's Ulysses unbanned in the United States.

What isn't that well known is Bennett was one of the greatest essayists American letters has produced. His lack of fame in this area is partly his fault since his essays are scattered through his books which are largely made up of humorous anecdotes and jokes. His best essays are from the 1930's through 1950 and include memoirs of people as varied as his good friend George Gershwin and his cantankerous acquaintance, Alexander Woollcott.

Bennett, though, like most writers would not hesitate to stretch the facts a bit if it made a better story. In his memoirs, At Random, he more or less admitted (albeit obliquely) that a story that he had told as first hand was really recycled and apocryphal. He was sitting in his office when his secretary knocked on the door. She said a young man who said he was the greatest writer in the world wanted to see Mr. Cerf. Bennett (the story goes) immediately told his secretary to send William Saroyan in.

By the way, does anyone still read William Saroyan?

Online Resources

As always be careful of on-line sources since they can be unstable, short-lived, and inaccurate (and this may seem like the pot calling the kettle black). But some of the better sites are given here.

Proslogion, Thomas Anselm. A number of editions of Tom's book are online. Check out:

http://www3.baylor.edu/~Scott_Moore/Anselm/Proslogion.html

http://www.ccel.org/ccel/anselm/basic_works.html

http://cla.umn.edu/sites/jhopkins/

Kurt Godel's Ontological Argument, Christopher Small, Department of Statistics and Actuarial Sciences, University of Waterloo, http://www.stats.uwaterloo.ca/~cgsmall/ontology.html. Very nice explanation of the problems with Tom's argument, and how Kurt did his best to fix it. Which he did logically speaking, although it can't be said Kurt convinced a lot of people, including himself (Kurt never published his findings).

For the best biography of Kurt see Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study by Ed Regis, Addison Wesley, 1988).

Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/ The articles on this site sometimes come off a bit much like personal essays and reflections (but unlike some other frivolous articles on philosophy do not contain cartoons). On the other hand, they do give a good introduction to the various philosophical topics. The article on the ontological arguments (and there's more than one type of argument) is at

http://plato.stanford.edu/entries/ontological-arguments/

One instructive section discusses parodies of the ontological argument. What the reader notices is that - like much of modern art - the parodies are often indistinguishable from the real thing.

The main point of this article is you can blow hot air all day about the relative merits of the arguments but none of them are of sufficient clarity or are definite enough that they will whop the heathen (i. e., convince the non-theist). And the really sharp reader will be tempted to argue that the "corrected" argument given above can be lumped with other "correct but uninteresting" resolutions to Tom's argument.

Pah! Philistines!

Acknowledgments

Actually it would be remiss not to note it was Professor Tom Boyd who taught great introductory philosophy courses way back in the 1970's and included the ontological argument in his class curriculum. He also made it clear that the great advantage to the field of philosophy is you do not need to have a degree to intelligently partake in its discussions and debates.

Tom, although retired, is still going strong as David Ross Boyd Emeritus Professor of Religious Studies at the University of Oklahoma. He was also a bonafide minister of a Presbyterian church during his professorial career and is a true rare bird. Although he lives in Oklahoma has always had the guts to believe in evolution - and say so publicly.

Anselm, Aquinas, and Boyd. Why are there so many religious philosophers named Tom?