Aristotelian indeterminacy and partial belief ( First draft , references and writing incomplete )

Aristotle is thought to have held a distinctive view about the openness of the future. Everything necessarily is or is not, and will be or will not be; but one cannot divide and say that one or the other is necessary. I mean, for example: it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for a sea-battle to take place tomorrow, nor for one not to take place. A standard interpretation of Aristotle's writings on the subject—one that goes beyond anything to which the above quote commits him—-has him accepting each instance of the law of excluded middle: p ∨ ¬p but denying future contingent instances of the law of bivalence: 1 T (p) ∨ T (¬p) Future contingents are but one arena among many one might think of as containing " open " or " unsettled " or " indeterminate " questions. It's useful to have a generic word for this 'open' status, officially neutral between various possible theoretical elaborations. I will use 'indefinite' in this role. Just as Aristotle is supposed to have linked the openness of the future contingents with failures of bivalence, one might in general associate indeterminacy with failures of bivalence. I will call a theory of indefiniteness that combines no revision of classical tautologies (such as the law of excluded middle) with failures of bivalence, " Aristotelian ". Of course, this might be unfortunate if exegesis shows Aristotle himself not to be an Aristotelian. Moreover, we should be aware that various views might be Aristotelian in preserving classical logic and dropping bivalence, while disagreeing profoundly with Aristotle as to the source or nature of the indefiniteness of, say, future contingents. Nevertheless, the label will be useful. Among contemporary theories of indefiniteness, one theory that is famously Aristotelian is supervaluationism. 2 The motivating thought of supervaluationism as standardly interpreted 1 An immediate question to ask about this formulation is whether 'p' is used or mentioned in this formulation. At points this matters—when it does, I discuss it in footnotes. For the most part, though, it is safe to read T (p) as the application of an object-language truth operator to p: i.e. " it is true that p ". 2 See in particular Fine (1975) and Keefe (2000). As will be mentioned below, there is much ambiguity about what theses the 'supervaluationist' is committed to. …