There are some propositions such as 1+1=2 that seem to be true in all possible worlds. That is, there is no possible world in which 1+1=2 is not true. Propositions like this that seem to be true in all possible worlds are said to be true necessarily.
There are two ways to interpret the claim that 1+1=2 is true necessarily, as epistemic modality and as metaphysical modality ("modality" is a general term to refer to necessity, possibility, and related concepts).
In the following, I'm going to abbreviate "necessarily true" as "necessary".
Epistemic modality is fairly unproblematic. Before I explain it, let me define another term: a proposition is said to be a priori if its truth can be determined without looking at any empirical evidence--that is, without looking at the actual world to see how things are. If you can determine the truth of a proposition without looking at the actual world, then that proposition must be true in all possible worlds--that is, necessary. Contrariwise, if you can determine that a proposition is necessary--true in all possible worlds--then it must be that you can determine the truth of that proposition without looking at the actual world, so that proposition must be a priori. Therefore, the epistemic approach to modality is that the necessary propositions are just the a priori propositions.
However, there are examples of propositions that are not a priori but are necessary. Consider the sentence,
In all possible worlds in which Jane Fonda exists, Jane Fonda is the daughter of Henry Fonda.
Note that I'm not saying that in all possible worlds having a woman named Jane Fonda, that woman has a father named Henry Fonda; there are possible worlds in which both names are different, but in order for the names to be different, the people have to be the same. That is, in any possible world in which Jane Fonda exists, regardless of her name in that possible world, she is the same person as Jane Fonda in this world. I'm using the name in the actual world to pick out two people in the actual world and saying that in any possible world, if those two people exist, then they have that relationship. Jane wouldn't be the same person as the Jane in this world if her father were not the same person as the Henry in this world.
Therefore, it is necessary that Jane Fonda is the daughter of Henry Fonda. She wouldn't be Jane Fonda if she had a different father. But it is not a priori that Jane Fonda is the daughter of Henry Fonda; that is not something that you could determine without looking at the actual world. So that proposition is necessary but not a priori, violating the claim of epistemic modality.
It seems then that there is another kind of modality, metaphysical modality, that is not dependent on knowledge, but dependent on the nature of things. This would seem to cause problems for two different groups of philosophers: empiricists and materialists.
It seems to cause problems for empiricists because it means that we can know things about possible worlds as a metaphysical reality. Where would this knowledge come from? It can't come from empirical experience because we can only experience the actual world and there doesn't seem to be any way that the actual world can give us knowledge about non-actual worlds.
It seems to cause problems for materialists because possible worlds are not material. Since only the material exists, how can you have true propositions about possible worlds?
Is this correct? Do empiricists and materialists have to reject metaphysical modality?