**Logic and Mathematics**

- Formal logic, logical argument based on form
- Formal cause, Aristotle's intrinsic, determining cause
- Formal power series, a generalization of power series without requiring convergence, used in combinatorics
- Formal calculation, a calculation which is systematic, but without a rigorous justification
- Formal set theory, as opposed to
*Naive set theory* - Formal derivative, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus

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“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of *mathematics* under the new names logicism, intuitionism, and formalism.”

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