1; Departments of Mathematics and Philosophy; Stanford University
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A notion of finitary inductively presented (f.i.p.) logic is proposed here, which includes all syntactically described logics (formal systems) met in practice. A f.i.p. theory FS 0 is set up which is universal for all f.i.p. logics; though formulated as a theory of functions and classes of expressions, FS 0 is a conservative extension of PRA. The aims of this work are (i) conceptual, (ii) pedagogical and (iii) practical. The system FS 0 serves under (i) and (ii) as a theoretical framework for the formalization of metamathematics. The general approach may be used under (iii) for the computer implementation of logics. In all cases, the work aims to make the details manageable in a natural and direct way. What is a logic? The question here is not "What is logic?", which (tendentiously) seeks to canonize some one distinguished system of reasoning as being the only true one. But also, here, we are not after any logic---only those that are syntactically described, or formal, as distinguishe...