Williamson's Modal Epistemology

Williamson believes that our knowledge about what might have been and what must be derives from our knowledge about counterfactuals. His rough idea is as follows. There are interesting biconditionals schemas that relate metaphysical possibility and necessity to certain kinds of counterfactuals. We can formulate these biconditionals as follows (please excuse my crude notation system. I hope everyone will be able to figure out what these are supposed to say):

17. []A iff (~A[]--> (P&~P))
18. <>A iff ~(A []--> (P&~P))

Since these biconditional schemas are true, if we can come up with an account of how we come to know certain counterfactuals, then we might be able to extend that account to say how we come to know that certain claims are necessary and that certain claims are possible. This is Williamson's project.

Williamson has a lot to say about how we come to know ordinary counterfactuals. I'd like to grant to him that we come to know ordinary counterfactuals in the way he indicated. However, I think there are still problems with his account of how we come to know that a claim is necessary or that a claim is possible.

My first objection to Williamson's account involves noting that the counterfactual schemas above involve strange, non-ordinary counterfactuals. Although Williamson has given us an account of how we come to know ordinary counterfactuals, he has not said much about how we come to know these strange counterfactuals. I might be willing to grant that we can come to know some of these non-ordinary counterfactuals. For example, I can come to know that if there were a barber who shaved all and only those who don't shave themselves, then there would be a barber who both shaves himself and does not shave himself. I can come to know this simply by drawing out the logical consequences of the antecedent of that counterfactual. But, suppose it is impossible for two objects to be co-located. Now, I'd like to know how I might come to know that if two things were co-located, then pigs fly and it is not the case that pigs fly. The claim that two objects are co-located is not inconsistent. So, I cannot draw the contradiction as a logical consequence of the claim that two objects are co-located. But, presumably some metaphysicians know that it is impossible for two objects to be co-located (given our supposition). So, how do they come to know this fact? It doesn't seem to me that Williamson has said much about this.

My second objection to Williamson's account is that his account seems to require that we know (17) and (18) above. If we did not know (17) and (18) then we would not be justified in believing that possibly P is true even through we are justified in believing that it is not the case that if P were true then P and not P would be true.

My third objection is merely an extension of one of the objections that Williamson considers. Williamson responds to the objection that his acocunt requires that all counterfactuals with necessarily false antecedents are vacuously true. However, the objector claims, there are some counterfactuals with necessarily false antecendents that are true and others that are false. Williamson gives several good explanations of why we might be mistaken in thinking that these counterfactuals are sometimes true and sometimes false. I find his explanations very plausible. However, the theorist who thinks that some counterfactuals with necessarily false antecedents are true while others false has more to say than simply that he has an intuition regarding certain counterfactuals. Such a theorist can say both that he has an intuition and that he has a prior commitment to an ersatzist account of worlds that allows for impossible worlds which can be used in an account of counterfactuals that satisfies his intuition. So, it seems to me that Williamson needs to say more in response to such a theorist. Not only does Williamson need to explain away our intuitions about these counterfactuals, but he needs to say why it is better to explain away our intuitions rather than accept an account of counterfactuals that satisfies those intuitions.