Formal System

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. Euclid’s Elements is often held to be the first formal system and displays the characteristic of a formal system. The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field (e.g. Euclidean geometry) consistent with the usage in modern mathematics such as model theory. A formal system need not be mathematical as such, Spinoza’s Ethics for example imitates the form of Euclid’s Elements.