General-Elimination Harmony

Stephen Read (St. Andrews) gives a talk at the MCMP Colloquium (2 Feb, 2012) titled "General-Elimination Harmony". Abstract: Michael Dummett introduced the notion of harmony in response to Arthur Prior's tonkish attack on the idea of proof-theoretic justification of logical laws (or analytic validity). But Dummett vacillated between different conceptions of harmony, in an attempt to use the idea to underpin his anti-realism. Dag Prawitz had already articulated an idea of Gerhard Gentzen's into a procedure whereby elimination-rules are in some sense functions of the corresponding introduction-rules. The corresponding conception of general-elimination harmony ensures that the introduction-rules are transparent in the meaning they confer, in that the elimination-rules match the meaning the introduction-rules confer exactly.