NoR 2.1: And

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 series of posts, I introduced radical interpretation as my favoured account of the “second layer” metaphysics of representation. It aims to specify the way in which the facts about what agents believe and desire is grounded, inter alia, in facts about what they experience and how they act (a story about the latter, “first layer” of representation remains on the to-do list). Radical interpretation tells us that what it is for an agent x to believe/desire that p is this: the correct interpretation of x attributes a belief/desire that p to x. It also says that the correct belief/desire interpretation of x is that which best rationalizes x’s dispositions to act in light of their experience. So a key question was how “best rationalization” is to be understood. To this point, I’ve used an underdetermination argument—the bubble puzzle—to show that we can’t read the relevant notion of rationalization in purely structural way. And I’ve argued that an alternative understanding of rationalization—substantive rationality, roughly glossed as the agent believing and acting as they ought, given their experience/desires—can pop the the bubble puzzle.

The aim here and in the next series of posts, is to draw out much more specific consequences of radical interpretation for specific kinds of representation. Across a series of posts, we’ll derive results that speak to well-known and challenging-to-explain features of representations. Among these are the referential stability of “morally wrong”, how it’s even possible to express absolute, unrestricted generality. More generally, I will show how patterns in the grounding of the denotation of this or that concept—causal patterns, inferentialist patterns and the like—emerge within the radical interpretation framework. I take the posts to follow to illuminate the relation between the kind of foundational theory of representation that I am pursuing, and the more local, less-reductive projects that sometimes go under the project “theory of reference”. That’ll bring me into dialogue with theorists like Peacocke (on logical concepts), Wedgwood (on moral concepts) and Dickie (on singular concepts). Towards the end, as attention turns to descriptive general concepts, I’ll investigate in a similar spirit the role that so-called “natural properties” can play, which brings me into contact with recent work in the Lewisian tradition by Weatherson, Schwarz and Pautz.

This is a big agenda! Any one of the following posts could generate a whole series of discussions on their own (indeed, the post about the reference-fixing of moral wrongness is going to be a short presentation of the ideas I set out and defend at length in a long, forthcoming paper). But I think there’s a virtue to laying out the essential ideas as cleanly and sparsely as possible, so the common patterns can emerge, and so I’ll stick to one manageably-sized post on each.

I start right now with the simplest case, but one which illustrates the moving parts at work in all that follows.  This is the case of the propositional logical connective and. And here, as ever, my focus is not on the word “and” in a natural or artificial language, but in the logical concept and as it appears in thought. Let me remind readers of a familiar story about how this a concept gets its meaning.

A connective-concept c is associated with the following inferential patterns:

  • from A, B derive  AcB.
  • from AcB derive A
  • from AcB  derive B.

The crucial claim is that what makes it the case that the connective concept c denotes the truth-function conjunction is the fact that it is associated the rules just mentioned.

Different versions of this idea will fill in the the two steps in more detail: saying more about the nature of the “association” between concept and the patterns expressed above with “derives”, and saying more about the recipe for getting from such patterns to denotation. For example, the A Study of Concepts-era Peacocke held that each concept figured in patterns of belief formation that were “primitively compelling”, and that for c, the relevant patterns of belief-formation were inferences mirroring the transitions labelled with “derive” above. He held that for c to denote the truthfunction f was for f to make valid the primitive compelling inferences configuring c.

My aim in this section is to capture what’s right about this inferentialist idea within the overarching theory of radical interpretation—to show in particular that radical interpretation can predict and explain what I think is quite an attractive view of the grounds of meaning of that particular logical concept.

Radical Interpretation unaided won’t get us there. And so here (and in following sections) I’ll be adding two kinds of auxiliary assumptions to the setup. These will comprise, first, assumptions about the specific cognitive architectures that our subject—Sally—possesses, and second, normative assumptions (epistemic or practical) involving specific kinds of content.The first and most basic architectural assumption (one crucial to securing our subject-matter) will be that Sally’s thinking consists in tokening state-types which have a language-like structure, within which we find analogues to the logical connectives “and”, “or”, “not” etc.

[Aside: The hypothesis that there is a ‘language of thought’ would vindicate this assumption, though it’s not the only thing that would do so.]

Second, I’ll be assuming also that the syntactical properties of the structured states in question, and the attitude-types they token  (e.g. flat-out-belief, supposition, degree of belief, degree of desire) , are grounded prior to and independent of the determination of content that they are paired with. The job of the interpretation that the radical interpreter selects is purely to assign content, which it does in a “compositional” way via assigning content to the atomic elements and specifying compositional rules.

[Aside: There is a tradition of appealing to functional role both to individuate the syntax of mentalese and word-types. In Fodor, for example, such assumptions are preliminaries to giving a causal metasemantics to pin down the content of the attitudes. That would be a suitable backdrop for this discussion, though of course, the metasemantics I explore is a rival to Fodor’s. If one thought that interpretations should do all these jobs holistically, then you can read what is to follow as a story about what, in substantive radical interpretation favours one interpretation over others among all those agreed on syntax and attitude-type, and there will have to be further discussion about how such local rankings interact with factors that fix the attitude-types.]

Third, I make the auxiliary assumption is that we can identify, prior to content-determination, which inferential rules involving c Sally finds primitively compelling.

The fourth and final architectural assumption is that such associated-entailments for the case of c turn out to be those given above and repeated here:

  • from A, B derive  A and B.
  • from AcB derive A
  • from AcB  derive B.

In the case of a fictional character like Sally, we can make such assumptions true by stipulation. But to hypothesize that we are like Sally in these respects would be a theoretical posit about our cognitive architecture, not something that is a priori or analytically obvious. So to emphasize: such assumptions are not essential to radical interpretation as such. Radical interpretation will have something to say about creatures who do possess this particularly clean sort of architecture—which for all we know from the armchair, includes us. And we want it to say plausible and attractive things about creatures with such an architecture. Let’s see if it does.

Radical interpretation tells us that the correct interpretation of mental states is one that maximizes the rationality of the individual concerned—where rationality in the relevant sense means that as far as possible the subject believes as they ought to, given their evidence, and acts as they ought, given their beliefs and desires. All else equal, an interpretation will score well on that measure to the extent that it makes the most basic patterns of belief formation ones that preserve justification (we don’t want leaky pipes!). And so, given the assumptions about cognitive architecture, we need our interpretation of the concept c to make rational our practice of treating the given rules as primitively compelling (inter alia, being willing to reason in accordance with them).

We can already see this desideratum has teeth. Interpreting c as disjunction, for example, makes a nonsense of the fact that Sally associates with it the rule that A is entailed by AcB. Having a basic disposition to infer A from A or B would be irrational! This is representative, and what we need to do is add more auxiliary assumptions, this time about what a rational agent could or could not be like—in order to derive specific predictions about what c denotes.

The following auxiliary normative assumptions will suffice to generate the prediction that c denotes conjunction:

  • A substantively rational agent would be such that they find primitively compelling the inference from A and B to A, they find primitively compelling the inference from A and B to B, and they find primitively compelling the inference from A, B jointly to A and B.
  • For no content X other than conjunction would a substantively rational agent would be such that they find primitively compelling the inference from AXB to A, they find primitively compelling the inference from AXB to B, and they find primitively compelling the inference from A, B jointly to AXB.

Notice here we use rather than mention the concept of conjunction. These are simply a couple of claims (very plausible ones) about what substantively rational agents equipped with a certain kind of inferential cognitive architecture are like.

The argument to the conclusion that Sally’s connective concept c denotes conjunction is as follows. First, we have the a posteriori assumption that c plays a distinctive cognitive role in Sally’s cognitive architecture, captured by the given rules. Second, we have substantive radical interpretation which tells us that the correct interpretation of c is one that maximizes (substantive) rationality of the agent. We now need, third, a “localizing” assumption, inferential role determinism for c, which says that the interpretation on which Sally is most rational overall is one on which the particular inferential dispositions captured by the rules just given for c are rational. Putting these three together we have the following: the correct interpretation of Sally is one that makes the inferential role associated with c most rational.

The final element to add to this is the pair of normative premises introduced above, which tell us that conjunction is the thing that (uniquely) makes those particular inferences rational. We then derive that Sally’s connective concept c denotes conjunction.

I finish by emphasizing a few things in this derivation. First, the assumptions about cognitive architecture are sufficient (given the other premises) to derive the metasemantic result that c denotes conjunction. There’s no suggestion here that they’re necessary, in order for c to denote conjunction. Remember—the aim was to show what radical interpretation predicts for a certain possible, contingent architecture, not about what is required in order to think conjunctive thoughts per se.

Second, the localizing assumption that I flagged up plays a very significant role. The most rationalizing global interpretation of an agent can in principle attribute local irrationalities—there could be other inferences Sally makes that involve c, which are irrational by the lights of the interpretation of c as conjunction. For example, the stated rules are silent about the way that conjunction figures in desires, and if figured in desires in a way that would be best rationalized by interpreting c as disjunction, then there would be an interpretative tension, and it is not at all clear that a plausible theory would predict that c picks out conjunction. Inferential role determinism assures us that we’re dealing a case where “all else is equal” where such pressures are absent.

Third, the normative assumptions themselves, even if accepted as true, are the sort of things we would expect to be backed by more detailed first-order normative (/epistemological) theory. That need for that kind of principled backing is something that I emphasized in a previous post. Why is it that it’s rational to perform, and find primitively compelling, the inferences involving conjunction? Surely the full story has something to do with the fact that those inferences are guaranteed to be truth-preserving, since they are valid. Why is it that no other connective content will do the job? Presumably this will be defended on the grounds that conjunction uniquely has the property of making the inferences in question valid. But why is validity required to rationalize those rules? Certain of the inferences we’re disposed to perform–even those that are plausibly basic—are not guaranteed to be truth-preserving, so it’s not clear why validity is required for rationalizing an inferential disposition. I think the reaction to this should be to strengthen the assumed inferential role in ways so that validity plausibly is required for rationalization—e.g. by making the inference indefeasible.

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