Abstract

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.