TOTAL LOGIC

AbstractA typical first stab at explicating the thesis of physicalism is this: physicalism is true iff every fact about the world is entailed by the conjunction of physical facts. The same holds,mutatis mutandis, for other hypotheses about the fundamental nature of our world. But it has been recognized that this would leave such hypotheses without the fighting chance that they deserve: certain negative truths, like the truth (if it is one) that there are no angels, are not entailed by the physical facts, but nonetheless do not threaten physicalism. A plausible remedy that has been suggested by Jackson and Chalmers is that physicalism boils down to the thesis that every truth is entailed by the conjunction of the physical facts prefixed by a “that’s it” or “totality” operator. To evaluate this suggestion, we need to know what that operator means, and—since the truth of physicalism hinges on what is entailed by a totality claim—what its logic is. That is, we need to understand the logic of totality, or total logic. In this paper, I add a totality operator to the language of propositional logic and present a model theory for it, building on a suggestion by Chalmers and Jackson. I then prove determination results for a number of different systems.