Williamson on modal knowledge
Apropos Williamson. The following question came up last year when we discussed The Philosophy of Philosophy in Canberra. I thought it had a sensible answer that we just couldn't figure out, but then Dorothy Edgington raised the same question at the recent phloxshop workshop in Berlin, and even though there were quite a few Williamsonians present, there was no agreement on what the answer is, and the proposals didn't sound very convincing.
The question is simply how, on Williamson's account, we can have knowledge of substantial metaphysical necessities, e.g. of the fact that gold necessarily has atomic number 79. Williamson explains that when we counterfactually imagine gold having atomic number 78 (knowing that it has number 79), we will "generate a contradiction", because we hold "such constitutive facts [as atomic number] fixed" (p.164). But the distinction between constitutive and not-constitutive facts can hardly be analysed as the distinction between whatever we happen to hold fixed and the rest, given Williamson's commitment to strong mind-independence of metaphysical modality. So what justifies our holding fixed the atomic number?
A natural thought is that we hold fixed such-and-such facts in counterfactual reasoning because we know that they are necessary. But according to Williamson, it is the other way round. Our knowledge of necessity is based on the attitude of "holding fixed" which we have towards certain propositions. So that attitude had better not be knowledge of necessity.
Someone suggested the attitude might be knowledge of constitutivity: we know that it is a "constitutive fact" that gold has atomic number 79. But then how do we know that? How do we know that it is not constitutive of this rock that it got stuck at the bush, so that what we imagine when we imagine it tumbling further is really a different rock, otherwise much like this one? And anyway, how would knowledge of contitutive facts help unless we also know that those facts are necessary and therefore can be held fixed in counterfactual reasoning?
It was also suggested that perhaps the relevant attitude towards the propositions we "hold fixed" is not knowledge at all. But whatever it is, the attitude is supposed to match mind-independent facts about necessity. And the match should not be an accident, otherwise counterfactual reasoning could not give us knowledge.
A third idea was that Williamson may not want to explain modal knowledge at all, but merely oppose philosophical exceptionalism. However, it seems that the relevant "holding fixed" attitude doesn't play much of a role in the evaluation of everyday counterfactuals. When I consider what would have happened if the rock had tumbled further, I obviously do hold a lot of things fixed, e.g. the depth of the valley. But this is not the right kind of holding fixed: when I entertain the possibility that the valley had been more shallow, I do not "generate a contradiction". So I do not hold the depth of the valley fixed in the unconditional sense in which, according to Williamson, I hold fixed the atomic number of gold -- in the sense that I hold p fixed even when I evaluate the counterfactual assumption that not-p. As far as ordinary evaluation of counterfactuals is concerned, it seems like we could do all that without ever holding anything absolutely fixed.
So what is Williamson's take on this peculiar, philosophical, knowledge-like attitude that provides us with knowledge of metaphysical necessities?
Hi Wo,
as to the third idea, does the philosophically relevant "holding fixed" attitude really not occur in everyday life? In other words, aren't there any propositions which even ordinary people in everyday counterfactual reasoning would "hold fixed" come what may? Of course, there would still be the more general epistemic problem, then, that there pretty much are no propositions which it would be rational to "hold fixed" come what may, even in the light of defeating considerations...