NoR 4.3: Subject-sensitive simplicity

This is one of a series of posts setting out my work on the Nature of Representation. You can view the whole series by following this link

In the previous post, I presented three underdetermination challenges. These amount to different ways of assigning the same truth-conditions to the sentences we use. Each is definitely incorrect, either because it assigns the wrong referents to words, or the wrong compositional rules to the language. But we can’t explain why it is incorrect by pointing to a lack of fit (or lack of strength) with the base facts (conventional associations between sentences and coarse-grained propositions). And for at least the last of the challenges—twisted compositional rules—we can’t explain why it is incorrect even if we suppose that our work on layer-2 intentionality earns us the right to a much more fine-grained set of facts about belief content.

My goal in this post is to review the obvious saving constraint: simplicity. I’ll recap the way that in Lewis’s hands, this turned into the idea that “natural properties” were “reference magnets” (we already saw this simplicity-naturalness connection as it arose in the context of inductive concepts). And I’ll put forward a very different treatment of simplicity, a “subject-sensitive” version on which each agent’s cognitive repertoire defines a set of contents that are reference-magnetic for their language. The effect is a new and better way to use the work already done on thought content to fix determinate linguistic content.

So first of all: simplicity. I have considered it once before. When considering concepts that were used in inductive generalizations, I sketched a way of deriving a constraint on content, via the rationality of inference to the best explanation. The best explanation, again, was determined by strength, fit with data, and simplicity. Applied to that case, the prediction was that the interpretation of the subject should be one which makes the content that they are treating as an explanatory generalization a simple hypothesis (all else equal). Overly “disjunctive”, less simple, interpretations of the concepts subjects deploy in such contexts are thus disfavoured.

Notice that in this case of belief/desire interpretation, there is no direct constraint that the interpreter’s story about “rationalization” should be simple. Rather, the constraint is that it rationalize the agent, inter alia making their beliefs justified. Simplicity entered the picture only when the subject’s cognitive architecture made simplicity epistemically relevant. By contrast, the proposal in the case of linguistic representation is that a role for simplicity is falling out of the fact that we appealed to best explanation directly in the selectional ideology itself. That will mean that the way that theses about simplicity play out here will be rather different to what we saw before. In particular, simplicity in content-assignment is non-contingently, always and everywhere a determinant of content—there are no restrictions to special classes of words, as there was to inductive concepts in the earlier account.

I will be assuming that simplicity is in the first instance a property of theories, not of abstract functions. So in order to make sense of that idea that ranking compositional interpretations (abstract functions, remember) as more or less simple, we need to do some work. We look to the ways those functions can be most concisely expressed—by an axiomatic specifications of the referents of lexical items, plus compositional rules. As well as some measure of the compactness of a given axiomatic specification, we will also need to make sure the specification is presented in some canonical language. In all this, I follow what I take to be Lewis’s treatment of simplicity (independently motivated, and deployed in e.g. his Humean theory of laws). And as I noted earlier, if we make one final move we can explain a famous feature of Lewis’s account of language.

That move is to identify the canonical language with “ontologese”, a language that features predicates only for metaphysically fundamental properties and relations (plus various bits of kit such as broadly logical concepts—Lewis was never very clear what resources were in the canonical language beyond the natural properties (the best guess is that he thought he would do enough by just listing them). Sider, the coiner of the term “ontolegese”, suggested that we get a more principled and satisfactory theory by generalizing the idea of fundamentality, so that quantifiers, connectives etc can be fundamental or not. On Sider’s version of the view, every primitive expression in the canonical language should denote something metaphysically fundamental.

Note the following (which I first presented in my “Eligibility and Inscrutability” paper from 2007). Suppose we have a pair of compositional interpretations of L, differing only in their interpretations of a single predicate “F”. The first says it denotes P, the second says it denotes Q. And suppose that the shortest way to define P in ontologese is longer than the shortest way to define Q in ontologese. Then the second interpretation will be more compactly expressable in ontologese—simpler—than the first. If the two theories are otherwise tied (on grounds of fit, predictiveness, etc) at the top as candidates for being the best interpretation of L, then on these grounds, the second will win. So we derive that length of definability in ontologese—what Lewis calls “relative naturalness”—of the semantic values assigned as referents to words is one of the determinants of correct interpretation. We can also see that compositional rules, no less than reference-assignments, can be evaluated for relative naturalness, and on exactly the same grounds: contribution to simplicity.

Consider the Kripkenstein problem of deviant compositional rules. We have every reason to believe that the deviant rule takes longer to write out than the original—after all, the way we have of writing it out is to write down the original, add a conjunct restricting its application, and then add a further disjunction. So we have every reason to believe it’s a less natural compositional rule. So the theory that uses it is less simple. Since it has no compensating virtues over the standard interpretation, it is incorrect. Similar stories can be run for the skolemite and permuted interpretations, if those have not already been dealt with at an earlier stage of the metaphysics of representation.

I highlight again that one can accept much of this putative resolution of the underdetermination challenges without going all the way to relative naturalness. The identification of simplicity with compactness of expression in ontologese is a theory: and a very contentious one (even in application to theories in metaphysics and fundamental physics, and certainly for higher-level theories of social phenomena like language). We might short-cut all this simply by stopping with the very first claim: that simplicity partially determines best explanation. Add the assumption that the Kripkensteinian compositional rule is less simple than the “straight” alternative. If that is true (never mind what grounds that fact) our problem is over. There is work to do for those with an interest in the theory of simplicity, but the metaphysician of content can pack up and go home. The same structure applies also to permuted and skolemite interpretation—those interpretations can be ruled out if we assume that the interpretations involved are less simple than the standard.

The needed assumptions about simplicity are very plausible. So there’s a good case to be made that at this level of description, the Lewisian solution just works. And if one is content to treat it as another working primitive, we are done. But of course, if simplicity turned out to be some kind of hyper-subjective property linked to what each of us feels comfortable working with, then there’s a danger that linguistic content will inherit this hyper-subjectivity. And one might worry that it will be impossible to articulate simplicity as it applies to linguistic theories, without appealing to facts about linguistic representation. So there’s good reason to dig a little deeper. That also has the advantage of making the account more predictive—it’s a great virtue of the full Lewisian package that we can start from on which we have an independent grip (what is more or less natural, in his sense) and derive consequences for linguistic representation. It would be nice to recover similar explanatory power.

One can dig deeper without going all the way to the point that Lewis reaches. Indeed, one can endorse the general identification of simplicity with compactness-of-expression-in-a-canonical-language without saying the canonical language is ontologese. Now in other work (“Lewis on reference and eligibility”, 2016), I floated the idea of “parochial” simplicity. This involves the theorist specifying—in a quite ad hoc and parochial manner—some language C that they favour for measuring simplicity. Relative to that choice of C, simplicity facts can be handled as before, and shortness of definability from C becomes a determinant of content (“reference magnetism”). Of course, if different theorists select different C, they may pick different interpretations as correct, and so in principle come up with different candidate accounts of semantic content. So this approach makes facts about linguistic content (insofar as they go beyond what we can extract from the constraint to “fit with the conventional base”), if not wildly subjective, at least parochial. I don’t find that as abhorrent as vast undetermination of reference. Indeed, I think it’s the best version of a deflationary approach to linguistic representation. But I do not think it counts as a realist theory of linguistic content—and that is my present target.

Accordingly, I float another option. Let the canonical language be fixed not by the theorist’s choice, but by the subject’s conceptual repertoire. For this to make sense, we need to know what their conceptual repertoire is, and it needs to be in some medium in which it makes sense to carry out definitions. So here I am going back to the work we did earlier in layer 2 metaphysics of representation, and adding the assumption that prior to public language, there is a sufficiently language-like medium for thought, whose components have fairly determinate content—the story of how they acquire that content is as given in the subsequence 2 of posts. I propose that ew now let the simplicity of a theory (for subject x) be the compactness of its expression in x’s medium of thought. So, if x’s medium of thought is mentalese, with a certain range of basic concepts, then we can let the simplicity of a property be its minimal length of definition in mentalese, from that basic range. When it comes to language, the things that each agent can think about via an atomic concept will be reference magnetic, for them. How this kind of subject-sensitive magnetism relates to naturalness is entirely deferred to to the level of metaphysics for thought-content.

(You might worry that the interpretation will be inexpressible for theorists who lack semantic and mathematical vocabulary involved in setting out the semantic theory. If that’s the case, then I will simply build into this account of simplicity for semantic theories that it should be judged by the subject’s conceptual repertoire supplemented with standard semantic and mathematical resource. This is analogous to Lewis’s supplementation of predicates with natural properties with other general-purpose resources, in fixing his “ontologese”).

My proposal gives up on the idea that “simplicity” is a subject-independent theoretical virtue, and so takes seriously the common idea that what is simple for me may not be simple for you, and vice versa. But given your conceptual repertoire and mind, we will both agree that the twisted compositional interpretation is less simple than the straight one, and that the permuted and skolemite interpretations are more complex than the standard. The agreement arises only because our differing conceptual resources overlap to a considerable extent: we both have the capacity to generalize unrestrictedly, for example.

There is a wrinkle in this proposal to make simplicity subject-sensitive. We are targeting a metaphysics of public language, and a public language involves a diverse population, each with a potentially idiosyncratic conceptual repertoire. So who within this population gets to set the standards of simplicity? I propose: no one person does. Simplicity relative to the population as a whole is indeterminate,  with each member of the population contributing their own precisification of the notion. Nevertheless, language-using populations will tend to overlap in conceptual resources, and so will agree on central verdicts about the relative simplicity of one theory over another—in particular, the permuted, skolemite and twisted interpretations are determinately less simple than the standard alternative.

(A good challenge to me, for enthusiasts to press: how can I see this about simplicity at the level of language, and also appeal to simplicity as a constraint on the content of inductive concepts. This is a challenge to which I hope to return.).




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