The Concept of Logical Consequence

The aim of this book is to correct a common misunderstanding of a technique of mathematical logic.

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The intuitive concept of consequence, the notion that one sentence follows logically from another, has driven the study of logic for more than two thousand years. But logic has moved forward dramatically in the past century - largely as a result of bringing mathematics to bear on the field. The infusion of mathematically precise definitions and techniques has turned a field dominated by homely admonitions into one characterized by illuminating theorems. The aim of this book is to correct a common misunderstanding of one of the most widely used techniques of mathematical logic. Central to the received view is Tarski's model-theoretic analysis of logical consequence, which Etchemendy argues is fundamentally mistaken. Save indirectly, by those who question classical principles, this standard analysis has gone unchallenged for half a century, with the result that it has come to seem a piece of common knowledge. Etchemendy's critique will shatter the complacency.