Laurenz Hudetz (LSE): “On Reduction”

Abstract: Many claims about intertheoretic reductions lack rigorous proofs (e.g., the claim that thermodynamics is reducible to statistical mechanics or even the widespread view that the Newtonian theory of gravitation is reducible to Einstein’s general theory of relativity). Apart from specific problems pertaining to individual theories, we also face the general issue that reducibility claims can only be proved or disproved if we have a rigorous and acceptable definition of reducibility. This talk aims to provide such an explication of reducibility.

On the proposed account, reductions may be complex. A complex reduction involves several reductive steps of potentially different types (such as taking limits of theories or logico-mathematically reconstructing models of one theory from models of another theory). I put forward a definition of logico-mathematical reconstruction that (1) is compatible with the best existing accounts of limiting-case relations in terms of topological structure or similarity structure on classes of models, (2) generalises and unifies various logical accounts of reduction (including the accounts by Nagel and Suppes), (3) is not committed to first-order logic or even the syntactic view of theories and (4) allows to explicate what it is for logico-mathematical reconstructions to preserve (empirical) interpretation.