Nature of Representation book draft

… is now fully in being. This is a much reworked version of the themes of the series of blog posts below, themselves a distillation of work over the last five years.

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NoR 4.5: the base–words, population, convention.

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

Previous posts in this subsequence have taken convention as basic, and worked forward from that to an account of languages in use, correct compositional interpretation, attitude expressed, and the like. In this post, I’m going to outline the account of base facts, to hook this account of layer-3 representational facts back in to the facts about mental representation established at layer-2. I’ll also sketch how (in joint work with Gail Leckie) we have proposed extending this account to give a treatment of some other elements of the “base” for selecting the correct linguistic interpretation: the words that are interpreted, and the language-using population.

Lewis’s account of convention was as follows. A regularity R is a convention in a population P iff within P, the following hold, with at most a few exceptions:

  1. Everyone in P conforms to R.
  2. Everyone in P believes that everyone in P conforms to R.
  3. This belief gives everyone in P a good reason to conform to R himself.
  4. There is a general preference in P for general conformity to R rather than slightly-less-than-general conformity to R
  5. There is an alternative possible regularity R’ such that if it met (1) and (2), it would also meet (3) and (4)
  6. All of (1-5) are common knowledge.

The relevant regularities, generalized to allow for states of acceptance of enriched content, are the following:

  • (Truthfulness) Members of P utter s only if they accept p, where L(s)=p.
  • (Trust) If a member of P hears another member of P utter s, she tends to come to accept p, where L(s)=p.

And so what naturally suggests itself is the following account the linguistic “source intentionality”, the language-in-use appealed to in our previous discussions:

  • (Lewis) Given an exogenously fixed specification of population P1 and typing of sentences, T1, L is the language of P1 for T1 iff there are conventions of (Truthfulness) and (Trust) in L in P1 for T1

Let me note some features of this. First, the characterization of convention is full of appeals to attitudes of members of the population: their beliefs and preferences, together with normative facts about reasons for conforming to a regularity. Together with Truthfulness and Trust and the way that they appeal to psychological facts about agents, clearly the work done to ground belief/desire and other facts about mental representation are being drawn on heavily at this point.

I am not going to engage in detail with the various worries one might have about this account of convention, or the modifications one might introduce to evade it. It doesn’t really matter to me whether this is a good account of convention in general, so long as it’s a good characterization of the features of regularities in language use that feed into linguistic source intentionality. And any other characterization of convention that appealed to intentional resources and delivered the same results on our target cases would do just as well, at least to this point. But just as my previous handling of mental source intentionality, my interest will be on extending the scope of the appeals to convention.

The need for extension is prompted by the appeal, in the account as currently formulated, for exogeneous typing of sentences and identification of language-using populations. But we don’t get facts about sentence-types of language using populations for free. But what grounds facts concerning when two blasts of sound are of the same sentence type, or when two people belong to a single language-using population? As is familiar in the specialist literature on this, it’s extremely implausible that we have any way to identify sentence-types by types of shapes or sounds (for an excellent review of problem cases and the relevant literature, Nick Tasker’s PhD thesis and papers should be a first port of call). The worry is that there’s no way to pick out sentence-types independently of semantic facts. What other than semantic facts makes ambiguous homophones/homographs “bank” and “bank” distinct words? It is no easier to imagine independent way of picking out a population that uses a single language, except by the fact that they are all users of that very language. But of course, the latter is a semantic fact that could not feature in a exogeneous characterization of populations (I’m grateful to Leeds’ Roger White for alerting me to that to several years ago).

Leckie and I suggest a different model:

  • (Endogenous) Given an utterance u, <P, T, L> is a language in use in utterance u iff P is a population and T a typing relation relative to which there are conventions of (Truthfulness) and (Trust) in L, and the speaker/hearer of u is a member of the population P; and u is a member of some equivalence class of the typing relation T.

Instead of determining L after fixing a particular population and typing relation, (Endogenous) treats the population and typing relation as variables whose values are fixed however is necessary to produce conventions of (Truthfulness) and (Trust). The correct word typing for English is as described by the T role in a language-in-use for a population that includes the utterance I am presently making. The membership of the language-using population of which I am a part is as described by the P-role in that same language-in-use. And finally, the content-sentence pairings that constitute linguistic source intentionality for English can be read off that same triple.

It is important to understand that endorsing this account does not foreclose saying other, more immediately illuminating things about words and populations. If you thought you had an exogeneous way of specifying a language-using population and a typing relation that feature in linguistic conventions, then all the better for (Endogeneous)—that typing relation and population will be an illuminating independent specification of a typing relation that features in a language-in-use, according to our formulation. But of course, pessimism on that front motivated the shift to this one. But it’s much more plausible is that one could, via appeal to semantic facts, give a more illuminating characterization of the language-using population and a typing relation. For example, Nick Tasker’s PhD dissertation an intriguing account of the nature of words is offered, building on work in the metaphysics of artefacts by Amie Thomasson. An account of word-individuation (or at least, various necessary and sufficient conditions) is offered as part of the package, built on the more general model of individuation of artefact-kinds. But Tasker is clear from the start that among the determinants of word-individuation for him are facts about the semantic properties of the individual word tokens, their recognizability to a certain audience, and so forth. Tasker’s account might be exactly what we need to understand how words work, but also entirely unsuitable to be slotted in as an “exogeneous” account of word-individuation as per the original model. But so long as word-types as he characterizes them figure in linguistic conventions, his account is consistent with (Endogenous).

In sum: since the reductive characterization of words and populations is given by (Endogenous) and not by an exogenous characterization, the project of saying interesting things about types and populations that figure in languages in use doesn’t have to be burdened by any reductive constraint. Metaphysically speaking, the bounds of the population, the relevant types, and the contents conventionally associated with sentences, are all jointly and simultaneously grounded in facts about patterns of linguistic usage and attitudes of speakers and hearers.

The worry about this kind of account is not that it’ll fail to count genuine sentences and language-using populations as sentences and populations. The worry to have is that it will overgenerate. After all, by choosing crazy typing relations and gerrymandered populations, we may be able to find all sorts of dubious regularities connecting uses of sentences (so typed) to attitudes. In the Leckie/Williams paper, we consider a number of different ways this might happen, for example, by subdividing genuine populations and types (typing utterances by brown-eyed people separately from blue-eyed people); merging separate types together, or tailoring the population or typing so as to bias the resulting regularity (e.g. by restricting it to population who apply “red” to more orangey things than is the norm). Our strategy in response is to work through such examples, and argue that none of them produces a genuine example of overgeneration. They are gerrymandered regularities of truthfulness and trust, sure—but we argue, they each violate one or more clauses of the characterization of convention Lewis gave.

Suppose the Leckie/Williams project succeeds. Then revised characterization of “language in use” means that we remove the need to list in addition the typing of sentences and the identification of populations as among our the base facts of the metaphysics of linguistic representation. And with that, the last tie between the layers of representation has been put in place.

 

 

 

NoR 4.4: Beyond belief.

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 three posts, I’ve given my favoured interpretationist account of linguistic content: fixed by that explanation fitting the base conventions of truthfulness and trust that best manages the trade off between (subject-sensitive) simplicity and strength.

The base facts were conventions linking utterances to belief. So as well as feeding into an account of how words get their meaning, the conventions give us an excellent handle on what it might mean to say that in asserting a sentence, we are “expressing a belief”. Notice, though, that the beliefs conventionally expressed in this way will not necessarily have the same content as that of the sentence—this is the phenomenon we covered in the post Fixing Fit.

Is the state of mind expressed by a sentence always a belief? Might moral sentences express pro and con-attitudes, epistemic modals a state of uncertainty, and conditional sentences states of conditional belief? There is a very natural way to understand what such claims mean, in this framework, respectively:

  • There is a conventional regularity of uttering “x ought phi” only if one’s contingency plan for x’s situation, is to phi, and coming to so plan when one hears the utterance “x ought phi”.
  • There is a conventional regularity of uttering “It might be that p” only if p is compatible with what one believes, and of adjusting one’s beliefs to make p compatible with them when one hears the utterance “It might be that p”.
  • There is a conventional regularity of uttering “if p, q” only if one believes q on the supposition that p, and of adjusting one’s beliefs to come to believe q on the supposition that p, when one hears the utterance “if p, q”.

These are not the only ways of formulating the connections in the conventional framework—for example, perhaps closer to the dialogical role of epistemic modals would be to present them as a test: the “sincerity” condition remains the same, but on the “trust” end, the convention is that the speaker checks that p is already compatible with their beliefs, or else challenges the utterer.

Are there regularities of this kind? One might wonder whether someone uttering the words “Harry ought to phi” regularly leads their audience to plan to phi in Harry’s circumstances. Attention is naturally drawn to cases where these normative claims are contested—where someone is saying that Harry ought to change career, or do more exercise, or avoid white lies. In those cases, we don’t respond to bare assertions simply by incorporating the plans expressed into our own—we would tend to ask for a bit more explanation and justification. But of course, the same could be said of contested factual claims. If someone claims that the government will fall next week, we want to know how they know before we’ll take them at their word. These are violations of the “trust” regularity for belief, unless we add the caveats mentioned in an earlier post: to restrict it to situations where the speakers have no interest in deception and hearers regard speakers as relevantly authoritative. The same qualifications are, unsurprisingly, necessary in this case. And once we make that adjustment, then it may well be that the cases above are indeed conventional regularities. (It’s worth remembering one can come to plan to phi in x’s situation, without changing your contingency plans for any situation. For example, if you hear someone say “Harry ought to change career”, one might hold fixed one’s opinion about the circumstances in which changing-career is the thing to do, and simply come to believe that Harry is now in one of those circumstances. Lots of information-exchange using normative sentences can take this form.)

So there is a plausible way of extending the talk about sentences expressing beliefs to a more general account of sentence-types expressing attitudes of various kinds.

Now, this is all perfectly compatible with following being true, at one and the same time:

  • There is a conventional regularity of uttering “x ought phi” only if one believes x ought to phi, and of coming to believe x ought to phi upon hearing “x ought phi”.
  • There is a conventional regularity of uttering “It might be that p” only if one believes it might be that p, and of coming to believe this upon hearing “it might be that p”.
  • There is a conventional regularity of uttering “if p, q” only if one believes that if p, q, and of coming to believe this upon hearing “if p, q”.

After all, I already flagged that on this account, sentences of any kind will be conventionally associated with many different beliefs. So why not beliefs and other attitudes too?

There are questions here, however, about the appropriate order of explanation, and it’s hear we make contact with work on broadly expressivist treatments of language. For one might think that our layer-2 story about fixing thought content did not get us to a point where we had a grip on thoughts with modal, deontic or conditional content. If that is the case, then although the later three conventional associations with belief will come out eventually as true commentaries on an agent, they are not something to which we had earned a right at layer 2 of our metaphysics of representation. On the other hand, we might think that from patterns of belief and desires, we will have a fix on states of belief, supposition and planning (planning states with factual content are not something that I’ve covered so far, but I’d be happy to add them as an additional element to the kind of psychology that radical interpretation will select).

That leaves us in the following position: as we approach linguistic content, for some sentences, we are not in a position to appeal to belief-centric conventions of truthfulness and trust, since the belief-states that they might express have not yet been assigned content. The semantic facts that we can ground by means of the story just given will then be restricted to a fragment of language that leaves out these problematic bits of vocabulary. So we need to go back to the grindstone.

Expressivists about deontic and epistemic modals and conditionals will tend to think that this is the situation we find ourselves in—and they have a solution to offer. Rather than building our metasemantics for the problematic terms by looking at features of the belief expressed, they propose to work directly on the other attitudes—the plans, suppositions or ignorance—that stand to these sentences just as ordinary beliefs stand to factual sentences. Let us consider how this might go.

To start with, the story I have been giving would need to be generalized. The key “datapoints” that a semantic theory had to “fit” were the range of propositions that I said were “conventionally associated” with each sentence. Those contents are associated with a sentence because by being the contents of the beliefs the sentence expresses (i.e. that figure in conventions of truthfulness and trust). We can’t just mechanically transfer this to other attitudes: for example, the content of the plan expressed by “Harry ought to change career” might: changing career in Harry’s circumstances. But we will get entirely the wrong results if we required our semantic content to assign to normative content the factual proposition that one changes career in Harry’s circumstances. The semantics needs to fit with a planning state, not a factual belief that the plan has been executed.

Let us take a leaf out of Gibbard’s book here. Let a world-hyperplan pair be the combination of a complete description of how the world is factually, together with function from all possible choice situations to one of the options available in that situation. To accept a world-hyperplan pair is to believe that the world fits the description given by the world component, and to plan to do x in circumstance c iff the hyperplan maps c to x. To accept a set of world-hyperplan pairs is to rule out any combination of world and hyperplan that is outside that set—this amounts, in the general case, to a set of conditional commitments to plan a certain way if the world is thus-and-such. (Okay, you might want more details here. This is not the place to defend the possibility of such a redescription: if it is not legitimate, then that’s a problem for Gibbardian expressivists independent of my kind of metasemantics).

I will assume that our metaphysics of layer-2 representations gets us to a point where we can read off what a subject’s conditional plans are, in this sense. We can then redescribe the combined belief/planning states of this agent in terms of which sets of world-hyperplan pairs they accept. And that means we will have earned the right to redescribe this:

  • There is a conventional regularity of uttering “x ought phi” only if one believes x ought to phi, and of coming to believe x ought to phi upon hearing “x ought phi”.

as follows for a suitable q (set of world-hyperplan pairs):

  • There is a conventional regularity of uttering “x ought phi” only if one accepts q, and of coming to accept q upon hearing “x ought phi”.

And once in this format, we can extract the data the semantic theory is to fit, since we now have a new, more general kind of conventionally associated content: the combined belief/planning states q. The correct compositional interpretation will then be as before: the (subject-sensitive) simplest, strongest interpretation that fits these base facts. And contemporary expressivist semantic theory is exactly a specification of functions of this kind.

The crucial technique here is the Gibbardian transformation of a description of a subject’s psychology as the acceptance of enriched content—that’s what allows us to articulate the convention in a way that provides a target for compositional interpretations. So if we want to replicate this metasemantics for other kinds of expressive content, we need to perform the analogous redescription. It might be, for example, that to underpin epistemic modals, we need to describe an agent as accepting a set of world-information state pairs, representing combinations of factual states of the world and states of their own factual information to which they are open. To underpin epistemic modals, we need to credit the agent as accepting a set of world-update function pairs. And if this is to be a single story across the board, we will need to combine these and others to a highly complex summary of a possible opinionated psychology: world-hyperplan-information-update-etc, and then, on the basis of the facts about mental content already established at layer 1 in more familiar terms, say which of these possible opinionated psychologies are ones to which the subject is open.

None of this is easy or uncontentious! The existence of the conventions that tie the target sentences to non-doxastic attitudes, the Gibbardian redescriptions, and the availability of compositional interpretations of language are all points at which one might balk. But those who favour an expressivist theory of the discourse in question are likely to be sympathetic to these kinds of claims, and my central point in this post has been to show that the convention-based metasemantics can underwrite that project just as much as it can underwrite more traditional cognitivist projects.

(I’m very grateful to discussions with Daniel Elstein and Will Gamester that have shaped my thinking about the above. They are not to be blamed.)

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.).

 

 

NoR 4.2: Fixing Fit

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

Let us suppose that the base facts about whole-sentence-content (for those sentences which feature in actual patterns of use) have been established. The story about how we fix word-content was the following: that the correct compositional interpretation was whatever “best explains” the facts about whole-sentence content.

So what makes one compositional interpretation of a language better than another?  I will work with a familiar model: that betterness is determined by the tradeoff between virtues of fit, strength and simplicity. If the datapoints are facts about linguistic content (for a constrained range of sentences) then the contents assigned by the compositional theory should explain that data, which minimally requires being consistent with it. The theory should be strong, in that it should predict as much of this data as possible. But this is balanced by simplicity. As in an earlier post, the model for this is compactness of expression, when the interpretation is expressed in some canonical language.

“Fitting” the base facts about sentential content does not mean the the compositional interpretation should assign the same content to whole sentences that the base facts supply. It would be bold to bet that there is a unique content conventionally associated with each sentence, and an even bolder bet that that will turn out to be the semantic content that can be generated compositionally. No, “fit” is a looser, more interesting criterion that this. The constraint as I understand it is the following: given the content that the compositional interpretation assigns to the sentence, plus suitable auxiliarly hypotheses (general information about rational agents and conventions of cooperation, special purpose pragmatic principles) as much as possible of the range of contents that are conventionally associated with the sentence should be explicable. It’s easy to explain why there will be a regularity of truthfulness and trust connecting “Harry is a bachelor” to the content that Harry is male, on the basis of a compositional interpretation of it as having the content that Harry is a bachelor, since generally we believe the obvious logical consequences of what we believe. The reverse would not be easy. Again, general information about Gricean conventions of orderliness together with the standard compositional content will explain why “Harry had five drinks and drove home” is conventionally associated with the content, inter alia that the drinking preceded the driving. So even if these regularities of truthfulness and trust count as conventions, the standard interpretations fit them well.

If Fit and Strength were the only determinants of “best explanation” of the language in use, then the account would be subject to counterexample. It is well known that the same sentence-level truth-conditions can be generated by a variety of lexical interpretations, some of which are obviously crazy. I introduced two in an earlier post:

  • Permuted interpretations. Where the standard interpretation has “Tibbles” referring to Tibbles, and “is sleeping” picking out the property of sleeping, the permuted interpretation says that “Tibbles” refers to the image under the permutation p of Tibbles, and “is sleeping” picks out the property of being the image under p of something which is sleeping. Systematically implemented, the permuted interpretation can be shown to produce exactly the same truth-conditions at the level of whole sentences as does the standard interpretation. But, apparently, that means that they fit with and predicts the same sentence-level facts about conventions. So we can’t explain on this basis the obvious fact that the permuted interpretation is obviously and determinately incorrect.
  • Skolemite interpretations. Where the standard interpretation has the quantifier “everything” (in suitable contexts) ranging over absolutely everything, the skolemite interpretation takes it to be quantify restrictedly only over a countable domain (this domain may vary counterfactually, but relative to every counterfactual situation its domain is countable). And (with a few caveats) we can show that the skolemite interpretation and the original are truth-conditionally equivalent. But, apparently, that means that they fit with and predict the same sentence-level facts about conventions. So we can’t explain on this basis the obvious fact that the skolemite interpretation is obviously and determinately incorrect.

We met these kind of deviant interpretations in the context of the metaphysics of mental representation. Under the assumption that thought had a language-like structure that allows us to pose such puzzles, I argued that normative facts about the way in which we handle universal quantification in thought and inductively generalize would solve the problem.

Now Lewis denied the starting point of this earlier story. He stuck resolutely to theorizing thought content in a coarse-grained way (as a set of worlds, and later a set of centred worlds/individuals), ignoring issues of individual representational states and any compositional structure they might have. That only delayed the day of reckoning, since once he reached this point in the story—with public language and its compositional structure—he had to face the challenge head on. Further, nothing that Lewis did earlier on helps him here. Remember, the the raw materials for selecting interpretations are conventions of the form: utter S only if one believes p; and come to believe p if one hears someone utter S. And since for Lewis the “p” here picks up a coarse-grained truth condition. But the permuted and skolemite interpretations fit that sort of data perfectly. So underdetermination looms for him.

(There is one way in which we might try to replay those earlier thoughts. Among the conventions of truthfulness and trust will be an association between, say, “everything is physical” and Jack being physical. That is obviously not going to be the semantic content, but we need to explain why there is a convention of truthfulness and trust there, given the semantic content we assign. Here is the suggestion: a restricted interpretation, even one that de facto includes Jack in the domain D of the quantifier, won’t afford such an explanation. That’s because the audience couldn’t rationally infer just from the information that everything in D is physical, to Jack being physical, except under the presupposition that Jack is in D (so what we should expect, under a restricted interpretation, is that we only get conventional association with: if Jack is in D, then he’s physical). This is a natural way to try to lever the earlier account I gave into the current setting. But unfortunately, I don’t think Lewis can appeal to it. For him, the contents that everything is physical and that everything in D is physical are identical—since they’re truth conditionally equivalent, denoting the same set of worlds. So it’s not an option for Lewis to say that believing one supports believing Jack is physical, while believing the other supports believing only the conditional—that’s a distinction we can only make if we presuppose a finer-grained individuation of the two contents.)

So Lewis needs something more than fit and strength in his account of better explanation. But so does everyone else. At first it might not seem this way. After all, if we’ve already solved these puzzles at the level of thought-content, then surely linguistic content should be able to inherit this determinate content? There are two problems with the proposal. First, it’s surprisingly tricky to get a workable story of how determinate content is inherited by language from thought. And second, there are further underdetermination challenges beyond the two just mentioned for which this strategy won’t help.

On the first point, let us assume, pace Lewis, that the structure of thought was itself language-like, and that we confronted and solved the problem of permuted and skolemite interpretations as it arose at this lower layer of representation in the way I described earlier. We will have already earned the right to ascribe to agents, for example, a truly universal belief that everything is physical (modelled perhaps by a structured proposition, rather than a Lewisian set of worlds).  The “inheritance” gambit then works as follows: there will be a regularity of uttering “everything is physical” only when the utterer believes that truly universal structured content. And to the extent that this regularity is entrenched in the beliefs and preferences of the community so that it counts as a convention (plausible enough), the constraint on linguistic interpretation will not simply be that we fit/predict data characterized by coarse-grained content, but that it fits and predicts fine-grained data. Ta-da!

But we have already seen that “fit” cannot simply be a matter of identity between the content of thought and language. And theorizing thought in a fine-grained way amplifies this. None of our assumptions entail that for each sentence in public language, there is a belief whose content exactly matches its structured content. Here’s a toy example: suppose we have no single concept “bachelor” in our language, but do have the concepts “unmarried” and “adult male”. Then the fine-grained belief content conventionally associated with “Harry is a bachelor” may be a conjunctive structured proposition: Harry is unmarried and Harry is an adult male. But we shouldn’t require a semantic theory to compositionally assign that particular proposition to the atomic sentence in question—it may be impossible to do that. What seems attractive is to say that the assignment of the stuctured proposition <Harry, being a bachelor> to the sentence explains the conventional data well enough: after all, at the level of truth-conditions, it is obviously equivalent to the conventionally associated content. But certainly the structured contents ascribed by the permuted interpretation are also obviously truth-conditionally equivalent to the structured contents conventionally associated with the sentence, so fit equally well. Maybe matters are less obvious in the case of the skolemite interpretation, but it’s still necessarily and a priori equivalent. Given the needed flexibility in how to measure “fit”, it’s far from obvious we are on solid ground in insisting that the fine-grain content of thought must be the semantic content of the sentences. (There are moves one can make, of course: arguing that something fits better the closer the content assigned is to conventional content. But this is not obviously independently motivated, and as we’re about to see, won’t do all the work).

But the real killer is the following challenge:

  • Compositionally twisted interpretations. O’Leary-Hawthorne once asked Lewis to say what fixed the compositional rules that must be part of any compositional interpretation. One version of this challenge is as follows: the standard compositional rules say, for example, that if the semantic value of “a” is x, and the semantic value of “F” is the function f (at each world, mapping an object to a truth value), then the semantic value of the sentence “Fa” is the function that maps a world w to the True iff at w, f maps o to the True (or, if one wants a fine-grained content, then it is the structured proposition <f,a>). But a twisted rule might take the following disjunctive form: if “Fa” is a sentence that is tokened in the community, the semantic value of the whole is determined just as previously. But if “Fa” is never tokened, then its semantic value is a function that maps a world w to the False iff at w, f maps o to the true (respectively for fine-grained content: it is the structured proposition <neg(f),a>, where neg(f).

Now, the trouble here is that the standard and the twisted interpretation agree on all the datapoints. They can even agree on the fine-grained structured content associated with each sentence ever used. So they’ll fit and predict the sentential data equally well (remember: the language in use which provides the data is restricted to those sentences where there are actually existing regularities). The “constraining content” we inherit from the work we did on pinning down determinate thoughts is already exhausted by this stage: that at most constrains how our interpretation relates to the datapoints, but the projection beyond this to unused sentences is in the purview of the metaphysics of linguistic content alone. This “Kripkensteinian” underdetermination challenge will remain, even if we battle to relocate some of the others to the level of thought.

Something more is required. And if what determines best explanation is fit, strength and simplicity, it looks like simplicity must do the job.

 

NoR 4.1: Fixing linguistic interpretation.

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

The non-representational world contains causes and functions. From these primordial elements arises the intentionality of perception and (contrastive) intention. Perceptions and intentions in the life of a single creature then ground beliefs and desires. What mediates between perception/intention and belief/desire is rationalization. If the states that will end up as vehicles of content are patterned in interesting ways, then truths about rationality allow us to derive succinct explanations why the elements of those states represent what they do.

In this new subsequence of posts, I’m going to extend this to “third layer” of representation, the representational properties of artefacts.  I will be concerned specifically with linguistic representation: the representational properties of words, sentences and utterances.

Just as my starting point for the metaphysics of belief and desire was David Lewis’s brief brief remarks on (mental) radical interpretation, I will base my story on Lewis’s (much more developed) theory of linguistic representation. In the case of mental representation, the metaphysical story took this form: there is a space of abstract interpretations, which map states or stages of agents to contents. The job of the metaphysician of mental representation is to give an illuminating story about which of these abstract interpretation is correct. And then we “read off” facts about what a person believes or desires, for example: that a person believes that p iff they are in a state which the correct interpretation maps to the ordered pair: <belief,p>. In the case of linguistic representation, the situation is similar. There is a space of abstract interpretations (what Lewis calls “languages”) which map sentences to contents. The job of the metaphysician of linguistic representation is to give an illuminating story about which of these abstract interpretations is correct.

As well as this story, however, one needs to delimit the right space of abstract interpretations. Will the vehicles of linguistic content be individual utterances, utterance-types, sentence-types or individual words? We make this choice when we stipulate the domain of the abstract interpretations that we select between. In the same way, we might target the sentences of an idiolect, or a whole public language.

Framing the problem as involving interpretations that map public language sentence-types to propositions, Lewis offered the following account of correctness.

  • The correct interpretation of a set of public sentence-types Z of population P is one that, for each sentence-type S in Z, maps S to p iff there is a conventional regularity within P for someone utter a token of type S only if they believe p (truthfulness), and a conventional regularity for someone to come to believe that p if they hear another utter a token of type S (trust).

The basis on which an interpretation is selected consists of (i) patterns connecting acts of uttering to agent’s beliefs; (ii) the entrenchment of those patterns in communal beliefs and desires—whatever is involved in making a regularity a “convention” within a given population. The appeals to conventions, sentences and populations is something to which we return in a later post. For now, they are working primitives.

People are not always honest, nor always trusting. Some sentences (“I did not do it”) may be more often used dishonestly than honestly. Audiences may rightly fail to trust certain speakers, ask for further evidence. Some sentences might be particularly prone to provoking distrust. Following Lewis, we may appeal to the attitudes of speaker and audience to refine the regularities we are looking for to “serious communicative situations” where the speaker has no interest in deception, and the audience takes the speaker to be an authority. I take such restrictions as read: they will not make regularities exceptionless, but they’ll ensure that generically, they hold.

Some further observations:

  1. There are many regularities of truthfulness and trust for any given sentence. I will utter “Harry is a bachelor” only if I believe Harry is unmarried. And someone hearing me utter this will likewise form that belief. Perhaps this regularity will not count as conventions (there are many regularities involved in driving—e.g. driving on the right for the first half of each hour—which are entailed by but not themselves conventions). But prima facie, there are a multitude of candidates for being “the” content conventionally associated with a sentence.
  2. Among these, the strongest content conventionally associated with sentences are not necessarily what we think of as what the sentence literally “means”. “He had three drinks and drove home” implies but does not state that the drinking preceded the driving. Speakers will utter this only if they believe in the temporal ordering, and audiences will come to believe the temporal ordering on hearing it. Absent a reason for thinking that only the regularity of truthfulness and trust involving the semantic content is conventional, we should be aware that Lewis’s account doesn’t lock us onto the literal meaning of sentences.
  3. Indexical sentences need special attention. A utters “I am sitting” while believing that A is sitting. B utters the same while believing B is sitting. C hearing one or the other utter that sentence, will form one or the other belief—or if the speaker is masked, he might form the descriptive belief “the utterer of that sentence is sitting”. Unless the account is tweaked (e.g. so that regularities of truthfulness and trust relate sentences to functions from contexts to contents, rather than contents directly) then it is not the semantic content, but the “diagonal” content, that figures in regularities of truthfulness and trust.
  4. This account is silent on the representational property of units of language below the level of a whole sentence. It is also silent on the representational properties of sentences that are never used, and so feature in no regularities connecting them to states of belief. So the scope of this account is constrained.

So this initial convention-based account leaves us very far from a full or satisfying account of the representational properties of linguistic artefacts. But it is the first staging post towards such an account. Conventionally associated content is the linguistic source intentionality—a layer of representational facts that form the raw materials for an interpretationist story about what ground (literal) meaning of words and more complex expressions.  This interpretationist account is not found directly in the above account of correct sentence-level interpretation (or as Lewis puts it: in the account of what makes an abstract “language” be “in use” by a population). Instead, it is found in his account of what makes something a “grammar” for such a language.

Let us frame the task anew. The space of interpretations now map words of the target public language onto objects (their “semantic values”: that is, the interpretation assigns a reference or denotation to each lexical item). Each now includes a rules that assigns semantic values to more complex sentences (as a special case: sentences). The simplest such rules are compositional, assigning contents to the wholes as a function of the contents already assigned to their parts. Nevertheless, I’ll call a member of this space of abstract interpretations a “compositional interpretation”.

  • The correct interpretation of a set of public words W of population P (and the semantic rules for the expressions they form) is the compositional interpretation which best explains the language in use in P.

Here “language in use in P” is just another way of saying “correct interpretation of the public sentence-types of the population”—and is to be explicated as above in terms of conventional regularities of truthfulness and trust.

This move is relevant to each of the four notes above. In the following, I will hold assume that the best explanation of the language-in-use is indeed compositional, and “not” is given its usual meaning.

  1. A compositional interpretation of “Harry is a bachelor” won’t assign it the content that Harry is unmarried. For (absent a deviant treatment of “not”) that would ultimately mean it had to assign to “Harry is not a bachelor” the content Harry is not unmarried. But that content doesn’t feature in regularities of truthfulness and trust: speakers are willing to utter the sentence when they believe Harry is unmarried and female.
  2. Similar constraints favour the compositional interpretation assigning intuitively “semantic” content over enriched “pragmatic” content.
  3. A compositional interpretation can use familiar means to associate indexical sentences both with “diagonal” contents that show up in the conventions, and account for the way that those sentences contribute as parts of larger wholes, delivering an account which has a place both for diagonal and contextually varying, semantic contents for such sentences.
  4. Even if the “language in use” just assigns content to those sentences that are actually uttered by members of the population, the compositional interpretation can in principle assign content that goes way beyond this. The correct assignment of referents to words, and compositional rules, are grounded in the properties of the finitely many sentences that are actually in use. But by recombining those words and applying the compositional rules, the compositional interpretation assigns compositional content to sentence-types that have never been uttered.

Lewis’s metaphysics of word-reference, then, has two stages: a sentence-level story that works by linking sentence-types to attitudes (belief) and having the sentences inheriting the content. And the key to understanding this is to understand what makes something a convention. The second stage uses the first like a set of datapoints, and interpolates subsentential content as whatever “best explains” that data. In the story I gave about layers 1 and 2, proper functions grounded source intentionality which grounded the intentionality of belief and desire. In parallel in this story conventions ground raw sentential content which ground word content. Just as radical interpretation appeals to the selectional-ideology of “rationalizing” interpretations of an agent, applied to a base of facts about perceptual and intententional content, Lewis’s metaphysics of word content appeals to the selectional-ideology of “best explanation”, applied to much sparser set of base facts about sentential content.

Our setup defines an agenda.

  • Say something about the selectional ideology of “best explanation”.
  • Say something about the base facts that fix sentential content: conventions of truthfulness and trust.
  • Say something about the how facts about words and populations factor into this story.

With the core of this approach to language on the table, we can move to more advanced themes.

  • Varying assumptions about the content inherited from belief.
  • Varying assumptions about the attitude conventionally linked to sentences.
  • Varying assumptions about the relative priority of thought and language.

 

NoR section three supplemental: Options as abilities?

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

I earlier followed Hedden in identifying an agent’s options with a certain range of basic intentions available to them. This theoretical setting—assumed but not argued for—illustrate us one way of connecting source intentionality to radical interpretation. But it is not the only way. Here I’ll sketch an alternative account.

The alternative is as follows: an agents options are not the intentions that they form, but their basic, specific abilities. Let me explain what one of those is.

The agents basic abilities I will understand as picking out those acts that are the execution of a basic intention. A basic intention, in turn, is an intention that has a function to produce a certain result. But as is now familiar, something can have the function to produce phi, and yet not produce phi. This will happen when circumstances are “abnormal”. For example, one mental state of mine has the function to produce my arm rising. If my arms are tied behind my back, then the existence of such an intention does no good: my arms stay resolutely stuck to my sides. So though I have the general ability to raise my arms, I lack the specific ability to raise my arms in these circumstances.

What then, are an agent’s basic specific abilities in circumstances c? I propose they are just those among the agent’s general abilities whose associated “normal conditions” are met in c. Unpacking this, x having a specific ability to phi will entail that x can form an intention whose function is to bring about phi, and also that circumstances are normal for this function, so that if it were formed, phi would be brought about.

Clearly this is an account of basic specific abilities that relies very heavily on our account of the content of intentions. It is not something we could reconstruct without an account of source intentionality, though unlike the previous account, we don’t identify options with the representational states themselves.

I call all these things “basic abilities” since I want to emphasize that not every true claim of the form “Sally can phi” or “Sally is able to phi” is an option in the relevant sense. We can use these phrases—agentive modals—to report on a richer range of ‘extended’ abilities that Sally possesses, which often depend on features of her circumstances not at all to do with Sally or her functioning. Example: given Suzy’s maximum pace, and the maximum pace of Orcs, Suzy can outrun the Orcs chasing her. But without any malfunction on Suzy’s part, the speed of the Orcs could be different, and so an intention to outrun them doesn’t guarantee success.

It is very natural to think that there should be a connection between basic abilities and “extended abilities”—that we enact the latter by way of enacting the former. Recent work on the semantics of agentive modals by Mandelkern, Schultheis and Boylan is suggestive of such a connection. According to their story, an agent x is able to phi just in case there is some practically available act A such were x to try to A, they would phi. Suppose we insist that practically available acts [for an agent in world w and context c] must be those that correspond to the agents basic abilities. We could then follow Manderkern et al in adding further constraints that narrow down this basic repertoire to produce the contextually relevant set of aviailable acts [the authors suggest an epistemic constraint: that an act is only available if the agent knows it is a way to phi; and also that the set of acts will contextually vary, and by default should be compatible with the agent’s prior plans]. If this were the way that the semantics and metasemantics of agentive modals works, then although our everyday ascription of abilities goes well beyond the basic set, nevertheless basic abilities remain at the core of ability-ascriptions.

If options were an agent’s basic, specific abilities, what would be the consequences for rational decision making?

Well, to begin with, by construction if the agent forms the intention to execute an option to phi, then the agent will phi. It would not be an option unless circumstances were normal, and intention-formation is guaranteed to bring about its content in all normal circumstances. So, in a certain sense, the possibility of “trying and failing” is excluded.

However, the agent may lack knowledge of this. She may not know, for example, if her hands are bound.  If that is the case, then she can credence to a scenario where she forms the intention to raise her hands, and her hands do not rise. This is where the account of options-as-intentions and the account of options-as-abilities differ. On the former, in such circumstances, the relevant option to evaluate is: forming the intention to raise one hands. The agent will assess various possible outcomes of this, including those where her hands are bound and do not rise. On the latter, in the same circumstances, the relevant option to evaluate is: raising one’s hands. The agent will then assess what will happen conditional on enacting this, which excludes the possibility of one’s hands not going up.

This is a case where the agent is ignorant of her options because she does not know whether conditions are normal, and so doesn’t know whether her general ability to raise her arm translates into a specific ability in this circumstance. Another way an agent can be ignorant of what options are open to her, on the options-as-abilities account, is by lacking knowledge of her general abilities. She might have never tried a particular stressful bodily motion, or not attending while she tried to do so, so that when asked to reflect on whether she would succeed if she tried, she is not confident.

You might think that its treatment of ignorance of one’s abilities is a strike against this theory of options: that rational decision-making should factor in the possibility of trying-and-failing, even if in fact, in all normal circumstances including the actual one, the agent would never try-and-fail. If we were building a theory of options for structural rationality, I would have sympathy. But notice that it is really hard to construct a theory of options that excludes the possibility of ignorance of what those options are. For example, if options are abilities, one might not know which intentions it is possible for you to form. And on the version of the Hedden view that I suggested in the previous post, one might be ignorant of options because one did not know, of a given intention, whether it was appropriately basic.

At some point we will need to hold the line, I think, and insist that ignorance of options is just ignorance of what rationality recommends. For other determinants of substantive rationality, that is already familiar. X may be ignorant of what is morally or all things considered permissible for her, due to her ignorance or (justified?) false belief about moral demands. The suggestion here is that ignorance of options can work like ignorance of value.

Suppose that the agent knows that raising their arms would bring about the best consequences, but is unsure whether their arms are tied. The verdict I am suggesting is that they should raise their arms: enact the ability they do possess. Their ignorance is normatively relevant only insofar  as it is a decent excuse for not doing as they ought.

A positive attraction of the view is that it enables a straightforward reading of the idea that “ought implies can”: specific abilities are exactly the things the agent can do. And it also avoids an unattractive feature of the options as intentions view: that in order to be rational, an agent needs be opinionated about the likely consequences of them being in the mental state of intending. It seems to me that the natural view is that an agent could be rational by forming intentions, but not thinking about forming intentions.

The view just sketched is less plausible as a theory of the options relevant for structurally rational action [I’m here very grateful to a series of discussions with Gary Mullen on which the following is based—though Mullen is not to blame for any mistakes in what follows]. The problem here is that structural rational evaluation is supposed to be a commentary on patterns in the agent’s mental states. But if options depend on the circumstances an agent finds themselves in (e.g. Whether arms are tied) two mental duplicates could differ in rationality while making the same choice. This seems odd. So I do think we need a more internalistic notion of option for structural rationality. Suppose it were this: that our options for structurally rational action are those things we think are our basic abilities. And suppose that the theory of rationality is that we should try to enact whichever one of these abilities we think would lead to the best results. Then, in the special case where we have full knowledge of our abilities, the option-set for structural rational decision making and substantively rational decision making will coincide. Further, there will be rational pressure on us to keep track of our abilities, in order to preserve the possibility that taking the structurally rational option is also to take the substantively rational one.

Notice that if we identified options with those abilities we believe ourselves to have, then our theory of options, which should be layer one intentionality, would depend on what we believe, a layer two fact. So it would be a considerable headache for my account if we tried to collapse the account of options to the single “internalistic” case.

I haven’t argued for the correctness of options-of-abilities, any more than I argued for the correctness of options-as-intentions. But together, they give us two very different ways that we can wield the resources of source intentionality to generate a suitable basis on which radical interpretation can be founded.