zondag 29 november 2015
A calculus for possible worlds
Many metaphysicians deploy the apparatus of possible worlds. Possible worlds are in principle complete descriptions of how the world is or could have been. So, there are many, perhaps infinitely many, possible worlds. One of them is the actual world. It reflects reality as it actually is. How do metaphysicians decide whether something may count as a possible world? In most, if not all cases, the only criterion used for deciding whether a proposed candidate may be considered a possible world is the criterion of conceivability. If we can conceive the sketched situation, then we may infer that it is indeed possible and therefore part of at least one possible world. Conceivability though is a rather vague notion. It seems to convey the idea that there must be a clear and comprehensible narrative that outlines how the situation in question could obtain. So what is needed is an reasonable recognizable account of how the situation could be actual. It is thus not enough to just stipulate a situation as being possible. Now, what I would like to propose is to develop a calculus for the generation of new possible worlds out of given ones. The conceivability criterion may become one of the rules of this calculus, but this is not necessary. Perhaps we are able to identify a set of rules for said calculus that together make the conceivability criterion superfluous. What sort of rules do I have in mind? Well, we need rules for the generation of new possible worlds out of existing ones. For example rules like the following one. If W1 is a possible world, and W2 can be construed by a finite, coherent and unproblematic pathway from W1 to W2, then W2 is a possible world as well. So, the actual world without the chair I'm sitting on is a possible world. And the same holds for the actual world without the planets Mars and Venus. Or a possible world in which there are twenty planets orbiting around the sun. And so on. We also need rules to ground an initial set of possible worlds. An example of such a grounding rule would be the rule that a world in which only God exists is possible. From these possible worlds we may construct many other possible worlds by using generation rules such as the aforementioned one. In this way we get for example a possible world in which God exists and brings a universe into being. Or a possible world in which God exists and creates a multiverse. And so on. It seems to me that we need a quite large number of generation and grounding rules in order to arrive at an adequate possible worlds calculus. It would be interesting to see how such a calculus looks like.