Friday, September 24, 2021

Being subject to a Dutch Book

I’ve periodically wondered why doing poorly when faced with a Dutch Book is supposed to be a sign of irrationality, but it’s not a sign of irrationality that rational people do poorly when faced with someone who hits all and only rational people on the head with a baseball bat.

This occurred to me today:

  1. One cannot get a rational person to act against their own interest except by force, luck or superior information.

  2. Putting a Dutch Book over someone with inconsistent credences does not require force, luck or superior information.

This seems to get at some of the intuition as to why being subject to a Dutch Book is supposed to be a sign of irrationality.

But I don’t know how much confidence we should have in (1). The exception clause already admits three exceptions. This sounds ad hoc. Would we be very surprised if more exceptions had to be added?

Still, there is some plausibility to (1), at least for self-interested rationality.

Wednesday, September 22, 2021

Consciousness of one's choices

Here is a plausible thesis:

  1. Consciousness of one’s choice is necessary for moral responsibility.

I go back and forth on (1). Here is a closely related thesis that is false:

  1. Knowledge of one’s choice is necessary for moral responsibility.

For imagine Alice who on the basis of a mistaken interpretation of neurosience thinks there are no choices. Then it could well be that Alice does not know that she is making any choices. But surely this mistake does not take away her moral responsibility for her choice.

Alice presumably still has consciousness of her choice, much as the sceptic still has perception of the external world. So Alice isn’t a counterexample to (1). But I wonder if (1) is very plausible once one has realized that (2) is false. For once we have realized that (2) is false, we realize that in Alice’s case the consciousness of her choice is not knowledge-conferring. And such consciousness just does not seem significant enough to matter for moral responsibility.

Against digital phenomenology

Suppose a digital computer can have phenomenal states in virtue of its computational states. Now, in a digital computer, many possible physical states can realize one computational state. Typically, removing a single atom from a computer will not change the computational state, so both the physical state with the atom and the one without the atom realize the same computational state, and in particular they both have the same precise phenomenal state.

Now suppose a digital computer has a maximally precise phenomenal state M. We can suppose there is an atom we can remove that will not change the precise phenomenal state it is in. And then another. And so on. But then eventually we reach a point where any atom we remove will change the precise phenomenal state. For if we could continue arbitrarily long, eventually our computer would have no atoms, and then surely it wouldn’t have a phenomenal state.

So, we get a sequence of physical states, each differing from the previous by a single atom. For a number of initial states in the sequence, we have the phenomenal state M. But then eventually a single atom difference destroys M, replacing it by some other phenomenal state or by no phenomenal state at all.

The point at which M is destroyed cannot be vague. For while it might be vague whether one is seeing blue (rather than, say, purple) or whether one is having a pain (rather than, say, an itch), whether one has the precise phenomenal state M is not subject to vagueness. So there must be a sharp transition. Prior to the transition, we have M, and after it we don’t have M.

The exact physical point at which the transition happens, however, seems like it will have to be implausibly arbitrary.

This line of argument suggests to me that perhaps functionalists should require phenomenal states to depend on analog computational states, so that an arbitrarily small of the underlying physical state can still change the computational state and hence the phenomenal state.

Functionalism and pain-likeness

Say that a functional property F is pain-like provided that a human is in pain if and only if the human has F.

Assuming functionalism, there is a functional property F0 which is pain. Property F0 will be pain-like, but it won’t be the only pain-like property. For there will be infinitely many ways of tweaking F0 to generate functional properties F1, F2, ... that in humans are instantiated precisely when F0 is, but that differ in instantiation among aliens. For instance, F1 could be F0 conjoined with the property of not currently thinking a thought that has seventeen levels of embedding (I take it that humans can’t think a thought with more than about three levels of embedding), while F2 could be F0 conjoined with the property of not consciously exercising magnetic sense, and so on.

There will thus be infinitely many pain-like properties that differ in when different aliens instantiate them. One of these pain-like properties, F0, is pain. And now we have a difficult question for functionalism: What grounds the fact that this particular pain-like property is pain? Why is it that having F0 is necessary and sufficient for hurting but having F1 isn’t? What’s so special about F0? Why is it that F0 picks out a phenomenally unified type, but the other properties need not?

Tuesday, September 21, 2021

Fading knowledge of qualia

I am one of those people who do not have vivid memories of pains.

Suppose I stub my toe. While the toe is hurting, I know what the toe’s hurting feels like. After it stops hurting, for a while I still know what that felt like. But I know it less and less well as my memory fades, until eventually I know very little how it felt like. The whole process might take only a few minutes.

Thus, that mysterious “knowing what it’s like” involving qualia is something that comes with a parameter that varies as to how well you know it.

This should worry physicalists. Thin physicalists should worry because it doesn’t seem that the fading corresponds to any knowledge of the underlying physical reality. Thick physicalists who think that Mary just acquires a new recognitional concept when she sees red should worry, because it does not seem that there is any gradual loss of a concept. I continue to have the same “that experience” concept (the demonstrative “that” points to the same past experience, and does so in a first-personal way) and the recognitional abilities it enables (I can tell if another pain is like that one or not), even as my knowledge of what “that experience” is like fades.

It’s also not completely clear what a dualist should say about the fading of the knowledge. Normally, when knowledge fades, what happens is either that we lose details (as when I forget much of what I once learned in school about the Metis uprising), or we find the dispositional knowledge harder to make occurrent. But the fading is neither of these. Maybe what is happening is that our present knowledge becomes a less good representation of what it is the knowledge of.

Monday, September 20, 2021

A posteriori necessities

The usual examples of a posteriori necessities are identities between kinds and objects under two descriptions, at least one of which involves a contingent mode of presentation, such as water (presented as “the stuff in this pond”, say) and H2O.

Such a posteriori necessities are certainly interesting. But we should not assume that these exhaust the scope of all a posteriori necessities.

For instance, Thomas Aquinas was committed to the existence of God being an a posteriori necessity: he held that necessarily God existed, but that all a priori arguments for the existence of God failed, while some a posteriori ones, like the Five Ways, succeeded.

For another theistic example, let p be an unprovable mathematical truth. Then p is, presumably, not a priori knowable. But God could reveal the truth of p, in which case we would know it a posteriori, via observation of God’s revelation. And, plausibly, mathematical truths are necessary.

For a third example, we could imagine a world where there is an odd law of nature: if anyone asserts a false mathematical statement, they immediately acquire hideous warts. In that world, all mathematical truths, including the unprovable ones, would be knowable a posteriori.

A defense of probabilistic inconsistency

Evidence E is misleading with regard to a hypothesis H provided that Bayesian update on E changes one’s credence in H in the direction opposed to truth. It is known that pretty much any evidence is misleading with regard to some hypothesis or other. That’s no tragedy. But sometimes evidence is misleading with regard to an important hypothesis. That’s no tragedy of the shift in the credence of that important hypothesis is small. But it could be tragic if the shift is significant—think of a quack cure for cancer beating out the best medication in a study due to experimental error or simply chance.

In other words, misleadingness by itself is not a big deal. But significant misleadingness with respect to an important hypothesis can be tragic.

Suppose I am lucky enough to start with consistent credences in a limited algebra F of propositions including q, and suppose I have a low credence in a consistent proposition q. Now two friends, whom I know for sure to speak only truth, speak to me:

  • Alice: “Proposition q is actually true.”

  • Bob: “She’s right, as always, but the fact that q is true is significantly misleading with respect to a number of quite important hypotheses in F.”

What should I do? If I were a perfect Bayesian agent, my likelihoods would be sufficiently well defined that I would just update on Alice saying her piece and Bob saying her piece, and be done with it. My likelihoods would embody prior probability assignments to hypotheses about the kinds of reasons that Alice and Bob could have for giving me their information, the kinds of important hypotheses in F that q could be misleading about, etc.

But this is too complicated for a more ordinary Bayesian agent like me. Suppose I could, just barely, do a Bayesian update on q, and gain a new consistent credence assignment on F. Even if Bob were not to have said anything, updating on q would not be ideal, because the ideal agent would update not just on q, but on the facts that Alice chose to inform me of q at that very moment, in those very words, in that very tone of voice, etc. But that’s too complicated for me. For one, I don’t have enough clear credences in hypotheses about different informational choices Alice could have made. So if all I heard was Alice’s announcement, updating on q would be a reasonable choice given my limitations.

But with Bob speaking, the consequences of my simply updating on q could be tragic, because Bob has told me that q is significantly misleading in regard to important stuff. What should I do? One possibility is to ignore both statements, and leave my credences unchanging, pretending I didn’t hear Alice. But that’s silly: I did hear her.

But if I accept q on the basis of Alice’s statement (and Bob’s confirmation), what should I do about Bob’s warning? Here is one option: I could raise my credence in q to 1, but leave everything else unchanged. This is a better move than just ignoring what I heard. For it gets me closer to the truth with regard to q (remember that Alice only says the truth), and I don’t get any further from the truth regarding anything else. The result will be an inconsistent probability assignment. But I can actually do a little better. Assuming q is true, it cannot be misleading about propositions entailed by q. For if q is true, then all propositions entailed by q are true, and raising my credences in them to 1 only improves my credences. Thus, I can safely raise my credence in everything entailed by q to 1. Similarly, I can safely lower my credence in anything that entails ∼q to 0.

Here, then, is a compromise: I set my credence in everything in F entailed by q to 1, and in everything in F that entails ∼q to 0, and leave all other credences for things in F unchanged. This has gotten me closer to the truth by any reasonable measure. Moreover, the resulting credences for F satisfy the Zero, Non-negativity, Normalization, Monotonicity, and Binary Non-Disappearance axioms, and as a result I can use a Level-Set Integral prevision to avoid various Dutch Book and domination problems. [Let’s check Monotonicity. Suppose r entails s. We need to show that C(r)≤C(s). Given that my original credences were consistent and hence had Monotonicity, the only way I could lack Monotonicity now would be if q entailed r and s entailed ∼q. Since r entails s, this would mean that q would entail ∼q, which would imply that q is not consistent. But I assumed it was consistent.]

I think this line of reasoning shows that there are indeed times when it can be reasonable to have an inconsistent credence assignment.

By the way, if I continue to trust the propositions I had previously assigned extreme credences to despite Bob’s ominous words, an even better update strategy would be to set my credence to 1 for everything entailed by q conjoined with something that already had credence 1, and to 0 for everything that when conjoined with something that had credence 1 entails ∼q.

Friday, September 17, 2021

Medical recommendations and informed consent

It is widely accepted that medical treatments require informed consent from the patient. This requires medical professionals to educate patients, to a reasonable degree, on the relevant scientific aspects of the treatment.

Interestingly, I have been told by a medical ethicist that it is not widely accepted that medical recommendations, whether from one’s individual physician or from a government body, are governed by similar informed consent standards. Thus, before giving you an injection, the physician is required to give you both the medical pros and cons of the injection, but if the physician recommends exercise to you, there is no such education requirement (e.g., the physician is not required to tell a clueless patient that exercise can result in joint pain).

This view seems wrong to me. The main reason for requiring informed consent is patient autonomy. But autonomy can be compromised just as much by recommendations omitting salient information as by actual treatment. Let’s say that Jeeves is annoyed by Wooster’s ugly mustache, and recommends to a Wooster the deliciousness of a particular brand of chocolate, having heard from the factory owner's valet that this brand has been contaminated with a chemical that makes one’s facial hair fall out. Jeeves has violated Wooster’s bodily autonomy through the recommendation almost as much as if Jeeves had shaved Wooster in the night.

Thursday, September 16, 2021

An ontological argument from the possible nondefectiveness of modality

  1. Necessarily, if it is necessary that there is no God, then modal reality is bad. (Making the existence of God impossible is terrible!)

  2. Necessarily, if something is bad, it is possible for it not to be bad. (The bad is a flaw in something that ought to be better than it is, and what ought to be can be.)

  3. So, if modal reality is necessarily bad, then it is possible for modal reality not to be bad. (by 2)

  4. So, if modal reality is necessarily bad, then modal reality is not necessarily bad. (by 3)

  5. So, modal reality is not necessarily bad. (by 4)

  6. So, possibly, modal reality is not bad. (by 5)

  7. So, possibly, it is not necessary that there is no God. (by 1 and 6)

  8. So, possibly, it is possible that God exists. (by 7)

  9. So, it is possible that God exists. (by 8 and S4)

  10. Necessarily, if God exists, it is necessary that God exists. (God is a necessary being and essentially divine.)

  11. So, it is possible that it is necessary that God exists. (by 9 and 10)

  12. So, God exists. (by 11 and Brouwer)

Wednesday, September 15, 2021

Two common intuitions

Here are two very common intuitions in the philosophy of mind:

  1. Our experiences of the same things are approximately qualitatively the same: your perceptual experiences of white, or squareness, or the beat of a drum are approximately like mine.

  2. It is metaphysically possible to remap all of one’s qualia, so that one could have had all the color perceptions in one’s life rotated by 120 degrees, say.

I find myself somewhat sceptical of each. Moreover, each claim makes the other less likely, so the probability that both are true is less than the product of the probabilities of each.

Of the two claims, the first seems fairly plausible to me, because I am attracted to the idea that the qualitative properties of my perceptions arise from typical interconnections (including, but perhaps not limited to, inferential ones) between them, and we all have roughly the same ones. But this line of thought, while supporting (1) also supports the denial of (2).

Moreover, our use of the same word “red” for your and my experiences of red tomatoes suggests that (1) is a part of our ordinary pre-theoretic beliefs. And I am inclined to trust our ordinary pre-theoretic beliefs.

On the other hand, it could turn out that (1) is false because it could turn out that how red things look is partly a function of features of brain organization that differ from individual to individual (and in the same individual over time). If so, then we might want to disambiguate ordinary language’s “looks the same” relation to mean either having the same qualitative experience or having an experience with the same representative content, so that we could continue to say that when you and I are looking at a red tomato, it looks the same to us in the representative but not qualitative sense.

But in any case all this is deeply mysterious stuff. I am strongly inclined to the idea that we should try to figure out the best theory of mind and perception we can, and then use that to figure out if (1) and (2) are true, rather than using (1) and (2) as constraints.

An ontological argument from justice

Buras and Cantrell have given a very clever ontological argument for the existence of God based on a desire for happiness. Here is a variant of their argument based on justice.

  1. Ought implies (metaphysical) possibility.

  2. There ought to be justice for humans.

  3. Necessarily, if there is justice for humans, it is possible that there is a human who has happiness.

  4. Necessarily, if there is a human who has happiness, God exists.

  5. So, possibly God exists. (1-4 and S5)

  6. So, God exists. (S5 and as God is essentially divine and necessarily exists.)

I want to expand a little on 3 and 4.

In any world where there is justice for humans, there is (a) a practical possibility of a human being innocent, and (b) a system that reliably rewards innocent humans with happiness. Items (a) and (b) taken together plausibly imply a practical, and hence metaphysical, possibility of happiness. That gives us (3).

Buras and Cantrell defend claim (4). My favorite defense of claim (4) is that human happiness, when we think through our deep desire for eternal life as well as the danger of boredom in eternal lfie, requires some sort of friendship with God.

Monday, September 13, 2021

Virtue ethics and peer disagreement

Aristotelian ethics is committed to the claim that the virtuous person knows what actions and habits are virtuous and is justified in holding on to that knowledge, and indeed should hold on to it. There is a deep stability to virtue. This means that an Aristotelian virtuous person ought not adopt a conciliationist response to those who disagree as to what is virtuous, suspending judgment over the disagreed-upon items.

Indeed, one imagines that Aristotle’s virtuous person could say of those who disagree: “They are not virtuous, and hence do not see the truth about moral matters.” Aristotle’s virtuous person would reject the idea that someone who disagrees with them about virtue could be an epistemic peer. Virtuous habits give epistemic access to moral (and not only moral) truth.

Of course, the disagreer may think themselves virtuous as well, and may think the same thing about the virtuous person as the virtuous person thinks about them. But that does not shake the Aristotelian virtuous person.

This means that if Aristotelian virtue ethics is correct, there is a clear thing that a Christian can say about religious disagreement. The Christian thinks faith is a virtue, albeit an infused rather than natural one. As such, faith gives epistemic access, and someone lacking faith is simply not an epistemic peer, since they lack a source of truth. The fact that a person lacking faith thinks they have the virtue of faith should not move the person who actually has the virtue.

Of course, one might turn all this around and use it as an argument against virtue ethics. But I think Aristotle’s picture seems exactly correct as to the kind of firmness of moral knowledge that the virtuous person exhibits, the kind of spine that lets them say, without pride or vanity, to vast numbers of others that they are simply wrong.

Moral bindingness and levels of jurisdiction

In the US, you are sometimes told that something “violates federal law”, and it is said in a way that suggests that violating federal law is somehow particularly bad.

This raises a moral question. I will assume, contrary to philosophical anarchists, that valid and reasonable laws are in some way morally binding. Other things being equal, is it morally worse to violate the laws that operate at broader levels of organization. In the US, an affirmative answer would imply that federal law is morally worse to break than state law, and state law than county law, and county law than city law.

One might think this: the power to make laws belongs to more local levels of organization by delegation from broader levels of organization, and hence violating the laws of a more local jurisdiction is less morally bad. But this argument does not fit with what I understand is the US consitutional system’s idea that sovereignty starts with the states which permanently delegate some of their authority to the federal system. And, in any case, it is not clear why it would be less bad to go against the laws of a more delegated authority: if x delegates some authority to y, then relevant disobedience to y is also disobedience to x.

A perhaps more plausible argument in favor of the laws of broader jurisdictions being morally more strongly binding is that in violating a law, one offends against the body of citizens. With a broader jurisdiction, that body of citizens is larger, and hence the offense is worse. But this can’t be right. It is not morally less bad to commit federal tax fraud in Canada than in the US just because in Canada the population is smaller! (This observation perhaps suggests that if we do adopt the view that violating the law offends against the body of citizens, we should not view the “offense against the body of citizens” as meaning an offense against the citizens taken severally—to offend against a body is different from offending against the body’s constituents taken severally, or else punching a bigger person would be a worse thing than punching a smaller, just because the bigger person’s body has more cells. Or, perhaps, we have to say that the offensiveness of a law breaking is diluted among the citizenry, so that in a larger body, each citizen is less offended against.)

I want to suggest that the idea that it is worse to offend against broader jurisdictions is backwards for multiple reasons:

  1. An offense against a narrower jurisdiction is an offense against a body of citizens who are more closely related to one, and hence is a greater breach of the duties of civic friendship.

  2. The laws of narrower jurisdictions can be reasonably expected to be on the hwole better fitted to the community, because there is less variation in circumstance within a narrower jurisdiction.

  3. One has a greater say in the laws of the laws of the narrower jurisdiction, and hence they better fit with the autonomy of the governed.

  4. It is typically less burdensome to choose which narrower jurisdiction one lives under than which wider one: it is easier to move to a different city than to a different country. Therefore, any implied consent to local laws is greater than to wider laws.

These considerations suggest that offending against a narrower body is worse. Interestingly, (3) suggests that in my earlier example of tax fraud in the US and Canada, it is even worse to commit tax fraud in Canada, because doing so violates laws one has a greater say in. That actually sounds right to me, but I do not feel the difference in moral badness is a very big one, so (3) is probably not a major factor (of course, in the special case of tax fraud, a lot of the immorality comes from the immorality of lying, which precedes law).

(These same considerations support the principle of subsidiarity.)

So far I have been thinking about geographically defined jurisdictions. But consider a very different jurisdiction: the body of a profession, such as physicians or lawyers or electricians. The standards of such a body have a great deal of moral force. When a doctor says that disclosing some information about a patient violates medical ethics, that carries a great deal of moral force. And yet it really is “just” a violation of the law of a body, because there would be no such moral duty of confidentiality without the standards of the body of physicians (there would be more limited duties of confidentiality, say when the doctor specifically promised the patient not to disclose something). The laws of the professional jurisdictions have a lot of moral force, and it is not implausible that 1-4 are at least partly explanatory of that force.

Saturday, September 11, 2021


It feels like I am constantly fixing computer mice. The most common issue is the wires breaking near the mouse, requiring me to shorten the cable and resolder it to the PCB. I usually also add some glue or heat shrink tubing as strain relief if I haven’t done so already. Switching the household to wireless mice would solve the problem, at the expense of having yet more batteries to deal with.

I started off today with a new fix: the plastic axle from a mouse wheel broke off. I drilled through the mouse wheel and put a toothpick in instead. We’ll see how long that holds up. If it doesn’t, I’ll have to see if I can find a screw or nail of the right diameter instead.

Likely near future task: my daughter complains of a mouse double clicking. When it earlier had that problem, it seemed to me that it was generating an extra click on release, which sounds to me like a debouncing failure. But then I took it apart and put it back together and the problem disappeared, so I didn’t have a chance to fix it. Apparently the problem has come back, but I can’t duplicate it. If and when I duplicate it, I plan to hook it up to an oscilloscope, and play around with capacitors to debounce the release.

I wonder if problems would decrease if we bought more expensive mice.

Friday, September 10, 2021

Comparing the epistemic relevance of measurements

Suppose P is a regular probability on (the powerset of) a finite space Ω representing my credences. A measurement M is a partition of Ω into disjoint events E1, ..., En, with the result of the experiment being one of these events. In a given context, my primary interest is some subalgebra F of the powerset of Ω.

Note that a measurement can be epistemically relevant to my primary interest without any of the events in in the measurement being something I have a primary interest in. If I am interested in figuring out whether taller people smile more, my primary interest will be some algebra F generated by a number of hypotheses about degree to which height and smiliness are correlated in the population. Then, the measurement of Alice’s height and smiliness will not be a part of my primary interest, but it will be epistemically relevant to my primary interest.

Now, some measurements will be more relevant with respect to my primary interest than others. Measuring Alice’s height and smiliness will intuitively be more relevant to my primary interest about height/smile correlation, while measuring Alice’s mass and eye color will be less so.

The point of this post is to provide a relevance-based partial ordering on possible measurements. In fact, I will offer three, but I believe they are equivalent.

First, we have a pragmatic ordering. A measurement M1 is at least as pragmatically relevant to F as a measurement M2, relative to our current (prior) credence assignment P, just in case for every possible F-based wager W, the P-expected utility of wagering on W after a Bayesian update on the result of M1 is at least as big as that of wagering of W after updating on the result of M2, and M1 is more relevant if for some wager W the utility of wagering after updating on the result of M1 is strictly greater.

Second, we have an accuracy ordering. A measurement M1 is at least as accuracy relevant to F as a measurement M2 just in case for every proper scoring rule s on F, the expected score of updating on the result of M1 is better than or equal to the expected score of updating on the result of M2, and M1 is more relevant when for some scoring rule the expected score is better in the case of M1.

Third, we have a geometric ordering. Let HP, F(M) be the horizon of a measurement M, namely the set of all possible posterior credence assignments on F obtained by starting with P, conditionalizing on one of the possible events in that M partitions Ω into, and restricting to F. Then we say that M1 is at least as (more) geometrically relevant to F as M2 just in case the convex hull of the horizon of M1 contains (strictly contains) the convex hull of the horizon of M2.

I have not written out the details, but I am pretty sure that all three orderings are equivalent, which suggests that I am on to something with these concepts.

An interesting special case is when one’s interest is binary, an algebra generated by a single hypothesis H, and the measurements are binary, i.e., partitions into two sets. In that case, I think, a measurement M1 is at least as (more) relevant as a measurement M2 if and only if the interval whose endpoints are the Bayes factors of the events in M1 contains (strictly contains) the interval whose endpoints are the Bayes factors of the events in M2.

Thursday, September 9, 2021

What question should I ask?

Epistemology is heavily focused on the question of evaluating a doxastic state given a set of evidence: is the state rational or irrational, is it knowledge or opinion, etc. This can be useful to the epistemic life of an agent, but there is something else that is at least as useful and does not get discussed nearly as much: the question of how we should go about gathering evidence or, equivalently, what experiments (broadly understood) we should perform.

[The rest of the post was based on a mathematical error and has been deleted. The next post is an attempt to fix the error.]

Wednesday, September 8, 2021

Has cultural relativism about norms of etiquette really been established?

Imagine a philosopher who argued that the norms of assertion are relative to culture on the grounds that in England we have the norm:

  1. Only assert “It’s snowing” when it’s snowing

while in France we have the norm:

  1. Only assert “Il neige” when it’s snowing.

This would be silly for multiple reasons. Foremost among these is that (1) and (2) are mere consequences of the norm of assertion:

  1. Only assert what it is true.

(Of course, you may disagree that truth is the norm of assertion. You may prefer a knowledge or justified belief or belief or high credence norm. But an analogous point will apply.)

It is widely held that while the norm of assertion is essentially the same across cultures, norms of etiquette vary widely. But the main reason people give for believing that the norms of etiquette vary widely is akin to the terrible argument about norms of assertion I began the post with. People note such things as that in some countries when one meets acquaintances one bows, and in others one waves; or that in some one eats fish with two forks and in others with a fork and knife.

But just as the fact that in England one should follow (1) and in France (2) is compatible with the universality of norms of assertion, likewise the variation in greeting and eating rituals can be compatible with the universality of norms of etiquette. It could, for instance, be that the need to eat fish with two forks in Poland and with a fork and knife in the USA derives simply from a universal norm of etiquette:

  1. Express respect for your fellow diners.

But just as one asserts the truth with different words in different languages, one expresses respect for one’s fellow diners with different gestures in different cultures.

Indeed, presumably nobody thinks that the fact that in France one says “Merci” and in England “Thank you” implies a cultural relativism in etiquette. In both cases one is thanking, but the words that symbolize thanks are different. But what goes for words here also applies to many gestures (there may turn out to be universal gestures, like pointing).

One object that among the norms of etiquette there are norms that specify which gestures signify, say, respect or thanks. But a specification of what signifies what is not the specification of a norm. That “Merci” signifies gratitude and that eating fish with two forks signifies respect are not norms, because norms tell us what to do, and these do not.

  1. “Merci” signifies thanks

is grammatically not a norm but a statement of fact. We might try to make it sound more like a norm by saying:

  1. Signify thanks with “merci”!

But that is bad advice when taken literally. For thanks are not to be signified always, but only when thanks are appropriate. A more correct norm would be:

  1. When a service has been done for you, signify thanks with “merci”!

But this is just a consequence of the general norm of etiquette:

  1. When a service has been done for you, signify thanks!

together with the fact (5).

So, we see that the mere variation in rituals should not be taken to imply that there is cultural relativity of norms of etiquette.

If there is to be a cultural relativity of norms of etiquette, it will have to be at a higher level. If in some cultures, etiquette requires one to show respect for all fellow diners and at others to show disrespect for some—say, those from an underprivileged group—then that would indeed be a genuine relativity of norms of etiquette.

But it’s not clear that me that in a culture where one is expected to show disrespect to fellow diners in some underprivileged group that expectation is actually a norm of etiquette. Not all social expectations, after all, are actually norms of etiquette, or even norms at all. A norm (of behavior) gives norm-based reasons. But an expectation that one show disrespect to members of an underprivileged group has no reason-giving force at all.

We can imagine a culture where there is no way to symbolize respect for members of an underprivileged group when dining. On the view I wish to defend, such a lack would not exempt one from the duty to show respect to all one’s fellow diners—it would just make it more difficult to do so, because it would require one to create new ways of showing respect (say, by adapting the forms of showing respect to members of privileged groups, much as in some European languages the polite forms of address are derived from forms in which one used to address nobility in less democratic times).

I am not sure if there is cultural variation in norms of etiquette. But if there is, that variation will not be proved by shallow differences between rituals, and may not even follow from deeper variation, such as a culture where it is not appropriate to thank one’s subordinates for work well done. For in the case of deeper variation, it could simply be that some in some cultures violation of certain norms of etiquette is nearly universal, and there are no accepted ways to show the relevant kind of respect.

In fact, it could even be the case that there is only one norm of etiquette, and it is culturally universal:

  1. Signify respect to other persons you interact with in ways fitted to the situation.

If this is right, then social rules designed to show disrespect, no matter how widespread, are not norms of etiquette.

Reasons from the value of true belief

Two soccer teams are facing off, with a billion fans watching on TV. Brazil has a score of 2 and Belgium has a score of 0, and there are 15 minutes remaining. The fans nearly unanimously think Brazil will win. Suddenly, there is a giant lightning strike, and all electrical devices near the stadium fail, taking the game off the air. Coincidentally, during the glitch, Brazil’s two best players get red cards, and now Belgium has a very real chance to win if they try hard.

But the captain of the Brazilian team yells out this argument to the Belgians: “If you win, you will make a billion fans have a false belief. A false belief is bad, and when you multiply the badness by billion, the result is very bad. So, don’t win!”
Great hilarity ensues among the Belgians and they proceed to trounce the Brazilians.

The Belgians are right to laugh: the consideration that the belief of a billion fans will be falsified by their effort carries little to no moral weight.

Why? Is it that false belief carries little to no disvalue? No. For suppose that now the game is over. At this point, the broadcast teams have a pretty strong moral reason to try to get back on the air in order to inform the billion fans that they were mistaken about the result of the game.

In other words, we have a much stronger reason to shift people’s beliefs to match reality than to shift reality to match people’s beliefs. Yet in both cases the relevant effect on the good and bad in the world can be the same: there is less of the bad of false beliefs and more of the good of true beliefs. An immediate consequence of this is that consequentialism about moral reasons is false: the weight of moral reasons depends on more than the value of the consequences.

It is often said that belief has a mind-to-world direction of fit. It is interesting that this not only has repercussions for the agent’s own epistemic life, but for the moral life of other parties. We have much more reason to help others to true belief by affecting their beliefs than by affecting the truth and falsity of the content of the beliefs.

Do the Belgians have any moral reason to lose, in light of the fact that losing will make the fans have correct belief? I am inclined to think so: producing a better state of affairs is always worthwhile. But the force of the reason is exceedingly small. (Nor do the numbers matter: the reason’s force would remain exceedingly small even if there are trillions of fans because Earth soccer was famous through the galaxy.)

There is a connection between the good and the right, but it is quite complex indeed.

Two spinners and infinitesimal probabilities

Suppose you do two independent experiments, A and B, each of which uniformly generates a number in the interval I = [0, 1).

Here are some properties we would like to have on our probability assignment P:

  1. There is a value α such that P(A = x)=P(B = x)=α for all x ∈ I and P((A, B)=z)=α2 for all z ∈ I2.

  2. For every subset U of I2 consisting of a finite union of straight lines, P((A, B)∈U) is well-defined.

  3. For any measurable U ⊆ I2, if P((A, B)∈U|A = x)=y for all x ∈ I, then P((A, B)∈U)=y.

  4. For any measurable U ⊆ I2, if P((A, B)∈U|B = x)=y for all x ∈ I, then P((A, B)∈U)=y.

  5. The assignment P satisfies the axioms of finitely additive probability with values in some real field.

Here is an interesting consequence. Let U consist of two line segments, one from (0, 0) to (1, 1/2) and the other from (0, 1/2) to (1, 1). Then every vertical line in I2 intersects U in exactly two points. This is measurable by (2). It follows from (1) and (5) that P((A, B)∈U|A = x)=2α for all x ∈ I. Thus, P((A, B)∈U)=2α by (3). On the other hand, every horizontal line in I2 meets U in exactly one point, so P((A, B)∈U|B = x)=α by (1) and P((A, B)∈U)=α by (4). Thus, 2α = α, and so α = 0.

In other words, if we require (1)-(5) to hold, then the probability of every single point outcome of either experiment must be exactly zero. In particular, it is not possible for the probability of a single point outcome to be a positive infinitesimal.

Cognoscenti of these kinds of arguments will recognize (3) and (4) as special cases of conglomerability, and are likely to say that we cannot expect conglomerability when dealing with infinitesimal probabilities. Maybe so: but (3) and (4) are only a special case of conglomerability, and they feel particularly intuitive to me, in that we are partitioning the sample space I2 on the basis of the values of one of the two independent random variables that generate the sample space. The setup—say, two independent spinners—seems perfectly natural and unparadoxical, the partitions seem perfectly natural, and the set U to which we apply (3) and (4) is also a perfectly natural set, a union of two line segments. Yet even in this very natural setup, the friend of infinitesimal probabilities has to embrace a counterintuitive violation of (3) and (4).

Tuesday, September 7, 2021

Naturalism and lovability

  1. If naturalism is true, Stalin is not lovable.

  2. Everyone is lovable.

  3. So, naturalism is not true.

Here, by “lovable”, I don’t mean that it is possible to love the person, but that it is not inappropriate to do so.

Premise 2 follows the intuition that it is permissible for every parent to love their children. It also follows from the more controversial claim that everyone should love everyone.

The intuition behind premise 1 is something like this: Stalin’s actions were so horrible that the only plausible hypotheses on which he is lovable are that there is some deeply mysterious and highly valuable metaphysical fact about his being, such as that he is in the image and likeness of God, or that his Atman is Brahman, a fact incompatible with naturalism. For if all we have are the ordinary naturalistic goods in Stalin, these goods are easily outweighed by the horrors of his wickedness.

Friday, September 3, 2021

Impairment and saving lives

Bob and Carl are drowning and you can save only one of them. Bob is a human being in the prime of life, physically and mentally healthy, highly intelligent, and leading a happy and fulfilling life as a physicist committed to lifelong celibacy. To look at him, Carl is Bob’s identical twin. Carl has the same physical and mental powers as Bob, and leads a very similar happy and fulfilling life as a physicist committed to lifelong celibacy.

But there is one crucial difference that you know about, but Carl does not. Carl is actually a member of a superintelligent humanoid alien species. However, due to an unfortunate untreatable genetic condition, Carl suffers from a severe intellectual impairment, having merely the intelligence of a highly intelligent human. In order that Carl might avoid the stigma of the impairment, his parents had some highly sophisticated surgery done on him to make him fit into human society, and arranged for him to be adopted by a human family and raised as a human. No one except for you on earth will ever know that Carl isn’t human. You know because you happened to see the aliens arranging this (but you haven’t told anyone, because you don’t want people to think you are crazy).

Should you save Bob or Carl from drowning? My intuition is that if the above is all that you know, you have no reason to prefer saving one over the other. If one of them is slightly more likely to be saved by you (e.g., they are slightly closer to you), you should go for that one, but otherwise it’s a toss-up.

But notice that if you save Carl, there will be more natural evil in the world: There will be a severe intellectual impairment, which won’t be present if you choose to save Bob instead. It seems pretty plausible that:

  1. If you have a choice between two otherwise permissible courses of action, which result in the same goods, but one of them results in exactly one additional evil, you have a moral reason to choose the course of action that does not result in the evil.

Thus, it seems, you should save Bob.

So there is something paradoxical here. On the one hand, there seems to be no reason to pick Bob over Carl. On the other hand, the plausible general ethical principle (1) suggests you should pick Bob.

How can we get out of this paradox? Here are two options.

First, one could say that impairment is not an evil at all. As long as Carl leads a fulfilling life—even if it is merely fulfilling by human standards and not those of his species—his impairment is no evil. Indeed, we might even take the above story to be a reductio ad absurdum of an Aristotelian picture of species as having norms attached to them with it being a harm to one to fall short of these norms.

Second, one argue that principle (1) does not actually apply to the case. For there is a difference of goods in saving Carl: you are saving a member of a superintelligent species, while in the case of saving Bob, you are saving a mere human. For this to fit with the intuition that it’s a toss-up whether to save Bob or Carl, it has to be the case that what the superintelligence of his species adds to the reasons for saving Carl is balanced by what his abnormally low intelligence subtracts from these reasons.

Of these options, I am more attracted to the second. And the second has an interesting and important consequence: "mere" membership in a natural kind can have significant value. This has important repercussions for the status of the human fetus.

Wednesday, September 1, 2021

Models of libertarian agency, and some more on divine simplicity

Here is a standard libertarian picture of free and responsible choice. I am choosing between two non-mental actions, A and B. I deliberate on the basis of the reasons for A and the reasons for B. This deliberation indeterministically causes an inner mental state W(A), which is the will or resolve or intention to produce A. And then W(A) causes, either deterministically or with high probability, the extra-mental action A.

Now notice two things. First, notice that my production of the state W(A) is itself something I am morally responsible for. Imagine that I have resolved myself to gratuitously insult you. If it turns out that my vocal chords are paralyzed, my resolve W(insult) is itself enough to make me guilty.

Second, note that that my production of W(A) could involve the production of a prior second-order state of will or resolve, a willing W(W(A)) to will to produce A. For there are times when it’s hard to resolve ourselves to do something, and in those cases we might resolve ourselves to resolve ourselves first. But at the same time, to avoid an infinite regress, we should not adopt a view on which every time we responsibly produce something, we do so by forming a prior state of willing or resolve or intention. In light of this, although my production of W(A) could involve the production of a prior second-order state W(W(A)), it need not do so. In fact, phenomenologically, it seems more plausible to think that in typical cases of free choice, we do not go to the meta level of producing W(W(A)). We only go to the meta level in special cases, such as when we have to “steel” ourselves to gain the resolve to do the action.

Thus we have seen that, assuming libertarianism, it is possible for me to be responsible for indeterministically producing a state of affairs W(A) without producing a prior state of willing or resolving or intending in favor of W(A). The state W(A) is admittedly an inner mental state. But the responsibility for W(A) does not seem to have anything to do with the innerness of W(A). We are responsible for W(A) because our deliberation indeterministically but non-aberrantly results in W(A).

Here is a question: Could there be cases where we have libertarian-free actions where instead of our deliberation indeterministically non-aberrantly resulting in W(A), and thereby making us responsible for W(A) as well as A, our deliberation directly indeterministically and non-aberrantly results in the extra-mental action A, without an intervening inner mental state W(A) that deterministically or with high probability causes A, but with us nonetheless being responsible for A?

Once we have admitted—as a libertarian has to, on pain of a regress of willings—that we can be responsible for producing a state of affairs without a prior willing of that state of affairs, then it seems hard to categorically deny the possibility of us producing an extra-mental state of affairs responsibly without an intervening prior willing. And in fact phenomenology fits quite well with the hypothesis that we do that. We do many things intentionally and responsibly without being aware of a willing, resolve or intention to do them. If we stick to the initial libertarian model on which there must be an intervening mental state W(A), we have to say that either the state W(A) is hidden from us—unconscious—or that these actions are only free in a derivative way. Neither is a particularly attractive hypothesis. Why not, simply, admit that sometimes deliberation results in an extra-mental action that we are responsible for without an intervening willing, resolve or intention?

Well, I can think of one reason:

  1. It seems that you can only be responsible for what we do intentionally, and we cannot do something intentionally without intending something.

But note that if this reason undercuts the possibility of our responsibly directly doing A without an intervening act W(A) of intention, it likewise undercuts the possibility of our responsibly directly producing W(A) without an intervening W(W(A)) act, and sets us on a vicious regress.

I actually think (1) can be accepted. In that case, when we directly responsibly produce W(A), the intentionality in the production of W(A) is constituted by the non-aberrant causal connection between deliberation and W(A), rather than by some regress-engendering intention-for-W(A) prior to W(A). And the occurrence of W(A) means that we are intending something, namely A.

But what would it be like if we were to directly responsibly produce A, without an intervening act of intention W(A)? How would that be reconciled with (1)? Again, the intentionality of the production of A would be constituted by the non-aberrant causal connection between deliberation and A. And the content of the intention would supervene on the actual occurrence of A as well as on the reasons favoring A that were instrumental in the deliberation. (There are some complications about excluded reasons. Maybe in those cases deliberation can have an earlier stage where one freely decides whether to exclude some reasons.)

Call the cases where we thusly directly responsibly produce an extra-mental action A cases of direct agency.

A libertarian need not believe we exhibit direct agency. Perhaps we always have one level of resolve, willing or intention as an inner mental state. But the libertarian should not be dogmatic here, given the above arguments.

Our phenomenology suggests that we do exhibit direct agency, and indeed do so quite commonly. And if God is simple, and hence does not have contingent inner states, all of God’s indeterministic free actions are cases of direct agency.

In fact, independently of divine simplicity, we may have some reason to prefer the direct agency model in the case of God. Consider why it is that sometimes we go to the meta level of W(W(A)): we do so because of the weakness of our wills, we have to will ourselves to will ourselves to produce A. It seems that a perfect being would never have reason to go to the meta level of W(W(A)). So, the remaining question is whether a perfect being would ever have reason to go to the W(A) level. I think there is some plausibility in the idea that just as going to the W(W(A)) level is a sign of weakness, a sign of a need for self-control, going to the W(A) level is also a sign of imperfection—a sign that one needs a tool, even if an intra-mental tool, for the production of A. It seems plausible, thus, that if this is possible and compatible with freedom and responsibility, a perfect being would simply directly produce A (where A is, say, the action of the being’s causing horses to exist). And I have argued that it is possible, and it is compatible with freedom and responsibility.

Monday, August 30, 2021

Divine simplicity and responsibility for creation

Libertarians believes something like this:

  1. If an agent has primary responsibility for a state of affairs A, then the agent gained that resposibility by intentionally indeterministically causing A.

Here, primary responsibility is distinguished from the kind of derivative responsibility that someone who freely got drunk (and hence has primary responsibility for getting drunk) has for the accident caused while drunk.

Next, add this plausible thesis:

  1. If an agent gains primary responsibility for a state of affairs A by intentionally causing A, then the agent has primary responsibility for an intention relevantly connected to A.

Now, combine (1) and (2). Suppose Alice has primary responsibility for A. Then she had an intention I = I1 relevantly connected to A that she had primary responsibility for. Applying (1) and (2) to I1, we conclude that Alice had primary responsibility for an intention I2 relevantly connected to I, and primary responsibility for an intention I3 relevantly connected to I2, and so on, ad infinitum.

But of course we don’t have an infinite chain of intentions. So we must break out of the chain. I think there is only one way to do so: at some point, In = In + 1. In other words, the intention relevantly connected to In just is In once again: there is no further intention. Rather, one’s intention to produce In is just constituted by In.

This means that it is possible for one to be primarily responsible for a state of affairs A—say an intention In—when the intention with which one caused A is itself at least partly constituted by A.

Now, I take it that something like this is what happens when a simple God creates something: God’s intention to create horses is partly constituted by horses, rather than simply by some inner state of God’s.

There is a lesson here: The primary worry that one has about a simple God’s contingently creating things—namely, that a simple God cannot have contingent inner states—is mirrored by a parallel worry about a libertarian agent’s production of intentions.

Absence of evidence

It seems that the aphorism “Absence of evidence is not evidence of absence” is typically false.

For if H is a hypothesis and E is the claim that there is evidence for H, then E raises the probability of H: P(H|E)>P(H). But then (as long as P(E)>0, as Bayesian regularity will insist), it mathematically follows that P(∼H|∼E)>P(∼H). Thus the absence of evidence is evidence for the falsity (“absence”) of the hypothesis.

I think there is only one place where one can challenge this argument, namely the claim:

  1. If there is evidence for H, then the fact that there is evidence for H is itself evidence for H.

First, let’s figure out what (1) is saying. I think the best reading is that it presupposes some kind of notion of a body of first-order evidence—maybe all the stuff that human beings have ever observed—and says that if the actual contents of that body of first-order evidence supports H, then the fact that that body supports H itself supports H.

Here is a way to make this precise. We suppose there is some random variable O whose value (not real valued, of course) is all first-order observations humans ever made. Let W be the set of all possible values that O could take on. For simplicity, we can take W to be finite: there is a maximum number of observations a human can make in a lifespan, a finite resolution to each observation, and a maximum number of human beings who could have lived on earth. Let o0 be the actual value that O has. Let WH = {o ∈ W : P(H|O = o)>P(H)}.

Assuming we have Bayesian regularity, we can suppose O = o has non-zero probability for each o ∈ WH. Then the claim that there is evidence for H is itself evidence for H comes to this:

  1. P(H|O ∈ WH)>P(H).

And it is easy to check that this follows by finite conglomerability from the fact that P(H|O = o)>P(H) for each o ∈ WH.

There might be cases where we expect infinite conglomerability to be lacking. In those cases (1) would be dubious. Here is one such case. Suppose Alice and Bob each get a ticket from a fair infinite jar with tickets numbered 1,2,3,…. Alice looks at her ticket. Bob doesn’t look at his yet, but knows that Alice has looked at hers. Bob notes that whatever number Alice has seen, it is nearly certain that his number is bigger (there are infinitely many numbers bigger than Alice’s number and only finitely many smaller ones). Thus, Bob knows that the evidence available to humans supports the thesis that his number is bigger than Alice’s. But Bob’s knowing this is not actually evidence that his number is bigger than Alice’s, for until Bob actually observes one or the other number, he is in the same evidential position as before Alice looked at her ticket—and at that point, it is obvious that it’s not more likely that Bob’s ticket has a bigger number than Alice’s.

But apart from weird cases where conglomerability fails, (1) is true, and so absence of evidence is evidence of absence, assuming we have enough Bayesian regularity.

Perhaps a charitable reading of the aphorism that absence of evidence isn’t evidence of absence is just that absence of evidence isn’t always significant evidence of absence. That seems generally correct.

A tension in some of my recent work

Here is a tension in some recent work of mine. In Chapter 6 of Infinity, Causation, and Paradox, I argue that (a) the Axiom of Choice for countable sets of reals (ACCR) is true, and (b) this version of the Axiom of Choice plus causal infinitism implies a nasty paradox, so we should accept causal finitism instead. The argument for ACCR makes use of the premise that mathematical entities exist necessarily. But in “Might All Infinities Be The Same Size?”, I argue that for all we know, some mathematical entities exist contingently. Thus, the latter paper undercuts the argument of Chapter 6 of the book.

Fortunately, the argument of Chapter 6 of the book looks like it might be fixable. The argument for ACCR proceeded as follows:

  1. For any set of non-empty countable sets of reals, it is metaphysically possible that there is a choice function.

  2. If possibly there is a choice function, then necessarily there is a choice function.

The argument for (1) is elaborate, but it is (2) that the considerations in my article block.

But we can try to proceed as follows. The paradox in Chapter 6 of the book requires a choice function for a particular collection of non-empty countable sets of reals (reals generatable by a certain infinitary coin-tossing process). By (1), there is a possible world w′ where that particular collection of sets does have a choice function. So it seems all we need to do is to run the paradox in w′, and we should be done.

There are probably other areas in Chapter 6 where some tweaking (or more than that!) is needed to make things work with mathematical contingentism, and hence my cautious wording.

Friday, August 27, 2021

A superpower

Imagine Alice claimed she could just see, with reliability, which unprovable large cardinal axioms are true. We would be initially sceptical of her claims, but we could imagine ways in which we could come to be convinced of her having such an ability. For instance, we might later be able to prove a lot of logical connections between these axioms (say that axiom A12 implies axiom A14) and then find that Alice’s oracular pronouncements matched these logical connections (she wouldn’t, for instance, affirm A12 while denying A14) to a degree that would be very hard to explain as just luck.

Suppose, then, that we have come to be convinced that Alice has the intuitive ability to just see which large cardinal axioms are true. This would be some sort of uncanny superpower. The existence of such a superpower would sit poorly with naturalism. An intuition like Ramanujan’s about the sums of series could be explained by naturalism—we could simply suppose that his brain unconsciously sketched proofs of various claims. But an intuition about large cardinal axioms wouldn’t be like that, since these axioms are not provable.

Now as far as we know, there is no one exactly like Alice who just has reliable intuitions about large cardinal axioms. But our confidence in the less abstruse axioms of Zermelo-Fraenkel set theory—intuitive axioms like the axiom of replacement—commits us to thinking that either we in general, or those most expert in the matter, are rather like Alice with respect to these less abstruse axioms. The less abstruse axioms are just as unprovable as the more abstruse ones that Alice could see. Therefore, it seems, if Alice’s reliable intuition provided an argument against naturalism, our own (or our experts’) intuition about the more ordinary axioms, an intuition which we take to be reliable, gives us an argument against naturalism. Seeing the axiom of replacement to be true is just as much a superpower as would be Alice’s seeing that, say, measurable cardinals exist (or that they do not exist).

Thursday, August 26, 2021

Counting good and bad things

People sometimes wonder, perhaps in connection with the problem of evil, whether there is in total more good than evil in the world. The connection with the problem of evil is somewhat tenuous, of course. Even if it were agreed there is more good than evil, it could still be argued that there is gratuitous evil, inconsistent with the existence of God. And even if there is a God, there could presently be more evil than good, if, say, the evil is justified in connection with future good.

All that said, here is a question related to the question whether there is more good than evil:

  • Are there more good things than bad things in the world?

I will argue that on two different takes on “things”, there are vastly more good things than bad—or even bad or neutral—things in the world as we know it. Even if we can generalize from the world as we know it, this still does not show that there is more good than evil: perhaps there are more goods, but the bad things are so very bad that the total evil is greater than the total good. Nonetheless, I think the answer has evidential bearing on the existence of God, because it would intuitively be at least a little bit more likely for there to be vastly more good things than bad or neutral things in the observed part of the world if God existed than if God didn’t exist.

On to the argument. On a first take, “things” are substances. Now, I think the best story about substance is a neo-Aristotelian one on which in the part of the world we collectively know, the substances are the organisms and the fundamental physical entities.

Now, our three best theories as to what the fundamental physical entities are is that they are:

  1. particles,

  2. global entities like fields and the wavefunction of the universe, or

  3. particles and global entities.

Suppose that the correct answer is (a) or (c). Then in the known universe, the vast majority of substances are particles. There may be a lot of organisms in the world, but there are way more particles. And the number of global entities, like fields and the wavefunction, on our best theories is in the single digits. But every particle is good: it perfectly fulfills its nature, which is to dance its dance according to the beautiful mathematical laws of the universe. So, on (a) and (c), the vast majority of substances are good. (Maybe good in a very minor way.)

Suppose that the correct answer is (b). Then the substances of the known universe consist of organisms and probably a handful of global entities like fields or the wavefunction. The organisms outnumber the global entities so much that we can neglect the global entities and, besides, the global entities are good, for the same reason the particles are. Among the known organisms there are some that are bad. The clearest cases are a sizeable proportion of humans.

Whether there are any bad non-human organisms on earth (essentialy the only place we know of with organisms) depends on whether we count instrumental value. For if we limit ourselves to intrinsic badness, plausibly all organisms that aren’t persons are good (and there are many good persons), and non-personal organisms vastly outnumber personal ones. If badness (and goodness), however, includes instrumental assessment, then there are bad organisms. But how many? There may be some species most of whose members are bad: perhaps some mosquito species are like that. But it seems very plausible that such species form a very small portion of the whole, and that the vast majority of species are such that the vast majority of their members are good. (Quick thought experiment: Suppose by pressing a button you could wipe out a randomly chosen non-human species? Surely it would be a very, very bad idea to press the button.) So, it seems quite plausible that the vast majority of organisms are good.

On a second take, “things” include events in addition to substances. Well, now, the vast majority of events in the known universe seem to be purely physical events that are neither good nor bad for living things, and they do no harm to non-living things either. But they are an intrinsically good part of the dance of nature according to beautiful mathematical laws. So, it seems, the vast majority of events is good.

Wednesday, August 25, 2021

Analog photography

For over a decade, all my photography has been digital, but this spring I finally pulled out the 1939 Voigtlaender Vito 35mm camera I inherited from my grandfather, checked with an oscilloscope (photo-detector on one side, flashlight on the other) that the shutter timer was still correct, loaded it up with 100 ISO black and white film, and took a bunch of pictures around Waco over several months. 

I had the pictures developed and scanned by OneStopDeveloping on Etsy.

Last years, Waco installed a bunch of animal-themed sculptures near the zoo. Though one of the pictures is of real animals.


"Despite" explanations

The phenomenon of contrastive explanations has been explored by a number of authors. There is another phenomenon in the vicinity, that of explanations of despite-claims, that has not received as much attention, even though it’s also interesting. Suppose Bob hates bananas and eats a banana.

  1. Why did Bob eat a banana? – Because he was hungry.

  2. Why did Bob eat a banana despite hating bananas? – Because he was very hungry.

A contrastive request for explanation, say

  1. Why did Bob eat a banana rather than an apple?

doesn’t so much ask for an explanation of a special contrastive proposition, but rather constrains what kind of answer is acceptable—an answer that provides a contrastive answer. Thus, saying that Bob was hungry is not an acceptable answer since it fails to be contrastive between the banana and apple options, while saying that Bob was hungry and a banana was closer at hand is an acceptable answer. However, whenever one constrains what kind of an explanation is acceptable, one runs the risk that—even without any violation of the Principle of Sufficient Reason—there is no answer. For instance, the question

  1. Who killed the mayor and why?

is a request for explanation that has no answer if the mayor died from a tornado, because (4) constrains us to agentive explanation, and in this case there is no agentive explanation.

Are requests for explanations-despite like requests for contrastive or agentive explanations, requests that constrain the type of explanation that is acceptable, rather than simply modifying the proposition to be explained?

I am inclined to think that the answer is negative. Here is a preliminary analysis for what is going on when we ask:

  1. Why p despite r?

First, the question carries a presupposition that the fact that r is antiexplanatory of p or that it has a tendency against p. If that presupposition is false, the question has no answer, being akin to one of the standard trick questions with false presuppositions (like “Have you stopped beating your spouse?”).

Second, what we are asking is something like this:

  1. How was the antiexplanatory force of the fact that r against its being the case that p countered such that p is true?

And this seems to be a straightforward request for an explanation of an admittedly complex proposition, without any constraints being placed on what explanations are acceptable.

If I am right about this, then while a failure to have a good answer to contrastive explanation question does no damage to the Principle of Sufficient Reason (PSR), a failure to have a good answer to an explanation-despite question, when the presuppositions of the question are correct, would be a violation of the Principle. This suggests that some of the attention focused on contrastive explanation in connection with critique of the PSR should be redirected towards explanation-despite. I think the PSR can survive such attention, but the investigation is worthwhile.

Tuesday, August 24, 2021

Theism and abundant theories of properties

On abundant theories of properties (whether Platonic universals or tropes), for every predicate, or at least every predicate satisfied by something, there is a corresponding property expressed by the predicate.

Here is a plausible sounding argument:

  1. The predicate “is morally evil” is satisfied by someone.

  2. So, on an abundant theory of properties, there exists a property of being morally evil.

  3. The property of being morally bad, if it exists, is thoroughly evil.

  4. So, on an abundant theory of properties, there exists something that is thoroughly evil.

  5. If theism is true, nothing that exists is thoroughly evil (since every entity is the perfect God or created by the perfect God).

  6. So if theism is true, an abundant theory of properties is false.

If I accepted an abundant theory of properties, I would question (3). For instance, maybe properties are concepts in the mind of God. A concept of something morally evil is not itself an evil concept.

Still, it does seem to me that this argument provides a theist with a little bit of a reason to be suspicious of abundant theories of properties.

An argument for nominalism

Assume theism. Then, there is nothing in existence that is intrinsically bad. For everything that exists is either God or created by God, and neither God nor anything created by God is intrinsically bad.

On radical nominalism, all that exist are substances: there are no relations, properties, tropes, accidents, essences, etc. And it is very plausible that no substance is intrinsically bad. The most plausible candidates for intrinsically bad things are non-substances, like properties (being in pain) or relations (being mistaken about something). Thus, radical nominalism has a neat and elegant way of preserving the theistic commitment to there not being anything in existence that is intrinsically bad.

This seems to me to be a significant advantage of radical nominalism over other theories.

Of course, this is not a decisive argument for radical nominalism: there are other ways of preserving the commitment to there not existing intrinsically bad entities, such as Augustine’s privation theory.

Monday, August 23, 2021

Anecdotal reasoning

Suppose I see a hypothetical click-bait article that says: “One thing you can do that science says doubles your chance of living past a hundred.” I foolishly click on it, and from the first paragraph find out that supposedly that thing is a serious photography hobby. Now, the idea isn’t crazy: having a serious hobby that can be pursued over a lifetime and that involves artistic and intellectual skills could well increase your lifespan. But I am reasonably sceptical.

Suppose for simplicity that after reading the first paragraph, I assign a credence of 1/2 to the null hypothesis N that there is no correlation between photography and living to a hundred and a credence of 1/2 to the hypothesis H that serious photography doubles the chance of living past 100.

Suppose I now tell my mother about the article, and she says: “Your great-grandma Alice was an avid photographer and she lived past 100!”

This is paradigmatically anecdotal evidence. But let’s do a quick and dirty Bayesian analysis. I just learned the fact E1 at least one of my eight great-grandparents was both a serious photographer and lived past 100. Let’s say for simplicity that each of my great-grandparents was born more than 100 years ago and had a 1% chance of living past 100 (some actual data is here), and that 15% of people are serious photographers. Then the conditional probability of my evidence E1 on the null hypothesis N is 1 − (1 − 0.01 ⋅ 0.15)8 or 1%, but on the doubling-chance hypothesis H it is 1 − (1 − 2 ⋅ 0.01 ⋅ 0.15)8 or 2.4%. Plugging these into Bayes’ theorem, I get a 67% posterior probability of H, and now I have a significant degree of credence in a photography-centenarianism link.

But suppose that instead of talking to my mother, I read further on in the article, and find after reading whatever scientific study spawned the article, the author found and interviewed a centenarian Bob who has been an avid photographer for half his life. What does that piece of anecdotal data do to my credence in the link between photography and a long life? Nothing! To a first approximation, the relevant fact I learned from the interview is the fact E2 that there exists at least one person in the world who was an avid photographer and lived past 100. And the conditional probability of E2 is very close to 1 on both H and N, so by Bayes’ theorem it doesn’t change my credences in H and N. (To a second approximation, I learned that the there was one person accessible to the author who was an avid photographer and lived past 100. And that is presumably slightly more likely on H and N. So I should get a slight boost in H, but only a slight one, since in the modern world we have access to lots of people.)

Now consider an intermediate case. Instead of talking to relatives, I share the article with a hundred people, and one of them writes back: “Wow! My tennis partner’s great-uncle Carl was an avid photographer and lived past 100.” Let’s over simplify by supposing that each of my hundred correspondents read the article and on average contributes ten people born more than 100 years ago to the sample. So from the first response, I have learned the fact E3 that in this sample of 500, there is at least one person who is a centenarian and a serious photographer. The probability of this on H is 95% and on N it is 78%. Plugging these into Bayes’ theorem, my credence in the photography-centenarianism link is 55%, which is a rather modest boost over my initial 50%. (The crucial point was that in the initial grandparents sample, the probability on H was double than on N, but now as both probabilities approach 100%, the ratio gets less impressive.)

There are some lessons here: If we are careful with our reasoning, anecdotal data can actually be quite relevant. Moreover, while it’s presumably been ingrained in us since high school science classes that larger sample sizes are better, for certain kinds of anecdotal data, smaller sample sizes are better. This is because the relevant information given by certain kinds of anecdotal data is positive: it is information that some sample contains at least one instance of some sort that is rare on both the null hypothesis and the alternate hypothesis (say, a photographer centenarian). In those cases, once the sample size gets large enough, the probability of the evidence on either hypothesis gets close to 1, and the evidential force disappears.

What this means is that for certain kinds of anecdotal data it makes perfect sense to be more impressed by an anecdote about oneself (a sample of one) than by an anecdote about a relative, and by an anecdote about a relative than by an anecdote about a friend’s friend, and to be essentially unmoved by an anecdote about a stranger on the Internet. And that is, I suspect, how most people actually proceed, notwithstanding blanket condemnations of anecdotal reasoning.

How can we do even better? Well, we should try to enrich our positive anecdotal data with other kinds of anecdotal data: Did I have centenarian relatives who weren’t photographers or photographer relatives who weren’t centenarians? All that would ideally be taken into account. But, nonetheless, if all I have is one positive anecdote, Bayesianism requires me not to dismiss it.

Thursday, August 19, 2021

A philosophical advantage of quantum mechanics over Newtonian mechanics

We often talk as if quantum mechanics were philosophically much more puzzling than classical mechanics. But there is also a deep philosophical puzzle about Newtonian mechanics as originally formulated—the puzzle of velocities—which disappears on quantum mechanics.

The puzzle of velocities is this. To give a causal explanation of a Newtonian system’s behavior, we have to give the initial conditions for that system. These initial conditions have to include the positions and velocities (or momenta) of all the bodies in the system.

To see why this is puzzling, let’s imagine that t0 is the first moment of the universe’s existence. Then the conditions at t0 explain how things are at all times t > t0. But how can there be velocities at t0? A velocity is a rate of change of position over time. But if t0 is the first moment of the universe’s existence, there were no earlier positions. Granted, there are later positions. But these later positions, given Newtonian dynamics, depend on the velocities at t0 and hence cannot help determine what these velocities are.

One might try to solve this by saying that Newtonian dynamics implies that there cannot be a first moment of physical reality, that physical reality has to have always existed or that it exists on an interval of times open at the lower end. On either option, then, Newtonian dynamics would have to be committed to an infinite temporal regress, and that seems implausible.

Another solution would be to make velocities (or, more elegantly, momenta) equally primitive with positions (indeed, some mathematical formulations will do that). On this view, that the velocity is the rate of change of position would no longer be a definition but a law of nature. This increases the number of laws of nature and the fundamental properties of things. And if it is a mere law of nature that velocity is the rate of change of position, then it would be metaphysically possible, by a miracle, that an object standing perfectly still for days would nonetheless have a high velocity. If that seems wrong, we could just introduce a technical term, say “movement propensity” (that’s kind of what “momentum” is), in place of “velocity”, and it would sound better. However, anyway, while the resulting theory would be mathematically equivalent to Newton’s, and it would solve the velocity problem, it would be a metaphysically different theory, since it would have different fundamental properties.

On the other hand, the whole problem is absent in quantum mechanics. The Schroedinger equation determines the values of the wavefunction at times later than t0 simply on the basis of the values of the wavefunction at t0. Granted, the cost is that we have a wavefunction instead of just positions. And in a way it is really a variant of the making-momenta-primitive solution to the Newtonian problem, because the wavefunction encodes all the information on positions and momenta.

Wednesday, August 18, 2021


If an explanation is a truth or hypothesis that removes or would remove mystery from the proposition to be explained, then an antiexplanation is a truth or hypothesis that adds or would add mystery to the proposition to be explained. Like in the case of explanations, we need to be sensitive to context with antiexplanations. That Alice dislikes bananas is, in typical contexts, antiexplanatory of why Alice ate the banana. But if we add to the background that it’s Lent and Alice wishes to do penance, then Alice’s dislike of bananas becomes explanatory.

It is widely held, though still moderately controversial, that:

  1. The fact that a hypothesis p is explanatory of some known truth is evidence for p.

A parallel claim about antiexplanations would:

  1. The fact that a hypothesis p is antiexplanatory of some known truth is evidence against p.

This sounds even more plausible than (1). In a typical context, the antiexplanatoriness of a dislike of bananas to actual consumption of a banana provides evidence that Alice who ate a banana does not dislike bananas. Similarly, the fact that Bob is in perfect health is antiexplanatory of Bob’s death, and hence if Bob has died, we have evidence that Bob’s health was imperfect.

There are lots of explanatory arguments in philosophy based on (1). But it would be worth exploring whether one can’t also give antiexplanatory arguments based on (2).

In fact, I think some fairly intuitive arguments can be rephrased as antiexplanatory arguments. For instance:

  1. Materialism is antiexplanatory of consciousness.

  2. Consciousness is a known fact.

  3. So, we have evidence against materialism.

The thought behind (3) is simply that there is intuitively something particularly mysterious about a purely material thing having a conscious point of view.

C. S. Lewis’s version of the moral argument for theism can be taken to be in part an antiexplanatory argument.

  1. Atheism is antiexplanatory of moral law.

  2. Moral law is a known fact.

  3. So, we have evidence against atheism.

Further evaluation of such arguments would call for a deeper philosophical analysis of antiexplanation and an examination of (2). This is a task worth doing. Someone should do it.

Thursday, August 12, 2021

Does general relativity lead to non-locality all on its own?

A five kilogram object has the determinable mass with the determinate mass of 5 kg. The determinate mass of 5 kg is a property that is one among many determinate properties that together have a mathematical structure isomorphic to a subset of real numbers from 0 to infinity (both inclusive, I expect). Something similar is true for electric charge, except now we can have negative values. Human-visible color, on the other hand, lies in a three-dimensional space.

I think one can have a Platonic version of this theory, on which all the possible determinate properties exist, and an Aristotelian one on which there are no unexemplified properties. There will be important differences, but that is not what I am interested in in this post.

I find it an attractive idea that spatial location works the same way. In a Newtonian setting the idea would be that for a point particle (for simplicity) to occupy a location is just to have a determinate position property, and the determinate position properties have the mathematical structure of a subset of three-dimensional Euclidean space.

But there is an interesting challenge when one tries to extend this to the setting of general relativity. The obvious extension of the story is that determinate instantaneous particle position properties have the mathematical structure of a subset of a four-dimensional pseudo-Riemannian manifold. But which manifold? Here is the problem: The nature of the manifold—i.e., its metric—is affected by the movements of the particles. If I step forward rather than back, the difference in gravitational fields affects which mathematical manifold our spacetime is isomorphic to. If determinate position properties are tied to a particular manifold, it means that the position of any massive object affects which manifold all objects are in and have always been in. In other words, the account seems to yield a story that is massively non-local.

(Indeed, the story may even involve backwards causation. Since the manifold is four-dimensional, by stepping forward rather than backwards I affect which four-dimensional manifold is exemplified, and hence which manifold particles were in. )

This is interesting: it suggests that, on a certain picture of the metaphysics of location, general relativity by itself yields non-locality.

Wednesday, August 11, 2021

Free will and the PSR

Even though I think one of the biggest challenges to the Principle of Sufficient Reason (PSR) is the feeling that something is unexplained in the case of free actions. I think this can be answered: see Section 4 here. But in this post I want to make a very small and simple point that just occurred to me.

The puzzle of free actions is not the lack of reasons. It is a surfeit of reasons. Suppose I eat a donut rather than an apple. It is easy to give a reason: the donut is more delicious. If that’s all we had, there would be no felt difficulty about the explanation. But the felt difficulty comes from the fact that while the donut is more delicious, the apple is more nutritious, and hence while I have a reason for eating the donut rather than the apple, I also have a reason for eating the apple rather than the donut.

But while a shortage of reasons would be a problem for a principle like the PSR that affirms the existence of reasons, a surfeit of reasons is not a problem for it!

So whatever one might say about the puzzle of free will, it is not problem for the PSR.

Tuesday, August 10, 2021

The Theotokos and personhood

Catholics and the Orthodox insist that Mary is the Theotokos—the Godbearer. The child in her womb was God.

It follows that this child she bore in her womb was a person. For the child was God by virtue of the Incarnation, and the Incarnation consists precisely of the union of two natures in one person. Moreover, the Incarnation is a process of God becoming a human being. So that person in her womb was also a human being.

Thus, the human being Jesus, while in Mary’s womb, was a person. Now, Jesus is like us in all things but sin. So, while we are in our mothers’ wombs, we already are persons.

A theory of personhood or personal identity that requires human persons to have developed human mental functioning—like Warren’s theory of personhood or Locke’s theory of personal identity—conflicts with the Catholic and Orthodox teaching on Mary the Mother of God.

My mother gave birth to me

  1. My mother gave birth to me.

  2. I have no memory connection, direct or indirect, to me at birth.

  3. Therefore, the memory theory of identity is false.

Eternalism and future non-existence

I go back and forth on whether this is a strong argument against eternalism:

  1. Given eternalism, it is guaranteed to be eternally the case that one exists simpliciter, even if one’s existence comes to an end.

  2. Given eternalism, one’s existence coming to an end is just finitude in the forwards temporal direction.

  3. If it is guaranteed to be eternally the case that one exists simpliciter, finitude in the forwards temporal direction would not be something to be dreaded.

  4. So, given eternalism, one’s existence coming to an end would not be something to be dreaded. (1–3)

  5. One’s existence coming to an end would be something to be dreaded.

  6. So, eternalism is false. (4–5)

(As a theist, I think our existence does not come to an end. Hence the hypothetical “would” in (5).)

The intuition behind (3) is that finitude in the forwards temporal direction, given that one exists simpliciter, is akin to finitude in the backwards temporal direction or along a spatial axis, and these are clearly not to be dreaded.

But, on reflection, I think the eternalist can make very good sense of the appropriate attitudes to an end of existence. Consider this: If I were threatened with amputation of the part of me below the head—i.e., with being reduced to a head in a life-support tank—that would be something to be dreaded. It would be something to be dreaded, because the kind of functioning that is natural to human beings requires the below-the-head portion of the body. On the other hand, we could imagine sessile aliens that are very much like human heads, and there is nothing dreadful about the life of these aliens. These aliens’ lack of the below-the-head functioning normal humans enjoy would not be a deprivation.

Thus, human flourishing has spatial requirements: we require all of our body to fully flourish. Similarly, human flourishing has a robust temporal requirement: it requires an eternal future. This is because of the nature of human flourishing. Plausibly, human flourishing has a drive to infinity, requiring endless growth knowledge of reality and relationship with others. (This is probably not the whole story, but it will do for this post.) But our flourishing does not require spatial unlimitedness—on the contrary, there is a maximum size along each spatial axis such that a human being that is too big along that axis is not a fully flourishing human being.

We are four-dimensional beings, and we require a specific four-dimensional shape to flourish: a shape that is not too small and not too large in the three spatial directions and that is infinite in the forwards temporal direction. A finite future is a terrible truncation.

Now not every animal is like humans. Brute animals do not require an eternal future to be fully flourishing: they can achieve complete flourishing in a finite life, say because the lack the drive to the infinite that humans have. If we were like that, it would not be appropriate for us to dread future non-existence. Not being inclined to dread future non-existence is hard for us to imagine, because the drive to the infinite arises from such deep features of our nature. But philosophically, it makes perfect sense to think that there could be beings that can complete their flourishing in a finite compass.

The eternalist’s seeing a future end of existence of a human as a terrible truncation, but as not necessarily a terrible truncation in a non-human, seems very compelling. On the other hand, I think it is harder for a presentist to make sense of the difference here. Future non-existence seems really bad, because future non-existence on presentism would imply that eventually one will not exist simpliciter, and that seems dreadful. But the dreadfulness of this seems to have to do with the value of existence simpliciter, and not with our nature. Thus, we may have a story as to why it would make sense for a presentist to dread an end to existence, but that story proves too much: for that story would apply even if the presentist were the kind of non-human that doesn’t need an infinite future for flourishing.