Coherence and Reduction

Synchronic intertheoretic reductions are an important field of research in science. Arguably, the best model able to represent the main relations occurring in this kind of scientific reduction is the Nagelian account of reduction, a model further developed by Schaffner and nowadays known as the generalized version of the Nagel–Schaffner model (GNS). In their article (2010), Dizadji-Bahmani, Frigg, and Hartmann (DFH) specified the two main desiderata of a reduction á la GNS: confirmation and coherence. DFH first and, more rigorously, Tešic (2017) later analyse the confirmatory relation between the reducing and the reduced theory in terms of Bayesian confirmation theory. The purpose of this article is to analyse and compare the degree of coherence between the two theories involved in the GNS before and after the reduction. For this reason, in the first section, I will be looking at the reduction of thermodynamics to statistical mechanics and use it as an example to describe the GNS. In the second section, I will introduce three coherence measures which will then be employed in the comparison. Finally, in the last two sections, I will compare the degrees of coherence between the reducing and the reduced theory before and after the reduction and use a few numerical examples to understand the relation between coherence and confirmation measures.