The Hermes in the marble

A substance’s existence does not ontologically depend on the state of anything beyond the substance. But a typical artifact depends on absences of materials beyond itself. A classic example is a statue that comes into existence when the surrounding marble is removed. The statue’s existence is grounded in part in the absence of the surrounding marble. Similarly, even if a knife blade is made by forging rather than by removal of material, one can destroy the blade by encasing it in a block of steel: the existence of the knife is grounded in part in the absence of surrounding steel.

Thus, it seems, typical artifacts are not substances.

But this argument was too quick. What if the laws of nature are such that the following is true? When the sculptor chips away the surrounding marble to make the Hermes, a non-physical component, a form, of the Hermes comes into existence. That form is united with the Hermes’ matter. And what makes the statue be itself is not the absence of surrounding matter, but the presence of the form. It may be that by the laws of nature the form only comes into existence as a result of the removal of material, but it would be logically possible for the form to come into existence without any removal: the statue causally but not ontologically depends on the absence of surrounding material. God could make the statue within the block of marble, without any removal of material, simply by creating a form for a Hermes-arranged subset of marble molecules.

(One could also have a non-Aristotelian version of this account in terms of Markosian’s brute theory of composition.)

I think the above Aristotelian story is implausible. One reason is that the story conflicts with our intuitions as to the survival conditions for artifacts. A statue is essentially a statue. But the Hermes-shaped bundle of atoms in the block marble, even if distinguished by a metaphysical union with a form, are not a statue. Maybe God could make a form for these atoms, but it wouldn’t be the form of an artifact.

Riots and textualism

I keep on wondering about how it is that legislators seem to be completely oblivious to obvious counterexamples. Take the definition of a riot in Texas law:

For the purpose of this section, “riot” means the assemblage of seven or more persons resulting in conduct which: (1) creates an immediate danger of damage to property or injury to persons; (2) substantially obstructs law enforcement or other governmental functions or services; or (3) by force, threat of force, or physical action deprives any person of a legal right or disturbs any person in the enjoyment of a legal right.

Note some curious things. First, there is no restriction in (1) to unauthorized damage to property. Thus, a team of seven demolishing an old building or a party of seven friends eating up a pizza constitute a riot, no matter how sedately they go about their business.

Second, neither is there a restriction to reasonably expected danger to property or persons. Thus, it counts as a riot when seven people walk on an unsound bridge, even when they do not know the bridge to be unsound. Fortunately, in this case, although the definition of a riot is satisfied, such participation in a riot is not an offense, since according to the what comes later, it’s only an offense when one “knowingly participates in a riot”.

There are counterexamples to (2) as well. Thus, consider a team of seven building inspectors who inform a local government office that the office walls are full of black mold. As a result, the office closes for a week while relocating to a temporary location. The conduct of the building inspectors substantially obstructed “governmental functions or services”.

Maybe governments should have bug trackers for laws, aimed solely at cases where the law’s wording does not match the intent.

Or maybe this is just an argument for originalism over textualism in legislative interpretation. One assumes that the Texas legislature did not wish to criminalize the consumption of a meal by seven or more people, even if the plain sense of the words classifies such consumption as a riot. (Though there is a potentially tricky interpretive question in the “knowingly participates in a riot”. Is it enough to know that one’s conduct satisfies conditions (1), (2) or (3), or does one have to know explicitly that it satisfies the definition of a “riot”. A typical group of seven people eating a meal do know that the food they eat is property that is being destroyed, but unless they are lawyers or law geeks, they don’t know that the law classifies such destruction as a riot. Perhaps the legislature wished to outlaw meals had by seven or more lawyers or law geeks?)

Behaviors that look like risk aversion but aren't

Technically, risk aversion is the phenomenon of valuing risky propositions at a value lower than their expected value. But I think in ordinary use of the phrase “risk averse”, we mean something different.

I consider myself a pretty risk-averse individual. Not infrequently, when I consider the possibility of myself or a child engaging in some activity, I spend a significant amount of time looking up the data on the risks of that activity, and comparing those to risks of other activities. And I spend time worrying about bad things that might happen. Thus, even though deaths from brain-eating amoebae are very rare (one per 1.2 years in Texas), if I were to swim with head submersion in a Texas lake or river, I know I would worry for the next week and a half (especially if I had anything approximating the symptoms of an amoeba infection, say a crick in the neck) in a way that would make the swim not have been worth it.

But while both my risk-investigation and risk-worrying make me “risk averse” in the ordinary sense, neither makes me clearly risk averse in the technical sense.

For risk-investigation behavior to count as risk averse in the technical sense, it would have to be that the expected value of the results of the investigation is lower than the value of the time I am willing to invest in the investigation. Whether this is true is a difficult to say. Sometimes at least the investigation concerns an activity that, if engaged in, would likely be engaged in repeatedly. In such a case, it might well be worth-while to devote a fair amount of time to investigating the risk-profile of the activity. If my child were to play soccer, they would likely be playing soccer for multiple years, each time undertaking the concussion risks from heading the ball (I would not allow a child of mine to play soccer unless I knew they were willing to consistently stand up to their coach and refuse to head the ball). The cost of spending an hour or two looking at sports-medicine research does not seem to be excessive as compared to the expected value of making a less-informed versus a more-informed decision. Moreover, the investigation itself is often interesting—I learn things that are interesting to know that offset much if not all the cost of the investigation. Finally, if the investigation leads to the conclusion that the risks of an activity are low, my future worries will be less.

Risk-worrying, on the other hand, does not even prima facie classify one as risk averse in the technical sense. Positive and negative emotional outcomes of a decision are simply a part of the utilities. Suppose that I am willing to pay $10 in order to avoid a situation where I have a 0.5 chance of losing $1000 and a 0.5 chance of gaining $1000, because if I don’t pay, I will worry that I will lose $1000. In that case, paying the $10 has an expected disvalue of $10, while not paying has an expected disvalue of $0 plus the disvalue of my negative emotional state. That emotional state might well be worth paying $10 to avoid, but if so, there is nothing risk averse in the technical sense about this decision.

So, some of the behaviors that intuitively would classify one as risk averse do not in fact show one to be risk averse in the technical sense. It would be interesting to see if there is a correlation between those behaviors, however, and risk aversion in the technical sense. There might be.

A related interesting empirical question is how to tell technical risk aversive behavior apart from simply taking worry-like states into account in one’s expected utility calculations. I think it can be done. For instance, if my main reason for avoiding risks is the disvalue of worrying, then I will be less willing to take risks that are resolved in the distant future than to take risks that are resolved in the near future. For with the distant risks, I have more time to worry, while the near risks will be resolved quickly, so the total amount of worry should be rather less. Interestingly, most people aren’t like that: they are more risk-avoidant in the case of immediately resolving risks than in the case of risks with temporally distant resolution. Hence, their risk avoidance is not based on simply rationally weighing the disvalue of worrying.

What I think of ontological nihilism

A commenter asked me what I thought of ontological nihilism, the view that there are no subjects. Here’s what I think: Everybody who accepts this view is wrong.

1. Ontological nihilism is true or false.

2. If ontological nihilism is true, nobody exists.

3. If nobody exists, then there is nobody who accepts ontological nihilism.

4. If nobody accepts ontological nihilism, then everyone who accepts ontological nihilism is wrong.

5. So, if ontological nihilism is true, then everyone who accepts it is wrong. (2-4)

6. If ontological nihilism is false, then everyone who accepts it is wrong.

7. So, everyone who accepts ontological nihilism is wrong. (1,5,6)

Existence

In his famous critique of the ontological argument, Kant said that existence is not a property. Frege and Russell gave a very influential response to Kant (though not framed as such): the existence of an object is not a property of the existent object, but it is a second-order property of an abstract object. Thus, the existence of Biden is the second-order property of being instantiated possessed not by Biden himself but by the abstract object Bidenness.

But now consider this very plausible principle:

1. The existence of an object is explanatorily prior to all the (other) properties of that object.

The parenthetical “other” is included to make (1) acceptable both to Frege-Russell and to “pre-Kantians” who think existence is a property of the existent object.

But combining (1) with the Frege-Russell account leads to an explanatory priority regress:

• Biden’s maleness is posterior to Biden’s existence.

• Biden’s existence is Bidenness’s being instantiated.

• Bidenness’s being instantiated is posterior to Bidenness’s existence.

• Bidenness’s existence is Bidennessness’s being instantiated.

• Bidennessness’s being instantiated is posterior to Bidennessness’s existence.

• Bidennessness’s existence is Bidennessnessness’s being instantiated.

• …

How can we arrest this regress? A natural move is to restrict the Frege-Russell view of existence to contingent entities. Thus, Biden’s existence is the instantiation of Bidenness, but Bidenness is a necessary entity, and its existence is not the instantiation of some further entity. Indeed, perhaps, the pre-Kantian view holds of Bidenness: Bidenness’s existence could just be a property of Bidenness.

Note that if the pre-Kantian view holds of necessary beings, then Kant’s critique of the ontological argument falls apart, since God is a necessary being.

But let’s think through the pre-Kantian view a little bit. Suppose that x is an object and e is its existence, and suppose e is a property of x. But how can x possess e without already existing prior to having e? (I.e., surely, (1) is true with the parenthetical “other” removed.) There seems to be one possible move here: perhaps x = e. That would be a view on which some objects are identical with their own existence—a view very much like St. Thomas’s, who held that God, and God alone, was identical with his own existence.

So, interestingly, thinking the Frege-Russell view through leads fairly naturally to a view like Thomas’s.

I am attracted to this variant of the Thomistic view:

2. Uncaused objects are identical with their existence.

3. The existence of a caused object is its being caused.

The worry that an object cannot possess a property without “already” existing does not appear pressing when the property in question is being caused.

Moreover, we might even more speculatively add:

4. An object’s being caused is its cause’s causing of it.

On this view, a contingent thing’s existence, like on the Frege-Russell view, is a property of something other than the thing: it is a property of the cause (perhaps an extrinsic property of the cause, when the cause is God, so as not to violate divine simplicity).

Contrast, Serif and Justify

I was trying to read Locke online, but was annoyed by the fact that the font was dark gray instead of black and sans serif, neither of which is great for extended reading. So I made two bookmarklets: Contrast and Serif. Just drag them to your bookmark bar and click on them to run them on a page. The Contrast one snaps all fonts to white or black (depending on background color) or blue (if it's a link) and adjusts near-black/white page backgrounds to black/white.

Update 1: Justify may also help. And, finally, Reader combines all three functions.

Update 2: Sepia is sometimes nice.

Update 3: See also my Blacker Text extension.

Cartesian-style ontological arguments

Cartesian-style ontological arguments run like this:

1. God has all perfections.

2. Existence is a perfection.

3. So, God exists.

These arguments are singularly unconvincing. Here is a simple reason they are unconvincing. Suppose we are undecided on whether there are any leprechauns and, if so, whether they have a king, and someone tells us:

4. The leprechaun king is very magical.

This sure sounds plausible in a certain frame of mind, and we may accept it. When we accept (4), while remaining undecided on whether there are leprechauns and, if so, whether they have a king, what we are accepting seems to be the conditional:

5. If the leprechaun king exists, he is very magical.

By analogy, when the agnostic accepts (1), it seems they are accepting the conditional:

6. If God exists, God has all perfections.

Given premise (2), we can conclude:

7. If God exists, God exists.

But every atheist accepts (7).

It seems to make little difference if in (2) we replace “existence” with “necessary existence”. For then we just get:

8. If God exists, God necessarily exists.

That’s not quite as trivial as (7), but doesn’t seem to get us any closer to the existence of God.

The above seems to perfectly capture why it is that Cartesian-style ontological arguments are unconvincing.

Even if the above is adequate as a criticism of Cartesian-style ontological arguments, I think there is still an interesting question of what sort of a conditional we have in (5)–(8)?

It’s not a material conditional, for then (5) would be trivially true given that there are no leprechauns, while (5) is non-trivially true.

Should it be a subjunctive conditional, like “If the leprechaun king existed, he would be very magical”? I don’t think so. For suppose that in the closest possible leprechaun world to ours, for some completely accidental reason, the leprechaun king is very magical, but in typical possible worlds with leprechauns, leprechaun kings are are actually rather a dud with regard to magicality. Then it’s true that if the leprechaun king existed, he would be very magical, but that shouldn’t lead us to say that the leprechaun king is very magical.

Perhaps it should be a strict conditional: “Necessarily, if the leprechaun king exists, he is very magical.” That actually sounds fairly plausible, and in light of this we would actually want to deny (4). For it is not necessary that the leprechaun king be very magical. But if we take it to be a strict conditional, we still have a triviality problem. Imagine an atheist who thinks that God is impossible. Then the strict conditional

9. Necessarily, if God exists, God has all perfections

is true, but so is:

10. Necessarily, if God exists, God has exactly 65% of the perfections.

But while it seems that our atheist would be likely to want to say that God has all perfections (indeed, that might be a part of why the atheist thinks God necessarily does not exist, for instance because they think that the perfections are contradictory), it doesn’t sound right to say that God has exactly 65% of the perfections, even if you think that necessarily there is no God.

I think the best bet is to make the conditional be a strict relevant conditional:

11. Necessarily and relevantly, if God exists, God has all perfections.

It is interesting to ask whether (11) helps Cartesian-style ontological arguments. Given (11), if all goes well (it’ll depend on the modal relevance logic) we should get:

12. Necessarily and relevantly, if God exists, God exists.

That sounds right but is of no help. We also get:

13. Necessarily and relevantly, if God exists, God necessarily exists.

Again, that sounds right, and is less trivial, but still doesn’t seem to get us to the existence of God, barring some clever argument.

Being a (counter)example

Consider a case where there is a spectrum of behaviors such that without considering influence on others A is bad, B is moderately good and C is the best. It seems likely (by analogies to the studies on political opinions hardening in the face of opposition) that sometimes when people see someone engaging in behavior radically different from theirs, this strengthens their commitment to their own behavior. Thus, someone who does A upon seeing someone do C might be hardened in doing A. One might easily think about the person doing C: “That behavior is really out there, and so only crazy people don’t do A”. On the other hand, seeing someone do B might actually shift one’s behavior away from A.

And so we can imagine a case where although C is best when one doesn’t consider influence on others, the difference between B and C is sufficiently narrow, that overall it is better to do B, because one is more likely to influence others for good by doing B rather than the “crazy” C.

On the other hand, no doubt there are cases where seeing the radicality of another’s behavior, and the contrast between that radicality and one’s behavior, could shake one up. Thus, when I was a teenager, I was converted from some of my sins upon reading Augustine’s Confessions and seeing the contrast between my sinful ways and the radical holiness that Augustine strove for. Had Augustine only striven for B in contrast to my A, I perhaps wouldn’t have been converted. But he strove for C, and that impressed me.

What’s the lesson? I don’t know. Maybe just this: Absent specific data about the likely influence of one’s actions in a particular case, maybe we do best to do what’s best without considering the influence.

Theism and Natural Law

One occasionally wonders what theism adds to Natural Law ethics. Here is one example.

• Q1: Why are artistic endeavors good?

Here, Natural Law answers by itself, without any help from theism:

• A1: Because they fulfill the human nature.

We can ask another question:

• Q2: Why do artistic endeavors fulfill the human nature?

Again, Natural Law answers by itself in a not very informative way:

• A2: Because necessarily the human nature teleologically directs its possessors to artistic endeavors.

But we can now ask a different question:

• Q3: Why are there beings with a nature that teleologically directs its possessors to artistic endeavors?

Natural Law by itself has no answer. Theism can go on to answer Q3:

• A3: God created beings with such a nature because artistic endeavors imitate God, who is the Good Itself.

One might say that Q3 is an etiological rather than normative question, and hence lies beyond the scope of value theory. But A3 also answers a value-theoretic variant of Q3:

• Q3a: What is it about artistic endeavors that makes them apt for being intrinsically good for a being, apt for being the telos of a nature?

To see the force of Q3a, imagine that we meet aliens and they spend a lot of time and energy on some activity that does not seem to conduce to or constitute any biological end of theirs, and does not seem to promote any end that we can understand. We ask the aliens about why they do this activity, and they say: “It’s good for us in and of itself, and our observation of your culture shows that you have no concept of this type of good.” They are otherwise smart and morally sensitive, so we trust that the activity is good for them, that it is a telos of their nature.

But even after we have learned that the activity is a telos of their nature and hence intrinsically good for them, we would be puzzled by the activity, and what makes it apt for being a good for them. A theistic story about how this good imitates God provides an answer to this kind of a question.

The question suggests, too, that not everything is apt for being good for a being, that not everything is apt for being the telos of a nature. And that, too, seems right. It does not seem that one could have a being for which the production of ugliness or the promotion of the suffering of others is intrinsically good. But I think only a theist can say something like that.

Indeed, this last point suggests another way in which theism helps Natural Law. Consider this objection to Natural Law:

• Cruelty would be wrong even for beings whose nature it was to be cruel, but according to Natural Law, if a being’s nature were to be cruel, cruelty would be right for that being.

But the theist can do something to help with this: cruelty is just not the sort of thing that a nature could aim at, since it is counterimitative of God. So the conditional about beings whose nature is to be cruel is a per impossibile one. And it is not surprising if strange results follow from impossible suppositions.

The weird view that particles don't survive substantial change

I have a weird view: when a dog or another substance ceases to exist, all its particles cease to exist, being replaced by new particles with very similar physical parameters (with the new physical parameters being predictable via the laws of nature). Similar things happen when a new substance comes into existence, and when a particle is incorporated into or leaves a substance: no particles survive such things.

I have good Aristotelian reasons for this view. Particles are not substances, since substances cannot have substances as parts, and hence ontologically depend on substances for their existence. Thus, when the substance perishes, the particles do as well.

The view seems preposterously unparsimonious. I disagree. Let’s compare the view to some competitors. First of all, it’s clear to me that some version of four-dimensionalism is true, so let’s start with four-dimensionalist views.

A standard four-dimensionalism is perdurantism: four-dimensional objects are made up of instantaneous temporal parts—infinitely many of them if time is continuous. These instantaneous temporal parts come in and out of existence all the time, with very similar physical parameters to their predecessors. My weird view is compatible with the idea that particles actually all exist only instantaneously, akin to the perdurantist’s temporal parts. Such a view could be more parsimonious than standard perdurantism for two reasons: first, it needn’t posit temporal parts of substances, and, second, it needn’t posit wholes made up of the instantaneous particles.

An alternate version of my weird view says that particles do not survive change of substance, but live as long as they recognizably remain in the same substance. Imagine a particle that is eaten by a dog and some months later sloughed off. On my view, there are three particle-like objects in the story: the pre-dog particle, the in-dog particle, and the post-dog particle. On standard perdurantism, there are as many particle-like objects as moments of time in this story. Granted, some may think it weirder that the temporal boundaries in the existence of particles are determined by their allegiances to substances rather than by instants of time. But there is nothing weird about that if one takes seriously the priority of substances to their parts.

My view is admittedly less parsimonious than a four-dimensionalist view on which substances and particles are temporally extended, have no temporal parts, and particles outlast their substances. But such a four-dimensionalist has an implausible consequence. Many people will find plausible the idea that in some exceptional cases substances can share parts: conjoined twins are a standard example. But on this version of four-dimensionalism, it is now a matter of course that distinct substances share parts. The dog dies and some of its particles become a part of a flower: so the dog and the flower, considered as four-dimensional entities, have these particles as common parts. You and I share probably share parts with dinosaurs. So while my weird view is less parsimonious than a no-temporal-parts four-dimensionalism with particles that outlive substances, it is not less plausible.

The main alternative to four-dimensionalism is presentism. Is a presentist version of my view less parsimonious than a typical competing presentist view? In one sense, not. For at the present time, my view doesn’t posit additional present particles over and beyond those present particles posited by competing presentist views. And only present particles exist according to presentism! But more seriously, my view does posits that particles cease to exist and come into existence more than on typical presentist alternatives. So in that sense it is less parsimonious.

Thus, parsimony cuts against my view on presentism, but it may actually favor it on four-dimensionalism.

Is our universe of sets minimal?

Our physics is based on the real numbers. Physicists use the real numbers all over the place: quantum mechanics takes place in a complex Hilbert space, and the complex numbers are isomorphic to pairs of real numbers, while relativity theory takes place in a manifold that is locally isomorphic to a Lorentzian four-dimensional real space.

The real numbers are one of an infinite family of mathematical objects known as real closed fields. Other real closed fields than the real numbers could be used in physics instead—for instance, the hyperreals—and I think we would have the same empirical predictions. But the real numbers are simpler and more elegant: for instance, they are the only Dedekind-complete and the minimal Cauchy-complete real closed field.

At the same time, the mathematics behind our physics lives within a set theoretic universe. That set theoretic universe is generally not assumed to be particularly special. For instance, I know of no one who assumes that our set theoretic universe is isomorphic to Shepherdson’s/Cohen’s minimal model of set theory. On the contrary, it is widely assumed that our set theoretic universe has a standard transitive set model, which implies that it is not minimal, and few people seem to believe the Axiom of Constructibility which would hold in a minimal model.

This seems to me be rationally inconsistent. If we are justified in thinking that the mathematics underlying the physical world is based on a particularly elegant real closed field even though other fields fit our empirical data, we would also be justified in thinking it’s based on a particularly elegant universe of sets even though other universes fit our empirical data.

(According to Shipman, the resulting set theory would be one equivalent to ZF + V=L + “There is no standard model”.)

From naturalism to divine command theory by way of vagueness

Plausibly:

1. There is a collection K of atoms forming an early stage of the developmental history of a particular human, where it is vague whether it is morally permissible to disperse the atoms in K.

Pro-choice readers might take K to be the collection of atoms in a late fetus or an early newborn. Pro-life readers might take K to be the collection of atoms at some early point during the fusion of gametes. (Note that (1) does not say that the atoms in K form a human.)

It is widely held that:

2. Vague matters always depend on semantic plasticity.

But:

3. Whether it is permissible to disperse the atoms in K does not depend on any semantic questions.

Claims (1)–(3) look incompatible. So we should abandon at least one of them. Personally, as a pro-life Aristotelian dualist, I am happy to abandon (1)—whether it is permissible to disperse the Ks depends on whether there is a human form uniting the Ks, and that’s not a vague matter. But apart from a Markosian-style brute fact view of composition—a view that seems implausible—it seems hard for a naturalist to deny (1).

Claim (2) is pretty plausible.

This means that if we accept (1), we should deny (3). But how to deny (3)? How could the question of whether it is permissible to disperse the atoms at some developmental stage depend on semantic questions? Surely it is a totally abhorrent idea that whether it is acceptable to disperse the atoms in K is determined by our linguistic performances?

Indeed! But it need not depend on the semantics of our linguistic performances. There is exactly one major moral theory that make that allows for a reasonable denial of (3): divine command theory. Commands are linguistic performances. Whether some act violates a command is in part a linguistic matter. Given divine command theory, semantic plasticity in the terms of the commands can ground vagueness in the obligations constituted by the commands. If your commander says: “Shave until you’re bald”, your obligation seems to be vague precisely because of the vagueness of language.

And that the semantics of God’s linguistic performances matters to the right to life of K is far from as objectionable as some claim on which our linguistic performances have the determining role. (Though our linguistic performances have some role to play, since they may help define the words that God is using if God speaks our language.) Thus, we can imagine that God says: “Thou shalt not murder.” But perhaps “murder” is vague. And the vagueness in this word then translates to vagueness as to whether the dispersal of the atoms in K is permissible.

If the above is right, then we have an argument for a very surprising thesis:

4. If physicalism (about us) is true, then divine command theory is the correct moral theory, and hence God exists.

This is yet another in a series of observations that I’ve been making over the years, that theistic naturalism has resources that its atheistic cousin lacks.

All that said, I think physicalism (even about us) is false, and divine command theory is not the correct moral theory. Though I do think God exists.

Vagueness about moral obligation

There is a single normative property that is normatively above all others, that overrides all others: moral obligation.

I think the above intuition entails that there cannot be any non-epistemic vagueness about moral obligation.

There are two main non-epistemic approaches to vagueness: deviant logic and supervaluationism. Deviant logic is logically unacceptable. :-) That leaves supervaluationism. But on supervaluationism, there would have to be many acceptable precisifications of our concept of moral obligation. Each such precisification would presumably be a normative property. But only a precisification that was normatively above all others could be an acceptable precisification of our concept of moral obligation. And there can only be one precisification above all others. So there can only be one acceptable precisification of moral obligation.

The above argument is too quick. The supervaluationist can say that in the claim “Moral obligation is above all other normative properties”, we have another candidates for vagueness: “above” (or “overrides”). Then we need to engage in coordinated precisification of “moral obligation”, as well as “above”. For each coordinated precisification, the aboveness claim will be true: “Moral obligation_i is above_i all other normative properties.”

I think, however, that once we allow for a variety of precisifications of “above”, we betray the intuition behind the aboveness thesis. That in some sense moral obligation is above personal convenience is not the bold and bracing intuition of the overridingness of morality. Thus, I think that if we are to be faithful to that intuition, we cannot allow for non-epistemic vagueness about moral obligation.

And this, in turn, greatly limits how much non-epistemic vagueness there can be. For instance, if there is no vagueness about permissibility, then it cannot be vague whether something is a person, since vagueness about personhood leads to vagueness about moral obligations of respect. Indeed, it is not clear that there can be any non-epistemic vagueness if there is no non-epistemic vagueness about moral obligation. Suppose I promise to become bald, and I have a small amount of hair. Then I am non-bald if and only if I am obligated to remove some hair.

Personal escape?

I'm now fully vaccinated, so through the wonders of modern medicine I'm deeming myself to have likely escaped COVID-19, while sadly aware that so much of the world is still struggling (I pray that vaccine patent waivers will go through and help).

I've been so very fortunate, unlike so many. Starting with August, the pandemic had little negative personal impact. On the contrary, being masked and distanced made me feel more comfortable around other people, and having conference and lecture travel be replaced with online events was wonderful. It would be great, for convenience, cost and environmental reasons, if conferences continued online indefinitely, hopefully with technical progress on getting informal interactions working better. (My experience is that the formal discussions at conferences are intellectually every bit as good when online, at least when the same people are in attendance.)

Since April 2020, I had exactly four occasions where I was within two meters of someone not from my household for 15 minutes or more in a 24-hour period. Two of them were dental visits. And two were Uber rides between home and the car repair shop. For the two Uber rides, I wore my "industrial-looking" elastomeric 3M P100 respirator (with an added exhalation filter), so I was quite safe--alas, it wasn't practical to do that for the dental visits.

For church and grocery stores, I usually used the 3M respirator. For the gym, I have a Trend woodworking N100 respirator (eventually modified to remove valves and block the exhale port). In both cases, I was quite safe and so were others around me.

Apart from one lecture moved online due to snow and one online due to a false COVID alarm (on the basis of two negative tests, I eventually concluded it was just a bad cold), I taught in person in both fall and spring. For teaching, I used cheap but heavily modified five-layer KN95 masks, because I was much more audible through them than through cloth, not to mention elastomeric respirators. Of course, I usually had some students Zooming in, often for COVID-related reasons but sometimes probably for more minor reasons.

I am not quite sure how I will modify my protocols now that I am fully vaccinated. My 3M and Trend elastomeric masks are very breathable, and keep the filter material away from my sweaty face, so I may end up still using the Trend mask for the gym. I may replace its N100 filters with 3D printed filters based on surgical mask material, though. I have considered continuing social distancing for the rest of my life in order to reduce the transmission of all respiratory diseases. Neither the flu nor even the common cold are enjoyable, and my personal utilities are such that if social distancing were to prevent the flu, it would be worth it, since given my white collar occupation and given that I live in a smallish town, it's only a slight inconvenience to distance myself under most circumstances, and it's intrinsically pleasant to have more personal space. However, since other people in my household aren't going to distance themselves from strangers once the pandemic is over, I suspect that my personal distancing would not do much to keep me from getting respiratory diseases at that point. I may make an effort to try for at least a meter of distance in most circumstances when interacting with people outside the household--but that is anyway within the range of North American proxemic zones.

Unicorns and error theory

Kripke famously argued that unicorns cannot exist. For “unicorn” would have to refer to a natural kind. But there are multiple non-actual natural kinds to which “unicorn” could equally well refer, since it’s easy to imagine worlds w₁ and w₂ in each of which there is a natural kind of animal that matches the paradigmatic descriptions of unicorns in our fiction, but where the single-horned equines of w₁ are a different natural kind (at the relevant taxonomic level) from the single-horned equines of w₂. The proposition p expressed by “There are unicorns” is true in one of the worlds but not the other, or in both, or in neither. Symmetry rules out its being true in one but not the other. It can’t be true in both, because then “unicorn” would refer to two natural kinds (at the relevant taxonomic level), while it arguably refers to one (at least if we index it to a sufficiently specific body of fictional work). So, the proposition must be true in neither world, and by the same token, there will be no world where it’s true.

It seems to me, however, that rather than saying that the proposition expressed by “There are unicorns” is impossible, we should say that “There are unicorns” fails to express a proposition. Here’s why. We could imagine Rowling enriching the Harry Potter stories by introducing a new species of animals, the monokeratines. Suppose she never gives us enough detail to tell the two species apart, so all the descriptions of “unicorns” in her stories apply to “monokeratines” and vice versa, but she is clear that they are different species (perhaps the story hinges on one of them being an endangered species and the other not).

Now, if “There are unicorns” in these (hypothetical) stories expresses a proposition, so does “There are monokeratines”. But if they express propositions, they express different propositions (neither entails the other, for instance). Thus, suppose “There are unicorns” expresses p while “There are monokeratines” expresses q. But no reason can be given for why it’s not the other way around—why “There are unicorns” doesn’t express q while “There are monokeratines” expresses p. In fact, the exact same reasoning why Kripke rejected the hypothesis that “There are unicorns” is true in one of w₁ and w₂ but not in the other applies here. Thus, we should reject the claim that either sentence expresses a proposition.

But if we do that, then we should likewise reject the claim that in the actual world, where Rowling doesn’t talk about monokeratines, “There are unicorns” expresses p (say). For it could equally well express q.

Maybe.

But maybe there is another way. One could say that “There are unicorns” is vague, and handle the vagueness in a supervaluationist way. There are infinitely many species u such that “There are unicorns” can be taken to be precisified into expressing the proposition that there are us. Thus, there is no one proposition expressed by the sentence, but there are infinitely many propositions for each of which it is vaguely true that the sentence expresses it.

This might be a good response to my old argument that error theorists should say that “Murder is wrong” is nonsense. Maybe error theorists can say that “Murder is wrong” has infinitely many precisifications, but each one is false, just as “There are unicorns” has infinitely many precisifications, but each one is false.

This suggests a view of fiction on which claims about fictional entities always suffer from vagueness.

An interesting thing is that on this approach, we need to distinguish between in-story and out-of-story vagueness. Suppose a Rowling has a character say “There are unicorns.” In-story, that statement is not vague. I.e., according to the story there is a specific species to which the word “unicorn” as spoken by the character definitely refers. But out-of-story, we have vagueness: there are infinitely many possible species the claim could be about.

This suggests that the error theorist who takes the vagueness way out is not home free. For it is a part of our usage of “(morally) wrong” that it refers fairly unambiguously to one important property. But the error theorist claims vagueness. If the statements about wrongness were made in a story, then the error theorist could handle this by distinguishing in-story and out-of-story vagueness. But this distinction is not available here.

A similar problem occurs for a real-world person who claims that there are unicorns. Maybe one could say that the person intends in saying “There are unicorns” to express a single specific proposition, but fails, and vaguely expresses each of an infinity of propositions, all of them false. If so, then a similar move would be available to the error theorist. But I am sceptical of this move. I wonder if it’s not better to just say that “There are unicorns” as said by someone who intended to express an existential claim about a single definite species is nonsense, but there is a neighboring sentence, such as “There is an extant species of single-horned equines”, that makes sense and is true.

A constraint on metaethics

Suppose that we lived lives like ours in a world (possible or not) whose metaphysics included nothing like moral duties except that there was a loving God and he issued commands. If in that world we used the phrase “morally wrong”, that phrase would refer to the property of being forbidden by God.

Or suppose that we lived lives like ours in a world (possible or not) whose metaphysics included nothing like moral duties except that we had Aristotelian forms and they specified what the will should will, the phrase “morally wrong” would refer to the property of being contrary to what our form says the will should will.

But suppose now we lived in a world where there was nothing like moral duties, no God, no forms, but buried underground and unseen by humans there was a stone tablet that arose from a random volcanic process millions of years ago. On these tablets by chance there were markings that looked just like French sentences, and when interpreted as French sentences, they stated imperatives, like the Golden Rule, that that fit very well with our intuitions about what are the core moral duties. I doubt that the phrase “morally wrong” would refer to the property of being contrary to what the stone tablet would enjoin if it were interpreted as French. (I am careful in my wording, because strictly speaking the stone tablet, being the product of random processes, does not contain any sentences—it only contains markings that look like sentences of French.)

Suppose my intuition is right. What is the difference between the third case and the first two? Here is a hypothesis. In the divine command world, presumably our beliefs about what we call “morally wrong” have some sort of a connection to the commands of that God. In the Aristotelian world, our beliefs about the “morally wrong” presumably come in some way from the Aristotelian forms. But in the stone tablet world, the “morally wrong” beliefs have no connection to the stone tablets, except that the stone tablets happen to fit them.

This suggests an important constraint on metaethics: our beliefs about the morally wrong had better have a real connection—perhaps even a real causal connection—with their grounds. If this constraint is right, then evolutionary debunking arguments against morality cut more deeply than is recognized: if the arguments correctly show that our “moral concepts” lack a relevant connection with any grounds, then our “moral beliefs” not are not knowledge, but they are in fact just nonsense.

Of course, I want to turn this around: given that our moral beliefs are not mere nonsense, it follows that they have a real connection with grounds, and this undercuts the idea that we are mere products of completely unguided evolution.

A Biblical argument for epistemicism

1. If God knows the exact number of hairs we have on our head, then there is a definite number of hairs we have on our head.

2. If there is a definite number of hairs we have on our head, vagueness is at most epistemic.

3. God knows the exact number of hairs we have on our head. (Luke 12:7)

4. So, vagueness is at most epistemic.

Premise 2 is based on observing that the number of hairs we have on our heads involves similar kinds of vagueness to more paradigmatic cases of vagueness. Think here about these questions:

• What’s the cut-off between hairs on the head and hairs on the upper neck?

• How much keratin needs to come out of a hair follicle before that keratin counts as a hair?

• How far must the molecules of a hair separate from the molecules of the skin before the hair counts as no longer attached?

One might worry that Premise 3 relies on biblical data too literalistically. Jesus is emphasizing the impressiveness of God’s knowledge. Suppose that instead of God knowing the exact number of hairs on my head, God knew the exact vagueness profile for the hairs on my head. That would be even more impressive. I see some force in this objection, but it implies that epistemicism holds at the level of vagueness profiles, and it seems (but perhaps isn’t?) ad hoc to go for epistemicism there rather than everywhere.

On reflection, I think premise 1 might be the most questionable premise. Perhaps God’s knowledge definitely matches the number of hairs: for every natural number n, it’s definitely true that: God believes I have n hairs if and only if I have n hairs, but there is no natural number n such that God definitely believes I have n hairs. In other words, the vagueness profile concerning God’s beliefs exactly matches the vagueness profile in reality. I am sceptical of this solution. It doesn’t feel like knowledge to me if it’s got this sort of vagueness to it.