Daniel_Burfoot comments on Open Thread, Sept 5. - Sept 11. 2016 - Less Wrong

6 Post author: Elo 05 September 2016 12:59AM

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Comment author: Daniel_Burfoot 06 September 2016 06:51:02PM *  1 point [-]

Can anyone give a steelman version of Chomsky's anti-statistics colorless green ideas sleep furiously argument? The more I think about it, the more absurd it seems.

Here's my take on Chomsky's argument:

  • The phrase "colorless green ideas sleep furiously" is extremely improbable from a statistical perspective.
  • However, it is also entirely consistent with the rules of grammar.
  • Therefore, one cannot use statistical reasoning to draw conclusions about the rules of grammar.

Naively, this seems plausible enough. But consider the following mirror-image argument, about physics:

  • Consider the event "a sword fell out of the sky" (not the sentence, the physical event).
  • This event is extremely improbable from a statistical perspective.
  • However, it is entirely consistent with the laws of physics; if a sword were dropped out of a hot air balloon, if would obviously fall to the ground.
  • Therefore, one cannot use statistical reasoning to draw conclusions about the laws of physics.

The mirror image argument seems patently absurd, but it follows the exact same line of reasoning.

Comment author: ChristianKl 06 September 2016 07:39:02PM *  1 point [-]

The problem is that "the laws of physics" is a phrase that means two different things:
(1) Rules like Newton's laws.
(2) What the world does.

Rules of grammar are formal rules like (1) and not about (2). You can use statistics to see whether (1) matches (2) but there's a lot that can be said with math about formal rules. You can use math to show that two kind of theories are equivalent or that they are different.

There's a lot about the rules of mathematics that you can't learn via statistics. You can't prove NP=/=P by looking at a bunch of examples and using statistics.

Chomsky invented the Chomsky hierachy and from what I remember from my classes at university there's no statistics involved in that way of thinking about grammar. It's still a model of grammar important enough to be taught in computer science classes.

Comment author: Douglas_Knight 09 September 2016 06:43:29AM 0 points [-]

The passage seems silly. It is easy to make statistical models that contradict Chomsky's claim. But I think he means something else, that whether a sentence is grammatical, while not a binary, admits sharply discrete levels. The concept of grammar cuts human understanding of language at its joint and statistical understanding is largely on the other side. At least, that is the claim; I think introspection is difficult and usually turns statistical understanding into an illusion of discreteness.

Comment author: Lumifer 06 September 2016 08:31:10PM 0 points [-]

Therefore, one cannot use statistical reasoning to draw conclusions about the rules of grammar.

Is this, actually, the argument Chomsky made? Because looking at Wikipedia, it says

This was used then as a counter-example to the idea that the human speech engine was based upon statistical models

which is a very different thing.

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