TOTAL LOGIC

STEPHAN LEUENBERGER
2014 The Review of Symbolic Logic  
A 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 hypothese 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
more » ... , 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. Author 2 The metaphysics of outstripping As mentioned above, a sketch for a semantics of the totality operator is offered in Chalmers and Jackson (2001) . They specify the truth-conditions of the operator in terms of the notion of a world's being minimal in a certain class of worlds, and 1 My regimentation of "that's-it" talk with an operator does not commit me to the claim that there is such an operator in English, nor to the claim that if there is such an operator, it is conceptually primitive, rather than understood in terms of some "totality predicate". Thanks to Kevin Mulligan for discussion on this point. 2 Totality facts-as opposed to totality statements and totality operators-had been discussed already in Armstrong (1989).
doi:10.1017/s1755020314000124 fatcat:lbbcmubpqnaipovzdtvtmzr5gi