1. Another term for a logical calculus.

2. In the philosophy of mathematics, a formalist holds that mathematical statements are to be thought of as uninterpreted strings of symbols. Mathematics has a syntax but no semantics. The formalism is useful only in enabling us to pass from some observations to other empirical conclusions, but it introduces no subject-matter of its own. The position is widely thought to be inadequate to the use of numbers in the empirical procedures of counting and measuring. A modified formalism may hold that some numerical statements (for example, those involving only finite numbers and finite classes of them) are interpretable, whereas the rest of classical mathematics is a kind of black box, or purely formal machine for taking us from some interpretable statements to others. An example would be the use of imaginary numbers in calculations designed to get us to useful real numbers, but not themselves thought of as corresponding to any physical magnitudes.