Barriers to Entailment

A barrier to entailment exists if you can't get conclusions of a certain kind from premises of another. One of the most famous barriers in philosophy is Hume's Law, which says that you can't get normative conclusions from descriptive premises, or in slogan form: you can't get an ought from an is. This barrier is highly controversial, and many famous counterexamples were proposed in the last century. But there are other barriers which function almost as philosophical platitudes: no Universal conclusions from Particular premises, no Future conclusions from premises about the Past, and no claims that attribute Necessity from premises that merely tell us how things happen to be in the Actual world. Barriers to Entailment proposes a unified logical account of five barriers that have played important roles in philosophy, in the process showing how to diagnose proposed counterexamples and arguing that the case for Hume's Law is as strong as that for the platitudinous barriers.The first two parts of the book employ techniques from formal logic, but present them in an accessible way, suitable for any reader with some background in first-order model theory (of the kind that might be taught in a first class in logic). Gillian Russell introduces tense, modal, indexical, and deontic formal logics, but always avoids unneeded complexity. Each barrier is connected to broader philosophical topics: universality, time, necessity, context-sensitivity, and normativity. Russell brings out under-recognised connections between the domains and lays the groundwork for further work at the intersections.The last part of the book transposes the formal work to informal barrier theses in the philosophy of language, in the process doing new work on the concept of logical consequence, and providing new responses to proposed informal counterexamples to Hume's Law which employ hard-to-formalise tools from natural language, such as speech acts and thick normative expressions.

Each of these various barrier issues has had its own distinctive flavour, and its own associations and repercussions in the history of philosophy. This makes Barriers, quite aside from its intrinsic interest and its many expository virtues, the perfect way of illustrating to a student whose penchant may be-not just for ethics, as in the Is/Ought case-but equally for metaphysics, epistemology or the philosophy of mind, how useful a formal approach to the conceptual fundamentals of the favoured territory can be. This makes it much more valuable,motivationally, than any dry, purely technical introduction to contemporary logical work could ever be. But students aside, any reader with logical interests will find Barriers to be bristling with imaginative curiosity, resourcefully pursued. Lloyd Humberstone, Australasian Journal of Logic
This book's proof of the Strong General Barrier Theorem is a landmark achievement in twenty-first century philosophy. Not since Ludwig Wittgenstein's Tractatus (1921) has such an important contribution been made to philosophical logic. Russell has shown the limits of deductive inference, which means, the limits to the very expression of thought. The proof she presents is integral to understanding how and why logical inferences can or cannot be legitimately made based on the properties of the premises involved. If ever there was a litmus test for philosophers to gauge the validity of their arguments, this ought to be it. My only hope is that this work does not go unnoticed. Christopher John Searle, Philosophy Now
Her proposed account has evolved over the years. This book is the culmination. It achieves a notable degree of success. Even those who quarrel with aspects of her approach will findformal foundations to build on, and an extensive database of formal and informal examples. The book is as reader friendly as it reasonably could be, given the trickiness of the relevant issues. Russell explains the technicalities accessibly, taking very little for granted. Anyone who wants to get up to speed on these problems could not do better than read it.'She [Russell] has made an impressive contribution to our understanding of this tricky area. Timothy Williamson, Journal of Philosophy

Since gaining her PhD in philosophy at Princeton University in 2004, Gillian Russell has been a postdoc at the University of Alberta, Assistant and Associate Professor at Washington University in St Louis, Professor and Alumni Distinguished Professor at the UNC Chapel Hill, and a Professorial Fellow at the University of St Andrews. She has recently moved to Australia, where she works for the Dianoia Research Institute in Analytic Philosophy at Australia Catholic University in Melbourne. Her work focuses on the philosophy of language and logic, and her previous books include Truth in Virtue of Meaning: A Defence of the Analytic/synthetic Distinction.

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