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4 Logic and Mathematics

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Chapter Summary

This chapter presents outline of the history of modern logic from George Boole. A unified idea of logic entails that every aspect of the domain of the theory could be clarified and justified by the tools and laws of the theory. Different philosophies of logic rose from this idea: logicism, formalism and intuitionism. The chapter briefly explores the situation of the logical currents before and after the Second World War. Strucuturalism focuses on structures that are common to a system of objects. Willard van Orman Quine is the main proponent of naturalism. Penelope Maddy is one of the main proponents of a new naturalist view in the philosophy of mathematics. The most influential theory of truth is the "semantic" theory, following the great Polish logician Alfred Tarski. Tarski's semantic theory of truth is at the root of model theory, which is one of the most important branches of contemporary logic.

Keywords: Alfred Tarski; formalism; George Boole; intuitionism; logicism; Penelope Maddy; Second World War; semantic theory; Willard van Orman Quine



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