Generally credited as the father of logic, Aristotle (384-322 BC) first devised a systematic criteria for analyzing and evaluating arguments. His logic, classified as syllogistic logic, stated that the fundamental elements of arguments are terms. Arguments could be evaluated as good or bad depending on the arrangement of terms in an argument. In addition to this system, Aristotle catalogued thirteen informal fallacies that he divided into two groups.
After Aristotle's death, Chrysippus (279-206 BC), one of the founders of the Stoic school, developed a logic in which fundamental elements were whole propositions. Chrysippus treated every proposition as either true or false and developed rules for determining the truth or falsity of compound propositions from the truth or falsity of the components. In developing this idea, he laid the foundation for the truth functional interpretation of logical connectives and introduced the notion of natural deduction.
The next major logician did not appear until the Middle Ages. Relatively little creative work was done in logic, and for the most part philosophers confined themselves to writing commentaries on the works of Aristotle and Chrysippus. The noted exception during this time was a physician named Galen (129-199 AD), who developed the theory of the compound categorical syllogism.
Peter Abelard (1079-1142) was the first major logician of the Middle Ages. By refining and reconstructing the logic of Aristotle and Chrysippus, he originated a theory of universals that traced the universal character of general terms to concepts in the mind rather than to "natures" existing outside the mind, as Aristotle had believed. Additionally, he distinguished between the validity of arguments in form and in content. However, he held that only formal validity is the "perfect" or conclusive variety.
After Abelard, the study of logic flourished through the works of numerous philosophers during the Middle Ages. Probably the most noted work was expressed in the writings of William of Occam who devoted much of his attention to modal logic. He also conducted an exhaustive study of forms of valid and invalid syllogisms and contributed to the development of the concept of a metalanguage.
Despite the growth in creative work on logic during the Middle Ages, by the middle of the fifteenth century a reaction set in against logic and was largely displaced by rhetoric as the primary focus of attention. For two hundred years new work in logic ceased until Gottfried Wilhelm Leibniz (1646-1716). Leibniz is generally credited as the father of symbolic logic. He attempted to develop a symbolic language or "calculus" that could be used to settle all forms of disputes including theological.
By the middle of the nineteenth century logic had begun an extremely rapid period of development that continues today. Work in symbolic logic was done by a number of philosophers and mathematicians, including Augustus DeMorgan (1806-1871), George Boole (1815-1864), and John Venn (1834-1923). During this time, John Stuart Mill (1806-1873) also initiated a revival of inductive logic.
The foundations of modern mathematical logic were laid by Gottlob Frege. His work was continued into the twentieth century by Alfred North Whitehead and Bertrand Russell whose monumental work Principia Mathematica attempted to reduce the whole of pure mathematics to logic. This work was one of the things that interested Ludwig Wittgenstein leading to his work Tractatus Logico Philosophicus.
Logicians during the twentieth century have spent much of their time focusing on the formalization of logical systems and on questions dealing with the completeness and consistency of such systems. Logic has also made a major contribution to technology by providing a conceptual foundation for the electronic circuitry of digital computers.