The aim of this paper is to determine the plausibility of Robert Kirk’s strict implication thesis as an explication of physicalism and its relation to Jackson and Chalmer’s notion of application conditionals, to the notion of global supervenience and to a posteriori identities. It is argued that the strict implication thesis is subject to the same objection that affects the notion of global supervenience. Furthermore, reference to an idealised physics in the formulation of strict implication threatens to make the thesis vacuous. Third, Kirk’s claim that the strict implication thesis does not entail reduction of the mental to the physical (excluding phenomenal properties) is untenable if a functional model of reduction is preferred over Nagel’s classical model. Finally, Kirk’s claim that the physical facts entail in an a priori way the fact that certain brain states feel somehow seems to be unfounded.