Mathematical logic is the study of logic as a mathematical theory. Following the usual procedure of applied mathematics, we construct a mathematical model of the system to be studied, and then conduct what is essentially a pure mathematical investigation of the properties of our model. Since this book is intended for mathematicians, the system we propose to study is not general logic but the logic used in mathematics. By this restriction, we achieve considerable simplification, because we do not have to worry about precise meanings of words—in mathematics, words have precisely defined meanings. Furthermore, we are free of reasoning based on things such as emotive argument, which must be accounted for in any theory of general logic. Finally, the nature of the real world need not concern us, since the world we shall study is the purely conceptual one of pure mathematics.
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