Weak ontic necessity is the ontic necessity expressed by “should/ought to” in English. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds at the present world is irrelevant to whether its prejacent holds at the present world. In this paper, by combining premise semantics and update semantics for conditionals, we present a logical theory for conditional weak ontic necessity based on context update. A context is a set of (...) ordered defaults, determining expected possible states of the present world. Sentences are evaluated with respect to contexts. When evaluating the conditional weak ontic necessity with respect to a context, we first update the context with the antecedent, then check whether the consequent holds with respect to the updated context. We compare this theory to some related works. The logic’s expressivity is studied. (shrink)

The thin red line theory is a form of branching indeterminism. It entails that, among the many possible developments that reality might take, one is privileged: the actual history. The thin red line theory is naturally paired off with a semantic thesis that may be called ‘the actuality principle’: a statement is true as used at a moment if and only if it is true at that moment on the actual history. The actuality principle has been challenged, for it would (...) be wrong about several counterfactual reasonings. On the one hand, the actuality principle should entail that any statement uttered at a merely possible moment is untrue. On the other hand, the actuality principle should be at odds with the way we use subjunctive conditionals. This paper argues that both objections rely on an inadequate understanding of the notion of the history of use. As for the first objection, the paper argues that to assume the actuality principle amounts to taking the actual history as the history of use. As a consequence, one cannot consistently take the actual history as the history of use and, at the same time, a merely possible moment as the moment of use. As for the second objection, the paper shows that the actuality principle is consistent with any reasonable treatment of subjunctive conditionals. (shrink)

In addressing the problem of the compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and (...) \ models, Restall Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \ models. In particular, Restall believes that the implication \ is not true in \ models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models ) the implication \ is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the \ and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models or can be accounted for by these models and so is not a problem for Molinists either. (shrink)