CuSithBell comments on Undiscriminating Skepticism - Less Wrong

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

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Comment author: wedrifid 22 January 2012 09:11:37AM *  1 point [-]
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.

Not only is it valid it is trivially so. It does not even rely on the possibility of there being valid inductive arguments. I made it the most simple of deductions from supplied premises.

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

Your problem here seems to be that you object to deducing a conclusion of 'likely to be' from a premise of 'likely to be'. By very nature of uncertain information things that are merely likely do not always occur and yet this does not make reasoning about likely things invalid so long as uncertainty is preserved correctly. (The premise could possibly be neatened up such that it includes a perfect technical explanation with ceritus paribus clauses, etc but the meaning seems to be clear as it stands.)

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

If the argument was in the form of a deduction when only an induction is possible from the information then the appeal to authority is invalid. If the argument is a carefully presented inductive claim then it most certainly can be valid.

Not all arguments are deductions. Not all arguments that are not deductions are invalid.

Comment author: CuSithBell 22 January 2012 05:26:56PM *  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.

Not only is it valid it is trivially so.

Jayson_Virissimo is talking about logical validity. The argument is not logically valid, because it is possible for "Z is likely to be correct" to be false, even if the other statements are true (for instance, add the premise "Z is incorrect"). Induction is not (in general) logically valid. It's valid in other senses, but not that one.

Comment author: wedrifid 22 January 2012 06:34:15PM *  0 points [-]

Jayson_Virissimo is talking about logical validity.

Yes, we both are. We have gone as far as to accept a shared definition of logical validity and trace the dispute from there.

The argument is not logically valid, because it is possible for "Z is likely to be correct" to be false, even if the other statements are true (for instance, add the premise "Z is incorrect").

This is simply false. The following premise:

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

... becomes invalid the moment there is in fact a "thing said <etc, etc>" that is not likely to be correct. That's why I put it there! It is an instance of the class of premise "ALL G ARE W" and so just like all other premises in that class it is false if there is a G that is NOT W. it just so happens that 'likelyhood' is the subject matter here.

The above serves to make the premise in question rather brittle. While it does means that the whole argument can be treated as deductive reasoning (about the subject of likelyhoods) it is also means that there are very few worlds for which that premise is true and meaningful.

Comment author: CuSithBell 22 January 2012 08:11:53PM 0 points [-]

I interpreted your premise as: (Things said about Y by a person who has a reputation for being an expert on Y) are likely to be (correct.) as opposed to (Things said about Y by a person who has a reputation for being an expert on Y) are (likely to be correct.)

If, as you seem to be agreeing, a thing cannot be "likely to be correct" and "incorrect" (as known by the same reasoner), then the premise reduces to "Things said about Y by a person who has a reputation for being an expert on Y are correct".

Is this really what you intended?

Comment author: wedrifid 22 January 2012 09:25:30PM -1 points [-]

I interpreted your premise as: (Things said about Y by a person who has a reputation for being an expert on Y) are likely to be (correct.) as opposed to (Things said about Y by a person who has a reputation for being an expert on Y) are (likely to be correct.)

The second was the intended meaning.

If, as you seem to be agreeing, a thing cannot be "likely to be correct" and "incorrect" (as known by the same reasoner), then the premise reduces to "Things said about Y by a person who has a reputation for being an expert on Y are correct".

Given the 'as known by the same reasoner' clause wouldn't that imply that it is '<...> cannot be known to be incorrect'? Either way it is clear that the encapsulation of the probabilistic parts is woefully inadequate here.

Is this really what you intended?

No, but it does seem to be the implication.