Weakened Versions of Hume’s Thesis in a.d.1- Logics with Bridge Principles

Abstract

Though it is doubtful whether BPs can be regarded as analytical, and thus, whether logics with bridge principles can be regarded as logics “in the philosophical sense”, it is nevertheless interesting to investigate Hume’s problem also in a.d.1-logics with bridge principles. It turns out that some BPs are such that even if they are added to standard a.d.1-logics, the resulting logics enable only is-ought inferences which are trivial in a certain sense — in other words, a weakened version of Hume’s thesis holds in these logics. This is in particular true of two prominent BPs, which shall now be investigated — the ought-can principle (OC), which says that all obligatory propositions (or actions) are possible, and the must-ought principle (MO), which says that all necessary propositions are obligatory.