Given that it’s the end of the decade, a time when “best of” lists appear all over the place, I thought I’d weigh in with my two pence. Obviously there has been a phenomenal amount of good work done during the 00s, and things like Knowledge and Its Limits are rightly getting making many people’s “best-of” lists. But one thing that is totally striking, at least to me, is the amount of excellent work that’s been done on the semantic paradoxes during the decade. We’ve had not one, not two, but three groundbreaking books: Tim Maudlin’s Truth and Paradox, Hartry Field’s Saving Truth From Paradox and J.C. Beall’s Spandrels of Truth. If you think about where we began at the start of the decade, we’re in such a better position now. At least to my mind, this is the main area that’s been greatly advanced during the decade.

Not all properties were born equal. Some are more elite; more fundamental; more natural than others. Even if we think this distinction is primitive, we can still characterize these special properties by means of their theoretical role. Natural properties figure in the fundamental description of reality, their instances are objectively similar, they occur in laws of nature, they are more eligible to be the semantic values of predicates, and the total qualitative state of the world is supervenient upon their collective pattern of instantiation. Predicates expressing natural properties “carve nature at its joints.” Other predicates carve elsewhere.

Friends of natural properties, then, think that they can help us solve certain problems. If we think that natural things are somehow more eligible to serve as the semantic values of expressions, perhaps appealing to naturalness can help us block Quinean arguments for the inscrutability of reference, or Putnam’s paradox, or various other vexed problems.

Now, one friend of all things natural, David Lewis, famously thinks that naturalness can help us block the arguments that Kripkenstein develops in order to argue for “semantic skepticism”, the claim that it isn’t true of any expression that it express some particular concept or meaning. Thus the thought goes that there is just no fact of the matter whether Billy’s use of the term “plus” picks out the addition function as opposed to the quaddition function. But, the friend of naturalness says, addition is more eligible to serve as a semantic value, and whilst Billy’s previous use of the expression doesn’t determine whether he means addition or quaddition, naturalness breaks the tie.

I’ve been lecturing on the rule-following considerations of late, and one question that it’s important to get clear on is whether naturalness really helps us to answer Kripke’s skeptic. In particular, we should get clear on whether naturalness is any better an answer than the “simplicity”-based proposal Kripke briefly discusses.

The simplicity thought that the addition-hypothesis can be justified over the quaddition-hypothesis on the grounds of simplicity. The thought would be that the devious hypotheses are less likely to be true since they are more complicated, and just as we might try to justify a scientific hypothesis on grounds of simplicity, we could try to pull of the same trick in the context of Kripkean skepticism.Kripke argues against this thought on two grounds.

Firstly, he argues that simplicity is hard to define and that judgements of simplicity are somehow too subjective to play a role in a solution to Kripkean skepticism. Now this worry isn’t going to fly in the context of naturalness-based solutions, since naturalness is an objective distinction. So put that to one side.

Secondly, he suggests that anyone who is tempted to appeal to simplicity hasn’t really understood the skeptical scenario. It’s this point which is important in the present context. Kripke tells us that whilst simplicity considerations “can help us decide between competing hypotheses,” they can never “tell us what the competing hypotheses are. If we do not understand what two hypotheses state, what does it mean to say that one is“more probable” because it is “simpler”? If two competing hypotheses are not genuine hypotheses, not assertions of genuine matters of fact, no “simplicity” considerations will make them so.”

The point is that the skeptical scenario shouldn’t be understood as though we have two hypotheses about what is meant and that whatever facts fix meaning don’t fix which hypothesis is the right one. That Kripke initially develops things like that is just a dramatic device. Rather, the real conclusion is that no content can be attached to a given expression — so if two hypotheses lack truth-conditions, no sense can be made of the idea that one of them is more likely to be true because its simpler. So the point is that its not like we’ve got a kind of indeterminacy in which rule is being following — i.e. we have two rules and its indeterminate which rule we’re following — rather, we’re bringing into question the very idea of a rule. In this way, the problem is “constitutive” in character.

Now, there is at least a prima facie case for thinking that naturalness is in the same boat as simplicity. To adapt Kripke: if two competing hypotheses aren’t genuine hypotheses, what sense can be made of the thought that one of them is better because it is more natural? If two competing hypotheses are not genuine hypotheses, not assertions of genuine matters of fact, no “naturalness” considerations will make them so. I can see how naturalness would help if we had some kind of indeterminacy in which rule was being followed, but since the problem is supposed to be constitutive in character, it’s not immediately obvious how appealing to naturalness helps.

But Lewis’s idea isn’t that naturalness solves the problem all by itself. Rather, the Lewisian metasemantic proposal is that meaning is fixed by use plus naturalness. So the point is that we initially look at the facts about Billy’s past usage of the term “plus”, and that settles a range of hypotheses — and then considerations of naturalness come in to break ties. It’s a good question whether naturalness gets us down to a unique hypothesis, but that’s a different issue.

This suggests that Kripke is attacking a straw man when he considers the simplicity-based solution. The friend of simplicity doesn’t think that meaning is fixed by simplicity, any more than the friend of naturalness thinks that meaning is fixed by naturalness. Rather, the thought will be some independent factors — use, most likely — give us a range of hypotheses, and then facts about simplicity help us to break the tie. Now, I’ve got no truck with the simplicity-based solution, but what I do think is that Kripke’s major objection against it doesn’t fly.