Lumifer 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: 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.