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 identified valid and invalid forms of argument and 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.
Melvyn Bragg discusses logic and its history in this BBC episode of In Our Time with guests A.C. Grayling, Professor of Philosophy at Birkbeck, University of London, Peter Millican, Gilbert Ryle Fellow in Philosophy at Hertford College at the University of Oxford, and Rosanna Keefe, Senior Lecturer in Philosophy at the University of Sheffield.