The Boundary Stones of Thought: An Essay in the Philosophy of Logic

New book by Professor Ian Rumfitt published by Oxford University Press.

Abstract

This book defends classical logic from a number of attacks of a broadly anti-realist character. The book is sympathetic to many of the premisses underlying these attacks. Indeed, it regards some of them as effective challenges to certain principles of classical semantics, notably the Principle of Bivalence. It argues, though, that they are ineffective against classical logic itself. The book starts by considering the general problem of how conflicts over logical laws may be rationally discussed and adjudicated. This leads to a consideration of the nature of logic: the book identifies the particular features that mark out logical consequence from other consequence relations, and it advances a new argument for the ancient thesis that there is a modal element in the notion of logical consequence. It develops a theory of that modal element in terms of perhaps incomplete possibilities, rather than fully determinate possible worlds. Several arguments against the validity of certain classical logical laws are then analysed in the light of this account of logic. Throughout, care is taken to separate lines of anti-classical argument that are often run together or confused. The analysis yields semantic theories for discourse about subatomic particles, the infinite, infinitesimals, and sets; it also presents a distinctive treatment of vague discourse. The book concludes by defending its stance of accepting classical logic while rejecting Bivalence against Aristotle’s argument that a classical logician is committed to Bivalence. The ultimate aim is to liberate classical logic from the dead hand of classical semantics.

Further information: Oxford Scholarship online