Précis of The Boundary Stones of Thought - Rumfitt, I (Springer Verlag, 2018)
If pressed, I could sum up The Boundary Stones of Thought in six words: classical logic good; classical semantics bad. However, somewhat less telegraphically… The book aims to advance rational debate between adherents of rival logics of conjunction, disjunction, and negation. For the most part, the rivalry I focus on is classicists versus intuitionists (although classicists clash with quantum logicians in §6.6). Debates over basic logical laws tend to fall prey to a vitiating circularity: in giving metalogical arguments for the soundness of their preferred system, adherents appeal to rules which their rivals do not accept. I aim to avoid this by finding semantic theories which are stable in the sense of delivering the same verdicts as to the validity of arguments even after switching from one set of metalogical rules to its rival. (Clearly, a stable theory cannot be homophonic.) The book interweaves assessments of various candidate semantic theories with analyses of particular arguments against classical laws, especially Excluded Middle and Double Negation Elimination. Even when those arguments cast serious doubt upon the Principle of Bivalence, I contend, they are ineffective against classical logic per se.