Peter Vranas

The Principal Principle (PP) says that, for any proposition A, given any admissible evidence and the proposition that the chance of A is x%, one's conditional credence in A should be x%. Humean Supervenience (HS) claims that, among possible worlds like ours, no two differ without differing in the spacetime-point-by-spacetime-point arrangement of local properties. David Lewis (1986b, 1994a) has argued that PP contradicts HS, and the validity of his argument has been endorsed by Bigelow et al. (1993), Thau (1994), Hall (1994), Strevens (1995), Ismael (1996), Hoefer (1997), and Black (1998). Against this consensus, I argue that PP might not contradict HS: Lewis's argument is invalid, and every attempt – within a broad class of attempts – to amend the argument fails.

Besides pure declarative arguments, whose premises and conclusions are declaratives, and pure imperative arguments, whose premises and conclusions are imperatives, there are mixed-premise arguments, whose premises include both imperatives and declaratives, and cross-species arguments, whose premises are declaratives and whose conclusions are imperatives or vice versa. I propose a general definition of argument validity: an argument is valid exactly if, necessarily, every fact that sustains its premises also sustains its conclusion, where a fact sustains an imperative exactly if it favors the satisfaction over the violation proposition of the imperative, and a fact sustains a declarative exactly if, necessarily, the declarative is true if the fact exists. I argue that this definition yields as special cases the standard definition of validity for pure declarative arguments and my previously defended definition of validity for pure imperative arguments, and that it yields intuitively acceptable results for mixed-premise and cross-species arguments.

"Surrender; therefore, surrender or fight" is apparently an argument corresponding to an inference from an imperative to an imperative. Several philosophers, however (Williams 1963; Wedeking 1970; Harrison 1991; Hansen 2008), have denied that imperative inferences exist, arguing that (1) no such inferences occur in everyday life, (2) imperatives cannot be premises or conclusions of inferences because it makes no sense to say, for example, "since surrender" or "it follows that surrender or fight", and (3) distinct imperatives have conflicting permissive presuppositions ("surrender or fight" permits you to fight without surrendering, but "surrender" does not), so issuing distinct imperatives amounts to changing one's mind and thus cannot be construed as making an inference. In response I argue inter alia that, on a reasonable understanding of 'inference', some everyday-life inferences do have imperatives as premises and conclusions, and that issuing imperatives with conflicting permissive presuppositions does not amount to changing one's mind

There is widespread agreement, even among those who accept the possibility of backward causation, that it is impossible to change the past. I argue that this agreement corresponds to a relatively uninteresting understanding of what changing the past amounts to. In one sense it is indeed impossible to change the past: in no possible world is an action performed which makes the past in that world different from the past in that world. In another sense, however, it may be possible to change the past: maybe in some possible world an action is performed which makes the past in that world different from the actual past. I argue that those who accept the possibility of backward causation are committed to accepting the possibility that the past changes in the latter sense.