The Grounds of Logic: Response to Sascha Bloch, Martin Pleitz, Markus Pohlman, and Jakob Wrobel

Abstract

“The Justification of Deduction” was written more than forty years ago; so probably I should begin by saying that it wasn’t I who wrote this, but my younger sister—the same young lady who wrote Deviant Logic. Now, however, since this younger sister is no longer around, it falls to me to say a few words on her behalf.Neither my little sister nor I ever for a moment imagined that modus morons was a good rule of inference—of course it isn’t; that’s why it’s called modus morons! But Bloch et al. have done a nice job of articulating some ways in which it is, in their phrase, a “rogue” rule. They call primarily on the notion of “harmony,” a term they attribute to Michael Dummett, and describe as going back to an idea of Gerhard Gentzen’s: that the elimination rule for a connective is (or should be) a mere “consequence” of the introduction rule for the same connective. Using Dag Prawitz’s concept of reducibility, Neil Tennant’s “inferential truth-theory,” and considerations about the truth-table for “→,” Bloch et al. show that the introduction rule and the elimination rule for modus morons are, to put it mildly, not in harmony. No wonder, then that (like Arthur Prior’s rogue connective, “tonk”) modus morons would wreak havoc in any logical system. My sister and I thank Bloch and Co. for this careful work.