nshepperd comments on Undiscriminating Skepticism - Less Wrong

97 Post author: Eliezer_Yudkowsky 14 March 2010 11:23PM

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Comment author: Jayson_Virissimo 22 January 2012 08:21:26AM *  0 points [-]

The following is an example of a valid argument form:

  • Person X has reputation for being an expert on Y.
  • Things said about Y by a person who has a reputation for being an expert on Y are likely to be correct.
  • Person X said Z about Y.
  • Z is likely to be correct.

That argument is not valid. Valid arguments don't become invalid with the introduction of additional information, but the argument you provided does. For instance, compare these two arguments:

1.)

  • All men are mortal.

  • Socrates is a man.

  • Therefore, Socrates is mortal.

2.)

  • All men are mortal.

  • Socrates is a man.

  • Socrates is in extremely good health for his age.

  • Therefore, Socrates is mortal.

This argument will stay valid no matter how many additional premises we add (provided the premises do not contradict each other). Here is a variation of the argument you provided with additional information:

  • Person X has reputation for being an expert on Y.

  • Things said about Y by a person who has a reputation for being an expert on Y are likely to be correct.

  • Person X said Z about Y.

  • Person X said Z because he was paid $1,000,000 by person A.

  • Person X doesn't really believe Z.

  • Z is likely to be correct.

There is no contradiction between an argument having arbitrarily high inductive strength (like the very best arguments from authority) and still being invalid.

Comment author: nshepperd 22 January 2012 09:17:34AM *  0 points [-]

The following is an example of a valid argument form:

  • Person X has reputation for being an expert on Y.
  • Things said about Y by a person who has a reputation for being an expert on Y are likely to be correct.
  • Person X said Z about Y.
  • Z is likely to be correct.

That argument is not valid. Valid arguments don't become invalid with the introduction of additional information, but the argument you provided does.

What? Of course it's valid (logically). The first three statements are premises and the final statement is the conclusion, which is entailed by the premises. If things said about Y by person X are likely to be correct and person X says Z about Y then Z is likely to be correct. That's a trivial deduction.

The argument is however not necessarily sound, because the premise "Things said about Y by a person who has a reputation for being an expert on Y are likely to be correct" is not universally true, for example if the person is saying stuff which blatantly contradicts other far stronger evidence.

Edit: Okay, enough silliness. Here is a formalised version of the above argument. You could run it through a proof checker, probably.

  1. Person A is an expert on B
  2. forall{X, Y, Z} (Person X is an expert on Y & Person X says Z about Y) => (Z is probably correct)
  3. Person A says C about B
  4. therefore: (Person A is an expert on B & Person A says C about B) [conjunction:1, 3]
  5. therefore: (Person A is an expert on B & Person A says C about B) => (C is probably correct) [instantiation:2, A, B, C]
  6. therefore: (C is probably correct) [modus ponens:4, 5]

This argument is valid. It is not sound, because premise 2 is false. This is basic logic.

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