Overview

Logic in the broadest sense is the study of the methods and principles used to distinguish correct from incorrect reasoning. Over the centuries many societies have produced thinkers who have been concerned with the study of logic. In the Western intellectual tradition, for example, the formal study of logic was pioneered by the ancient Greek philosopher Aristotle and by various early Stoic philosophers including Zeno of Citium, Cleanthes, and Chrysippus. Inspired by Aristotle’s work, Islamic philosophers (particularly the philosopher Al-Farabi) developed a systematic and through treatment of the relationships between logical theory and language.

The late nineteenth and early twentieth centuries witnessed an explosion of interest and research into logic theory and the theory of symbolism, culminating in the development of various algebraic or symbolic devices for representing, testing, and evaluating the structure of reasoning. These developments in ‘symbolic’ logic, as it has come to be called, have had a profound impact on the computer revolution of the second half of the twentieth century, as computer designers and programmers work at designing the logic systems and programming languages upon which modern microcomputers operate. Logic continues to be of major importance both for its own sake and in terms of its application to computer technology.

Logic is a huge discipline, with many branches, specialties, and variations. There is simply not enough time in the course of a semester to cover everything that logic encompasses. Rather than sample too lightly, what we will do in this class is to focus on five topics in logic: (1) the relationship between arguments in ordinary language and symbolic representations of the logical form of those arguments; (2) Aristotle’s logic; (3) recognizing common forms of fallacious or incorrect reasoning; (4) the use of truth-tables to evaluate the logical structure of reasoning; and (5) mastering a simple method of determining whether an instance of reasoning is correct or incorrect without using truth-tables – a method that will be familiar to you from the study of geometry.  

Why is This a Philosophy Course?

In a way, it is odd that this is a philosophy course. Modern symbolic logic, as you will soon see, has just about as much to do with mathematics as with philosophy. In fact, modern logic is often called ‘mathematical logic’. Unlike other philosophy courses, we will not be concerned too much with arguing about logic itself (we could do this, I suppose – there is a branch of philosophy called ‘the philosophy of logic’ or ‘metalogic’ that concerns itself with various enduring philosophical questions regarding logic).

Rather than talk about philosophical issues in logic, we will concern ourselves exclusively with learning the techniques and principles of modern symbolic logic. In that way, learning about logic in this class will feel more like, say, learning about algebra or geometry. In short, our business will be more practical than philosophical.