ec429 comments on Arguing "By Definition" - Less Wrong

44 Post author: Eliezer_Yudkowsky 20 February 2008 11:37PM

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Comment author: ec429 19 September 2011 04:53:46AM 2 points [-]

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)