Category Archives: Nature of Representation.

NoR: 1.1. Layers of Representation.

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 experience of running downhill. The recollection of the coffee you drank this morning. The belief that everything is grounded in the physical. The desire to stop eating meat. A photograph of your mother. The words “it’s behind you”.

All share a common feature. They are all representations of something else, they have the spooky feature of “aboutness”. The photograph is a thing that can be put in an album and stored on a shelf. But it represents something else entirely—an individual human being. The belief (let’s assume) is a certain configuration of your brain, but it represents a general feature that that the world we inhabit as a whole might have or fail to have. We have one thing (states of our brain, other biological systems or artefacts) representing quite different things: hills, coffee, monsters, or whatever. You won’t be able to think of anything that can’t be represented (suppose you were able to: then in thinking about it, you’d be representing it).

I want to know about the nature of representation—what representation is, how it gets generated, and how different kinds of representation relate to one another. What is the basis for representation and how does it arise out of (“get grounded in”, “reduce to”) that basis?

In this series of posts, I’m going to present an answer to that question. Here is the overarching structure of how the story goes.

(1) The most primitive kind of representation is the “aboutness” we find in perception and action/intention—the two most basic modes in which we and the world interact. This layer of representation consists in states of our head which if functioning properly are produced by particular aspects of our environment (perception) or bring about changes in our environment (action/intention). It is to be analyzed, say I, into a combination of teleological (“functioning properly”) and causal (“produced by/bringing about”) features of things. We can understand how this kind of representation can exist in a fundamentally physical world so long as we have an independent, illuminating grip on functions and causation.

(2) The next kind of representation is the “aboutness” of (degrees of) belief and desire. Where the representational content of perception and action was tightly bound to visible or manipulable features of the immediate environment, beliefs and desires can represent anything (certainly anything you can think of). This layer of representation consists in states of our head which (inter alia) update in response to the information that comes in from perceptual states, and which in combination lead to the formation of states of intention. It is to be analyzed, say I, by giving a story about the correct belief/desire interpretation of the agent—with the critical question being giving an illuminating gloss on what makes an interpretation “correct”. This is where the layering comes in. In my telling of the story, the correct interpretation of an agent is that one which makes their actions/intentions, given their perceptual evidence, most reasonable. Accordingly, the story about belief and desire presupposes a prior and independent story about perception and action. We can understand how the belief and desire kinds of representation can exist in a fundamentally physical world so long as we have an independent illuminating grip on “reasonableness” and so long as the first layer of representation is available to cash out appeals to perception and action/intention.

(3) The final layer of representation I discuss is the “aboutness” of words and sentences. So here, I’ll be stepping outside the head to consider the representational features of a very special class of human artefacts. This layer of representation consists in blasts of sound, bodily movements or marks on paper which express mental states, as for example, asserting “grass is green” expresses a belief that grass is green.  It can be analyzed by analyzing the notion of a sentence “expressing” an attitude and, say I, this is a matter of what conventional regularities relate sentences to thoughts in the linguistic community in question. We can understand how this kind of representation can exist in a fundamentally physical world, so long as we have an independent illuminating grip on conventions and the attitudes expressed and so long as the second layer of representation is available to cash out the appeal therein made to representational mental states.

So that’s the overview from 60,000 feet. The reality is a bit more complex than this simple three-layer structure suggests. There are many more details to be given, loose ends to be tied, puzzles and objections to be sorted through, and applications to be explored. The macro-structure itself may need some qualification, once we’ve worked this through—for example, it may be that for some attitudes and parts of language, the relative priority of layers (2) and (3) will be reversed. There will be time enough to sort through this later, so I won’t say more now.

NoR, 1.1b. Precedents and methodology.

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 last post, I introduced the question of the nature of representation, and introduced the way I propose to tackle three core “layers” of representation. Layer (1) concerns the representational properties of perception and action/intention. Layer (2) concerns the representational properties of belief and desire. Layer (3) concerns the representational properties of language.

Precedents.
The strategies that I sketched have two main precedents. The approach to layer (1) is an a teleoinformational account of content. Indeed, in the case of perception, to a first approximation I will just borrow Karen Neander’s teleoinformational account of the content of sensory-perceptual representations. I will have things to say about ways to adjust and tweak the theory of perceptual content into my favoured setting, but the main thing I need to do is convince my readers that the teleoinformational view (Neander-style) has a natural generalization to action-intentional content, and so can serve as a complete theory of first-layer representation.

My approach to layers (2) and (3) are instances of interpretationist accounts of representation. Here the central precedent, for me, is David Lewis’s fascinating, highly influential but at times frustratingly incomplete work on the topic. Lewis separated layers (2) and (3), and at least at the level of generality spelled out above, he gave very similar analyses to those I outline above. When we dive into the details, however, we find that Lewis’s account is schematic in many ways. What we can extract from Lewis is a space of theories of the nature of representation to explore, not a single, fully-fleshed out account. The project here is to work up a specific theory, and tease out specific predictions. It will make sense to compare and contrast to Lewis’s work (especially given the way that it has been picked up, endorsed and applied in the literature), but my project is not exegetical. I will riff on a theme that Lewis provides. Even just looking at the overview we have so far, we already see the first case of this, since Lewis never gave us details of how he proposed to handle layer (1), or explained how to do without such a layer.

Scope.
My three layers leave much unsaid. I cover only three of the examples that introduced this section (you won’t find a discussion either of photographs nor memories in what follows). Along with memories, there are many other mental states that are not discussed—among them affective intentional states like fearing the blob, hoping for release, and objectual states like admiring Nelson or attending to a laser-pointer. Some of these states may be analyzed into combinations of the representational states I do analyze, plus other material. Some of them could be given their own grounding using the resources herein deployed (it’s natural to try out a teleoinformational account for memories as a widening of stage 1, and to try covering additional intentional attitudes by adding extra dimensions to the interpretations grounded at stage 2). But it may be that new ideas are needed.

The human-made world is replete with further representations beyond the words and sentences that are my focus. There are non-verbal signals where a generalization of my favoured approach to sentences—conventional expression of thoughts—has long been a popular option. Other artefacts may be better treated by an extension of the teleoinformational approach. Photographs, prima facie, seem more informational and less conventional. Within linguistic representation, there are plenty more challenges to explore. Consider stretches of dialogue, which surely have representational properties whose relation to the representational properties of the words and sentences used is complex (consider the mechanisms by which anaphor is fixed, or co-indexing of variables). Or consider novels and stories: what is represented to be the case by a written work of fiction surely relates in some way to what its sentences say, but the generation of fictional truths is a complex business that is rightly a topic of study in its own right. And who’s to say what the best story would be about the representational content of a (more or less abstract) painting? But again and again, in thinking through such cases it is natural to draw on a toolkit of experience, intention, belief, desire and language. So I think of my chosen topics as a core. If we can get the nature of these kinds of representation right, that will be a platform for generalization and reduction, and a necessary foil for any autonomous treatment of the metaphysics of other sorts of representational phenomena.

The role of empirical data
I make few appeals to empirical results in cognitive science, biology, psychology or linguistics in building up my theory. Though the teleoinformational tradition—and the work of Neander that I borrow—does draw upon this, I won’t be relying on this aspect of that work. That is not because I think these things are philosophically irrelevant; on another day, engaged in another project, I would happily dive into the details. But there are trade offs in each research project, and by suppressing certain questions, we can focus more intently on others. The question I set myself here is a “how possible” one. How is possible, in principle, for facts about philosophically central sorts of representation to arise in a fundamentally physical world? I offer an account of one way that it could happen. That account will work for creatures with a certain kind of belief/desire psychology that relates in the ways I will go on to describe to perception/action and language. As we will see, articulating this in adequate detail already generates a fascinating landscape of questions.

Let’s suppose you agree that my project has been successful. Then there’ll be a further question—is this the way it works in us flesh and blood human beings? Is it the way it works in frogs? Does it go for the hyperintelligent aliens inhabiting yonder distant planet? It could turn out that the model I worked with really is a good description of some or all such cases, but more likely, it will need tailoring to fit the details of this or that case. (So I here distance myself from the “analytic” version of a project like mine, where the models I construct in the armchair have special authority because they are laying out what is implicit in the very concept of belief/desire/representation, etc). It would be nice if the tailoring proved to be modest, involving “more of the same”, for example, further kinds of layer-1 teleoinformational states, a more complex interpretation with more subtly interrelated attitude types in layer-2, and refinements at level-3 to suit the latest developments in linguistic semantics. Perhaps the surgery could be more radical. In the limit, maybe, although representation could arise in the way I describe, perhaps it arises in a quite different configuration in our case. So be it! Theorists need to speculate to accumulate, and I am happy taking the theoretical gamble involved in the how-possible project in which I am engaged.

There is a place in my project where some more specific, and contingent, assumptions become important. Though the layer-2 story about belief and desire is compatible with many different assumptions about the underlying cognitive architecture of the states which carry this kind of content, we get much more specific predictions about certain species of belief/desire (singular thought, general thought, normative thought, etc) when we add in specific assumptions. So at various points I’ll be assuming that beliefs and desires have vehicles with language-like “conceptual” structure, which enter into inferential relations (I’ll go on to specify what these “inferential roles” might be). Together with the general radical interpretation framework, this allows me to derive results about what the posited “concepts” pick out. What I’m aiming to establish in these sections are conditionals: that if such-and-such a cognitive architecture is present, then so-and-so content will be assigned. Those conditionals are of interest to those who have independent arguments for the cognitive architecture in question, for they can modus ponens to get the results. Those neutral on the architecture but sympathetic to the conclusions about content derived, on the other hand, can view this as indirect support for the architecture in question—an explanatory/predictive success.

NoR: 1.2 Radical 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 core layers of representation I will be talking about are (1) preception/action; (2) belief/desire and (3) language. I start in the middle, with layer (2). In the next few posts, I will lay out in more detail the metaphysics of belief/desire representation that I favour, develop the sharpest form of criticism of it that I know, and explain how the theory should be refined to avoid that criticism. After this, I’ll get to work in expanding on this refined theory, with an eye to making predictions about particular species of representation.

Let’s start from general principles. Abstract interpretations of someone—functions that map points in the history of that person (“person stages”) to a set of beliefs and desires—are ten a penny. There is, for example, one abstract interpretation that maps you right now inter alia to a belief that the Earth is run by lizard people. Another attributes an overwhelming ambition to count the grains of sand in the Sahara. Most of these abstract interpretations bear no relation to what you actually believe or desire, and make no sense of what you say and do. They are, after all, just pieces of mathematical machinery.

Somewhere among this space of abstract interpretations, however, there is one that gets things right—which maps you right now to those beliefs and desires that you do in fact possess (and similarly for every other stages of your existence). Similarly, one of those abstract interpretations gets things right for each stage of my existence, and so on.

A metaphysics of mental representation (at layer 2) will give a story in two parts. In the first part, it gives further details about a relevant space of abstract interpretations. Here we need to answer questions such as the following. (1) what kinds of things get interpreted (at a time)—the whole temporal stage of a person, or internal states that the person is in at that time? That’s a question about the domain of the functions that are the abstract interpretations. (2) What attitude-types does an interpretation ascribe—flat out beliefs/desires, comparative belief/preference or numerical degrees of belief/desire, for example? Are there other attitudes also ascribed, such as the subject’s attitude to risk? These are questions about the co-domain of the function that are the abstract function. In short: exactly what is to be interpreted and what information does an interpretation deliver? With the domain and co-domain spelled out, the space of of abstract interpretations can be defined as arbitrary mappings from one to the other.

In the second part of the story, the metaphysics gives an illuminating account of what the world has to be like for one of these abstract interpretations to be the correct interpretation of an individual x. In giving this story, one will of course cite certain facts about x—this could be almost anything, in principle, from their inner cognitive processing, to their causal relations to the surrounding relation, to features of the species to which x belongs, to facts about what they perceive or how they choose to behave. These cited facts I’ll call the basis of correct interpretation. The rest of the story about how a function is selected as correct given the basis I’ll call the selectional ideology.

Consider the following pair of (very schematic) accounts:

  • The correct interpretation of an agent x is that one which maps x at t to a set of beliefs and desires that best accountsfor x’sdispositions toactat t given courses of experiencex undergoes up to t.
  • The correct interpretation of an agent x is that one which maps an inner state s of x to a belief that p iff the state’s function within x’s cognitive system is to carry the information that p, for the purposes of controlling behaviour.

illustrate some of the possible divergences between different stories about the nature of representation.

(a) The first seems to be working with a space of abstract interpretations which map whole time-slices of agents to beliefs/desires. The second has to work with interpretations that map individual states of a person to beliefs (some other clauses would be needed if we wanted to ground desires too).

(b) In the first, the basis of correct interpretation includes dispositions to act and courses of experience undergone.(It also includes, implicitly, the reidentification of the agent over time and counterfactual scenarios). in the second, the basis are facts about the functions of components of cognitive systems, and specifically, information-carrying functions.

(c) In the first, there is selectional ideology. Given full information about the basis (action, experience) we need in addition facts about how interpretation do better and worse in “accounting for” the basic facts. In the second, there is no sign if selectional ideology (all the work is done by the “iff”).

I’ve said that the metaphysics will have to give some illuminating story, but left it open what counts as illuminating. The paradigmatic unilluminating story about correctness is one that just redeploys concepts of the very attitudes being ascribed by an interpretation in characterizing correctness. The following is true, but not illuminating: the correct abstract interpretation maps x-at-t to a belief that p iff the agent believes p at t. You can pick out the correct interpretation by laying down such platitudes for each attitude-type the interpretation covers, but we need some independent route to correctness that doesn’t mention beliefs, desires, etc. Such platitudes do have a role within the overall metaphysics here, but the key thing is that rather than use facts about belief and desire to explain correctness, the proposal is that we use our grip on correctness to explain facts about belief and desire. So the platitudinous biconditional has a role, but the direction of explanation, on this account, flows from left to right, and stands in need of an independent story about in what correctness consists.

The metaphysics of mental representation I am exploring is a version of radical interpretation,and a slight elaboration of the first option introduced above:

  • The correct interpretation of an agent x is that one which best rationalizes x’s dispositions to act in the light of the courses of experience x undergoes.

This will be further refined later. But even at this stage, we can see that the basis includes actual and counterfactual experiences and dispositions to act, and that the selectional ideology includes a notion of better and worse rationalization. Also notice the things it does not contain. For example, there’s no relativization to any actual or ideal interpreter or interpretative stance. Insofar as its an objective [non-stance-relative] matter how an agent acts and what they experience, and an objective matter what rationalizes what to what degree, then it’ll be an objective matter what the correct interpretation is, and so what the agent believes and desires.

My favoured story about correctness, as stated, would not by itself reduce the representational facts about belief/desire to purely physicalistic, naturalistic or even non-representational facts. After all, that one perceives the presence of a red ball, or that one’s limbs moving along a certain trajectory is youhailing a taxi are themselves representational facts. And whether or not a cluster of belief/desires rationalize certain choices, in a certain context, is prima facie a normative fact, and whether normative facts are physicalistic or naturalistic is very much sub judice. It is not something I will take a stand on here. I offer it as an account of how one kind of intentionality—that of perception and action-gets transformed, via normative truths, into the intentionality of belief and desire. I favour supplementing this with a physicalistic/naturalistic account of the intentionality of experience and action, and together the two stories would reduce the representational to the non-representational. But radical interpretation as presented here need not be yoked to that broader project. We might, as Adam Pautz has advocated, combine this story of the transformation of perceptual and agential content into belief/desire content with the positing of metaphysical primitive representation in experience.

The story about the metaphysics of representation just given defines a theoretical agenda: to get clear on each of these three elements: experience, action and rationalization. Experience and action are deferred to a later sub-sequence of posts where I discuss the way the metaphysics of layer-1 representational facts. But it is rationalization that will be our primary focus for the time being.

NoR: 1.3 Rationalization. Structural vs. Substantive.

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

Radical Interpretation tells us: the correct interpretation of x is one which best rationalizes x’s dispositions to act in the light of the courses of experience x undergoes. But what is it for an interpretation to rationalize such things? There are thinner and thicker ways of understanding “rationalization” of actions/experiences, and this generates two very different versions of radical interpretation.

The first option is to identify rationality with structural rationality. A structurally rational agent is one whose mental states are patterned in the right way. For example, a paradigm constraint of structural rationality is formal consistency of belief. One violates this if one simultaneously believes that grass is green and believes that it is not green. Another paradigm of structural rationality is means-end coherence between beliefs/desires/actions. One violates that if one desires above all to get smarties, believes the only way to get smarties is to open the cupboard, yet fails to open the cupboard.

Such rational constraints are “structural” in that they’re insensitive to the specific contents of attitudes involved. It’s not anything to do with grass or greenness that makes it problematic to believe grass is green and that grass is not green. Schematically, for any p, it’s problematic to believe that p and that not-p. Likewise for the means-end constraint. Schematically, for any proposition q and act A, it’s problematic to desire (above all) to bring about q, believe that the only way to bring about q is to A, and yet fail to A. Structural rational constraints are characteristically topic-neutral, relying only on very abstract and formal specifications of the relations between attitudes/acts/experiences, for example, their logical forms (e.g. that the content of one belief is the negation of another).

Structural rationality constraints lend themselves to formal modelling. For a concrete example this consider (a minimal version of) Bayesianism.  The Bayesian starts from a distinctive take on the space of abstract interpretations. The version I’ll consider takes interpretations to map person-stages to an assignment of degree of belief in each proposition (probability) and degree of desirability in each proposition (utility). My Bayesian’s proposal for structural rational constraints include:

  • Rationality constraints on beliefs over time: that they are updated by conditionalization on content extracted from experience.
  • Rationality constraints on beliefs at a time: that they are probabilistic (i.e. satisfy the axioms of probability theory).
  • Rationality constraints on final/instrumental desires and beliefs: that they fit means-end constraints articulated by (Jeffrey-style) decision theory.
  • Rationality constraints on choices: that the agent chooses to do the thing they most desire to do, among the things they think they’re able to do.

This gives us a candidate metaphysics of representation: structural radical interpretation (Bayes-style). An interpretation will be correct if and only if it comes closest to making the agent’s dispositions to act (at t) dispositions to select the option that maximizes expected desirability (at t), and to making the beliefs and desires attributed evolve under the impact of experiences in the way the Bayesian demands.

These Bayesian constraints do not rule out wild initial belief states. It is rational, so far as the above constraints go, to have high conditional confidence that the world will explode tomorrow, given the course of experience you have undergone to this point—and so rational, after undergoing that experience, to end up believing that the world will explode tomorrow. Nor do Bayesian constraints rule out wild final desires, e.g. basic desires for a saucer of mud or indifference to what happens to you on future Tuesdays. That is by design: the core Bayesian story as articulated above was developed as a theory of the formal patterns that a well-run mind should exhibit, not about the particular contents that we have most reason to believe or desire. It would be a surprise if one could rule out wild initial belief states or desires on the basis of formal features alone (perhaps some have aspired to this, but it would be headline news if they really succeeded). I will take Bayesian structural rationality to be in this respect representative of structural rationality accounts more generally.

Yet there’s something crazy about a basic desire for a saucer of mud, or future-Tuesday indifference, and about humdrum experience triggering paranoid beliefs—something deeper and more alien than what’s wrong with commonplace false beliefs or unwholesome desires. In addition to constraints of rationality based on purely formal patterns among our attitudes, perhaps there are rational constraints that are sensitive to the particular contents we think or want. These would be constraints of substantive rationality. (Just to note: it’s perfectly in order for someone who advocates the Bayesian story above as an account of structural rationality, to think that there are in addition substantive rationality constraints floating around).

This generates our second option. Substantive radical interpretation is a metaphysics of content on which the correct interpretation of an agent is the one that does the best job of making her substantively as well as structurally rational. This is what Lewis (1974, 1992) explicitly advocates, as recent authors such as Pautz, Weatherson and Schwartz have emphasized. Unfortunately, Lewis never told us much about what these constraints of substantive rationality were, beyond a few examples (similar to those I have just mentioned: the saucer of mud, future-Tuesday indifference). What metaphysics of representation we get out will depend on what account of substantive rationality we feed in.

The view I will be developing here is substantive radical interpretation. Some of the work to be done is in describing what substantive rationality constraints amount to, and using this to predict and explain results in the philosophy of mind. But before I get into this level of detail, the next couple of posts will review the reasons that structural rational interpretation (unsupplemented) is untenable, and locate substantive radical interpretation as a natural reaction to this problem.

NoR 1.4: The Bubble Puzzle

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

Structural radical interpretation does not work: perhaps the correct interpretation meets all its constraints, but David Lewis in “New work for a theory of universals” very briefly sketched an argument that wildly inaccurate interpretations do so too. The argument demands detailed scrutiny. I will describe my favoured version of this “bubble” argument here. (I examine it in much greater detail within the formalism of Evidential and Causal Decision Theories in “Representational Scepticism: the Bubble Puzzle”, Philosophical Perspectives 2017). There are lots of more famous “underdetermination” arguments out there, due to Putnam, Quine, Kripke, and others, and I’ll have more to say about those anon. But many of those don’t have direct application to this setting, as they target language (layer 3 intentionality, in my scheme) or fine-grained representational content rather than the coarse-grained content of though radical interpretation aims to ground. So the bubble puzzle, in my view, is where the action is.  

Without looking into the details, we can think of Lewis’s argument as a black box which takes as input any sensible interpretation of Sally (Original) and outputs a deviant variant (Deviant). Original and Deviant coincide on what attitudes Sally adopts concerning the goings-on in a local space-time bubble surrounding her. If Original ascribes to Sally a belief that there is a house in the road they are standing in, so does Deviant. If Original ascribes to Sally a desire to purchase that house she is confronting, so does Deviant.

In our ordinary case, our beliefs and desires concerning the local bubble are a piece in a much larger jigsaw. Exit the road, and you continue to believe that there’s a house on the corner. And much of the time (perhaps not always!) your desire to purchase it persists even once you’ve turned the corner. In line with this, suppose Original ascribes to Sally many beliefs and desires that are about the goings-on outside her local bubble.

At this point, however, Deviant diverges, depicting Sally as agnostic and indifferent to matters outside that bubble.

  • Agnosticism: while both interpretations ascribe to Sally a belief (on Monday, standing in the road) that it contains a house, and both ascribe a belief (on Tuesday, on the train heading south) that there was a house on the corner of that road the day before, Deviant unlike Original will depict Sally as utterly uncertain, on Tuesday, about whether there is still a house there.
  • Indifference: while both interpretations ascribe to Sally a desire (on Monday, standing in the house) to purchase that very house, Deviant unlike Original fails to ascribe to Sally the desire (on Tuesday, on the train heading south) to purchase that house.

Now Original and Deviant agree on the content of Sally’s attitudes insofar as they concern matters inside her local bubble. So according to Deviant, Sally does possess the following:

  • a desire that she be in possession of a key which opens the front door to the house.
  • a desire to live in the house.
  • a desire for congratulatory messages to appear on her social media stream.

In short, she wants to be in a world where her local bubble is exactly as if she purchased the house. Similarly for her beliefs and expectations. She is confident that if she retraced her steps to that same road, she would see the house—she believes her bubble was and will be exactly as if there is a house on that corner. But according to Deviant, she is open to the world being void everywhere outside her local bubble.

It will help in what follows to introduce a third interpretation of Sally: Paranoid. Where Deviant depicts Sally as agnostic over whether the world is uniform inside and outside her bubble, or regular inside her bubble and void outwith, Paranoid attributes to her a definite belief about the character of the world outside her bubble: it is all void. Accordingly to Paranoid, Sally believes she is in a world where houses disappear when she is no longer present, and reappear (exactly as if they had aged and evolved naturally) when she revisits them. According to Paranoid, Sally desires are for the local bubble to be as-if it were embedded in a world where the world outside the bubble is this way or that (that she owns a house, that distant friends are happy, that there is peace between nations), though the content of the desires are for local apparent indications of such things, as she is fully convinced that outside the bubble is only void.

Thus deviant bubble-interpretations of Sally. And here’s the payoff: if we demand only that we make her *structurally* rational, in the way formalized by the Bayesian canon, we cannot eliminate the Deviant or Paranoid interpretation. Structural radical interpretation makes it indeterminate at best which of these is the correct interpretation of Sally. So it makes it indeterminate at best whether Sally believes in a regular world outside her bubble, believes that outwith the bubble all is void, or is agnostic between those hypotheses.

I’ll sketch a prima facie case for what I’ve just asserted. To tighten this up beyond the prima facie case, we’d need to choose a specific, rigorous formulation of rationality constraints and a formalize Deviant and Paranoid. That’s what I do in the paper cited at the beginning of the post. But the danger of moving too quickly to formalisation is that it can look as if it is of relevance only to those who buy into the specific rationality constraints. So it’s best to start by articulating the driving thought behind any specific formalization. 

Remember what we need is to secure the structural rationality of interpretations, with the relevant three constraints for the Bayesian radical interpreter being: belief consistency at a time, belief evolution over time under the influence of experience, and means-end coherence between action, belief and desire. Let us take each constraint in turn.

1. The constraint that Sally’s beliefs-at-each-time be consistent. We can dispense with this quickly. There is no reason at all to suspect that the ‘as-if; bubble beliefs of the Deviant or Paranoid interpretation shouldn’t be as internally consistent as those attributed by Original. One might think that Sally’s beliefs according to Paranoid or Deviant are unreasonable (I would agree). But unless one can identify formal incoherence in the attributed belief states, then the unreasonability shouldn’t be classified as a failure of structural rationality.

2. The constraint that Sally’s beliefs over time evolve in ways that are rational given the experience that has come in. This turns crucially on the content of the experience that has come in. Sally sees the house in front of her, views congratulatory messages on her phone, and so forth. I will suppose that the canonical description of the experience is restricted to Sally’s local bubble. For example, we might loosely describe Sally as seeing a congratulatory message from a distant friend. So described, the experience would be accurate only in a world where the distant friend exists, and is the causal origin of the various flashings on Sally’s phone. But I will suppose that in the sense relevant here, the content of Sally’s experience is the various flashings on her phone, which (we ordinarily think) she will combine with background beliefs about the typical origins and meaning of such flashings, to support a belief that her friend has just sent a congratulatory message. I am assuming, in short, that the accuracy of the experiences is vindicated or violated by the way the local bubble is.

If that is true, then there is no inconsistency between accepting the deliverances of experience as accurate, and maintaining the Paranoid view that all outside the bubble is void, or maintaining the agnosticism on this matter that Deviant recommends. But now, since Original, Deviant and Paranoid all attribute the same attitudes as far as the local bubble is concerned, each accepts as accurate the content of a given experience if and only if the others do.

So at each point in time, Sally on the Paranoid interpretation has consistent beliefs, and has incorporated into her beliefs the accuracy of her experience just as much as Sally on the Original interpretation did.

3. The final relevant constraint is that Sally’s beliefs, desires and actions means-end cohere. So, for example, Sally takes the following action: picking up a pen and signing a house purchase contract. As with experience, some descriptions of this act may invoke the world beyond Sally’s bubble (a purchase contract for a house seems to require the house exist). But I assume that the canonical description of this action will not be like this: instead, they describe how Sally manipulates her local environment. Accordingly, whether or not Sally performs the action turns on how things stand with the local bubble.

Original gives one means-end coherent story about why Sally picked up the pen and signed: she wished to purchase the house, she believed that the way to do this was to pick up the pen and sign. Since she had no countervailing desires or beliefs, these caused and rationalized her action. Paranoid has an alternative but parallel story: she wished her local environment to be as-if she had purchased the house, she believed the way to make her local bubble be this way would be to pick up the pen and sign. Since she had no countervailing desires or beliefs, these attitudes caused and rationalized her action. Deviant’s story piggybacks on these two. Sally was agnostic as to whether her world is uniform or bubble-and-void, and wishes in the first scenario to purchase a house, and on the second to make her bubble as-if she has purchased a house. A means-end story ensues. On the supposition that the world is uniform, reasoning like Original’s would rationalize signing. On the supposition that it is bubble-and-void, reasoning like Paranoid’s rationalizes signing. Reasoning by cases (and the absence of countervailing considerations) causes and rationalizes signing).

In each case, as far as the structural patterns go, Paranoid and Deviant are in just as good order as Original.

As the reader will have noted, central to all this are assumptions that the canonical description of experience and action–the basic data that radical interpretation has to work with–are restricted to the local bubble. This will be examined in much greater detail later. For now, I simply note that throughout this argument, I have been silent on how `local’ the local bubble is. At one extreme, one might think that the canonical descriptions of experiences are patterns of sense-data, and canonical acts are internal volitions. The argument will then proceed with a `local bubble’ consisting of a trajectory of sense-data and strivings. At the other, one might be very externalist, and even allow descriptions in terms of distal causes of experiences and remote goals of action (I doubt that this is something a structural radical interpreter can really allow, but set that aside). Still, one might set the boundaries of the bubble extremely wide, to include anything that turns up in such descriptions. So long as corners of remote galaxies are outside this bubble, a version of the argument above can be run.

Again, this is an informal presentation of the bubble argument, and we cannot hope to make it rigorous without a precise specification of what exactly structural rationality demands. Since that is a matter of first-order dispute, I start with this informal gloss, and invite the reader to identify where, if anywhere, it fails for their preferred version. My own preference is for the Bayesian articulation of structural rationality mentioned (the setting in which Lewis in “New work for a theory of universals” originally sketched this argument). I don’t want to underplay the significance of the details here! For example, in the cited paper I show that the argument just sketched for means-end coherence works nicely under one Bayesian model of means-end rationality (Evidential Decision Theory) but needs to be considerably adapted to work for another (Causal Decision Theory). The reader may well encounter similar prima facie obstacles in adapting the above line of thought for their favoured theory of structural rationality. I suspect, however, that they will also find (as I did) that there are workarounds available, and that there is no way for structural rationality alone to eliminate problematic interpretations such as Paranoid and Deviant.

But that is terrible for the structural radical interpretationist! For her analysis of `correct belief/desire interpretation’ was that such an interpretation structurally rationalizes dispositions to act in the light of experience. And if the above is right, then Paranoid and Deviant are just as correct as Original. But they aren’t! Sally could be you or me—she’s just an ordinary person, acting and experiencing in ordinary ways. Sally is a person who believes that the world is uniform, and who rejects the bubble-and-void scenario. Structural radical interpretation cannot capture this, and so must be amended or replaced. I vote for replacement, and in the next post, I’ll talk about the alternative I advocate. 

NoR 1.5a Substantive rationality

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 last post I argued that it’s possible to construct an interpretation on which an agent is agnostic and indifferent to the character of the world outside her local bubble (the part of the world she can directly perceive and manipulate). This can be done in a way that still makes her “structurally” rational–formally and means-end consistent, updating coherently in the light of experience, and so forth. That’s trouble for structural radical interpretation, which said that what it was for an interpretation of Sally to be correct was for it to rationalize her dispositions to act in light of her course of experience. But we’ve seen that structurally rationality alone can’t rule out obviously incorrect interpretations on which Sally is agnostic about extra-bubbular matters, or even takes the world outside her bubble to be void.

The bubble puzzle refutes structural radical interpretation. But it is only a problem because of the unforced error taking the ‘rationalization’ relevant to radical interpretation to be structural rather than substantive. Recall: there’s nothing structurally irrational with future Tuesday indifference or a basic desire for a saucer of mud, And we might now add: nothing structurally irrational with taking one’s local bubble to be radically different in character from the world outside that local bubble. But forming such beliefs or desires is nevertheless not a reasonable place to end up, given standard, mundane course of experiences. Such beliefs and desires are irrational (given the available evidence) in an ordinary, non-technical sense, and it is only when we refine the notion to focus on  attitudes whose badness is distinctively “formal” that we generate these difficulties. Structural rationality is I think an important normative notion but it is not the right tool for this project.

The trouble is that the ordinary, broader notion of rationality is at this point inchoate. In the case of structural rationality, we have many ideas about what sorts of things are in the offing to be rational constrains, and we have a century of development of formal articulations of these constraints to model the account being proposed. This level of detail makes structural radical interpretation a predictive theory, since we can apply our existing theory of structural rationality to patterns of acts and experiences, and see what interpretations pass the test. If it weren’t predictive, we wouldn’t get the kind of nasty surprises we’ve just been worrying about!

If substantive radical interpretation is to be a credible option, we need something similar. We need some body of theory about substantive rationality that we can bring to candidate interpretations of an agent, which we can use to see what the theory predicts. The bubble puzzle makes this pressing. Are the interpretations Deviant or Paranoid substantively irrational, or at least less substantively rational than Original? On what basis shall we adjudicate such questions?

In what follows I add content to this theory in a number of ways:

  1. By endorsing specific assumptions about what a substantively rational agent is like.
  2. By endorsing restricted identifications: for example, that a substantively rational agent will have justified beliefs.
  3. By giving general theoretical glosses on the notion of substantive rationality.

In the applications in future posts, strategy 1—specific assumptions about  will be centre-stage. Any reading of substantive rationality on which those specific assumptions follow will do. But specific assumptions may look ad hoc without the wider theoretical context provided by the second and third. The second and third themselves get their power by linking substantive rationality to existing normative accounts, and will tend to involve some contentious choices. So let me spend some initial time here talking a bit about substantive rationality, in the spirit of approaches 2 and 3.

As regards 2, I will indeed take it that a (perfectly) substantively rational agent is one whose every belief (disbelief, suspension of belief) is justified. Further, I assume that subjects are, all else equal, more substantively rational the more their beliefs are justified by the evidence they possess. Substantive radical interpretation tells us, therefore, that ceteris paribus, the correct interpretation of Sally is a justification-maximizing one.

Similarly, I take it that a (perfectly) substantively rational agent is moral, and that agents all else equal are more substantively rational the more their actions are ethically correct given their beliefs/desires. Substantive radical interpretation tells us, therefore, that ceteris paribus, the correct interpretation of Sally is a morality-maximizing one.

These are just two ways to add content to substantive radical interpretation. More such constraints could be added, further fleshing out substantive rationality—for example, prudence as well as morality may be a desiderata on the practical side. These restricted identifications give a lot of content to work with, but if they’re not to be a laundry list, we need some general sense of what virtues we should include or not within “substantive rationality. This is where an overarching type-3 gloss comes in.

My central theoretical gloss is the following: that a substantively rational agent believes as they ought (or as is permissible), given their evidence, and an ideally reason-responsive agent acts they as they ought (or as is permissible), given their options and beliefs. Further:

  • The “oughts” in question factor in the agent’s limited perspective. Consider a bomb-disposal expert who is perfectly justified in believing that cutting the green wire will defuse the bomb, but where this will in fact detonate it. In some sense, perhaps, they ought not cut the wire (since that would lead to an explosion!) But in the relevant sense, cutting the wire is The Thing To Do, given their evidence.
  • The ought is “all things considered”. On the practical side, it aggregates moral, prudential (etc) considerations with the agent’s subjective preferences (/tastes/context) in whatever way is appropriate.
  • We shouldn’t presuppose that there is exactly one thing it’s all-things-considered okay to do in decision situation, or exactly one attitude it’s okay to have to a particular context. In the case of acts, for example, we can have ties, incommensurabilities, supererogatory options, or individual differences in taste, etc, generating normative non-uniqueness. The permissibility gloss allows for this—so long as an agent isn’t acting (or believing) in a way that’s all-things-considered wrong, they’ll count as substantively rational. For ease of exposition, I’ll drop the caveat here, and only reintroduce it where non-uniqueness is particularly salient.

Principles that favour justification-maximization fit this overarching gloss. Principles that favour truth-justification do not (even if on some reading or other, one ought to believe what’s true). Principles that favour morality-maximization fit this overarching gloss so long as the moral-ought in question factors in the agent’s factual uncertainty–overly “objective” moral oughts would not.

So when it comes to determining the correct interpretation, we should ideally find an interlocking hierarchy. Specific normative principles explain why this interpretation is favoured over that one. The specific normative principle is backed up by some general first-order normative theory (e.g. theory of justification, theory of morality), which is a determinant of substantive rationality via the kind of “restricted identifications” recently illustrated. And those restricted identifications need to be defensible as determinants of what the agent ought to believe and ought to do, on an appropriately information/evidence-sensitive reading of “ought”.

Turning back to our earlier examples of specific constraints of substantive rationality we can set them in context. Counterinductive belief formation is structurally rational, but doesn’t lead to epistemically justified beliefs. What you ought to believe is determined (at least in part) by what you’re epistemically justified in believing. So counterinductive beliefs are not substantively rational, and interpretations that attribute them are disfavoured. Being indifferent to what happens on future Tuesdays is structurally rational, but leads to imprudence—a failure to properly respect your own future interests. What you ought to do is determined (at least in part) by what it is prudent to do. So such desires are not substantively rational, and interpretations that attribute them are disfavoured. What about basic desires for saucers of mud? The underlying idea here, I take it, is that even idiosyncratic desires need to be for something valuable, and so substantively rational agents, though they may differ in their preferences, would always lock onto goals that are of value. Personally, I don’t know if I accept this piece of normative theory — or if it is a constraint on what the agent all things considered ought do, in the appropriate sense. So I’m agnostic, at this point, about whether this really is an example of something that would make an interpretation disfavoured. That shows that the framework I’ve introduced has teeth, and that we are no longer just dealing with an ad hoc list of psychological features that strike us as odd. To figure out whether desires for saucers of mud are to count as substantively irrational, we need to get into first-order normative theory.

 

 

Okay, so I think we have enough here to flesh out what substantive rationality is to be, and hence the content of substantive radical interpretation. In the next post, I’ll discuss how this resolves the bubble puzzle.

NoR 1.5b: Popping the bubble puzzle.

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

To recap: I distinguished two forms of radical interpretation: structural and substantive, based on a distinction between two corresponding readings of “rationalization”. Structural radical interpretation has a counterexample in the bubble puzzle: obviously wrong interpretations of an agent can perfectly structurally-rationalize her actions given her course of experience. Attention turns then to substantive radical interpretation, but that’s going to be no good if all we have to offer by way of fleshing out “substantive rationality” is an ad hoc laundry list of odd-seeming psychological states. But I’ve set out a principled framework which we use to explain and predict which interpretations will be counted as substantively rational, and which not. In this post, I’ll turn back to the bubble puzzle, and show why it isn’t a problem for substantive radical interpretation.

What the construction provides us with are (structurally-rational) candidate interpretations Deviant and Paranoid. Now this was a counterexample to structural radical interpretation, but because we deny that all structurally rational interpretations are substantively rational, they are not (at this point) a counterexample to substantive radical interpretation. However, they still serve generate a challenge: to pin down what constraints of substantive rationality they violate.

Consider the case of a character to whom Deviant would truly apply, who really is agnostic and indifferent about matters outside her local bubble. You might think of her—at least as far as her beliefs are concerned—as someone who read too many classic Cartesian and Humean sceptical arguments and, convinced, ends up suspending judgement on the character of the wider world beyond her local surroundings. This suggests a way of identifying what’s wrong with Deviant. Take your favourite anti-sceptical story about how and why agents are justified in their (standard) beliefs about the world around them, given their evidence. Cite the anti-sceptical story to defend the view that the beliefs attributed by the interpretation Original are justified by the agent’s course of experience, but suspending belief or having paranoid beliefs is not. Then (via a restricted identification of kind 2 above, e.g. that substantive rationality of beliefs coincides with justification) we explain on this basis why Original is more substantively rational than Deviant or Paranoid (all else equal).

To illustrate, suppose the local bubble around an agent encompasses a region of space time varying from a few metres to a several miles (perhaps on occasion, when gazing at the stars, it is much more extensive). We believe that the world outside that bubble—in the region now behind the wall that blocks my view, in the years before I was born and after my death—is similar in character to the world in my bubble. That belief in the spatio-temporal uniformity of nature, across the boundaries of the bubble of my experience and action, is a presupposition of my reasons for holding more specific beliefs, e.g. that the hose I left in the yard yesterday is still there now, that there was some decent popular music recorded in the 1960s, and that pouring chemicals in the local streams will cause environmental damage that will last centuries.  What justification we have for believing that nature is uniform in this way is a familiar, Humean, question, to which first-order epistemology owes us an answer. Perhaps it is this: a belief in the uniformity of nature is the best, simplest explanation of the uniformity that we do see within our local bubble. Add to this the claim that we are justified in believing the best explanation of the phenomenon we observe, and that we are not so justified in believing a worse explanation/no explanation, or in suspending judgement, and we have a epistemic principle we can wield in defence of substantive radical interpretation.

Suppose that the local bubble is more “Cartesian”, including only the agent’s pattern of sense-data and inner volitions—this on the basis that sense-data constitute the sphere of experiential evidence and volitions the sphere of basic action. In that context, we will need to look to epistemology to tell us what justifies ordinary beliefs about the material world around us (insofar as that is not an idealist construct out of sense-data and volitions). We need an answer to what justifies the agent in thinking that there is a solid material chair in which she is sitting, given her evidence consists of a mosaic of colour patches in visual space, pressure patches in bodily space, etc. Andgiventhe starting assumption about the character of basic experiential evidence, then unless the sceptic is going to win, there must be some good answer to it. Perhaps, as Russell thought, inference to the best explanation is again the key. Or perhaps there are simply a priori justified “dogmatic” conditionals, that experience as of a material object so-shaped justifies the belief that there is a material object so-shaped. Having got to the material contents of the local space-time region, we are at the starting blocks of the Humean puzzle just discussed, and by chaining the stories together our first-order anti-sceptical epistemology again is the source of the detailed story about why the bubble puzzle is answered.

It is characteristic of the approach that the necessary first-order epistemology will be a matter of controversy. It is not uncontroversial that justification in the uniformity of nature proceeds by inference to the best explanation. It is not uncontroversial that suspending judgement in the uniformity of nature is unjustified. And even once the operative principles are accepted, there is of course a lot of work to be done in understanding the most foundational epistemic principles on which the epistemic principle operative here—inference to the best explanation—is based. Substantive radical interpretation, for better or worse, simply doesn’t offer many autonomous predictions, independent of the details of first-order epistemic or practical normative theory. But the case of the bubble puzzle, since it’s linked to familiar sceptical scenarios, is a special one, since we are entitled to assume that some anti-sceptical story or other will be forthcoming, and however this plays out, the bubble puzzle will have an answer.

One caveat to the above. An anti-sceptical epistemology is not quite enough. We need an intolerant anti-sceptical epistemology, that is, one that doesn’t simply say that it’s okay (epistemically permissible) to believe in the material world around you and the uniformity of nature, given a standard course of experience, but that such beliefs are epistemically obligatory. Subjective Bayesianism, as an epistemic theory, denies this. They are not classic sceptics, and might even endorse the letter of inference to the best explanation. But for subjective Bayesians, having prior probabilities that favour explanations with such-and-such character in response to a standard course of experience is simply one rational option among many. Sure, our priors are like this, and perhaps there’s a good, non-rational, evolutionary explanation about how we come to be disposed to react to evidence like this. But on this view, there’d be no normative defect in having very deviant priors that favour more complex explanations over simpler ones, and priors that favour e.g. the beliefs attributed by Paranoid, over those attributed by Original. Subjective Bayesians, at least as I’m understanding them here, essentially deny there’s a category of “substantive rationality” in epistemology that can’t be analyzed as the joint upshot of structural rationality constraints plus facts about the priors that are typically shared among creatures like us, but which are not normatively privileged. It is not immediate that the subjective Bayesian reduction of “substantive” rationality would reinstitute the bubble puzzle, since Paranoid and Deviant attribute paranoid and deviant desires as well as beliefs, and one might combine the subjectivist epistemology with a more objectivist account of practical normativity. But I think that’s a faint hope, and we should simply insist that a demanding anti-sceptical epistemology, as opposed to be the permissivist one just sketched, is a presupposition of the project.

This brings us to the end of this initial presentation of my favoured approach to type-2 representation, the grounding of facts about what an agent believes and desires, and to the end of part 1 of my series of posts. As promised, we’ve concentrated on the selectional ideology of “rationalization”. Nothing has been said about the base facts on which the metaphysics of belief/desire is grounded—experience and action. In part 3, I’ll be looking in more detail at the metaphysics of these, more basic, representational facts. Facts about linguistic representation, or other representational artefacts, have not been mentioned. Because of this, the story that has been presented is itself an appropriate basis for going on to theorize those “third-layer” representational facts, and part 4 will cover this. Before all that, though, I want to extract more mileage out of the story of belief and desire than we have seen hitherto, and show the way that this foundational story can predict and explain in a detailed and nuanced way aspects of particular kinds of representational states. Part 2, then, will be deploying the framework I’ve just set out to explain aspects of the way we think about the logically complex, the general, individual objects, and their normative and categorical features.

 

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.

NoR 2.2: Everything

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 turn now to another logical concept: generality. Specifically, I am interested in unrestricted generality.

For starters, we do seem able to express thoughts that range over everything without  restriction. Our ability to do so is, furthermore, significant to us. The philosophical thesis of physicalism is that absolutely everything is physical, not that everything-around-here is physical. Without the ability to talk about absolutely everything, such theses would be ineffable. The moral rule is that all people should be treated fairly, not that all people-who-meet-some-further-condition should be so treated. The “all” still needs to be absolutely unrestricted in force in order to capture the intended thought, and this illustrates that even explicitly restricted quantification (“all people”) presupposes that we are not missing out on absolutely anything in the underlying domain from which the restricted class is selected.

But against this, there are formal results that show there are deviant, restricted interpretations of the generality of “everything” and “all” on which our interpretee Sally doesn’t quantify over absolutely everything. It turns out that we can construct such restricted interpretations in ways that pass most tests we can muster for what makes an interpretation correct. For example, we can find a deviant interpretation that agrees with the correct, unrestricted, interpretation of Sally on the truth value of every thought she can think. And we can choose the interpretation so it agrees with the distribution of truth values over thoughts not just in the actual world, but at every possible situation. Further, such deviant interpretations diverge from the correct interpretation only on the domain of the quantifiers. So they assign the same denotation to singular concepts, predictive concepts and the propositional connectives.

Because of the matching truth values/truth conditions, you won’t be able to rule out the deviant interpretation of Sally on the grounds that it makes her thoughts any less reliable than the original interpretation. Because of way the interpretations on everything-except-quantifiers, side-constraints on the interpretation of singular terms and the like won’t help at all. The challenge for us is to explain how, despite the existence of such “skolemite” interpretations, Sally manages to generalize unrestrictedly, in the way that philosophy and morality presupposes she can.

Aside. I’m here skating over a number of technical issues in constructing the construction of these deviant “skolemite” interpretations. So let me just flag, in lieu of getting into details, that it may be that the challenge is restricted to those whose conceptual repertoire is expressively limited in some ways. While the technicalities (involving higher order quantifiers and modal resources) are interesting in their own right, and I have things to say on the topic, I don’t find it at all credible that our ability to quantify restrictedly depends on our ability to think thoughts whose logical form goes beyond that of the first-order extensional calculus. So I’m happy setting these aside.

While I’m flagging side-notes, let me also highlight the point just made that skolemite interpretations aren’t ruled out by imposing side-constraints on the denotation of singular or predicative concepts or propositional connectives. While we’re talking about radical interpretation specifically here, notice that this feature means that the skolemite challenge is relevant to theorists who start from a quite different place, since there’s a laser-like focus on the denotation of quantifiers here—the problems won’t come out in the wash just because you have some interesting things to say about the denotation of concepts in other categories. End Aside. 

Following the pattern of the last post, I will make some architectural assumptions about the way that quantificational thoughts figure in our psychology, and explore what radical interpretation will predict under those assumptions. The first three architectural assumptions I will make are just as before—that belief states are structured, that facts about syntax are grounded prior to questions of content arising, and that we can pick out inferential dispositions interrelating belief-types, again prior to questions of content being determined. I will continue to use the Peacockian idea that certain core inferences are treated as primitively compelling.

The fourth architectural assumption is about the character of the inferential role associated with the quantifier concept everything which I write as q. I’ll concentrate on just one of these rules:

  • From qx:Fx  derive  Fa

Our interpretee, Sally, endorses an instance of this for every individual concept a that she possesses. We’ll come back in a moment to the question of whether this is all the relevant facts relating Sally to tokens of this inference-type.

If the story rolled on from this point as it did for conjunction, we might expect that we’d find radical interpretation predicting something along the same lines as the Peacockian “determination theory” for conjunction, that is, the semantic value for q will be the quantifier, whatever it is, that make all instances of the above instances of a valid type. Just as before, Radical interpretation will approximate an interpretative constraint of this kind.  Sally’s rationality, which includes maximizing justified beliefs, which ceteris paribus includes interpreting q so as to make the inferences justification-preserving. Making them valid looks just the ticket.

If this is all we can extract from the story, we’d be in trouble. There are every-so-many ways of choosing restricted quantifiers as an interpretation of q to make all instances of the above truth-preserving. The ones that are constructed by the skolem procedure are among them, since the skolemite interpretation’s restricted domain includes every object for which the subject has an individual concept a.

In some special restricted cases, we have devices that allow us to construct concepts for every member of a restricted domain (as in our procedure for constructing numerals for natural numbers). But that’s not so in the general case. It’s not even so in very large restricted domains, for example for quantifiers over the real numbers, over space-time points, or sets.

Aside. One reaction in the literature has been to double down on the idea of making instances of the above scheme valid, and argue that more “instances” are relevant than one might at first think. Thus, one might argue that Sally is disposed to find compelling not just instances of the above scheme for singular concepts she currently has available, but also for potential singular terms not currently within her ken. I think, though, that this is ultimately not a productive approach. Although the general idea that Sally’s endorsement of the inference pattern above is “open-ended” when she’s using an absolutely unrestricted quantifier is a good one, I do not think that this is best factored into the theory of how denotation is fixed by an insistence that those  extra token inferences be interpreted so as to be instances of a valid type. (I consider the approach at length elsewhere, but briefly, the problem is that consistently with this constraint, one can interpret the agent as deploying a contingent and contextually flexible restricted quantifier whose domain “expands and contracts” in sync with the agent’s available singular conceptual resources. In a slogan: using counterfactual pegs to fix quantifier domains only end up constraining the counterfactual domains. End Aside. 

Radical Interpretation can explain how finding tokens of the elimination rule above primitively compelling can fix a truly unrestricted interpretation of our quantificational concepts. It can do so by appeal to the epistemological character of even a single token instance of the inference-type.

Take an interpretation where Sally uses a quantifier tacitly restricted to some skolemite domain S, and see what we think of the epistemological status:

From Everything (psst… in S) is beautiful. Derive Toby is beautiful.

Now, Toby is among the items in the skolemite domain S, we may assume. So the inference preserves truth, on the suggested interpretation. But what’s striking is that Sally is not interpreted as having or utilizing any information either way about this fact. To state the obvious: that’s not the usual way we would think of restricted quantification as going. For example, in order to justify my belief that “Toby should be treated fairly” by inference from my (justified) belief that “All people should be treated fairly”, I surely also need to have the justified belief that Toby is a person. After all, if I wasn’t justified in thinking that Toby was a person—if my evidence was that he’s my neighbour’s cat—then the justification for the derived claim would be undercut. The same goes for ordinary, tacitly restricted quantification. From “everyone has some marking to do” (contextually restricted to faculty members) I can’t be justified in believing “Toby has some marking to do” unless I have some justification for believing that Toby is a member of faculty. What’s striking and central about Sally’s deployment of an unrestricted quantifier is that her inference is not enthymetic in this way. She doesn’t pause to check whether or not Toby has this or that feature before inferring that he’s beautiful.

In sum: Sally’s justification for the belief that everything is beautiful transfers to Toby is beautiful without mediation. The lack of mediations explains why her acceptance of the inference rule is “open ended”, as theorists like McGee and Lavine have emphasized. But what matters for grounding facts about quantifier-meaning is not the way this open-endedness manifests in the piling up of accepted instances of the inference across counterfactual scenarios, but the lack of mediation in the epistemological structure of the inference, a feature that is already present the actual cases.

I propose the following piece of epistemology. Consider an elimination rule for a restricted quantifier—whether restricted explicitly (all people) or restrictedly tacitly (either by contextual mechanisms or in the way proposed by the skolemite construction. If deployments of that rule are to transfer justification, then that rule will have to include a side-premise, to the effect that the object in question has the feature that defines the restriction. This is not the case for an unrestricted quantifier.

This piece of epistemology then tells us why we wouldn’t be interpreting Sally as substantively rational if we interpreted her as using a skolemite quantifier—we’d be representing her as constantly engaging in inferences that involve enthymetic premises for which she has no justification.

This story gives us a satisfying resolution of long-standing skolemite puzzles about what grounds our ability to quantify unrestrictedly. Methodologically, it illustrates the virtue of thinking through what radical interpretation require in detail—in the case of conjunction, we only needed to make the primitively compelling inferences valid in order to pin down the denotation. That is insufficient here, since making valid the elimination rule (and indeed, the analogous introduction rule) wouldn’t eliminate the deviant interpretations.

I finish by running through the derivation of Sally’s q denoting the unrestrictedly general universal quantifier. First, we have the a posteriori assumption that c plays a distinctive cognitive role in Sally’s cognitive architecture, captured by the unmediated elimination rule. Second, we have substantive radical interpretation which tells us that the correct interpretation of q is one that maximizes (substantive) rationality of the agent. We add the “localizing” assumption, inferential role determinism for q, 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 q are rational. Putting these three together we have the following: the correct interpretation of Sally is one that makes the inferential role associated with q most rational. And now we add the conclusion of the discussion we’ve just been having: that the way to make the inferential role that consists in the elimination rule without side-premises most rational (especially to make it most justification-preserving) is to make it denote the unrestricted quantifier.

Edited 12/9/17

NoR: supplement to 2.1/2.2: Peacocke 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

This post compares what I have said so far about the concepts of conjunction (which should be the easiest case) and unrestricted universal quantification (which is a notoriously hard case) to what Christopher Peacocke says on the same topics.

Peacocke’s account of logical concepts is something of a moving target. There is a “partial” treatment given in his 1986 book Thought. There are some important elaborations in his 1987 British Academy lecture “Understanding logical constants”. And there’s yet more on this in his 1992 book A Study of Concepts (ASOC). His thinking continued to develop after this, but one theme of his later work is the appeal to “implicit understandings” of concepts which make him less comparable to what I’m doing here. So I’ll concentrate on the the remarks he makes in these three early pieces, concentrating in particular in the account presented in the 1992 work, and using the earlier two works to fill in the account where the 1992 book is inexplicit.

One immediate contrast between the ideas I have been presenting and ASOC is the intended subject matter. Peacocke is assuming a Fregean account of thought, on which thoughts are structured entities whose components are Fregean senses. He calls these thought-components concepts. Each concept then determines (perhaps in context) a referent. He makes some standard Fregean assumptions about the division of labour between sense and reference. So we’d expect to see, for example, differences in cognitive significance of thoughts explained by difference in some component sense.

Peacocke’s project in ASOC is to give an account of what it is for a person to possess a concept. And he does this by setting out “possession conditions” for a target concept (be that conjunction or universal quantification). In the cases that concern us, these possession conditions consist simply in the subject finding relevant inferences primitively compelling (and the subject needs to be finding the token inferences primitively compelling because they have the right form). With this account of what it is for a subject to possess the concept conjunction, or quantification, or whatever, Peacocke then goes on to offer what he calls a “determination theory”, for each individual concept i.e. an account of what the concept refers to (or “has as its semantic value”). For conjunction he offers the following:

  • The truth function that is the semantic value of conjunction is the function that makes transitions of the form mentioned in its possession conditions always truth-preserving. (p.10).

The relevant transitions are of course the familiar conjunction-introduction and conjunction elimination rules.

Though each determination theory is a determination theory of one particular concept, Peacocke says we should expect such determination theories to have a general form.

  • The determination theory for a given concept (together with the world in empirical cases) assigns semantic values in such a way that the belief-forming practices mentioned in the concept’s possession condition are correct. That is, in the case of belief formation, the practices result in true beliefs, and in the case of principles of inference, they result in truth-preserving inferences, when semantic values are assigned in accordance with the determination theory”. (p.19)

Let me work this through for the various things that Peacocke says about quantifiers. In ASOC, the leading example is quantification restricted to the natural numbers C. At p.7, he states that the possession conditions are that the thinker find suitable instances of the form primitively compelling:

  • from Cx: Fx derive Fn

The suitable instances are are “those involving a concept n for which the content n is a natural number is uninformative”. In addition, the thinker is (a) required to find these inferences compelling because of the given form; and (b) the thinker is not required to find any other inferences essentially involving C primitively compelling. The determination theory is then

  • The semantic value of this quantifier is the function from extensions of concepts (true or false of natural numbers) to truth values that makes elimination inferences of the form mentioned in the possession condition always truth-preserving.

Now, clearly validity is playing a major role in Peacocke’s determination theory for conjunction and (numerical) quantification. But notice also that in both cases the requirement to make the inferences valid selects a semantic value from restricted pool of candidates (truth functions in the first case, quantifiers over natural numbers in the second). The general form of determination theory he gives doesn’t say anything about how we narrow down to this particular pool, and (as later authors have emphasized) this is an extremely substantive step. For example, in the case of quantification over the natural numbers, the elimination rule will be valid on any domain that includes the natural numbers, whether it includes also the integers, or is absolutely unrestricted.

This is one place where Peacocke’s 1987 work may be relevant. There, for cases of concepts whose possession conditions are spelled out in terms of elimination rules only (/introduction rules only) he suggests that the concept denotes the weakest (/strongest) semantic value that makes the rules valid (p.161). In application to the possession conditions for numerical quantification, for example, interpreting the quantifier as ranging over a more inclusive domain than the naturals would be, intuitively, to give it a stronger interpretation than is required to make the elimination rules valid. That would allow us to drop the ad hoc constraint to quantifiers over natural numbers in the determination theory for numerical quantification, but it wouldn’t bring that determination theory into line with Peacocke’s “general formulation” of determination theories, since that doesn’t provide for constraints of strength or weakness. So this is an area where it’s a little unclear how to mesh the different eras of Peacocke).

Let me mention one last thing. In ASOC, Peacocke explicitly discusses radical interpretation a few times. He is thinking of it, though, as a rival account of concept possession, and though he allows that radical interpretation may say nothing false, he complains that it doesn’t have the right formal features to provide the kind of illumination of concept possession he is targetting. So Peacocke’s conception of radical interpretation at this point contrasts with my own, where radical interpretation is conceived as a theory of reference-fixing, not (Fregean) concept-possession.

I’ll now compare and contrast this setup to my own.

First, unlike Peacocke, I say nothing about Fregean sense. I do talk about “concepts” as components of structured mental states, but for me these are vehicles of mental content, not constituents of content (they are more like Fodorian concepts than Fregean ones, and indeed, thinking of them as words in the language of thought is one model I’ve suggested). So the whole enterprise of articulating “possession conditions” and worrying about them having the right form is just absent from my story. What I have said is consistent with additional assertions that the “inferential roles” I have been appealing to are possession conditions in Peacocke’s sense. But I’ve left open that enacting these inferential roles might be either unnecessary or insufficient for possessing a concept of conjunction, of numerical or unrestricted quantification.

Second, and connectedly, there may be nothing terribly natural about the inferential roles which figure in my explanations of why our concepts have the reference that they do. They may be carved out of our cognitive economy in quite artificial ways. For my purposes, I’m just saying that finding (at least!) those rules primitively compelling is sufficient (given the rest of the background) to explain why the concept denotes what it does.

Third, Peacocke’s determination theories are stated in an unqualified way—e.g. “the semantic value of C *is* that truth-function which makes the conjunction rules valid”. What you get from my framework at this point will have to be caveated with a “ceteris paribus” clause, since everything depends on the assumption that the particular patterns encapsulated in the conceptual role aren’t “overridden” by the way the concept figures elsewhere in the cognitive economy. For some reason I don’t understand, the Peacockian privileges the way that the conjunction-concept figures in belief, rather than other kinds of thought, so that if a concept figures in the conjunction-way in beliefs, and in the disjunction-way in desires, it would determinately be a concept of conjunction. My account (correctly I think) makes no strong predictions about such conflicted cases. The caveats in my theory are a feature, not a bug.

Fourth, what I say is consistent with the thesis that there is a only a small range of concepts which have neatly specifiable inferential/conceptual roles of the kind I’ve been talking about. For all I’ve said there’s no such patterns to be found for many of our concepts. This relaxed attitude is possible since I already have my story about what fixes the content of thought, and so for me the Peacocke-style theorizing is not an essential part of articulating what grounds representation, but a matter of illuminating some special cases.

Fifth, Peacocke alludes to the “general form” of determination theories, which raises the question: why should determination theories have a common form? Radical interpretation answers this by starting with an account of what it takes, generally, for a thought to have content, and then the analogues we get to his “determination theories” are accounts of what the account requires when applied to a particular case. This feels to me like a better direction of explanation than a bottom-up approach on which the convergence on a common form would appear as a cosmic coincidence

Sixth, even when working through cases where inferential rules are central, the emphasis on their validity I think ties our hands. I mentioned above Peacocke’s 1987 constraints of strength and weakness, so it appears that more than validity is going on—and if this is not to be mere monster-barring, we need a sense of why such constraints turn up in theories of reference. Radical Interpretation is well equipped to give principled underpinnings for these extra sorts of constraints.

To illustrate. In response to my earlier post on conjunction, my colleague Jack Woods asked me what ruled out hyperintentionally deviant interpretations of the conjunction c. I asserted that no rational agent would find the conjunction rules for c primitively compelling unless they were working with conjunction. But what if the c they had in mind was something where we read “pcq” as p and q and I am here now? Or indeed, conjunction supplemented by any tautology? The answer I want to give to this sort of challenge is that such an interpretation would not make the agent’s practices justified. Let’s accept that “I am here now” is itself a priori. Still, there is a story to be told about what one has to be like to be justified in believing it (we just know that these conditions aren’t empirical ones). If we believe a thought—even one that is a priori justifiable— merely “en passant” on irrelevant grounds, then we are not forming a justified belief. So the crucial feature is that the raw data is that the inference from p,q to pcq is felt to be primitively compelling. The requirement that we make the primitively compelling rules valid isn’t fine grained enough, since there are many valid arguments we are not justified in taking as primitive. So it’s crucial that the story really incorporates the constraint of making the practice a justified one (which is indeed something that features in Peacocke’s “general formulations” of determination theories) and don’t cash it in too quickly for constraints of making-the-inference-valid (as Peacocke himself does when citing particular determination theories).

A second illustration will open up some further complex issues in Peacocke interpretation. My discussion of unrestricted quantification made essential appeal to epistemological claims about the conditions under which non-enthymetic universal instantiation is justified. Validity alone, I said, wouldn’t knock out skolemite interpretations of the quantifier, but nevertheless, considerations of maximizing justification do so. So I take this to illustrate the same moral of the importance of full justificatory structure in getting the story about reference-fixing right.

Now, Peacocke’s discussion spirals around the issue of what fixes unrestricted interpretation, without ever (in what I’ve read) really nailing it. Let me outline what I’ve found him saying on this topic.

Peacocke discusses unrestricted quantification in the 1986 book Thought. But he acknowledges there (p.36) that he has not given a full account of what determines the denotation of an unrestricted quantifier. More generally, I see no new resources in what he says there or in the later works to rule out skolemite interpretations, given only the resources of validity and completeness.

It could be that he envisages the possession conditions of unrestricted “everything” as tying the subject to every instance of the elimination scheme, for every individual concept whatsoever—even those currently beyond the subject’s conceptual repertoire and which it might be  physically impossible for the subject to possess. On the (substantive!) assumption that there is an individual concept for every object whatsover, the constraint to make all such instances valid would “peg out” the domain to be absolutely universal. There is an echo of that in the way he talks of “open ended” inferential dispositions (pp.33-34). But insofar as Peacocke has to appeal to what we’re disposed to do in counterfactual circumstances where our conceptual repertoire is expanded, this account is vulnerable to an interpretation on which our quantifier has an always-restricted but counterfactually-varying domain, just as McGee and Lavine’s appeals to open-endedness are.

In the later work ASOC (particularly in chapter 5) there is material that may speak to the issue, but ultimately not enough is said to resolve it.  Let’s spot ourselves that Sally both treats particular dated transitions from the thought “Everything is physical” to the thought “Roger is physical” as primitively compelling, and treats as primitively compelling the inference-type inferring Roger is physical from everything is physical (perhaps one or other is more basic, but it won’t matter for our purposes). Peacocke insists, further, that part of the explanation for why we find such inferences primitively compelling is that they have a certain form: inferences just mentioned are said to have the form “Cx:Fx” to “Fa”. Peacocke’s idea is that the determination theories for “C” will say (I think!) insist that the semantic value assigned to C make every (token or type) instance of this form always truth-preserving, i.e. valid.

Now, if this “form” is one shared by absolutely all instances of universal instantiation, including those involving singular concepts outside Sally’s conceptual repertoire, then you might think that Peacocke here has just pulled the rabbit out of the hat. For even in a single case, Sally is related to a particular inference form of universal instantiation (since it part of the explanation of why she finds the token/type inference primitively compelling). And making all instances of the form valid will pin down the quantifier to be the absolutely unrestricted one—the instances “peg out” the unrestricted domain. But of course, this is only good if we can undergird the claim that this the “form” which plays a causal explanatory role in Sally’s psychology is general in this way, rather than a more restricted “form” whose instances are only those individual concepts within Sally’s present ken. If she’s related to the latter “form”, or its indeterminate which “form” is playing the role in her psychology, we get no new leverage here.

In fact, Peacocke raises exactly the relevant issue at ASOC p.137—not in the case of unrestricted quantification, but in connection to the question about whether certain inferential rules for numerical quantification have a form that ranges over all singular concepts for natural numbers, or only over “surveyable” ones. Unfortunately, all he says there is that the issue is “far beyond” the scope of that book to resolve. We can at least take it that he doesn’t view the resources he’s provided in ASOC as giving an easy resolution of the sort of form-determination issue which would be utterly central to the success of this strategy.

Despite these differences, it is striking that the story that falls out of radical interpretation (modulo empirical and normative assumptions) is a recognizable variation of what Peacocke says about his parade cases, which after all were not developed with (my kind of) radical interpretation in mind. Obviously something in this ballpark has independent appeal—and so it’s a big bonus that radical interpretation can predict and explain why something like Peacockian determination theories are in force for logical concepts such as conjunction and quantification.