Against SIC

I will present four reasons why the SIC-Based strategy does not work: 1- It makes for an implausibly gerrymandered semantics; 2- The logic is still too weak, by non-vacuist’s lights; 3- A principle like SIC is hard to establish; 4- SIC is intuitively false. Let me present each of these objections in turn.

First, accepting SIC predicts that there is a big difference between the logi- cal behavior of counterfactuals with possible antecedents and counterpossibles. While counterfactuals with possible antecedents obey the exact same logic that the vacuist takes them to obey, counterpossibles are nearly logically anarchic. As we saw on the introductory chapter, hybrid semantics, in the sense of pos- tulating very different mechanisms of semantic evaluation for counterpossibles, are undesirable. The non-vacuist must claim that this is not the case here. But this requires some justification. Here is how Williamson puts the point:

[Non-vacuists] treat it as a virtue of their account that it preserves a strong logic of counterfactuals with possible antecedents. How- ever, from an abductive perspective, that puts increased pressure on their reasons for rejecting the standard rules in the first place [...]. Those reasons had better be robust enough to justify the sacrifice of a strong and simple theory such as Stalnaker or Lewis’s logic of counterfactuals, in favour of one patched up with messy adjustments and repairs. In particular, given that counterfactuals have a com- positional semantics, we should be suspicious of the idea that their behaviour is radically different on the rare occasions when the an- tecedent is impossible. For how are we supposed to have come to be using so oddly contoured a conditional? (Williamson 2017: 208)

The justification Williamson is looking for should have the form of an expla- nation of why the counterfactual supposition of a metaphysical supposition can take us “beyond logical bounds”, as Berto et al. (2017: 7) put it.

This brings me to my second objection. Why is the line drawn precisely there? Why is itmetaphysical impossibility that affects the logical behavior of counterfactuals? I do not see any such strict connection between weakness of logic and metaphysical impossibility as plausible. In fact, it seems to me, the non-vacuist’s counterfactual logic with SIC is still too weak from the non-vacuist perspective.

Let us focus on (P-Closure). Intuitively, it amounts to saying that you can use logic to figure out what is true under a counterfactual supposition, as long as the supposition is metaphysically possible. This does not cover the deductive behavior of metaphysicians when arguing using counterfactuals. Metaphysicians will sometimes proceed by accepting a metaphysical proposition counterfactu- ally in order to show that it has unpalatable consequences of some kind. In their arguments they can use deductive reasoning based on classical logic. However, if it turns out that the counterfactual supposition is false, it will be impossi- ble. Therefore, (P-Closure) cannot validate these deductions of metaphysicians. This is the kind of weakness of logic that is relevant for Williamson’s argument

to go through. Moreover, accounting for the way in which metaphysicians use counterfactuals is one of the initial motivations for non-vacuism.

Third, SIC is a very hard principle to establish. Restrictions on similarity metric come in two varieties. If they are intended to apply to some contexts but not all, they can be said to be restricted. If they are intended to apply to all contexts, they can be said to beunrestricted. SIC is unrestricted, as it must be in order to be the basis of a counterfactual logic. It amounts to saying that metaphysical possibility is themaximally important measure of similarity in every context of evaluation. Compare this claim to the principle of (Weak Centering) we considered above. It seems that (Weak Centering) follows from our understanding of the notion of similarity. Whatever other problems using the notion of similarity might bring, we are at least entitled to this formal con- straint on our models by using it. In contrast, why would the notion of similarity behave in accordance to SIC? It seems like we would need some convincing to be in a position to accept SIC. And it seems plausible that the only way to establish an unrestricted similarity principle would be to show how it follows from the notion of similarity we are using. The reason better not be because it gives us a robust counterfactual logic, otherwise this seems just like anad hoc

move. We need an argument. And no such argument has been given.8

Someone can reply to the objection of the last paragraph as follows. The notion of similarity used in the semantics of counterfactuals is not exactly the ordinary notion of similarity. It is partly a theoretical construction designed to produce the right results with regards to the truth-values of particular counter- factuals in context. As such, SIC may yet be true if it is the best systematization of our truth-value intuitions. Though I am unsure about the merits of this ar- gument in the present context, it faces a bigger problem: our intuition tells us that there are some counterexamples to SIC.

A counterfactual is a counterexample to SIC if it has a possible antecedent and an impossible consequent. If such a counterfactual is true, then all the closest worlds where the antecedent is true must be impossible worlds - they make the impossible consequent true, after all. But, since the antecedent was possible, this is a direct violation of SIC. Consider the following example by Daniel Nolan:9

Suppose I have been playing a game with a boy called Oliver, where we arrange balls into a square grid, then tip the balls into a bag, then count the balls that come out. [. . . ] While playing it, I introduce Oliver to the idea of a square number, in the obvious way. On a

8_{You might think that Kment (2006; 2014) has offered such an argument. Kment analyses}

metaphysical modality using the notion of similarity: a proposition is metaphysically possible if, and only if, it is true at all the members of a certain similarity sphere around actuality. It seems that SIC is built into the analysis. This, however, is too quick, even if the analysis is

correct. Kment (2006:271) intends this to be valid only instandard contexts. As such, the

sphericality principle you can derive by accepting his analysis is not unrestricted and therefore insufficient for purposes of builidng a counterfactual logic.

9_{See Nolan (1997: 550 and 569) and Vander Laan (2004) for more examples in the same}

particular occasion, we come up with a count of 63 balls from the bag. ‘If the bag had 63 balls in it, 63 would have been a square number’ seems like an appropriate thing for me to say in explaining why I think we miscounted: and I think a true thing to say, in that context. But, of course, it is possible for that bag to contain 63 balls, and impossible for 63 to be square. So at least in some contexts of utterance of counterfactuals, SIC fails. (Nolan 2017:29)

There seems to be a clear reading of the counterfactual in question where it has a possible antecedent and an impossible consequent. The non-vacuist that wants to keep SIC in place must be involved in the negative project of rejecting these linguistic intuitions. This is dialectically uncomfortable - the point of the addition of impossible worlds, points where impossibilities can be true, seems to be precisely that of avoiding situations like this.

We can conclude that the SIC-based counterfactual logic is built using very shaky foundations. I take it that this would represent a significative cost for the non-vacuist. In what follows I will defend a non-vacuist semantics which can provide a counterfactual logic that is robust enough in another way.