After discussing historical formalism, a revised version, ‘neo-formalism’, is introduced, utilizing the informational/metaphysical content distinction. Mathematical utterances effect truth-valued assertions, made true or false by the existence of proofs and disproofs though this content is not part of the informational content. Mathematical assertions are made in a non-representational mode, formal rather than projective. A simple illustration, using decimal arithmetic, is given and distinctions drawn between the purely formal game level, the content level, where utterances are truth-valued, and the metatheory which explains how the content level sentences are made true or false by the existence of proofs. The question of how the language can be extended to accommodate logical complexity is raised, a Basic Semantics for logical operators given, and problems in ensuring a good mesh between a semantics of proof and the meaning which logical terms have outside formal contexts highlighted.
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