This post began life as a comment responding to Peer Gynt's request for a steelman of non-correspondence views of truth. It ended up being far too long for a comment, so I've decided to make it a separate post. However, it might have the rambly quality of a long comment rather than a fully planned out post.

Evaluating Models

Let's say I'm presented with a model and I'm wondering whether I should incorporate it into my belief-set. There are several different ways I could go about evaluating the model, but for now let's focus on two. The first is pragmatic. I could ask how useful the model would be for achieving my goals. Of course, this criterion of evaluation depends crucially on what my goals actually are. It must also take into account several other factors, including my cognitive abilities (perhaps I am better at working with visual rather than verbal models) and the effectiveness of alternative models available to me. So if my job is designing cannons, perhaps Newtonian mechanics is a better model than relativity, since the calculations are easier and there is no significant difference in the efficacy of the technology I would create using either model correctly. On the other hand, if my job is designing GPS systems, relativity might be a better model, with the increased difficulty of calculations being compensated by a significant improvement in effectiveness. If I design both cannons and GPS systems, then which model is better will vary with context.

Another mode of evaluation is correspondence with reality, the extent to which the model accurately represents its domain. In this case, you don't have much of the context-sensitivity that's associated with pragmatic evaluation. Newtonian mechanics may be more effective than the theory of relativity at achieving certain goals, but (conventional wisdom says) relativity is nonetheless a more accurate representation of the world. If the cannon maker believes in Newtonian mechanics, his beliefs don't correspond with the world as well as they should. According to correspondence theorists, it is this mode of evaluation that is relevant when we're interested in truth. We want to know how well a model mimics reality, not how useful it is.

I'm sure most correspondence theorists would say that the usefulness of a model is linked to its truth. One major reason why certain models work better than others is that they are better representations of the territory. But these two motivations can come apart. It may be the case that in certain contexts a less accurate theory is more useful or effective for achieving certain goals than a more accurate theory. So, according to a correspondence theorist, figuring out which model is most effective in a given context is not the same thing as figuring out which model is true.

How do we go about these two modes of evaluation? Well, evaluation of the pragmatic success of a model is pretty easy. Say I want to figure out which of several models will best serve the purpose of keeping me alive for the next 30 days. I can randomly divide my army of graduate students into several groups, force each group to behave according to the dictates of a separate model, and then check which group has the highest number of survivors after 30 days. Something like that, at least.

But how do I evaluate whether a model corresponds with reality? The first step would presumable involve establishing correspondences between parts of my model and parts of the world. For example, I could say "Let m_S in my model represent the mass of the Sun." Then I check to see if the structural relations between the bits of my model match the structural relations between the corresponding bits of the world. Sounds simple enough, right? Not so fast! The procedure described above relies on being able to establish (either by stipulation or discovery) relations between the model and reality. That presupposes that we have access to both the model and to reality, in order to correlate the two. In what sense do we have "access" to reality, though? How do I directly correlate a piece of reality with a piece of my model?

Models and Reality

Our access to the external world is entirely mediated by models, either models that we consciously construct (like quantum field theory) or models that our brains build unconsciously (like the model of my immediate environment produced in my visual cortex). There is no such thing as pure, unmediated, model-free access to reality. But we often do talk about comparing our models to reality. What's going on here? Wouldn't such a comparison require us to have access to reality independent of the models? Well, if you think about it, whenever we claim to be comparing a model to reality, we're really comparing one model to another model. It's just that we're treating the second model as transparent, as an uncontroversial proxy for reality in that context. Those last three words matter: A model that is used as a criterion for reality in one investigative context might be regarded as controversial -- as explicitly a model of reality rather than reality itself -- in another context.

Let's say I'm comparing a drawing of a person to the actual person. When I say things like "The drawing has a scar on the left side of the face, but in reality the scar is on the right side", I'm using the deliverances of visual perception as my criterion for "reality". But in another context, say if I'm talking about the psychology of perception, I'd talk about my perceptual model as compared (and, therefore, contrasted) to reality. In this case my criterion for reality will be something other than perception, say the readings from some sort of scientific instrument. So we could say things like, "Subjects perceive these two colors as the same, but in reality they are not." But by "reality" here we mean something like "the model of the system generated by instruments that measure surface reflectance properties, which in turn are built based on widely accepted scientific models of optical phenomena".

When we ordinarily talk about correspondence between models and reality, we're really talking about the correspondence between bits of one model and bits of another model. The correspondence theory of truth, however, describes truth as a correspondence relation between a model and the world itself. Not another model of the world, the world. And that, I contend, is impossible. We do not have direct access to the world. When I say "Let m_S represent the mass of the Sun", what I'm really doing is correlating a mathematical model with a verbal model, not with immediate reality. Even if someone asks me "What's the Sun?", and I point at the big light in the sky, all I'm doing is correlating a verbal model with my visual model (a visual model which I'm fairly confident is extremely similar, though not exactly the same, as the visual model of my interlocutor). Describing correspondence as a relationship between models and the world, rather than a relationship between models and other models, is a category error.

So I can go about the procedure of establishing correspondences all I want, correlating one model with another. All this will ultimately get me is coherence. If all my models correspond with one another, then I know that there is no conflict between my different models. My theoretical model coheres with my visual model, which coheres with my auditory model, and so on. Some philosophers have been content to rest here, deciding that coherence is all there is to truth. If the deliverances of my scientific models match up with the deliverances of my perceptual models perfectly, I can say they are true. But there is something very unsatisfactory about this stance. The world has just disappeared. Truth, if it is anything at all, involves both our models and the world. However, the world doesn't feature in the coherence conception of truth. I could be floating in a void, hallucinating various models that happen to cohere with one another perfectly, and I would have attained the truth. That can't be right.

Correspondence Can't Be Causal

The correspondence theorist may object that I've stacked the deck by requiring that one consciously establish correlations between models and the world. The correspondence isn't a product of stipulation or discovery, it's a product of basic causal connections between the world and my brain. This seems to be Eliezer's view. Correspondence relations are causal relations. My model of the Sun corresponds with the behavior of the actual Sun, out there in the real world, because my model was produced by causal interactions between the actual Sun and my brain.

But I don't think this maneuver can save the correspondence theory. The correspondence theory bases truth on a representational relationship between models/beliefs and the world. A model is true if it accurately represents its domain. Representation is a normative relationship. Causation is not. What I mean by this is that representation has correctness conditions. You can meaningfully say "That's a good representation" or "That's a bad representation". There is no analog with causation. There's no sense in which some particular putatively causal relation ends up being a "bad" causal relation. Ptolemy's beliefs about the Sun's motion were causally entangled with the Sun, yet we don't want to say that those beliefs are accurate. It seems mere causal entanglement is insufficient. We need to distinguish between the right sort of causal entanglement (the sort that gets you an accurate picture of the world) and the wrong sort. But figuring out this distinction takes us back to the original problem. If we only have immediate access to models, on what basis can we decide whether our models are caused by the world in a manner that produces an accurate picture. To determine this, it seems we again need unmediated access to the world.

Back to Pragmatism

Ultimately, it seems to me the only clear criterion the correspondence theorist can establish for correlating the model with the world is actual empirical success. Use the model and see if it works for you, if it helps you attain your goals. But this is exactly the same as the pragmatic mode of evaluation which I described above. And the representational mode of evaluation is supposed to differ from this.

The correspondence theorist could say that pragmatic success is a proxy for representational success. Not a perfect proxy, but good enough. The response is, "How do you know?" If you have no independent means of determining representational success, if you have no means of calibration, how can you possibly determine whether or not pragmatic success is a good proxy for representational success? I mean, I guess you can just assert that a model that is extremely pragmatically successful for a wide range of goals also corresponds well with reality, but how does that assertion help your theory of truth? It seems otiose. Better to just associate truth with pragmatic success itself, rather than adding the unjustifiable assertion to rescue the correspondence theory.

So yeah, ultimately I think the second of the two means of evaluating models I described at the beginning (correspondence) can only really establish coherence between your various models, not coherence between your models and the world. Since that sort of evaluation is not world-involving, it is not the correct account of truth. Pragmatic evaluation, on the other hand, *is* world-involving. You're testing your models against the world, seeing how effective they are at helping you accomplish your goal. That is the appropriate normative relationship between your beliefs and the world, so if anything deserves to be called "truth", it's pragmatic success, not correspondence.

This has consequences for our conception of what "reality" is. If you're a correspondence theorist, you think reality must have some form of structural similarity to our beliefs. Without some similarity in structure (or at least potential similarity) it's hard to say how one meaningfully could talk about beliefs representing reality or corresponding to reality. Pragmatism, on the other hand, has a much thinner conception of reality. The real world, on the pragmatic conception is just an external constraint on the efficacy of our models. We try to achieve certain goals using our models and something pushes back, stymieing our efforts. Then we need to build improved models in order to counteract this resistance. Bare unconceptualized reality, on this view, is not a highly structured field whose structure we are trying to grasp. It is a brute, basic constraint on effective action.

It turns out that working around this constraint requires us to build complex models -- scientific models, perceptual models, and more. These models become proxies for reality, and we treat various models as "transparent", as giving us a direct view of reality, in various contexts. This is a useful tool for dealing with the constraints offered by reality. The models are highly structured, so in many contexts it makes sense to talk about reality as highly structured, and to talk about our other models matching reality. But it is also important to realize that when we say "reality" in those contexts, we are really talking about some model, and in other contexts that model need not be treated as transparent. Not realizing this is an instance of the mind projection fallacy. If you want a context-independent, model-independent notion of reality, I think you can say no more about it than "a constraint on our models' efficacy".

That sort of reality is not something you represent (since representation assumes structural similarity), it's something you work around. Our models don't mimic that reality, they are tools we use to facilitate effective action under the constraints posed by reality. All of this, as I said at the beginning, is goal and context dependent, unlike the purported correspondence theory mode of evaluating models. That may not be satisfactory, but I think it's the best we have. Pragmatist theory of truth for the win.

Thought of this after reading the discussion following abcd_z's post on utilitarianism, but it seemed sufficiently different that I figured I'd post it as a separate topic. It feels like the sort of thing that must have been discussed on this site before, but I haven't seen anything like it (I don't really follow the ethical philosophy discussions here), so pointers to relevant discussion would be appreciated.

Let's say I start off with some arbitrary utility function and I have the ability to arbitrarily modify my own utility function. I then become convinced of the truth of preference utilitarianism. Now, presumably my new moral theory prescribes certain terminal values that differ from the ones I currently hold. To be specific, my moral theory tells me to construct a new utility function using some sort of aggregating procedure that takes as input the current utility functions of all moral agents (including my own). This is just a way of capturing the notion that if preference utilitarianism is true, then my behavior shouldn't be directed towards the fulfilment of my own (prior) goals, but towards the maximization of preference satisfaction. Effectively, I should self-modify to have new goals.

But once I've done this, my own utility function has changed, so as a good preference utilitarian, I should run the entire process over again, this time using my new utility function as one of the inputs. And then again, and again... Let's look at a toy model. In this universe, there are two people: me (a preference utilitarian) and Alice (not a preference utilitarian). Let's suppose Alice does not alter her utility function in response to changes in mine. There are two exclusive states of affairs that can be brought about in this universe: A and B. Alice assigns a utility of 10 to A and 5 to B, I initially assign a utility of 3 to A and 6 to B. Assuming the correct way to aggregate utility is by averaging, I should modify my utilities to 6.5 for A and 5.5 for B. Once I have done this, I should again modify to 8.25 for A and 5.25 for B. Evidently, my utility function will converge towards Alice's.

I haven't thought about this at all, but I think the same convergence will occur if we add more utilitarians to the universe. If we add more Alice-type non-utilitarians there is no guarantee of convergence. So anyway, this seems to me a pretty strong argument against utilitarianism. If we have a society of perfect utilitarians, a single defector who refuses to change her utility function in response to changes in others' can essentially bend the society to her will, forcing (through the power of moral obligation!) everybody else to modify their utility functions to match hers, no matter what her preferences actually are. Even if there are no defectors, all the utilitarians will self-modify until they arrive at some bland (value judgment alert) middle ground.

Now that I think about it, I suspect this is basically just a half-baked corollary to Bernard Williams' famous objection to utilitarianism:

The point is that [the agent] is identified with his actions as flowing from projects or attitudes which… he takes seriously at the deepest level, as what his life is about… It is absurd to demand of such a man, when the sums come in from the utility network which the projects of others have in part determined, that he should just step aside from his own project and decision and acknowledge the decision which utilitarian calculation requires. It is to alienate him in a real sense from his actions and the source of his action in his own convictions. It is to make him into a channel between the input of everyone's projects, including his own, and an output of optimific decision; but this is to neglect the extent to which his projects and his decisions have to be seen as the actions and decisions which flow from the projects and attitudes with which he is most closely identified. It is thus, in the most literal sense, an attack on his integrity.

Anyway, I'm sure ideas of this sort have been developed much more carefully and seriously by philosophers, or even other posters here at LW. As I said, any references would be greatly appreciated.

I just read a paper by Gerhard Schurz proposing an interesting resolution to the problem of induction. Download a PDF here.

Here's the abstract:

This article suggests a ‘best alternative’ justification of induction (in the sense of Reichenbach) which is based on meta‐induction. The meta‐inductivist applies the principle of induction to all competing prediction methods which are accessible to her. It is demonstrated, and illustrated by computer simulations, that there exist meta‐inductivistic prediction strategies whose success is approximately optimal among all accessible prediction methods in arbitrary possible worlds, and which dominate the success of every noninductive prediction strategy. The proposed justification of meta‐induction is mathematically analytical. It implies, however, an a posteriori justification of object‐induction based on the experiences in our world.

Here's Schurz's description of meta-inductivism:

The meta‐inductivist (MI) applies the inductive method at the level of competing prediction methods. More precisely, the meta‐inductivist bases her predictions on the predictions and the observed success rates of the other (non‐MI) players and tries to derive therefrom an ‘optimal’ prediction. The simplest type of MI predicts what the presently best prediction method predicts, but one can construct much more refined kinds of meta‐inductivistic prediction strategies.

One should expect that for meta‐induction the chances of demonstrating optimality are much better than for object‐induction. The crucial question of this article will be: is it possible to design a version of meta‐induction which can be proved to be an (approximately) optimal prediction method? The significance of this question for the problem of induction is this: if the answer is positive, then at least meta‐induction would have a rational and noncircular justification based on a mathematical‐analytic argument. But this analytic justification of meta‐induction would at the same time yield an a posteriori justification of object‐induction in the real world: for we know by experience that in the real world, noninductive prediction strategies have not been successful so far, hence it would be meta‐inductively justified to favor object‐inductivistic strategies.

Here's the conclusion:

While one‐favorite meta‐inductive strategies are optimal only under certain restrictions, weighted‐average meta‐induction has turned out to be universally optimal...

In conclusion, I think the achieved optimality results on meta‐induction are strong enough to show that a noncircular justification of (meta‐)induction can be successful. This justification does not show that meta‐induction must be successful (in a strict or probabilistic sense), but it favors the meta‐inductivistic strategy against all other accessible competitors. This is sufficient for justificational purposes, without being in dissent with any of Hume’s skeptical arguments. The given justification of meta‐induction is mathematically‐analytic (or ‘a priori’), insofar it does not make any assumptions about the nature of the considered worlds except from practically evident assumptions about prediction games, such that its players can perform calculations, can observe past events, and are free to decide. However, as we have explained in Section 2, this analytic justification of meta‐induction implies an a posteriori justification of object‐induction in our real word, because so far object‐induction has turned out to be the most successful prediction strategy. This argument is no longer circular, given that we have a noncircular justification of meta‐induction—and we have it.

The major advantage of the meta‐inductivistic approach is its radical openness towards all kinds of possibilities. In my view, this radical openness is a sign of all good foundation‐oriented (instead of ‘foundationalistic’) programs in epistemology. Unlike in Rescher’s “initial justification” of induction (1980, 82), meta‐induction does not exclude esoteric world‐views or prediction methods from the start. Such an a priori exclusion would prevent a constructive dialog between a scientific philosopher and an esoteric‐minded person. Meta‐induction takes all these possible world‐views initially seriously and argues: wherever the ‘ultimate truth’ lies, you should in any case employ meta‐induction because it is universally optimal among all accessible prediction methods.

Many readers will still uphold skeptical reservations. They will ask: how can it ever be possible to prove that a strategy is optimal with respect to every other accessible strategy in every possible world—without assuming anything about the nature of alternative strategies and possible worlds? My heuristic answer to this skeptical challenge is as follows: this is possible for meta‐inductive strategies because these strategies are universal learners: whenever they are confronted with a so far better strategy, they can imitate the better strategy (output‐accessibility) or even learn to reproduce it (internal accessibility).

Laws as Rules

We speak casually of the laws of nature determining the distribution of matter and energy, or governing the behavior of physical objects. Implicit in this rhetoric is a metaphysical picture: the laws are rules that constrain the temporal evolution of stuff in the universe. In some important sense, the laws are prior to the distribution of stuff. The physicist Paul Davies expresses this idea with a bit more flair: "[W]e have this image of really existing laws of physics ensconced in a transcendent aerie, lording it over lowly matter." The origins of this conception can be traced back to the beginnings of the scientific revolution, when Descartes and Newton established the discovery of laws as the central aim of physical inquiry. In a scientific culture immersed in theism, it was unproblematic, even natural, to think of physical laws as rules. They are rules laid down by God that drive the development of the universe in accord with His divine plan.

Does this prescriptive conception of law make sense in a secular context? Perhaps if we replace the divine creator of traditional religion with a more naturalist-friendly lawgiver, such as an ur-simulator. But what if there is no intentional agent at the root of it all? Ordinarily, when I think of a physical system as constrained by some rule, it is not the rule itself doing the constraining. The rule is just a piece of language; it is an expression of a constraint that is actually enforced by interaction with some other physical system -- a programmer, say, or a physical barrier, or a police force. In the sort of picture Davies presents, however, it is the rules themselves that enforce the constraint. The laws lord it over lowly matter. So on this view, the fact that all electrons repel one another is explained by the existence of some external entity, not an ordinary physical entity but a law of nature, that somehow forces electrons to repel one another, and this isn't just short-hand for God or the simulator forcing the behavior.

I put it to you that this account of natural law is utterly mysterious and borders on the nonsensical. How exactly are abstract, non-physical objects -- laws of nature, living in their "transcendent aerie" -- supposed to interact with physical stuff? What is the mechanism by which the constraint is applied? Could the laws of nature have been different, so that they forced electrons to attract one another? The view should also be anathema to any self-respecting empiricist, since the laws appear to be idle danglers in the metaphysical theory. What is the difference between a universe where all electrons, as a matter of contingent fact, attract one another, and a universe where they attract one another because they are compelled to do so by the really existing laws of physics? Is there any test that could distinguish between these states of affairs?

Summary: There are claims that Boltzmann brains pose a significant problem for contemporary cosmology. But this problem relies on assuming that Boltzmann brains would be part of the appropriate reference class for anthropic reasoning. Is there a good reason to accept this assumption?

Nick Bostrom's Self Sampling Assumption (SSA) says that when accounting for indexical information, one should reason as if one were a random sample from the set of all observer's in one's reference class. As an example of the scientific usefulness of anthropic reasoning, Bostrom shows how the SSA rules out a particular cosmological model suggested by Boltzmann. Boltzmann was trying to construct a model that is symmetric under time reversal, but still accounts for the pervasive temporal asymmetry we observe. The idea is that the universe is eternal and, at most times and places, at thermodynamic equilibrium. Occasionally, there will be chance fluctuations away from equilibrium, creating pockets of low entropy. Life can only develop in these low entropy pockets, so it is no surprise that we find ourselves in such a region, even though it is atypical.

The objection to this model is that smaller fluctuations from equilibrium will be more common. In particular, fluctuations that produce disembodied brains floating in a high entropy soup with the exact brain state I am in right now (called Boltzmann brains) would be vastly more common than fluctuations that actually produce me and the world around me. If we reason according to SSA, the Boltzmann model predicts I am one of those brains and all my experiences are spurious. Conditionalizing on the model, the probability that my experiences are not spurious is minute. But my experiences are in fact not spurious (or at least, I must operate under the assumption that they are not if I am to meaningfully engage in scientific inquiry). So the Boltzmann model is heavily disconfirmed. [EDIT: As AlexSchell points out, this is not actually Bostrom's argument. The argument has been made by others. Here, for example.]

Now, no one (not even Boltzmann) actually believed the Boltzmann model, so this might seem like an unproblematic result. Unfortunately, it turns out that our current best cosmological models also predict a preponderance of Boltzmann brains. They predict that the universe is evolving towards an eternally expanding cold de Sitter phase. Once the universe is in this phase, thermal fluctuations of quantum fields will lead to an infinity of Boltzmann brains. So if the argument against the original Boltzmann model is correct, these cosmological models should also be rejected. Some people have drawn this conclusion. For instance, Don Page considers the anthropic argument strong evidence against the claim that the universe will last forever. This seems like the SSA's version of Bostrom's Presumptuous Philosopher objection to the Self Indication Assumption, except here we have a presumptuous physicist. If your intuitions in the Presumptuous Philosopher case lead you to reject SIA, then perhaps the right move in this case is to reject SSA.

But maybe SSA can be salvaged. The rule specifies that one need only consider observers in one's reference class. If Boltzmann brains can be legitimately excluded from the reference class, then the SSA does not threaten cosmology. But Bostrom claims that the reference class must at least contain all observers whose phenomenal state is subjectively indistinguishable from mine. If that's the case, then all Boltzmann brains in brain states sufficiently similar to mine such that there is no phenomenal distinction must be in my reference class, and there's going to be a lot of them.

Why accept this subjective indistinguishability criterion though? I think the intuition behind it is that if two observers are subjectively indistinguishable (it feels the same to be either one), then they are evidentially indistinguishable, i.e. the evidence available to them is the same. If A and B are in the exact same brain state, then, according to this claim, A has no evidence that she is in fact A and not B. And in this case, it is illegitimate for her to exclude B from her anthropic reference class. For all she knows, she might be B!

But the move from subjective indistinguishability to evidential indistinguishability seems to ignore an important point: meanings ain't just in the head. Even if two brains are in the exact same physical state, the contents of their representational states (beliefs, for example) can differ. The contents of these states depend not just on the brain state but also on the brain's environment and causal history. For instance, I have beliefs about Barack Obama. A spontaneously congealed Boltzmann brain in an identical brain state could not have those beliefs. There is no appropriate causal connection between Obama and that brain, so how could its beliefs be about him? And if we have different beliefs, then I can know things the brain doesn't know. Which means I can have evidence the brain doesn't have. Subjective indistinguishability does not entail evidential indistinguishability.

So at least this argument for including all subjectively indistinguishable observers in one's reference class fails. Is there another good reason for this constraint I haven't considered?

Update: There seems to be a common misconception arising in the comments, so I thought I'd address it up here. A number of commenters are equating the Boltzmann brain problem with radical skepticism. The claim is that the problem shows that we can't really know we are not Boltzmann brains. Now this might be a problem some people are interested in. It is not one that I am interested in, nor is it the problem that exercises cosmologists. The Boltzmann brain hypothesis is not just a physically plausible variant of the Matrix hypothesis.

The purported problem for cosmology is that certain cosmological models, in conjunction with the SSA, predict that I am a Boltzmann brain. This is not a problem because it shows that I am in fact a Boltzmann brain. It is a problem because it is an apparent disconfirmation of the cosmological model. I am not actually a Boltzmann brain, I assure you. So if a model says that it is highly probable I am one, then the observation that I am not stands as strong evidence against the model. This argument explicitly relies on the rejection of radical skepticism.

Are we justified in rejecting radical skepticism? I think the answer is obviously yes, but if you are in fact a skeptic then I guess this won't sway you. Still, if you are a skeptic, your response to the Boltzmann brain problem shouldn't be, "Aha, here's support for my skepticism!" It should be "Well, all of the physics on which this problem is based comes from experimental evidence that doesn't actually exist! So I have no reason to take the problem seriously. Let me move on to another imaginary post."