Multiple-conclusion systems, I submit, are illegitimate from an in- ferentialist point of view. I argue that, given our inferentialist commit- ments, a defence of classical logic based on the adoption of multiple-conclusion sequent calculi is misguided. Such arguments purport to show that the principle of harmony supports broadly intuitionistic revisions of our logic. In the final part I examine the consequences of these results for so-called proof-theoretic arguments. I then advance my own version of harmony, which not only avoids the difficulties that plagued the accounts mentioned, but also boasts additional advantageous features. In particular, I show that Michael Dummett’s and Stephen Read’s theories are unsatisfactory and I present a counterexample to Neil Tennant’s principle of harmony. After giving an analysis of the notion, I review and criticize existing accounts of harmony in the literature.

The second part offers a comprehensive treatment of the notion of harmony. Having spelled out its founding assumptions, I defend inferentialism against the charge that, contrary to its defining motto, the meanings of the logical operators are not fully determined by the rules of inference they obey, but also in part by structural assumptions. I begin by laying out the fundamental meaning-theoretic principles that underpin logical inferentialism: it is use-theoretic it subscribes to the two-aspect theory of meaning as the name makes plain, it is inferentialist in approach and it is committed to a weak form of molecularism. What are the assumptions about meaning that underpin logical inferentialism? What is the correct formulation of the principle of harmony? And finally: What follows from logical inferentialism? Accordingly, the dissertation falls into three parts. My thesis is an attempt to supply answers to what I take to be the three central questions facing inferentialism about the logical constants (which I call logical inferentialism).

Logic without ex falso quod libet