Williamson wants to argue that (a) counterfactuals are intimately tied up with modality, (b)counterfactual thought plays a pivotal role in our everyday reasoning and consequently (c) a modal epistemology comes along with our everyday reasoning for free. To strengthen his argument he tries to show that we cannot make due without counterfactuals and that we cannot reduce them to anything that breaks their tie to modality. As a particular instance of the latter, Williamson argues that counterfactuals cannot be reduced to “habituals”. He attempts to drive a wedge between the two by producing a case in which a counterfactual has a different truth-value from a parallel habitual. The details of Williamson’s argument are as follows:
Consider the sentences:
(i) If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show.
(iH) If Jones takes arsenic, he [normally] shows just exactly those symptoms which he does in fact show.
(1) If a situation S can be produced in which (i) and (iH) differ in truth value, then (iH) cannot do the same work (i) does in all situations.
(2) Let S be the case in which Jones’ symptoms are not those he would normally show in arsenic poisoning but those he would show given that he had, unusually, been fasting for the previous 72 hours.
(3) S is a case in which (i) is true when (iH) is false, that is a case in which they differ in truth value.
(4) Thus, (iH) cannot do the same work (i) does in all situations.
Now I don’t know anything about habituals and a fortiori I lack knowledge about habitual semantics. However, I would imagine them to be something like: the habitual conditional A [h]->B is true iff in A circumstances, B normally comes about. This seems to line up with Williamson’s evaluation of (iH) as false. The problem I have is with TWs evaluation of (i) as true under S.
It seems to me that if Jones had taken arsenic he would *not* have shown just exactly those symptoms which he does in fact show under S, since the symptoms in S are *not* those he would normally show in arsenic poisoning but those he would show given that he had, unusually, been fasting for the previous 72 hours.
Even spelling this out in terms of possible world semantics seems to point to the falsity of (i). A non-insane principle is the following: worlds where “normal” situations occur are closer to the actual world than worlds in which “non-normal” situations occur. But given this principle and S, if we go to the closest world where Jones takes arsenic, it is not the case that he exhibits the symptoms he currently exhibits at @ (since the @-symptoms are not arsenic symptoms). Hence, (i) is false.
Williamson is super good at logic, so I’m pretty sure I’m the one in error but I do not currently see how his counterexample works.