The requirement of proof-theoretic harmony has played a pivotal role in a number of debates in the philosophy of logic. Different authors have attempted to precisify the notion in different ways. Among these, three proposals have been prominent in the literature: harmony–as–conservative extension, harmony–as–leveling procedure, and Tennant’s harmony–as–deductive equilibrium. In this paper I propose to clarify the logical relationships between these accounts. In particular, I demonstrate that what I call the equivalence conjecture—that these three notions essentially come to the same thing—is erroneous.
"On the Equivalence Conjecture for Proof-Theoretic Harmony." Notre Dame J. Formal Logic 54 (1) 79 - 86, 2013. https://doi.org/10.1215/00294527-1731398