Tuesday, 8 April 2014

Language isn’t like that

At Language Log, Geoffrey Pullum has drawn attention to another argument for why Google Translate, though often very effective, tell us very little about how language actually works.  GT operates based on statistical distributions of word sequences, primarily three-word sequences (so-called ‘trigrams’).  But this is not a good model for how human knowledge of language works.

I have noticed myself that it is extraordinarily easy to take, say, the emails you received this morning, and verify for particular three-word sequences that they seem never to have occurred before in the history of the web. […]

[I]t really is true that the probability for most grammatical sequences of words actually having turned up on the web really is approximately zero, so grammaticality cannot possibly be reduced to probability of having actually occurred. Not even for word trigrams is that a reasonable equation.

As I said in a previous post,

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?

Pullum goes on to make the point that this doesn’t mean that n-gram data can’t help linguists: corpora are sources of data.  But we shouldn’t confuse the data with the theory.

Thursday, 3 April 2014

Farewell Ugley Vicar

I’m really sad to learn that Rev. John Richardson, aka the ‘Ugley Vicar’, died on 31 March.  I didn’t know him personally but I found his blog to be informative and sometimes challenging, and his witness as a Bible-believing Christian minister within the Church of England (and within what used to be my Diocese) to be thoughtful and encouraging.  He will be missed.

David Banting at Anglican Mainstream has written a more detailed obituary than I’ve been able to give.

Jesus said to her, “I am the resurrection and the life. Whoever believes in me, though he die, yet shall he live, and everyone who lives and believes in me shall never die. Do you believe this?” (John 11:25-26)

John Richardson certainly did.

Friday, 7 February 2014

Film review: The Armstrong Lie

As is well known by now, the way that Lance Armstrong managed to ‘win’ his 7 Tour de France titles was with the aid of a huge amount of doping.  As is also fairly well known, he got away with it for so long because of a combination of an overriding will to believe on the part of fans, journalists and sponsors with some pretty serious bullying and intimidatory tactics on the part of Armstrong himself and his entourage.

In 2009, though, Armstrong still had all his TdF titles, and his legend was still just about intact.  He had decided to come out of retirement and attempt to win the Tour again, and filmmaker Alex Gibney was invited to make a documentary of that season and the Tour in particular, with the working title ‘The Road Back’.  That documentary was all but finished when Armstrong’s downfall scotched plans to release it.  So what they’ve done is re-used a lot of the footage from it, cut together with more recent interviews with Armstrong himself and other talking heads from the world of cycling.

First I'm going to say what I liked about the film:

  • Some of the behind-the-scenes footage of Armstrong training and racing in 2009, particularly the interactions between him, Johan Bruyneel and Alberto Contador.  Even though we now know that Contador was (is?) also a doper, you can't help but like him for metaphorically sticking two fingers up to the pair of them and riding off they way he does.
  • Betsy Andreu.  She is the wife of one of Armstrong's former teammates, who ends up going public with evidence she has against him and getting a huge amount of grief as a result (including being sued, as Mark mentions).  She is one of the talking heads in the documentary.  There is a moment where Gibney says that her husband Frankie "decided to stop doping" – he neglects to mention that it was basically because Betsty issued him with an ultimatum (or so I heard David Walsh say in an interview).
  • The interviews with Michele Ferrari, the doping doctor par excellence.  This is another scumbag that you can't help but like a bit because he's so charming!
  • The footage of a 16-year-old Armstrong being interviewed after a triathlon and saying "I just lurve beatin' people, man!" (Incidentally, wasn't it interesting how his accent became less and less Texan over the years?)

But there are serious limitations.  Firstly, if you’re a road cycling fan, or for some other reason have been following the Lance Armstrong blowup over the last three years since Floyd Landis spilled the beans, then this film won’t really add anything to your understanding.  Also, if you watched the 2009 Tour de France the first time around, you won’t appreciate so much of the film being dedicated to Gibney telling us in voiceover about how the race panned out on the road.

Secondly, I agree with Deborah Ross that Gibney goes far too easy on Armstrong, even in the post-confession stage.  My brother, who is not particularly a cycling fan, liked the film a lot more than me, saying that it was a ‘classic Greek tragedy’ and wondering aloud whether or not Lance Armstrong was clean throughout his 2009 comeback (as he still maintains).  For me, Armstrong does not have the redeeming qualities of a tragic hero, and so if he comes across like that in the film it can only mean that the filmmaker has been played.  (And no, I don’t for one second believe that he was clean in 2009!)

In a segment of the post-confession interview with which the film opens, Armstrong says ‘we haven’t heard [the full story] yet’.  The thing is, after watching this film, we still haven’t, not by a long shot.

Monday, 25 November 2013

Monday, 11 November 2013

More on mindlessness

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.

Thursday, 19 September 2013

Maydole on Anselm’s argument

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.

  1. The definite description ‘that than which it is not conceivable for something to be greater’ is understood. (Premise)
  2. ‘That than which it is not conceivable for something to be greater’ refers to that than which it is not conceivable for something to be greater. (Premise)
  3. If a definite description is understood, then the concept of what it refers to has existence-in-the-understanding. (Premise)
  4. Therefore, the concept of that than which it is not conceivable for something to be greater has existence-in-the-understanding. (From 1, 2, 3)
  5. If something lacks a great-making property that it would be conceivable for it to have, then it is conceivable that something is greater than it. (Premise)
  6. Existence-in-reality is a great-making property. (Premise)
  7. Therefore, if something that could conceivably have existence-in-reality lacks existence-in-reality, then it is conceivable that something is greater than it. (From 5, 6)
  8. If the concept of something has existence-in-the-understanding, then it is conceivable that that thing has existence-in-reality. (Premise)
  9. Therefore, it is conceivable that that than which it is not conceivable for something to be greater has existence-in-reality. (From 4, 8)
  10. Therefore, if that than which it is not conceivable for something to be greater does not have existence-in-reality, then it is conceivable that something is greater than that than which it is not conceivable for something to be greater. (From 7, 9)
  11. It is not conceivable that there is something greater than that than which it is not conceivable for something to be greater. (Premise)
  12. Therefore, that than which it is not conceivable for something to be greater has existence-in-reality. (From 10, 11)

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:

  1. It is not conceivable that there is something greater than the island than which it is not conceivable for some island to be greater. (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.

  1. It is not conceivable that there is some island greater than the island than which it is not conceivable for some island to be greater. (Premise)

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.

  1. If some island lacks a great-making property that it would be conceivable for it to have, then it is conceivable that some island is greater than it. (Premise)

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).

Friday, 13 September 2013

The mindlessness of Google Translate

‘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?

'The boy ate the apple'
Nul points

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?