A simplified account of validity and implication for quantificational logic

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Abstract
As those of us who instruct him are well aware, customary accounts of validity and implication for quantificational logic often bewilder the novice. For his benefit, I present here an account of validity, due (in effect) to the late E. W. Beth, and two accounts of implication, one my own, the other Jaakko Hintikka's, which add up to what the better textbooks say, but, making no mention whatever of domains, say it far more simply.

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