The Oxford Handbook of Philosophy of Mathematics and Logic

This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the bookbegins with a historical section, consisting of a chapter on the modern period, Kant and hisintellectual predecessors, a chapter on later empiricism, including Mill and logicalpositivism, and a chapter on Wittgenstein. The next section of the volume consists of sevenchapters on the views that dominated the philosophy and foundations of mathematics in theearly decades of the 20th century: logicism, formalism, and intuitionism. They approachtheir subjects from a variety of historical and philosophical perspectives. The next sectionof the volume deals with views that dominated in the later twentieth century and beyond: Quine and indispensability, naturalism, nominalism, and structuralism. The next chapter inthe volume is a detailed and sympathetic treatment of a predicative approach to both thephilosophy and the foundations of mathematics, which is followed by an extensivetreatment of the application of mathematics to the sciences. The last six chapters focus onlogical matters: two chapters are devoted to the central notion of logical consequence, oneon model theory and the other on proof theory; two chapters deal with the so-calledparadoxes of relevance, one pro and one contra; and the final two chapters concern second-order logic (or higher-order logic), again one pro and one contra.