What Is Logic?

When someone who was attending his school said to him, ‘Convince me of the usefulness of logic,’ he replied: Would you like me to demonstrate it to you?—‘Yes.’ —Then I must employ a demonstrative argument? And when the questioner agreed, he asked: How will you know, then, whether I’m trying to mislead you with a sophism? The man offered no reply. So do you see, continued Epictetus, how you yourself are conceding that logic is necessary, since without it you can’t even tell whether it is necessary or not?

- Epictetus, Discourses, II, 25

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Logic, the study of reasoning and argument, first became a serious area of study in the 4th century BC through the work of Aristotle. He created a formal logical system, based on a type of argument called a syllogism, which remained in use for over two thousand years. In the nineteenth century the German philosopher and mathematician Gottlob Frege revolutionised logic, turning it into a discipline much like mathematics and capable of dealing with expressing and analysing nuanced arguments. His discoveries influenced the greatest mathematicians and philosophers of the twentieth century and considerably aided the development of the electronic computer. Today logic is a subtle system with applications in fields as diverse as mathematics, philosophy, linguistics and artificial intelligence.

Listen to the In Our Time episode on Logic

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Here’s an idea many philosophers and logicians have about the function of logic in our cognitive life, our inquiries and debates. It isn’t a player. Rather, it’s an umpire, a neutral arbitrator between opposing theories, imposing some basic rules on all sides in a dispute. The picture is that logic has no substantive content, for otherwise the correctness of that content could itself be debated, which would impugn the neutrality of logic. One way to develop this idea is by saying that logic supplies no information of its own, because the point of information is to rule out possibilities, whereas logic only rules out inconsistencies, which are not genuine possibilities. On this view, logic in itself is totally uninformative, although it may help us extract and handle non-logical information from other sources.

The idea that logic is uninformative strikes me as deeply mistaken, and I’m going to explain why...

Continue reading Timothy Williamson's article: Logic and Neutrality

Further Reading

For centuries, the study of logic has inspired the idea that its methods might be harnessed in efforts to understand and improve thinking, reasoning, and argument as they occur in real life contexts: in public discussion and debate; in education and intellectual exchange; in interpersonal relations; and in law, medicine and other professions. Informal logic is the attempt to build a logic suited to this purpose. It combines the study of argument, evidence, proof and justification with an instrumental outlook which emphasizes its usefulness in the analysis of real life arguing...

Continue reading the Stanford Encyclopedia of Philosophy article on Informal Logic by Leo Groarke

Related Topics

Mathematics | Metaphysics | Philosophy

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