Topics Logic

Question Hello, I would like to ask a kind of multiple angled question I have noticed a "lack of" while studying logic. Is "the process of elimination" a sound "Rule of Inference"? (Perhaps, we've all used this "process of elimination" in taking a multiple choice test.) I have read two books on Logic: one by Irving M.Copi & Carl Cohen as well as The Logic Book by Merrie Bergmann, James Moor, Jack Nelson. I have not seen a single logic text nor a logic website where "the process of elimination" appears as a inference rule. Why is this not included as a rule? Is it not considered Deductive? Does it go by another name? What is the deal? Thank you for considering this question in advance.

Accepted:
December 20, 2011

Comments

It goes by another name, sometimes "argument by cases" or "argument by dilemma" or "the disjunctive syllogism". The basic rule is:

A ∨ B
~A
∴ B

Obviously, this can be extended to any number of disjuncts, e,g.:

A ∨ B ∨ C ∨ D
~A ∧ ~B ∧ ~C
∴ D

So the disjuncts represent the possibilities you have before you, and the negations represent your ruling out all but one of them.

There are quantificational versions as well, e.g.:

∀x(Fx → x = a ∨ x = b ∨ x = c)
~Fa ∧ ~Fb
∴ Fc

This would normally be derived from one of the propositional versions.