strict adherence to, or observance of, prescribed or traditional forms, as in music, poetry, and art.
Religion. strong attachment to external forms and observances.
Ethics. a doctrine that acts are in themselves right or wrong regardless of consequences.
Logic, Mathematics. a doctrine, which evolved from a proposal of David Hilbert, that mathematics, including the logic used in proofs, can be based on the formal manipulation of symbols without regard to their meaning.
British Dictionary definitions for formalistically
scrupulous or excessive adherence to outward form at the expense of inner reality or content
the mathematical or logical structure of a scientific argument as distinguished from its subject matter
the notation, and its structure, in which information is expressed
(theatre) a stylized mode of production
(in Marxist criticism) excessive concern with artistic technique at the expense of social values, etc
the philosophical theory that a mathematical statement has no meaning but that its symbols, regarded as physical objects, exhibit a structure that has useful applications Compare logicism, intuitionism