portal: Logic Logic is the study of the principles of valid demonstration and inference. The word derives from Greek λογική (logike), fem. of λογικός (logikos), "possessed of reason, intellectual, dialectical, argumentative", from λόγος logos, "word, thought, idea, argument, account, reason, or principle". As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of validity, fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory.

Traditionally, logic is considered a branch of philosophy, a part of the classical trivium of grammar, logic, and rhetoric. Since the mid-nineteenth century formal logic has been studied in the context of foundations of mathematics, where it was often called symbolic logic. In 1879 Frege published Begriffsschrift : A formula language or pure thought modelled on that of arithemetic which inaugurated modern logic with the invention of quantifier notation. In 1903 Alfred North Whitehead and Bertrand Russell attempted to establish logic formally as the cornerstone of mathematics with the publication of Principia Mathematica. Alfred North Whitehead and Bertrand Russell, Principia Mathematical to *56, Cambridge University Press, 1967, ISBN 0-521-62606-4 However, except for the elementary part, the system of Principia is no longer much used, having been largely superseded by set theory. Fact: date=October 2008 At the same time the developments in the field of Logic since Frege, Russell and Wittgenstein had a profound influence on both the practice of philosophy and the ideas concerning the nature of philosophical problems especially in the English speaking world (see Analytic philosophy). As the study of formal logic expanded, research no longer focused solely on foundational issues, and the study of several resulting areas of mathematics came to be called mathematical logic. Fact: date=October 2008 The development of formal logic and its implementation in computing machinery is fundamental to computer science. Logic is now widely taught by university philosophy departments, more often than not as a compulsory discipline for their students, especially in the English speaking world.

Nature of logic

Form is central to logic. It complicates exposition that 'formal' in "formal logic" is commonly used in an ambiguous manner. Symbolic logic is just one kind of formal logic, and is distinguished from another kind of formal logic, traditional Aristotelian syllogistic logic, which deals solely with categorical propositions.