I have uploaded a new paper to my Work in Progress section. The title is Counterfactuals and Modal Epistemology. Basically this is a paper criticising Timothy Williamson’s account of modal epistemology, familiar from his recent book The Philosophy of Philosophy. Williamson claims that the epistemology of metaphysical modality is a special case of the epistemology of counterfactuals. I have two problems with his account, one concerns the basis of what he calls ‘background knowledge’ and ‘constitutive facts’, one concerns his use of imaginability or conceivability as an epistemic tool. Take one of Williamson’s examples:
You are in the mountains. As the sun melts the ice, rocks embedded in it are loosened and crash down the slope. You notice one rock slide into a bush. You wonder where it would have ended if the bush had not been there. A natural way to answer the question is by visualizing the rock sliding without the bush there, then bouncing down the slope. You thereby come to know this counterfactual:[CF] If the bush had not been there, the rock would have ended in the lake. (T. Williamson, The Philosophy of Philosophy, Oxford: Blackwell, 2007, p. 142.)
According to Williamson we come to know counterfactuals like (CF) with the help of our imagination. However, we are immediately faced with a problem: how are we supposed to choose the correct scenario given that our imagination can come up with the wildest of scenarios, such as ‘the rock rising vertically into the air, or looping the loop, or sticking like a limpet to the slope’ (ibid., 143). Williamson’s reply goes as follows:
You do not imagine it those other [irrelevant] ways because your imaginative exercise is radically informed and disciplined by your perception of the rock and the slope and your sense of how nature works. The default for the imagination may be to proceed as ‘realistically’ as it can, subject to whatever deviations the thinker imposes by brute force: here, the absence of the bush. Thus the imagination can in principle exploit all our background knowledge in evaluating counterfactuals. (T. Williamson, The Philosophy of Philosophy, Oxford: Blackwell, 2007, p. 143.).
The idea is presumably that our imagination will be restricted by our knowledge of the laws of nature so that we will omit scenarios that are physically impossible. There are some problems already here, but let’s focus on just one: what about scenarios that are physically impossible but metaphysically possible? More generally, if our background knowledge concerns the actual world, how can we restrict our imagination regarding scenarios that do not concern the actual world? It seems that Williamson does not even consider cases like this, but unless he implicitly assumes that the laws of physics are metaphysically necessary, then he must somehow be able to distinguish between physical possibilities and physical impossibilities which are metaphysically possible.
The figure on the right illustrates the situation. We are interested in the distinction between the left and the right half of the circle, i.e. between what is conceivable & metaphysically impossible, and what is conceivable & metaphysically possible. An example of the first could be that water is XYZ (if water has its actual molecular structure by necessity), an example of the latter could be a rock floating above a lake. Some further qualifications are needed though: the relationship between what is conceivable & metaphysically impossible, and what is conceivable & metaphysically possible is of course intransitive – the two are mutually exclusive – but the relationship between what is conceivable & metaphysically possible, and what is conceivable & physically possible is transitive, as everything that is physically possible is also metaphysically possible.
Obviously, there is an overlap between what is conceivable and what is metaphysically possible, but given that there is also an overlap between what is conceivable and what is metaphysically impossible, the previous overlap does not amount to very much. In fact, it seems clear that there will be a greater overlap between conceivability and metaphysical impossibility, due to the virtually infinite range of scenarios that we can imagine. Thus, when we compare the space of conceivable & metaphysically impossible scenarios to the space of conceivable & metaphysically possible scenarios, the previous will certainly dominate. If we hope to use conceivability as a guide to metaphysical possibility, we should somehow be able to distinguish between the two.
Now consider Williamson’s analysis of ‘gold is the element with atomic number 79’:
If we know enough chemistry, our counterfactual development of the supposition that gold is the element with atomic number 79 will generate a contradiction. The reason is not simply that we know that gold is the element with atomic number 79, for we can and must vary some items of our knowledge under counterfactual suppositions. Rather, part of the general way we develop counterfactual suppositions is to hold such constitutive facts fixed. (T. Williamson, The Philosophy of Philosophy, Oxford: Blackwell, 2007, p. 164.)
Williamson seems to provide a partial answer to the problem, for supposedly we can dismiss the conceivable but metaphysically impossible scenario of gold having some other atomic number than 79 with the help of ‘constitutive facts’, i.e. background knowledge that we do not vary when considering counterfactual scenarios. This enables us to distinguish between conceivable metaphysical impossibilities and metaphysical possibilities. But this solution will not work in all cases: it only works in cases where we are dealing with metaphysical necessities, such as ‘gold is the element with atomic number 79’. This is because in cases where we are dealing with mere metaphysical possibilities we should be able to vary many more, if not all items of our knowledge under counterfactual suppositions: in cases such as the rock sliding down a slope the possibilities for variation are much greater – even the laws of physics may be varied unless it is assumed that they are metaphysically necessary, which is something that Williamson does not argue for. Be that as it may, unless there are some metaphysically necessary conditions that serve as clear candidates for constitutive facts that should be held fixed, such as the fact that elements have their atomic number by necessity (if this is indeed the case), then there are no obvious reasons to decide which items of background knowledge should be held fixed.
There’s more to say about all this, see the actual paper for the details. One approach that might help Williamson is to draw on Kit Fine’s suggestion according to which metaphysical modality is a special case of essence. Accordingly, metaphysical modality could be grounded in the essences of the entities it concerns. But even if he did go this way, it seems that Williamson has left the most crucial part of the story untold.