Some hold that all genuine content is objective, and that the appearance of counterexamples is an illusion that can somehow be explained away. (See, e.g., "Stalnaker 1981, "Magidor 2015, or "Cappelen and Dever 2013.) Even those who accept that there is genuinely perspectival or self-locating information tend to treat it as a special case that requires special rules for integration with ordinary, non-perspectival information. (See, e.g., "Bostrom 2002, "Meacham 2008, "Moss 2012, "Titelbaum 2013, "Builes 2020, or "Isaacs, Hawthorne, and Russell 2022).

I think of this as the tyranny of the objective. (Compare "Chalmers 1998.)

In my view, all ordinary belief, and all ordinary information, is perspectival. Our senses tell us how things are here and now, around us. By scientific experiments and observations, we can find out more about our solar system or about the biology of organisms on our planet. When we learn such facts, we may also learn objective facts: by coming to know that it is raining, I also come to know that it is raining somewhere in the history of the world. But this objective belief is unusual and derivative. Ordinary confirmation is always confirmation of perspectival hypotheses by perspectival evidence.

"Lewis 1979 explained how this can be modelled formally. We simply need to replace the uncentred worlds of traditional confirmation theory with centred worlds.

The clearest sign that something is amiss with the objectivist mainstream is that it can't account for elementary facts about reasoning with perspectival information. As "Isaacs, Hawthorne, and Russell 2022, 252 put it: "All the precise theories we know of face very serious objections." I agree.

Of course, dropping the objectivist starting point doesn't automatically solve the difficult puzzles discussed in "Bostrom 2002 or "Isaacs, Hawthorne, and Russell 2022. But I think it sets the ground for a solution, and explains where certain arguments go wrong.

To see what I mean, let's have a closer look at "Isaacs, Hawthorne, and Russell 2022.

The paper explores whether our evidence supports the hypothesis that there are many universes. In the main part of the paper, the authors (henceforth, IRH) assume that centred credences are derived from uncentred priors by special rules. In Appendix B, IRH consider the possibility of starting with centred priors, but they argue that this doesn't affect the conclusion that our evidence supports the multiverse hypothesis.

Concretely, IRH prove two theorems. The theorems are complicated, but a simple example illustrates the key moves.

Let H1 be the hypothesis that there is exactly one universe, and H2 the hypothesis that there are two universes. Assume that each universe has a fixed chance p of being inhabited. Assume that p < 0.5. For simplicity, let's assume that an inhabited universe contains exactly one centre from which it is observed. The evidence that is received at such a centre is "local" insofar as it doesn't reveal anything about what might be the case in other universes. But it reveals (among other things) that this universe is inhabited.

Does such evidence support H2 over H1?

To answer this question, we need some assumptions about the (centred) priors.

Let Pr be a rational prior credence function. Let I=1 be the hypothesis that there is exactly one inhabited universe. Since the chance of any universe being inhabited is p, we might expect that

For (1), the idea is that if there's just one universe, and any universe has a fixed chance p of being inhabited, then the probability of this one universe being inhabited is p.

For (2), we assume that there are two universes, U1 and U2. Each has an independent chance p of being inhabited. There are two ways for there to be exactly one inhabited universe: U1 is inhabited and U2 isn't, or U2 is inhabited and U1 isn't. Each scenario has probability p(1-p). So the total probability of I=1 is 2p(1-p).

Now let E be our evidence. Plausibly,

The idea here is that our evidence E is not made any more or less probable by the presence of a second, uninhabited universe.

Since p < 0.5, it follows (by a little maths) that Pr(E | H2) > Pr(E | H1). And so E supports H2 over H1.

IRH's "Theorem 3" generalizes this result.

The point I want to make is that this line of reasoning is highly dubious if we take centred priors seriously.

Let's return to the priors. We have to make a choice: Should the prior Pr assign positive probability only to inhabited points, or can it also assign positive probability to uninhabited points?

This is a somewhat arcane theoretical question, since any evidence will immediately rule out uninhabited points anyway.

Suppose we decide that Pr assigns positive probability only to inhabited points. Then (1) is false. Given that there is exactly one universe, the prior probability that this universe is inhabited must be 1, not p. (2) is also false. In general, on this approach we can't assume that the prior probabilities align with the chances.

We can hold on to (1) and (2) only if we allow uninhabited points to have positive prior probability. But if we do that, we should give up (3).

To see why, let <E,-> be a two-universe world in which E is true at the first universe and the second universe is uninhabited. Let <E> be a one-universe world in which E is true. If Pr assigns positive probability to both locations in <E,-> then Pr(E | <E,->) is less than 1, while Pr(E | <E>) is 1. So Pr(E | H2 ∧ I=1) < Pr(E | H1 ∧ I=1).

There is no plausible view on which (1)-(3) are all true. So we don't get "Theorem 3". Nor do we get the stronger "Theorem 4".

IRH assume that the prior Pr assigns positive probability only to inhabited points, except in worlds that are entirely uninhabited: here, the prior assigns positive probability to a "dummy" centre. This is formally consistent and makes it possible to accept (1)-(3), but it is an entirely implausible account of rational priors.

1. A priori, simulation scenarios are less probable than non-simulation scenarios.

2. My evidence is more likely in non-simulation scenarios than in simulation scenarios.

3. So: It is highly improbable, given my evidence, that I'm in a simulation scenario.

By a "simulation scenario", I mean a scenario in which a subject's experiences of themselves and their environment are generated by a computer program that simulates an ordinary (non-simulated) subject and their environment.

I assume that it is a priori possible for a computer program to generate experiences (and a "subject") by simulating an ordinary subject with experiences. I'm not 100% sure this is true. (If not, premise 1 can be strengthened: simulation scenarios have probability 0.) But it seems plausible, especially if we're liberal about what qualifies as a computer program and as a simulation.

(Strictly speaking, a simulation scenario isn't just a scenario in which somebody lives in a computer simulation. It's a scenario in which I do.)

Now, why do I think that simulation scenarios are a priori less probable than non-simulation scenarios (assuming they are possible)? In short, because they are skeptical scenarios, and skeptical scenarios have low a priori probability.

Consider first a more standard type of skeptical scenario.

There are worlds that match our world in all the ways we have observed, but whose unobserved parts are utterly different. For example, there are worlds that are just like this world until today, but in which everything turns into plum jam tomorrow. On any way of counting possibilities, there are at least as many such "counterinductive" worlds as "inductive" worlds. But we shouldn't take them seriously. The plum jam extinction scenario deserves negligible credence, even though it is compatible with all our evidence. In a Bayesian framework, this implies that counterinductive scenarios must have much lower a priori probability than inductive scenarios.

Another type of skeptical scenario involves hallucinations and illusions. There are scenarios in which it visually seems to me as if I am looking at a dagger even though there's no real dagger there. For a more extreme version, there's a scenario in which I have all my actual experiences while I am living the external life of Napoleon Bonaparte: it seems to me as if I am quietly typing into my laptop at a cafe, but in fact I am standing on a battlefield in 1800s France, directing my troops. Such scenarios, too, deserve negligible credence, even though they are compatible with my evidence.

Back to simulation scenarios.

Many simulation scenarios are skeptical scenarios of the second type. My current experiences suggest to me that I have a physical body, that I move around in a physical space with tables and trees etc. If I'm in a simulation scenario, arguably none of that is true: my sensory experiences are radically deceptive. But rationality requires giving negligible credence to scenarios in which my experiences are deceptive. Hence simulation scenarios have low a priori probability.

This is a little too quick. David Chalmers has argued that our mundane positive beliefs about ourselves and our environment need not be false in simulation scenarios. (See, for example, "Chalmers 2018, and relevant parts of "Chalmers 2012 and "Chalmers 2022b.) Roughly, the idea is that all it takes for 'there are trees' to be true is that there are things that play a certain structural/causal role, linking the things to one another and to our experiences. I'm not convinced by these arguments, but I'm not fully convinced that the conclusion is false either.

So perhaps there are simulation scenarios in which my sensory experiences are not radically deceptive. These scenarios then don't belong in the second group of skeptical scenarios. But they still belong into the first. Such scenarios involve two layers of reality: a simulated layer (with genuine tables and trees, or so we assume) and an outer layer in which the simulation is running. We only have access to the simulated layer. How is this different from other counterinductive hypotheses that posit intricate events in unobserved parts of the world? There is a possible world in which this cafe is populated by angels made of ectoplasm that don't interact with ordinary matter. I can't rule out such a world, but I don't take it seriously. Layers of reality should not be multiplied without necessity.

So much for my first premise. In sum, simulation scenarios are scenarios in which our empirical methods don't work. Such scenarios deserve negligible a priori credence.

(Isn't this begging the question against someone who holds that we are living in a simulation? Of course it is. We shouldn't try to engage with a skeptic on their own ground.)

I also claim that my evidence is somewhat more likely in non-simulation scenarios than in simulation scenarios. This is my second premise. It's based on the thought that people in simulation scenarios generally don't have the kind of rich and coherent experiences that I have. "Most" computer programs that generate a simulation scenario would generate much poorer, more fragmented and chaotic experiences.

Objection: The people running these simulations would have an interest in generating rich and coherent experiences.

Response: Why should we assume this? Who said that there are people running these simulations anyway? Perhaps the computers that run the simulations are created by random fluctuations of matter in the outer universe. And even if there are people running the simulations, why are we entitled to any a priori views about their aims and interests?

This concludes my argument.

I need to say something about "the simulation argument", which supposedly proves that we are likely to live in a simulation. There are many versions of this argument. I'll focus on one problem that all of them seem to share.

Let's begin with a version that makes the problem especially obvious. The argument (intended to be a simplified version of the one in "Bostrom 2003) goes like this.

1. Given what we know about physics, the brain, computer technology, etc., it is likely that we will create lots of simulated beings, including beings with experiences just like mine.

2. Given that there are N beings in the world with experiences just like mine, it is equally likely that I am any one of them.

3. So: It is likely that I am simulated.

There's something odd about this line of reasoning. The central empirical premise (premise 1) says that there will probably be simulated beings in the future. From this, the argument seems to infer that I am probably one of these beings. But I know that I'm not in the future!

Let Physics be the (relatively) uncontroversial empirical assumptions invoked in the argument's first premise: that the laws of physics allow for the existence of computers to simulate a human brain, that we don't have such computers now but might have them in the future, and so on. To bring out the problem, let's pretend that Physics makes it highly probable that there will be simulated beings in the future and highly improbable that there are simulated beings now. (You might deny that we have such information, but let's pretend!) The first premise is then true. But the empirical information that it appeals to also entails that the conclusion is false. So there must be something wrong with this kind of argument, although it's not obvious where the mistake lies.

A similar problem arises for the following argument that we are Boltzmann brains.

1. Given what we know from physics, it is likely that there are many Boltzmann brains with experiences just like mine.

2. Given that there are N beings in the world with experiences just like mine, it is equally likely that I am any one of them.

3. So: It is likely that I am a Boltzmann brain.

The first premise mentions "what we know from physics". But let's list a few things we know from physics! We know, for example, that we live on a planet orbiting a star at a distance of about 150 million km. This is not true if we are Boltzmann brains. As before, the empirical information that is supposed to make the Boltzmann hypothesis probable belongs to a larger corpus of information that actually contradicts the Boltzmann hypothesis.

Intuitively, these arguments are self-undermining: if we accept the conclusion, we are no longer justified in accepting the first premise. But this doesn't explain where the arguments go wrong.

Well, the conclusion undermines the first premise because it implies that we can't trust the empirical methods on which that premise rests.

As before, let Physics comprise what we take ourselves to know about the physical world. Let's assume that Physics makes it highly likely that there are many Boltzmann brains with experiences just like mine. Let Boltzmann be the hypothesis that I am a Boltzmann brain.

Since Physics entails that we live on a planet, we have P(Physics | Boltzmann) = 0.

By the self-locating indifference principle in premise 2 of the Boltzmann brain argument, P(Boltzmann | Physics) is high.

It follows by elementary probability theory that P(Physics) must be low.

So we have two options. We must reject either the self-locating indifference principle or the trustworthiness of our empirical methods (i.e., take P(Physics) to be low).

I think it's clear which of these options we should choose. We should reject self-locating indifference.

This should be unsurprising from what I said above. I argued that skeptical scenarios deserve negligible a priori credence. Since skeptical scenarios can coexist with non-skeptical scenarios in the same world, we should not be indifferent between all scenarios in a world that we can't rule out. Boltzmann scenarios deserve negligible a priori credence.

The simulation argument fails for the same reason. Let's look at Chalmers's version (from "Chalmers 2022b, ch.5 and "Chalmers 2022a), which doesn't have the flaw of suggesting that we somehow live in the future.

The conclusion of Chalmers's official argument states that 'if there are no sim blockers, we are probably sims'. But he also indicates that he regards the antecedent as somewhat probable. So we can rephrase the argument as follows.

1. It is somewhat probable that most beings with experiences like mine are sims.

2. If most beings with experiences like mine are sims, I am probably a sim.

3. So: it is somewhat probable that I am a sim.

Premise 1 is supposed to be supported by empirical information about computer technology, the number of neurons in the human brain, etc. This assumes that our empirical methods are reliable. But the conclusion implies that our empirical methods are probably unreliable. Like the previous two arguments, this argument is self-undermining. And as in the previous two cases, the flaw lies in the second premise.

(I have no strong views about the first premise. This is an empirical matter.)

Again, this line of thought is a little too quick, if we consider Chalmers's view that our ordinary, positive thoughts about tables and trees are true in some simulation scenarios. Suppose for the sake of the argument that this is correct. In the relevant simulation scenarios, our empirical methods for arriving at positive conclusions may then be fairly reliable. It's only our methods for arriving at negative conclusions that are unreliable. (A "negative" conclusion is a conclusion about the non-existence of extra things or extra structure or extra layers of reality.) If the empirical information adduced in the first premise is entirely positive, the argument isn't self-undermining.

Of course, I would still say that premise 2 is false: rationality requires giving low credence to scenarios in which our empirical methods for arriving at negative conclusions are unreliable.

Curiously, Chalmers might argue that the simulation scenarios in question are ones in which our methods for arriving at negative conclusions are reliable as well. The argument would go as follows.

Our positive information suggests that there are more simulated beings with our present experience than non-simulated beings.

Our empirical methods include highly restricted indifference principles. In particular, they license indifference between sim and non-sim scenarios in which we have our present experiences.

So, our empirical methods imply that it is highly likely that we are simulated, and therefore that there is an extra layer of reality.

I guess this shows that there may be nothing inherently unstable or incoherent about believing in the simulation hypothesis on empirical grounds. But it doesn't persuade me that the hypothesis is plausible.

We can quibble over what exactly is part of the sensory information. We can also quibble over what "sensory information" is even meant to be. But it should be uncontroversial that we gain information from our senses. My point is that, on any plausible way of spelling this out, the information we receive is centred: it doesn't have parameters that fix a unique location in space and time. If I were unsure about what time it is or who I am, looking at the wall in front of me wouldn't help. The underlying reason, of course, is that photoreceptors are insensitive to differences in spatiotemporal location: they don't produce different outputs depending on where or when they are activated by photons.

Lewis "1979 and others have argued that belief contents are also centred. The idea is that there is a theoretically fruitful and intuitive sense in which our representation of the world assigns a special role to ourselves and the present time, like a map with a "you are here" marker. I find this plausible.

If belief contents are centred, one can give a simple account of how centred sensory information might update an agent's beliefs: the agent can simply accept the sensory information; they might conditionalize or Jeffrey-conditionalize on it.

But I don't think this simple account is correct.

When I'm holding a pencil right in front of my eyes, the information coming from my visual system might be something like pencil about 5 cm ahead. If I were to conditionalize on this, I would come to believe that there's a pencil about 5 cm ahead. But what I actually come to believe is that there's a pencil about 5 cm in front of my eyes.

Imagine your eyes are removed from your head and placed somewhere else, with radio signals replacing the nerve connections. How should you update on the visual information there's a red wall ahead?

Or suppose your eyes have been put at separate locations; your left eye sends a signal of a red wall; your right eye of a snowy mountain. What do you do with that?

One can even imagine that the eyes convey information about different times. Perhaps one eye is put behind a transparent medium in which light travels very slowly, so that its photoreceptors carry information about how things were on the other side of the medium many years ago. Or perhaps the radio signals from this eye travel with a long delay.

These are far-fetched scenarios. But they dramatise a real problem encountered by our nervous system. After all, our eyes really are at different locations. And since light travels faster than sound, our auditory information is not exactly in sync with our visual information: we hear the thunder after we see the lightning.

In short, our brain needs to integrate the sensory information provided by our sense organs into a unified representation of the world, and it shouldn't do that by simply accepting and conjoining the sensory information.

An analogous problem arises for linguistic communication. If beliefs are centred, how should we understand what is communicated by ordinary assertions? Naively, one would think that in a simple case of communication, the speaker utters a sentence that expresses a "proposition" which the speaker believes and which they want the hearer to believe. But on the centred-belief account, this simple model can't be right, unless we never communicate our centred beliefs. Some have concluded that we should reject the centred account of belief, or supplement it with an uncentred account. (See, e.g., "Perry 1977, "Stalnaker 1981, "Stalnaker 2008, "Caie and Ninan 2025.) I think we should instead revise the simple model of communication, roughly along the lines suggested in "Weber 2013.

In any case, the uncentred-content move looks really unappealing for the case of sensory integration. There must be a better solution.

Here is one idea. On closer inspection, our representation of the world might be multi-centred, with several "you are here" markers (compare, e.g., "Spohn 1996, "Torre 2010, "Ninan 2013). There could be one marker for each eye, one for each ear, and so on. It's then easy to update such a representation in response to centred sensory information. If, for example, the left eye "says" red wall ahead, one can rule out all multi-centred possibilities in which there's no red wall ahead of the marker for the left eye.

But multi-centred contents are revisionary. They don't neatly plug into standard formulations of Bayesian epistemology and decision theory. Can we do with a single centre?

Imagine first a creature with a single sense organ, an eye, to which it is connected by radio signals. If the eye says red wall ahead, the creature can update on red wall ahead of my eye.

More generally, we shouldn't think of the "you are here" marker as an arrow pointing at a precise spacetime point. The marker for belief contents usually singles out a temporal stage of a composite object. (In Lewisian terms: the properties that are the attitude contents are properties of stages of composite objects.) In unusual cases, the marker might point at an object that's scattered across spacetime. When sensory input arrives from the eye, all possibilities in the creature's doxastic space in which the received content isn't true at "my eye" – i.e., at the eye of the marked object – can be ruled out.

This assumes that the creature is aware that it has an eye. More generally, the update might rule out all possibilities in which the received content isn't true at some location from which "I" (i.e., the marked object) receive(s) sensory input.

Note that it doesn't matter if the creature considers this location as part of itself: it doesn't matter, for the purposes of integrating sensory information, if the belief arrow points to an object that includes the sense organ or not.

Things get more complicated if there are multiple sense organs. Here, it might help to give each input channel a tag indicating from which sense organ it comes, so that one can update on red wall ahead of organ A. These tags would play a similar role to the centres in the multi-centred account.

To spell this out more carefully, I suspect we should be more precise about how to understand the content that is received from the senses. On the account I describe in "Schwarz 2018, the "tags" could be folded into the "imaginary dimension" of the sensory content. Intuitively, each organ would get a distinctive phenomenal character by which it can be identified in the update.