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.