Logic is the study of valid reasoning. It asks what follows from what. A valid argument is one where the conclusion must be true if the premises are true. Logic provides the tools for distinguishing good arguments from bad ones. Aristotle systematized logic with the syllogism. Medieval logicians refined it. Frege and Russell developed modern symbolic logic, which uses formal languages to represent arguments and rules of inference to derive conclusions. Logic is used in mathematics, computer science, linguistics, and philosophy.

Logic is not the same as psychology. It studies normative principles, not how people actually think. People often reason illogically, but that does not change what validity requires. Logic is also not the same as rhetoric. Rhetoric aims to persuade. Logic aims to prove. The two can overlap, but they are distinct. Logic has many branches: propositional logic, predicate logic, modal logic, temporal logic, and many-valued logic, among others. Each branch has its own symbols, rules, and semantics. Logic is a formal science, like geometry, and it has applications in any field that requires precise reasoning.

Types of logic

• Propositional. Deals with whole propositions and connectives.
• Predicate. Deals with objects, properties, and quantifiers.
• Modal. Deals with possibility and necessity.
• Informal. Deals with reasoning in natural language.

Logic is not a body of knowledge about the world. It is a body of knowledge about what follows from what.