Inferring, splicing, and the Stoic analysis of argument
Peter Milne · Stirling Online Research Repository (University of Stirling) · 2012
RECENT YEARS, A NUMBER OF AUTHORS, including the dedicatee of this volume, have advocated the employment of general elimination rules in the presentation of harmonious natural deduction rules for logical constants.1 Motivated by different concerns, in (Milne 2008, Milne 2010) I have given natural deduction formulations of classical propositional and first-order logics employing what in (Milne 2012b) I call general introduction rules; there I show how general introduction and general elimination rules are in harmony and satisfy a certain inversion principle.Here I want to show how general introduction and general elimination rules narrow, perhaps even close, the gap between Gentzen's two ways of presenting logic: natural deduction and sequent calculus.I shall also describe a surprisingly close connection with the earliest account of propositional logic that we know of, that of the Stoic logicians.We are also led to ask after the significance of Gentzen's Hauptsatz.Until the final section, I shall consider only propositional logic.