Would it be accurate, then, to say that any valid use of “by definition” can be replaced by “a fortiori”?
As in, “Socrates is a [mortal, featherless, biped]. Therefore a fortiori Socrates is mortal.” is valid (though one might dispute the premise). But “Socrates is a [featherless, biped]. Therefore a fortiori Socrates is mortal.” is plainly obviously nonsense, even to people who think they can argue “by definition!”. The remaining problem, of course, being that not everyone accepts that a fortiori deserves the certainty that they have been claiming for by definition!.
(In classical logic, if A∧B, then a fortiori A. In Bayescraft, P(A) >= P(A∧B) a fortiori)
Would it be accurate, then, to say that any valid use of “by definition” can be replaced by “a fortiori”?
As in, “Socrates is a [mortal, featherless, biped]. Therefore a fortiori Socrates is mortal.” is valid (though one might dispute the premise). But “Socrates is a [featherless, biped]. Therefore a fortiori Socrates is mortal.” is plainly obviously nonsense, even to people who think they can argue “by definition!”. The remaining problem, of course, being that not everyone accepts that a fortiori deserves the certainty that they have been claiming for by definition!.
(In classical logic, if A∧B, then a fortiori A. In Bayescraft, P(A) >= P(A∧B) a fortiori)