Introduction to the Theory of Logic

Introduction to the Theory of Logic

Introduction to the Theory of Logic

Introduction to the Theory of Logic

Excerpt

Formal logic courses are widely taught in philosophy departments, often as compulsory components of undergraduate and graduate programs. This is as it should be, since the issues that formal logic deals with are among the central concerns of philosophy. Nevertheless, as students soon realize, sometimes to their dismay, formal logic is in many respects closer to mathematics than to other areas of philosophy.

The historical roots of this phenomenon lie in the second half of the nineteenth century, when logic underwent a revolution based to a large extent on the application of mathematical methods to the study of deductive reasoning. The formal languages and deductive systems studied in our introductory formal logic courses are the main achievements of the first stage of this revolution. Their basic features were presented by Gottlob Frege in his Begriffsschrift of 1879.

In the second decade of the twentieth century, contemporary logic entered a second phase, in which these formal systems ceased to be a mere tool for the study of deductive reasoning, and their scope and limits became the subject matter of logical research. This field is often known as metalogic. The main results in metalogic are of the greatest philosophical importance, and they are covered in more advanced courses in formal logic taught in many philosophy departments. Unfortunately, many of the best available textbooks at this level are written by mathematicians to be used in logic courses in mathematics departments, and presuppose a . . .

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