mantik

Mantik (mantık in Turkish) is the study of correct reasoning and argument. It encompasses the analysis of the structure of arguments, the determination of validity and soundness, and the formalization of systems that express inferential relationships. In Turkish usage, mantık covers both classical and modern approaches to logic, spanning ancient theories to contemporary formal frameworks.

Historically, logic originated in ancient Greece with Aristotle’s syllogistic, while Indian Nyaya and Chinese Mohist traditions developed parallel approaches to inference. In medieval Europe, scholastic logicians refined deductive methods. The modern era brought a transformation with Frege’s predicate logic, followed by work from Russell and Whitehead, Gödel’s incompleteness theorems, and the development of model theory, proof theory, and various non-classical logics such as modal, temporal, and fuzzy logics.

Subfields of mantik include formal logic, which covers propositional and predicate logic; modal logic, temporal logic, and other non-classical logics; as well as computational logic that underpins computer science. Applications extend to computer science, artificial intelligence, linguistics, mathematics, and philosophy, where logical methods support reasoning about truth, inference, and formal systems.

Key concepts in mantik include validity, soundness, deduction and induction, truth-functional connectives, and the relationship between syntax and semantics. Common methods involve formal proofs, truth tables, and model-theoretic semantics, along with axiomatic systems aimed at ensuring consistency and, within a given framework, completeness. Mantik thus provides tools for analyzing argument quality and for constructing well-founded formal theories.