The proofs for the existence of God were the centerpiece of Rational Theology for almost eighteen hundred years. They played an important part in the writings of the Scholastics, of course, but they also turned up in works by Descartes, Spinoza, Leibniz, and almost all of the other major [and minor] figures of the "modern" period -- which is to say the seventeenth and eighteenth centuries. And then, abruptly and with no regrets, the two greatest philosophers of the eighteenth century, David Hume and Immanuel Kant, killed Rational Theology. Hume began the slaughter in a series of extraordinary Dialogues Concerning Natural Religion ["natural" as opposed to "revealed."] I venture to suggest that Hume's Dialogues are the only fully successful example of that literary-philosophical form after Plato. Hume wrote the Dialogues relatively early in his career, but his friends, among them Adam Smith, were fearful that their publication would cause a scandal and irreparably damage Hume's literary reputation. They successfully prevailed upon Hume not to publish them, and it was left to his nephew and literary executor to see them into print in 1779, three years after Hume's death. [Trick question among graduate philosophy students: How can you remember that Hume died in 1776? Answer: it is the same year in which Adam Smith published An Inquiry into the Nature and Causes of the Wealth of Nations.] Hume lavishes his most hilarious flights of fancy on the Argument from Design, but he has no difficulty disposing of the Cosmological Argument in a few brief paragraphs, drawing on the analysis of causal inference that he had elaborated in Book I of A Treatise of Human Nature and in the Enquiry Concerning the Human Understanding. He also addresses the Ontological Argument in passing. Hume actually is forced to deploy considerable literary and polemical skill to keep the arguments afloat for the entire series of twelve dialogues. The truth is that he requires only a page or two of text to dispatch all of them.
Kant was aware of Hume's Dialogues. The same year that they appeared, the philosopher Hamaan prepared a partial translation into German and circulated them privately. Kant was at that point in the last stages of bringing his great Kritik der Reinen Vernunft to completion, and his treatment of the proofs for the existence of God, in the Chapter of the Transcendental Dialectic entitled The Ideal of Pure Reason, clearly shows the influence of Hume's arguments. But Kant's devastating refutation of the Ontological Argument was all his own.
The combined onslaught of Hume and Kant killed Rational Theology as a respectable branch of serious philosophy. Catholic philosophers were stuck, of course. They were ideologically committed, so to speak, to the scholasticism of St. Thomas [who, by the way, had no use for the ontological argument], and so they soldiered on, isolated from mainstream Anglo-American philosophy. God talk did not go away, of course, but it morphed into something a good deal more esoteric and hard to understand. The great nineteenth and twentieth century Protestant theologians found all manner of ways to go on saying the same old things while giving them new interpretations that protected them from the crushing objections of Hume and Kant. When I was a boy, studying philosophy, the Proofs were a standard topic in courses on the history of philosophy, but no serious analytic philosopher paid them any attention.
And yet. And yet. Mirabile dictu, just when we atheists thought the battle was won, up popped some smart, well-trained, logically au courant analytic philosophers to say that that old chestnut, the Ontological Argument, could be brought back to life with the aid of the latest advances in modal logic. My memory, which all these years later may be fallible, tells me that the first brave soul to advance this implausible claim was Alvin Plantinga. Plantinga is an interesting character in Philosophy. Wikipedia tells me that he spent 1950-51 studying philosophy at Harvard, which was my Freshman year, but I do not think I ever met him. At that time, the intellectual hothouse of Protestant theology was a little denominational college in Michigan called Calvin College. Plantinga studied there, and spent almost twenty years on the faculty before going to Notre Dame. He is back now at Calvin, apparently.
I thought the Ontological Argument bubble had burst long ago, but when I started this ill-advised series of posts on God talk, my old colleague Bruce Aune, now professor Emeritus in Philosophy at the University of Massachusetts, wrote to tell me that our former colleagues Gareth Matthews and Lynne Baker had collaborated two years ago on yet another effort to give a modern formal logical rendering of Anselm's chestnut. Aune has written a refutation of their attempt, and I think the very best way of concluding this short series of blog posts is by reproducing here, with his permission, Aune's statement and refutation of the Matthews/Baker argument. So here it is, with grateful thanks to Bruce.
Anselm’s “ontological argument,” one of the classical arguments for the existence of a theistic god, has recently been reconstructed by Lynne Baker and Gareth Matthews, who declare that it is sound: its premises, they believe, are true and its reasoning is valid. As I see it, the argument they present is only partially formalized; and although it is perhaps intuitively plausible as they present it, it is easily seen to be fallacious when its logical structure is fully exposed. In what follows, I outline their version of the argument and then identify the logical error involved in it.
The argument they present proceeds by reductio ad absurdum. They make four initial assumptions, which I quote almost exactly:
a. The theist and atheist refer to the same object of thought with the words, “that than which nothing greater can be conceived.”
b. That than which nothing greater can be conceived is an object that exists in both the theist’s and the atheist’s understandings.
c. Let S be the object that exists in the theist’s and the atheist’s understandings and is such that nothing greater can be conceived.
d. S exists in thought.
What they call “the main argument” is the following. Again, I follow their words almost exactly:
1. S exists in thought and does not exist in reality. [Premise for reductio]
2. An otherwise exact same thing as S that existed both in thought and in reality is conceivable.
3. If S exists in thought and not in reality and an otherwise exact same thing as S that existed both in thought and in reality is conceivable, then an otherwise exact same thing as S that existed in thought and reality would be greater than S. [By 1 and principle G.]
4. An otherwise exact same thing as S that existed in thought and reality would be greater than S. [1,2, conj., 3, MP.]
5. If an otherwise exact same thing as S that existed in thought and reality would be greater than S, then there can be a conceivable object that is greater than S [namely, an otherwise exact same thing as S that also existed in reality].
6. There can be a conceivable object that is greater than S [4,5, MP].
7. There can be no conceivable object that is greater than S [from assumption c].
8. Contradiction! [6,7 conjunction].
9. S does exist in reality [8, 1, IP]
The error here lies in the derivation of line 7. Line 7 is supposed to follow from assumption c, but this assumption contains a definite description that needs to be eliminated to obtain the conclusion concerning the object S. Let ‘Gx’ abbreviate ‘is such that nothing greater can be conceived.’ Line c then has the form of
C*: s = (ix)(x exists in both the theist’s and the atheist’s understanding and is such that nothing greater can be conceived.
There is a problem about how to eliminate the definite description here. If the definite description were understandable Russell’s way, then the sentence would be equivalent to "(for all x) [(there is a y) (Uxt & Uxa & Gx if and only if x = y) & s = x]", and line 7 could be validly inferred by quantifier logic. But on this reading C* asserts that there (actually) exists one and only one thing that is G, and this is what has to be proved (it can’t simply be assumed, since C* is an assumption). The best way to analyze C* is by means of Frege’s theory of descriptions. Frege assigned a denotation to every definite description: it was either the object in reality (as Anselm would say) satisfying the description (if such an object exists) or some arbitrary “don’t care” object, which Carnap represented by “a*”. To accommodate Anselm’s way of speaking, we can express this alternative by saying the denoted object exists merely in someone’s understanding. Understood this way, C* is equivalent to the following:
C**: (for all x)[(there is a y)(Uxt & Una & Gx iff x = y) & s =x] or ~[(for all x)(there is a y)(Uxt & Uxa & Gx iff x= y) & (s is merely thought of as G)].
It is easy to see that line 7 cannot be validly inferred from C**. To get it the requisite conclusion concerning S (that is, to get ‘S is the greatest conceivable thing’) we have to eliminate the second disjunct. But to do this, we have to know what we are trying to prove—that is, that S is not merely thought of but exists in reality as a unique object.
 See Lynne Rudder Baker and Gareth B. Matthews, “Anselm’s Argument Reconsidered,” Review of Metaphysics, 64.1 (September 2110), pp. 31-54.
 Principle G is as follows: For anything x that existed only in thought, an otherwise same thing that existed both in thought and reality would be greater (not just greater in thought) than x.
 Frege’s theory is conveniently set forth by Rudolf Carnap in Meaning and Necessity (Chicago, 1956), pp. 45ff.