Steve_Rayhawk comments on Guilt by Association - Less Wrong

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

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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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