A branch of mathematics concerned with the study of formal relationships between propositions – or formal propositions – independently of any interpretation they may be given or truth values that may be assigned to them.

Mathematics has been defined as the second degree of formal abstraction. Mathematical objects are abstracted from any sensible consideration; they become objects of the imagination. Despite mathematical logic’s formal methods, its purpose is not to define reality, but rather, to describe its ideal properties based on hypothetico-deductive rules. Right triangles and regular polygons do not exist in reality; they exist in the definitions and properties they have been given.

Logic is not considered to be a science, but rather, a fundamental working tool for all sciences.

### Historical note

Mathematical logic, a discipline introduced in the late 19th century, concerns the study of the linguistic aspect of mathematics.