logik

Logik, the German term for logic, is the systematic study of the principles of valid reasoning and inference. It seeks to distinguish correct reasoning from fallacious reasoning and to provide formal methods for analyzing the structure of arguments. In formal logic, reasoning is expressed through symbolic languages and rules that determine how conclusions follow from premises. Informal logic deals with everyday argumentation, argument structure, and rhetorical context.

Subfields include propositional logic, which studies how truth-functional connectives form complex sentences from atomic propositions; predicate logic, which extends this with quantifiers and predicates to discuss objects and their properties; and higher-order logic, which allows quantification over predicates and sets. Non-classical logics include modal logic (necessity and possibility), temporal logic (time-based reasoning), intuitionistic logic (constructive proof), many-valued and fuzzy logics (degrees of truth), and relevance logic.

History traces the discipline from Aristotle’s syllogistic, foundational for deductive reasoning, through later reforms by Frege, Russell, and Whitehead that established logic as a formal science. In the 20th century, David Hilbert pursued a program to formalize mathematics; Kurt Gödel demonstrated fundamental limits with his incompleteness theorems. Developments in model theory, proof theory, and computability—led by Tarski and Turing—further shaped the field.

Applications include the foundations of mathematics and computer science, where logic enables formal verification, programming language semantics, and automated reasoning. It also informs philosophy, linguistics, and cognitive science, providing tools for clarifying arguments, designing algorithms, and modeling information.