Alexander Hughes

The branching time analysis grounds the possibilities entailed by temporal indeterminism in a branching temporal structure. I construct a spatial analog of the branching time analysis – the branching space analysis – according to which the possibilities entailed by spatial indeterminism are grounded in branching spatial structure. The construction proceeds in such a way as to show the analogies between the branching space and branching time analyses. I argue that the two views are a package. In particular: the theoretical virtues of the one are theoretical virtues of the other and so if one ought to be accepted, then the other should also be accepted. And: if one ought to be denied, then the other ought to be denied as well. Thus, the branching space analysis functions either as a counterexample to the reductive strategy embodied in the branching time analysis or as a reasonable extension of it – as a lesson learned from it.

Inductive logic would be the logic of arguments that are not valid, but nevertheless justify belief in something like the way in which valid arguments would. Maybe we could describe it as the logic of “almost valid” arguments. There is a sort of transitivity to valid arguments. Valid arguments can be chained together to form arguments and such arguments are themselves valid. One wants to distinguish the “almost valid” arguments by noting that chains of “almost valid” arguments are weaker than the links that form them. But it is not clear that this is so. I have an apparent counterexample the claim. Though: as is typical in these sorts of situations, it is hard to tell where the problem lies.

I argue that mental descriptivism cannot be reasonably thought superior to rival theories on the grounds that it can (while they cannot) provide an elegant account of reference failure. Descriptivism about the particular-directed intentionality of our mental states fails when applied to desires. Consider, for an example, the desire that Satan not tempt me. On the descriptivist account, it looks like my desire would be fulfilled in conditions in which there exists exactly one thing satisfying some description only Satan satisfies (call it the Satanic Description). However, against this analysis, it is clearly compatible with desiring that Satan not tempt me that I also desire that there exist nothing satisfying the Satanic Description. The descriptivist has room for maneuver here, but the cost of accommodating this phenomenon is that the descriptivist shall no longer be able to use her theory to ameliorate the possibility of reference failure