Abstract
It is fashionable nowadays to characterize necessity or necessary truth in a Leibnizian manner as what is true in all possible worlds. But the brilliance of this heuristic device ought not blind us to the fact that, unlike God, we cannot suppose ourselves able to individuate all possible worlds. The sense of the notion of necessity is that, whatever we may suppose possible worlds to be, nothing we conceive as forming a compossible world could falsify a truth we rightly tendered as a necessary truth. Since to conceive or imagine a “particular” compossible world is to conceive or imagine a determinate state of affairs the details of which do not entail incompatible ascriptions among those details, there is reason to think that, whatever may be alleged to be the status of the formal principle of non-contradiction, conceptual compossibility is parasitic on the semantically rich natural languages with which in various ways we entertain possibilities relative to the actual world. If this much be conceded, then it is a very small step to grasp that if what we suppose to be possible relative to the actual world can be specified only within the scope of the particular conceptual schemes and theories that enable us to imagine determinate states of affairs of this sort or that, then: different conceptual schemes will permit us to entertain different and different ranges of compossible worlds; confined, within a given historical interval, to a particular conceptual scheme that does not yet feature or even know how to feature distinctions that are to become cognitively accessible at a later time, we cannot make sense of our ever being able to formulate in principle all possibilities with regard to the actual world—nor, therefore, all compossible worlds; and it would not be surprising that human investigators working in real-time terms with competing paradigms should find their paradigms at least provisionally incommensurable, as relating to differently conceived problems, differently conceived ways of construing events, and the like.