Steve_Rayhawk comments on Guilt by Association - Less Wrong

1 Post author: Annoyance 24 June 2009 05:29PM

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Comment author: thomblake 24 June 2009 06:06:00PM 7 points [-]

"If P, then Q. P. Therefore, Not-Q." is just as basic and elemental an error as "If P, then Q. Q. Therefore, P." is.

I'm not sure I'd grant that. The second can be sneaky, in that you can encounter countless arguments of that form with true premises and a true conclusion. In the first example, on the other hand, true premises guarantee that the conclusion is false.

I'm not sure if there's a word for the latter category, but there probably should be. "The conjunction of the premises is inconsistent with the conclusion" is not nearly as awesome as, say, "Antivalid"

Comment author: Steve_Rayhawk 25 June 2009 02:04:51AM *  4 points [-]

In Bayesian reasoning,

The probability of Q given P is 1. The probability of Q given Not-P is less than 1. The prior probability of P is not 0 and not 1. Q. Therefore, the posterior probability of P is higher than the prior probability of P.

and

The probability of Q given P is greater than 0. The probability of Q given Not-P is 0. The prior probability of P is not 0 and not 1. Not-Q. Therefore, the posterior probability of P is lower than the prior probability of P.

are valid.

The probability of Q given P is 1. The probability of Q given Not-P is less than 1. The prior probability of P is not 0 and not 1. Q. Therefore, the posterior probability of P is lower than the prior probability of P.

and

The probability of Q given P is greater than 0. The probability of Q given Not-P is 0. The prior probability of P is not 0 and not 1. Not-Q. Therefore, the posterior probability of P is higher than the prior probability of P.

are invalid and antivalid.

Is "If P, then Q. P. Therefore, Not-Q." also just as basic and elemental an error as "P is Fermat's Last Theorem. Therefore, P is false."?

Related: Absence of Evidence is Evidence of Absence or Absence of Evidence Is Too Evidence of Absence (Usually) and Conservation of Expected Evidence.

Comment author: Annoyance 25 June 2009 01:55:52PM 1 point [-]

Is "If P, then Q. P. Therefore, Not-Q." also just as basic and elemental an error as "P is Fermat's Last Theorem. Therefore, P is false."?

No, it's far more basic. "Fermat's Last Theorem" is a very complicated concept which is only being referenced here. The full logical description of the concept - which is what's necessary to evaluate the argument - would be much longer.

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