Michaelis Michael

Classical logic is explosive in the face of contradiction, yet we find ourselves using inconsistent theories. Mark Colyvan, one of the prominent advocates of the indispensability argument for realism about mathematical objects, suggests that such use can be garnered to develop an argument for commitment to inconsistent objects and, because of that, a paraconsistent underlying logic. I argue to the contrary that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity. Facing inconsistency does not force us to adopt an underlying paraconsistent logic. Moreover we will see that the argument to best explanation deployed by Colyvan in this context is unsuccessful. I suggest that Quinean approach which Colyvan champions will not lead to the revolutionary doctrines Colyvan endorses

David Lewis presented a celebrated argument for the identity theory of mind. His argument has provided the model for the program of analytic functionalism. He argues from two premises, that mental states are analytically tied to their causal roles and that, contingently, there is never a need to explain any physical change by going outside the realm of the physical, to the conclusion that mental states are physical. I show that his argument is mistaken and that it trades on a crucial ambiguity in the second premise. He argues for a weaker version of that premise and then uses a stronger version in the argument. The weaker version of that premise will not allow the inference and the stronger version is contested in the dialectical context. In general then this strategy for providing analytic reductions will not be guaranteed to succeed