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

Rumfitt's book is dense and rich. There is no doubt that it makes an important contribution to the debate between intuitionistic and classical logicians. ... Although the book defends classical logic, Rumfitt clearly takes the challenges posed by intuitionists seriously; this makes for a very engaging read. The Boundary Stones of Thought has much to offer to anyone interested in the philosophy of logic or philosophical logic, such as a sophisticated methodology for advancing a debate between competing logics, a novel account of the nature of logic, and several promising semantic theories. It is to be hoped that it finds a wide readership among philosophers and logicians, within but also beyond the debate about intuitionistic logic. (Peter Fritz, Mind)

The book is careful, insightful, and imaginative. I, for one, learned much from it. (Graham Priest, Journal of Philosophy)

The Boundary Stones of Thought exemplifies the breadth and depth involved in contemporary debates in the philosophy of logic. It is therefore a must read for those interested in this area. (John Wigglesworth, Philosophical Quarterly)

The Boundary Stones of Thought seeks to defend classical logic from a number of attacks of a broadly anti-realist character. Ian Rumfitt is sympathetic to many of the premisses underlying these attacks. Indeed, he regards some of them as effective challenges to certain principles of classical semantics, notably the Principle of Bivalence. He 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: Rumfitt identifies the particular features that mark out logical consequence from other consequence relations, and he advances a new argument for the ancient thesis that there is a modal element in the notion of logical consequence. He develops a theory of that modal element in terms of perhaps incomplete possibilities, rather than fully determinate possible worlds. Some prima facie powerful 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, although distinct, are often run together or confused.

The analysis yields, as by-products, semantic theories for a number of problematical areas of discourse. These areas include our talk about sub-atomic particles, about the infinite, about infinitesimals, about sets, and vague discourse. Rumfitt concludes by defending his 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.