The Construction of Possible Worlds
Possible worlds are often taken to be complete histories of everything. Insofar as there are temporary sentences that are true at some times and false at other times, evaluating a sentence at a possible world does not fix its truth-value. Moreover, if possible worlds are taken to be primitive, evaluating sentences at world-time pairs invalidates a perpetuity principle that what is necessarily the case is always the case where imposing model constraints cannot validate these principles without undermining the significance of the truth-conditions for the language. Rather, this paper takes world states to be maximal possible ways for things to be at an instant where the task relation encodes the possible transitions between world states. Possible worlds are then defined as functions from times to world states as constrained by the task relation. Since sentences are assigned truth-values at world states, times are exogenous to the truth-conditions for the language, eliminating unnecessary degrees of freedom from the definition of a model. By evaluating sentences at world-time pairs, the resulting semantic theory validates a logic for tense and modality in which the perpetuity principles are theorems, providing a logical foundation for reasoning about future contingency.