That key change you’re planning? Please reconsider.
In a recent post, I noted that
it is possible to write a computer program that mimics a human cognitive activity rather well, operating in a way that is nothing like the way that human cognition works.
Douglas Hofstadter has been bemoaning the fact that this is not just possible, but actually the mainstream of how ‘artificial intelligence’ research is conducted. The ‘imperative’ behind just about all current AI research is ‘to make machines perform in any way possible, with little regard for psychological plausibility’. Says Hofstadter,
Okay, Deep Blue plays very good chess—so what? Does that tell you something about how we play chess? No. Does it tell you about how Kasparov envisions, understands a chessboard? […] To me, as a fledgling AI person, it was self-evident that I did not want to get involved in that trickery. It was obvious: I don’t want to be involved in passing off some fancy program’s behavior for intelligence when I know that it has nothing to do with intelligence. And I don’t know why more people aren’t that way.
This is, in some ways, a refreshing perspective. But it does leave open the question of how you would know if a program’s behaviour does have something to do with intelligence.
The argument for the existence of God that Anselm gives in his Proslogion chapter II is as follows:
Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood, exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.
Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. hence, there is no doubt that there exists a being than which nothing greater can be conceived, and it exists in both the understanding and in reality.
In my recent post about ontological arguments, I included a link to the section of the Stanford Encyclopaedia of Philosophy article that shows various formal reconstructions of Anselm’s argument: those by Alvin Plantinga, Jonathan Barnes, Robert Adams, David Lewis and Paul Oppenheimer and Edward Zalta. However, the SEOP article doesn’t include Charles Hartshorne’s or Robert Maydole’s reconstruction of Anselm’s argument. Elsewhere on the net, Peter Suber has given a ‘refinement’ of Hartshorne’s formulation, along with some discussion. In what follows, I propose to do readers the same service with respect to Maydole’s formulation, which is found in chapter 10 of the Blackwell Companion to Natural Theology (Oxford: Wiley-Blackwell, 2009).
For those who don’t know, ‘that, than which nothing greater can be conceived’ is what Anselm proposes as the definition of God. In his discussion of the argument, Maydole rephrases this as ‘that than which it is not conceivable for something to be greater’ for technical reasons that I don’t think affect the merits or otherwise of the argument. The underlying idea is that God is the greatest conceivable being. See here for a defence of this definition by Peter van Inwagen.
More significantly, Maydole makes a fairly large concession on behalf of Anselm, as follows (p 555):
Either Anselm has been mistranslated or he misspoke and should have said that even the fool is convinced that the concept of something than which nothing greater can be conceived has existence-in-the-understanding; and instead of saying “whatever is understood, exists in the understanding,” he should have said “the concept of whatever is understood has existence-in-the-understanding” and so on.
We thus have to deal with at least two kinds of things: concepts (which potentially have the property of existence-in-the-understanding but cannot have the property of existence-in-reality) and objects (vice versa). In order to formalise the argument, according to Maydole, we also have to be able to refer to a third kind of thing: linguistic expressions. N.B. in order to state the argument (or anything at all), of course, we have to use linguistic expressions; the additional claim is that in this case we also have to talk about (mention) some of them as well, notably definite descriptions.
(Technical note: In the same vein, the formalisation includes a reference relation in the object language. Grelling’s paradox lurks here, but it can be avoided (I think) if we think of the formal language as sorted three ways according to the ‘kinds of things’ mentioned in the above paragraph, in such a way that ‘heterological’ is not well-sorted.)
(Further technical note: ‘exists in the understanding’ and ‘exists in reality’ are thus predicates, and quantification is without existential import.)
The preamble aside, then, let’s move on to Maydole’s version of Anselm’s argument. I’ve rephrased and re-ordered some of his premises and given verbal expressions of the deductive steps, which Madoyle represents symbolically.
Maydole notes that the argument thus formulated is not vulnerable to obvious parodies. For example, Gaunilo of Marmoutier famously countered Anselm’s original argument by contending that an argument with similar and equally-defensible premises could be formulated to prove that the greatest conceivable island (in our current terminology, the island than which it is not conceivable for some island to be greater) has existence-in-reality. However, in order to reformulate the above argument in such a way, you would need the following highly dubious premise:
xi is pretty obviously false, since it is conceivable for something to be greater than even the greatest conceivable island. The more plausible counterpart of 11 is XI.
XI is true (or at least, true if 11 is), but with XI in place instead of xi the reformulated argument is only valid if you also change 5 to V.
V is much less plausible than 5. To see this, consider the property of being connected by land to the mainland. Suppose that this is a great-making property (it doesn’t matter why). For some island i, we can conceive of it having this property; however, if it did have that property then it would ipso facto not be an island. From the conceivability of i having a great-making property that it lacks it follows that it is conceivable that there is something greater than i, but that thing is not necessarily an island and so it doesn’t follow that it is conceivable that there is some island greater than i. Therefore, the Gaunilo-esque parody of this argument fails.
Of course, there are very many other objections that might be raised against the premises and the underlying logic. But I still think that the argument is interesting and suggestive enough to merit whatever attention I can attract to it with this post.
(N.B. the argument presented here is not Maydole’s own ontological argument, discussed in various places around the web, which he summarises at the end of his chapter in the Blackwell Companion after having analysed various other ontological arguments, including those by Descartes, Leibniz and Gödel).
‘La pomme a mangé le garcon’ is a bizarre sentence, but an easily-comprehensible one (if you speak French). It means, ‘The apple ate the boy’. What does Google Translate make of it?
Bob Berwick at Faculty of Language has an explanation of why this is. In a nutshell: GT works by bombarding problems with corpus statistics, while paying very little attention at all to things like grammatical structure or thematic role. Since ‘the boy ate the apple’ is a statistically much more ‘likely’ sentence than ‘the apple ate the boy’, while both sentences contain English translations of all and only the words in the French source sentence, the former wins out. Berwick’s take-home message relates to the dangers of overusing statistics (Bayes’ Theorem in particular) in place of doing serious linguistics.
Notwithstanding mishaps like this, however, Google Translate is remarkably successful in general. Furthermore, overall it is significantly more successful than previous attempts at automated machine translation that paid much more attention to notions that are central in out best linguistic theories: things like grammatical structure (e.g. clause composition) and thematic role (e.g. verb subject/object).
It is possible to draw many morals from this scenario. At the very least, we can say the following: it is possible to write a computer program that mimics a human cognitive activity rather well, operating in a way that is nothing like the way that human cognition works. This is something to bear in mind amid the multifarious claims made on behalf of artificial intelligence.
N.B.: Of course, we really didn’t need this example to see that human cognition works nothing like Google Translate. Of course native speakers aren’t carrying n-grams around in their heads. Of course native speakers’ linguistic knowledge doesn’t amount to knowing statistical distributions of collocations of words … right?
Not according to John 1:18a…
No one has ever seen God
This is a perplexing claim coming from someone versed in the Old Testament. Didn’t Hagar see God?
So she [Hagar] called the name of the Lord who spoke to her, “You are a God of seeing”, for she said, “Truly here I have seen him who looks after me.”
Didn’t Abraham see God?
And the Lord appeared to him by the oaks of Mamre, as he sat at the door of his tent in the heat of the day. He lifted up his eyes and looked, and behold, three men were standing in front of him. When he saw them, he ran from the tent door to meet them and bowed himself to the earth […]
They said to him, “Where is Sarah your wife?” And he said, “She is in the tent.” The Lord said, “I will surely return to you about this time next year, and Sarah your wife shall have a son.” And Sarah was listening at the tent door behind him. […]
So the men turned from there and went towards Sodom, but Abraham still stood before the Lord. Then Abraham drew near and said, “Will you indeed sweep away the righteous with the wicked? […] Then he said, “Oh let not the Lord be angry, and I will speak again but this once. Suppose ten are found there.” He answered, “For the sake of ten I will not destroy it.” And the Lord went his way, when he had finished speaking to Abraham, and Abraham returned to his place.
Didn’t Isaiah see God?
In the year that King Uzziah died I saw the Lord sitting upon a throne, high and lifted up; and the train of his robe filled the temple. Above him stood the seraphim. Each had six wings: with two he covered his face, and with two he covered his feet, and with two he flew. And one called to another and said:
“Holy, holy, holy is the Lord of hosts;
the whole earth is full of his glory!”
And the foundations of the thresholds shook at the voice of him who called, and the house was filled with smoke. And I said: “Woe is me! For I am lost; for I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the Lord of hosts!”
Most of all, didn’t Moses see God? Well, there are apparently conflicting reports of this in Exodus 33:
Thus the Lord used to speak to Moses face to face, as a man speaks to his friend.
Moses said, “Please show me your glory.” And he [the Lord] said, “I will make all my goodness pass before you and will proclaim before you my name ‘The Lord’. And I will be gracious to whom I will be gracious, and will show mercy on whom I will show mercy. But,” he said, “you cannot see my face, for man shall not see me and live.”
Thankfully, the rest of John 1:18 puts all of this in context:
No one has ever seen God; the only God, who is at the Father's side, he has made him known.
No-one has ever seen God the Father, but some have seen God the Son, and he has made the Father known.
For God, who said, “Let light shine out of darkness”, has shone in our hearts to give the light of the knowledge of the glory of God in the face of Jesus Christ.
2 Corinthians 4:6
(Another thing I learned at the Keswick convention)
Look, even I think that this ↑ title sounds pretentious. I was going to call this post ‘the ontological argument as religious experience’, but then I thought that ‘religious’ didn’t quite convey what I was trying to convey. I rejected ‘existential’ for the same reason.
In the opening chapter of their mammoth Philosophical Foundations for a Christian Worldview (IVP), William Lane Craig and J.P. Moreland tell us that
The conventional wisdom says, “You can’t use arguments to bring people to Christ.” This has not been our experience.
It has not been my experience, either. Rational arguments played a significant role in my coming to faith, in particular the moral argument and the argument for the resurrection of Jesus. There is, however, one form of theistic argument featuring in that volume that I doubt has ever been used to bring someone to Christ: the ontological argument. Craig and Moreland define it (p 496) as follows:
The common thread in ontological arguments is that they try to deduce the existence of God from the very concept of God, together with certain other necessary truths.
However, I do believe that this argument can play a surprising role in the Christian life. In his journals, Søren Kierkegaard had the following to say about Anselm’s ontological argument for the existence of God:
Anselm prays to God in all sincerity that he may succeed in proving God's existence. He thinks he has succeeded and throws himself down to thank God: curious, he does not notice that this prayer and thanksgiving are infinitely more proof of God's existence than the proof.
If you didn’t know Kierkegaard better, you would suspect that his point may have simply been that Anselm’s argument is absolutely no good at all. It is entirely possible that Kierkegaard did think that, but I believe that that is not the only thing going on here. Nor do I think that Kierkegaard was rejecting rational argumentation in toto and advocating irrational fideism, as the caricature of him would have it. I think that there is a line of thought here that pulls Anselm’s argumentation and his prayers closer to each other than is initially apparent.
In order to try to get at this line of thought, let’s move from Kierkegaard’s journal to my own. A few weeks after I became a Christian, I made an entry in there that reads as follows:
The fact that this is such an important question means that the answer can't be meaningless. The very power to reason is based on this fact.
Looking at it now, this seems like a mangled attempt at ontological argumentation. But when I wrote it, it was not an attempt to prove that God exists; rather, it was an attempt to articulate the content of a religious experience in which I was certain of the existence of God. What was unusual (perhaps) is that the content of that experience was itself more like an argument than a felt presence – I didn’t see lights, hear voices or feel ecstatic; I was simply locked in to a certain kind of thinking.
Reading my diary entry, some readers might have thought of a particular xkcd comic:
I would say (from my own experience) that ‘getting existential’ is just a shade off of the religious experience I described above. I had ‘gotten existential’ before, and the quality of the two experiences was actually very similar. There was something vertiginous about them both. That is why, as I made clear in the very first post on this blog, I think that the instinct to ‘super soak’ people who ‘get existential’ is diabolical. In The Screwtape Letters, C.S. Lewis has a senior demon advise a more junior tempter that
By the very act of arguing, you awake the patient’s reason; and once it is awake, who can foresee the result? Even if a particular train of thought can be twisted so as to end in our favour, you will find that you have been strengthening in your patient the fatal habit of attending to universal issues and withdrawing his attention from the stream of immediate sense experiences. Your business is to fix his attention on the stream. Teach him to call it ‘real life’ and don’t let him ask what he means by ‘real’.
I suspect that there is a sound ontological argument out there somewhere, although I doubt that it can be recovered from my journal, and making the case for one has not been the point of this post. Rather, what I have tried to do is explain an attraction that ontological arguments hold for me apart from their apologetic potential or logical intricacy. It was prompted by a recent Doug Benscoter post in which he attempted to turn some of his own youthful thoughts into a valid ontological argument.