Against full panpsychism

I have access to two kinds of information about consciousness: I know the occasions on which I am conscious and the occasions on which I am not. Focusing on the second, we get this argument:

1. If panpsychism is true, everything is always conscious.

2. In dreamless sleep, I exist and am not conscious.

3. So, panpsychism is false.

One response is to retreat to a weaker panpsychism on which everything is either conscious or has a conscious part. On the weaker panpsychism, one can say that in dreamless sleep, I have some conscious parts, say particles in my big toe.

But suppose we want to stick to full panpsychism that holds that everything is always conscious. This leaves two options.

First, one could deny that we exist in dreamless sleep. But if we don’t exist in dreamless sleep, then it is not possible to murder someone in dreamless sleep, and yet it obviously is.

Second, one could hold that we are conscious in dreamless sleep but the consciousness is not recorded to memory. This seems a dubious skeptical hypothesis. But let’s think about it a bit more. Presumably, the same applies under general anaesthesia. Now, while I’m far from expert on this, it seems plausible that the brain functioning under general anaesthesia is a proper subset of my present brain functioning. This makes it plausible that my experiences under general anaesthesia are a proper subset of my present wakeful experiences. But none of my present wakeful experiences—high level cognition, sensory experience, etc.—are a plausible candidate for an experience that I might have under general anaesthesia.

Being known

The obvious analysis of “p is known” is:

1. There is someone who knows p.

But this obvious analysis doesn’t seem correct, or at least there is an interesting use of “is known” that doesn’t fit (1). Imagine a mathematics paper that says: “The necessary and sufficient conditions for q are known (Smith, 1967).” But what if the conditions are long and complicated, so that no one can keep them all in mind? What if no one who read Smith’s 1967 paper remembers all the conditions? Then no one knows the conditions, even though it is still true that the conditions “are known”.

Thus, (1) is not necessary for a proposition to be known. Nor is this a rare case. I expect that more than half of the mathematics articles from half a century ago contain some theorem or at least lemma that is known but which no one knows any more.

I suspect that (1) is not sufficient either. Suppose Alice is dying of thirst on a desert island. Someone, namely Alice, knows that she is dying of thirst, but it doesn’t seem right to say that it is known that she is dying of thirst.

So if it is neither necessary nor sufficient for p to be known that someone knows p, what does it mean to say that p is known? Roughly, I think, it has something to do with accessibility. Very roughly:

2. Somebody has known p, and the knowledge is accessible to anyone who has appropriate skill and time.

It’s really hard to specify the appropriateness condition, however.

Does all this matter?

I suspect so. There is a value to something being known. When we talk of scientists advancing “human knowledge”, it is something like this “being known” that we are talking about.

Imagine that a scientist discovers p. She presents p at a conference where 20 experts learn p from her. Then she publishes it in a journal when 100 more people learn it. Then a Youtuber picks it up and now a million people know it.

If we understand the value of knowledge as something like the sum of epistemic utilities across humankind, then the successive increments in value go like this: first, we have a move from zero to some positive value V when the scientist discovers p. Then at the conference, the value jumps from V to 21V. Then after publication it goes from 21V to 121V. Then given Youtube, it goes from 121V to 100121V. The jump at initial discovery is by far the smallest, and the biggest leap is when the discovery is publicized. This strikes me as wrong. The big leap in value is when p becomes known, which either happens when the scientist discovers it or when it is presented at the conference. The rest is valuable, but not so big in terms of the value of “human knowledge”.

Epistemically paternalistic lies

Suppose Alice and Bob are students and co-religionists. Alice is struggling with a subject and asks Bob to pray that she might do fine on the exam. She gets 91%. Alice also knows that Bob’s credence in their religion is a bit lower than her own. When Bob asks her how she did, she lies that she got 94%, in order to boost Bob’s credence in their religion a bit more.

Whether a religion is correct is very epistemically important to Bob. But whether Alice got 91% or 94% is not at all epistemically important to Bob except as evidence for whether the religion is correct. The case can be so set up that by Alice’s lights—remember, she is more confident that the religion is correct than Bob is—Bob can be expected to be better off epistemically for boosting his credence in the religion. Moreover, we can suppose that there is no plausible way for Bob to find out that Alice lied. Thus, this is an epistemically paternalistic lie expected to make Bob be better off epistemically.

And this lie is clearly morally wrong. Thus, our communicative behavior is not merely governed by maximization of epistemic utility.

More on averaging to combine epistemic utilities

Suppose that the right way to combine epistemic utilities across people is averaging: the overall epistemic utility of the human race is the average of the individual epistemic utilities. Suppose, further, that each individual epistemic utility is strictly proper, and you’re a “humanitarian” agent who wants to optimize overall epistemic utility.

Suppose you’re now thinking about two hypotheses about how many people exist: the two possible numbers are m and n, which are not equal. All things considered, you have credence 0 < p₀ < 1 in the hypothesis H_m that there are m people and 1 − p₀ in the hypothesis H_n that there are n people. You now want to optimize overall epistemic utility. On an averaging view, if H_m is true, if your credence is p₁, your contribution to overall epistemic utility will be:

• (1/m)T(p₁)

and if H_m is false, your contribution will be:

• (1/n)F(p₁),

where your strictly proper scoring rule is given by T, P. Since your credence is p₁, by your lights the expected value after your changing your credence to p₀ will be:

• p₀(1/m)T(p₁) + (1−p₀)(1/n)F(p₁) + Q(p₀)

where Q(p₀) is the contribution of other people’s credences, which I assume you do not affect with your choice of p₁. If m ≠ n and T, F is strictly proper, the expected value will be maximized at

• p₁ = (p₀/m)/(p₀/m+(1−p₀)/n) = np₀/(np₀+m(1−p₀)).

If m > n, then p₁ < p₀ and if m < n, then p₁ > p₀. In other words, as long as n ≠ m, if you’re an epistemic humanitarian aiming to improve overall epistemic utility, any credence strictly between 0 and 1 will be unstable: you will need to change it. And indeed your credence will converge to 0 if m > n and to 1 if m < n. This is absurd.

I conclude that we shouldn’t combine epistemic utilities across people by averaging the utilities.

Idea: What about combining them by computing the epistemic utilities of the average credences, and then applying a strictly proper scoring rule, in effect imagining that humanity is one big committee and that a committee’s credence is the average of the individual credences?

This is even worse, because it leads to problems even without considering hypotheses on which the number of people varies. Suppose that you’ve just counted some large number nobody cares about, such as the number of cars crossing some intersection in New York City during a specific day. The number you got is even, but because the number is big, you might well have made a mistake, and so your credence that the number is even is still fairly low, say 0.7. The billions of other people on earth all have credence 0.5, and because nobody cares about your count, you won’t be able to inform them of your “study”, and their credences won’t change.

If combined epistemic utility is given by applying a proper scoring rule to the average credence, then by your lights the expected value of the combined epistemic utility will increase the bigger you can budge the average credence, as long as you don’t get it above your credence. Since you can really only affect your own credence, as an epistemic humanitarian your best bet is to set your credence to 1, thereby increasing overall human credence from 0.5 to around 0.5000000001, and making a tiny improvement in the expected value of the combined epistemic utility of humankind. In doing so, you sacrifice your own epistemic good for the epistemic good of the whole. This is absurd!

I think the idea of averaging to produce overall epistemic utilities is just wrong.

Adding or averaging epistemic utilities?

Suppose for simplicity that everyone is a good Bayesian and has the same priors for a hypothesis H, and also the same epistemic interests with respect to H. I now observe some evidence E relevant to H. My credence now diverges from everyone else’s, because I have new evidence. Suppose I could share this evidence with everyone. It seems obvious that if epistemic considerations are the only ones, I should share the evidence. (If the priors are not equal, then considerations in my previous post might lead me to withhold information, if I am willing to embrace epistemic paternalism.)

Besides the obvious value of revealing the truth, here are two ways to reason for this highly intuitive conclusion.

First, good Bayesians will always expect to benefit from more evidence. If my place and that of some other agent, say Alice, were switched, I’d want the information regarding E to be released. So by the Golden Rule, I should release the information.

Second, good Bayesians’ epistemic utilities are measured by a strictly proper scoring rule. But if Alice’s epistemic utilities for H are measured by a strictly proper (accuracy) scoring rule s that assigns an epistemic utility s(p,t) to a credence p when the actual truth value of H is t, which can be zero or one. By definition of strict propriety, the expectation by my lights of what Alice’s epistemic utility for a given credence should be is strictly maximized when that credence equals my credence. Since Alice shares the priors I had before I observed E, if I can make E evident to her, her new posteriors will match my current ones, and so revealing E to her will maximize my expectation of her epistemic utility.

So far so good. But now suppose that the hypothesis H = H_N is that there exist N people other than me, and my priors assign probability 1/2 to there being N and 1/2 to its being n, where N is much larger than n. Suppose further that my evidence E ends up significantly supporting hypothesis H_n, so that my posterior p in H_N is smaller than 1/2.

Now, my expectation of the total epistemic utility of other people if I reveal E is:

• U_R = pNs(p,1) + (1−p)ns(p,0).

And if I conceal E, my expectation is:

• U_C = pNs(1/2,1) + (1−p)ns(1/2,0).

If we had N = n, then it would be guaranteed by strict propriety that U_R > U_C, and so I should reveal. But we have N > n. Moreover, s(1/2,1) > s(p,1): if some hypothesis is true, a strictly proper accuracy scoring rule increases strictly monotonically with the credence. If N/n is sufficiently large, the first terms of U_R and U_C will dominate, and hence we will have U_C > U_R, and thus I should conceal.

The intuition behind this technical argument is this. If I reveal the evidence, I decrease people’s credence in H_N. If it turns out that the number of people other than me actually is N, I have done a lot of harm, because I have decreased the credence of a very large number N of people. Since N is much larger than n, this consideration trumps considerations of what happens if the number of people is n.

I take it that this is the wrong conclusion. On epistemic grounds, if everyone’s priors are equal, we should release evidence. (See my previous post for what happens if priors are not equal.)

So what should we do? Well, one option is to opt for averaging rather than summing of epistemic utilities. But the problem reappears. For suppose that I can only communicate with members of my own local community, and we as a community have equal credence 1/2 for the hypothesis H_n that our local community of n people contains all agents, and credence 1/2 for the hypothesis H_n + N that there is also a number N of agents outside our community much greater than n. Suppose, further, that my priors are such that I am certain that all the agents outside our community know the truth about these hypotheses. I receive a piece of evidence E disfavoring H_n and leading to credence p < 1/2. Since my revelation of E only affects the members of my own commmunity, depending on which hypothesis is true, if p is my credence after updating on E, the relevant part of the expected contribution to the utility of revealing E with regard to hypothesis H_n is:

• U_R = p((n−1)/n)s(p,1) + (1−p)((n−1)/(n+N))s(p,0).

And if I conceal E, my expectation contribution is:

• U_C = p((n−1)/n)s(1/2,1) + (1−p)((n−1)/(n+N))s(p,0).

If N is sufficiently large, again U_C will beat U_R.

I take it that there is something wrong with epistemic utilitarianism.

Bayesianism and epistemic paternalism

Suppose that your priors for some hypothesis H are 3/4 while my priors for it are 1/2. I now find some piece of evidence E for H which raises my credence in H to 3/4 and would raise yours above 3/4. If my concern is for your epistemic good, should I reveal this evidence E?

Here is an interesting reason for a negative answer. For any strictly proper (accuracy) scoring rule, my expected value for the score of a credence is uniquely maximized when the credence is 3/4. I assume your epistemic utility is governed by a strictly proper scoring rule. So the expected epistemic utility, by my lights, of your credence is maximized when your credence is 3/4. But if I reveal E to you, your credence will go above 3/4. So I shouldn’t reveal it.

This is epistemic paternalism. So, it seems, expected epistemic utility maximization (which I take it has to employ a strictly proper scoring rule) forces one to adopt epistemic paternalism. This is not a happy conclusion for expected epistemic utility maximization.

An example of a value-driven epistemological approach to metaphysics

1. Everything that exists is intrinsically valuable.

2. Shadows and holes are not intrinsically values.

3. So, neither shadows nor holes exist.

Incompleteness

For years in my logic classes I’ve been giving a rough but fairly accessible sketch of the fact that there are unprovable arithmetical truths (a special case of Tarski’s indefinability of truth), using an explicit Goedel sentence using concatenation of strings of symbols rather than Goedel encoding and the diagonal lemma.

I’ve finally revised the sketch to give the full First Incompleteness theorem, using Rosser’s trick. Here is a draft.

What numbers could be

Benacerraf famously argued that no set theoretic reduction can capture the natural numbers. While one might conclude from this that the natural numbers are some kind of sui generis entities, Benacerraf instead opts for a structuralist view on which different things can play the role of different numbers.

The argument that no set theoretic reduction captures the negative numbers is based on thinking about two common reductions. On both, 0 is the empty set ⌀. But then the two accounts differ in how the successor sn of a number n is formed:

1. sn = n ∪ {n}

2. sn = {n}.

On the first account, the number 5 is equal to the set {0, 1, 2, 3, 4}. On the second account, the number 5 is equal to the singleton {{{{{⌀}}}}}. Benacerraf thinks that we couldn’t imagine a good argument for preferring one account over another, and hence (I don’t know how this is supposed to follow) there can’t be a fact of the matter about why one account—or any other set-theoretic reductive account—is correct.

But I think there is a way to adjudicate different set-theoretic reductions of numbers. Plausibly, there is reference magnetism to simpler referrents of our terminology. Consider an as consisting of a set of natural numbers, a relation <, and two operations + and ⋅, satisfying some axioms. We might then say that our ordinary language arithmetic is attracted to the abstract entities that are most simply defined in terms of the fundamental relations. If the only relevant fundamental relation is set membership ∈, then we can ask which of the two accounts (a) and (b) more simply defines <, + and ⋅.

If simplicity is brevity of expression in first order logic, then this can be made a well-defined mathematical question. For instance, on (a), we can define a < b as a ∈ b. One provably cannot get briefer than that. (Any definition of a < b will need to contain a, b and ∈.) On the other hand, on (b), there is no way to define a < b as simply. Now it could turn out that + or ⋅ can be defined more simply on (b), in a way that offsets (a)’s victory with <, but it seems unlikely to me. So I conjecture that on the above account, (a) beats (b), and so there is a way to decide between the two reductions of numbers—(b) is the wrong one, while (a) at least has a chance of being right, unless there is a third that gives a simpler reduction.

In any case, on this picture, there is a way forward in the debate, which undercuts Benacerraf’s claim that there is no way forward.

I am not endorsing this. I worry about the multiplicity of first-order languages (e.g., infix-notation FOL vs. Polish-notation FOL).

Theistic Humeanism?

Here’s an option that is underexplored: theistic Humeanism. There are two paths to it.

The path from orthodoxy: Start with a standard theistic concurrentism: whenever we have a creaturely cause C with effect E, E only eventuates because God concurs, i.e., God cooperates with the creaturely causal relation. Now add to this a story about what creaturely causation is. This will be a Humean story—the best I know is the David Lewis one that reduces causation to laws and laws to arrangements of stuff. Keep all the deep theistic metaphysics of divine causation.

The path from heterodoxy: Start with the metaphysics of occasionalism. Don’t change any of the metaphysics. But now add a Humean analysis of creaturely causation in terms of regularities. Since the metaphysics of occasionalism affirms regularities in the world, we haven’t changed the metaphysics of occasionalism, but have redescribed it as actually involving creaturely causation.

The two paths meet in a single view, a theistic Humeanism with the metaphysics of occasionalism and the language of concurrentism, and with creaturely causation described in a Humean way.

This theistic Humeanism is more complex than standard non-theistic Humeanism, but overcomes the central problem with non-theistic Humeanism: the difficulty of finding explanation in nature. If the fact that heat causes boiling is just a statement of regularity, it does not seem that heat explains boiling. But on theistic Humeanism, we have a genuine explanatory link: God makes the water boil because God is aware of the heat.

There is one special objection to theistic Humeanism. It has two causal relations, a divine one and a creaturely one. But the two are very different—they don’t both seem to be kinds of causation. However, on some orthodox concurrentisms, such as Aquinas’s, there isn’t a single kind of thing that divine and creaturely causation are species of. Instead, the two stand in an analogical relationship. Couldn’t the theistic Humean say the same thing? Maybe, though one might also object that Humean creaturely causation is too different from divine causation for the two to count as analogous.

I suppose the main objection to theistic Humeanism is that it feels like a cheat. The creaturely causation seems fake. The metaphysics is that of occasionalism, and there is no creaturely causation there. But if theistic Humeanism is a cheat, then standard non-theistic Humeanism is as well, since they share the same metaphysics of creaturely causation. If non-theistic Humeanism really does have causation, then our theistic Humeanism really does have creaturely causation. If one has fake causation, so does the other. I think both have fake causation. :-)

Autonomy and relativism

Individual relativism may initially seem to do justice to the idea of our autonomy: our moral rules are set by ourselves. But this attractiveness of relativism disappears as soon as we realize that our beliefs are largely not up to us—that, as the saying goes, we catch them like we catch the flu. This seems especially true of our moral beliefs, most of which are inherited from our surrounding culture. Thus, what individual relativism gives to us in terms of autonomy is largely taken away by reflection on our beliefs.

Asymmetry between moral and physical excellence

We can use a Mahatma Ghandi or a Mother Teresa as a moral exemplar to figure out what our virtues should be. But we cannot use an Usain Bolt or a Serena Williams as a physical exemplar to figure out what our physical capabilities should be. Why this disanalogy between moral and physical excellence?

It’s our intuition that Bolt and Williams exceed the physical norms for humans to a significant degree. But although Ghandi and Mother Teresa did many supererogatory things, I do not think they overall exceed the moral norms for human character to a significant degree. We should be like them, and our falling short is largely our fault.

My LaTeX "ide"

I haven’t found a LaTeX IDE that I am happy with (texmaker comes close, but I don’t like the fact that it doesn’t properly underline the trigger letter in menus, even if Windows is set to do that), and so I ended up defaulting to just editing my book and papers with notepad++ and running pdflatex manually. But it’s a bit of a nuisance to get the preview: ctrl-s to save, alt-tab to command-line, up-arrow and enter to re-run pdflatex, alt-tab to pdf viewer. So I wrote a little python script that watches my current directory and if any .tex file changes in it, it re-runs pdflatex. So now it’s just ctrl-s, alt-tab to get the preview. I guess it’s only four keystrokes saved, but it feels more seamless and straightforward. The script also launches notepad++ and my pdf viewer at the start of the session to save me some typing.

Teleology and the normal/abnormal distinction

Believers in teleology also tend to believe in a distinction between the normal and the abnormal. I think teleology can be prised apart from a normal/abnormal distinction, however, if we do something that I think we should do for independent reasons: recognize teleological directedness without a telos-to-be-attained, a target to be hit. An example of such teleological directedness is an athlete trying to run as fast as possible. There isn’t a target telos: for any speed the athlete reaches, a higher speed would fit even better with the athlete’s aims. But there is a directional telos, an aim tlos: the athlete aims in the direction of higher speed.

One might then say the human body in producing eyes has a directional telos: to see as well as possible. Whether one has 20/20 or 20/15 or 20/10 vision, more acuity would fulfill that directional telos better. On this view, there is no target telos, just a direction towards better acuity. If there were a target telos, say a specific level of acuity, we could identify non-attainment with abnormalcy and attainment with normalcy. But we need not. We could just say that this is all a matter of degree, with continuous variation between 20/0 (not humanly available) and 20/∞ (alas humanly available, i.e., total blindness).

I am not endorsing the view that there is no normal/abnormal in humans. I think there is (e.g., an immoral action is abnormal; a moral action is normal). But perhaps the distinction is less often applicable than friends of teleology think.

More on experiments

We all perform experiments very often. When I hear a noise and deliberately turn my head, I perform an experiment to find out what I will see if I turn my head. If I ask a question not knowing what answer I will hear, I am engaging in (human!) experimentation. Roughly, experiments are actions done in order to generate observations as evidence.

There are typically differences in rigor between the experiments we perform in daily life and the experiments scientists perform in the lab, but only typically so. Sometimes we are rigorous in ordinary life and sometimes scientists are sloppy.

The epistemic value to one of an experiment depends on multiple factors in a Bayesian framework.

1. The set of questions towards answers to which the experiment’s results are expected to contribute.

2. Specifications of the value of different levels of credence regarding the answers to the questions in Factor 1.

3. One’s prior levels of credence for the answers.

4. The likelihoods of different experimental outcomes given different answers.

It is easiest to think of Factor 2 in practical terms. If I am thinking of going for a recreational swim but I am not sure whether my swim goggles have sprung a leak, it may be that if the probability of the goggles being sound is at least 50%, it’s worth going to the trouble of heading out for the pool, but otherwise it’s not. So an experiment that could only yield a 45% confidence in the goggles is useless to my decision whether to go to the pool, and there is no difference in value between an experiment that yields a 55% confidence and one that yields a 95% confidence. On the other hand, if I am an astronaut and am considering performing a non-essential extravehicular task, but I am worried that the only available spacesuit might have sprung a leak, an experiment that can only yield 95% confidence in the soundness of the spacesuit is pointless—if my credence in the spacesuit’s soundness is only 95%, I won’t use the spacesuit.

Factor 3 is relevant in combination with Factor 4, because these two factors tell us how likely I am to end up with different posterior probabilities for the answers to the Factor 1 questions after the experiment. For instance, if I saw that one of my goggles is missing its gasket, my prior credence in the goggle’s soundness is so low that even a positive experimental result (say, no water in my eye after submerging my head in the sink) would not give me 50% credence that the goggle is fine, and so the experiment is pointless.

In a series of posts over the last couple of days, I explored the idea of a somewhat interest-independent comparison between the values of experiments, where one still fixes a set of questions (Factor 1), but says that one experiment is at least as good as another provided that it has at least as good an expected epistemic utility as the other for every proper scoring rule (Factor 2). This comparison criterion is equivalent to one that goes back to the 1950s. This is somewhat interest-independent, because it is still relativized to a set of questions.

A somewhat interesting question that occurred to me yesterday is what effect Factor 3 has on this somewhat interest-independent comparison of experiments. If experiment E₂ is at least as good as experiment E₁ for every scoring rule on the question algebra, is this true regardless of which consistent and regular priors one has on the question algebra?

A bit of thought showed me a somewhat interesting fact. If there is only one binary (yes/no) question under Factor 1, then it turns out that the somewhat interest-independent comparison of experiments does not depend on the prior probability for the answer to this question (assuming it’s regular, i.e., neither 0 nor 1). But if the question algebra is any larger, this is no longer true. Now, whether an experiment is at least as good as another in this somewhat interest-independent way depends on the choice of priors in Factor 3.

We might now ask: Under what circumstances is an experiment at least as good as another for every proper scoring rule and every consistent and regular assignment of priors on the answers, assuming the question algebra has more than two non-trivial members? I suspect this is a non-trivial question.