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.”?
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.
In Bayesian reasoning,
and
are valid.
and
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.
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.