Necessary Existence

Josh Rasmussen's and my Necessary Existence book is now complete. We just sent the final manuscript to Oxford. We're both quite happy with the book.

Freezing a hard drive

I had a hard drive that's around 15 years old fail to start a couple of months ago--I tried many times with no luck. Most but not all of the stuff was backed up, but not all (though what wasn't backed up wasn't very important). So yesterday I stuck the drive in a freezer, in two freezer bags without much air. Today I plugged it into an IDE-USB adapter. It didn't start up at first, but after a few minutes of warming it up, it started and I got all the data off without any difficulty.  This is the second time in my life that I've rescued data from an old hard drive using a freezer.

(Of course, there is always the chance that this time it would have worked without the freezer. I didn't actually check yesterday if the drive was still not working.)

Use 3D printer as a plotter/cutter

My 3D printer is fun, but I like to extend functionality, so I designed some additional snap-on parts that lets me also use it as a pen plotter and cutter. For instance, I had it draw a butterfly coloring sheet on a blank T-shirt for our four-year-old to color with fabric markers. Here are instructions.

Some weird languages

Platonism would allow one to reduce the number of predicates to a single multigrade predicate Instantiates(x₁, ..., x_n, p), by introducing a name p for every property. The resulting language could have one fundamental quantifier ∃, one fundamental predicate Instantiates(x₁, ..., x_n, p), and lots of names. One could then introduce a “for a, which exists” existential quantifier ∃_a in place of every name a, and get a language with one fundamental multigrade predicate, Instantiates(x₁, ..., x_n, p), and lots of fundamental quantifiers. In this language, we could say that Jim is tall as follows: ∃_Jimx Instantiates(x, tallness).

On the other hand, once we allow for a large plurality of quantifiers we could reduce the number of predicates to one in a different way by introducing a new n-ary existential quantifier ∃_F(x₁, …, x_n) (with the corresponding ∀_P defined by De Morgan duality) in place of each n-ary predicate F other than identity. The remaining fundamental predicate is identity. Then instead of saying F(a), one would say ∃_Fx(x = a). One could then remove names from the language by introducing quantifiers for them as before. The resulting language would have many fundamental quantifiers, but only only one fundamental binary predicate, identity. In this language we would say that Jim is tall as follows: ∃_Jimx∃_Tally(x = y).

We have two languages, in each of which there is one fundamental predicate and many quantifiers. In the Platonic language, the fundamental predicate is multigrade but the quantifiers are all unary. In the identity language, the fundamental predicate is binary but the quantifiers have many arities.

And of course we have standard First Order Logic: one fundamental quantifier (say, ∃), many predicates and many names. We can then get rid of names by introducing an IsX(x) unary predicate for each name X. The resulting language has one quantifier and many predicates.

So in our search for fundamental parsimony in our language we have a choice:

• one quantifier and many predicates
• one predicate and many quantifiers.

Are these more parsimonious than many quantifiers and many predicates? I think so: for if there is only one quantifier or only one predicate, then we can collapse levels—to be a (fundamental) quantifier just is to be ∃ and to be a (fundamental) predicate just is to be Instantiates or identity.

I wonder what metaphysical case one could make for some of these weird fundamental language proposals.

Life science and physical science

I've been thinking that in a nutshell one could put much of the distinctiveness of Aristotelian philosophy as follows: life science is at least as fundamental as physical science.

Double Effect in daily life

The Principle of Double Effect is often introduced in terms of weighty cases of killing, like bombing military installations or redirecting trolleys. But the importance of the distinction between intended and unintended but foreseen harms can be seen even more clearly in everyday cases.

Yesterday, my wife went grocery shopping, while I was home with some of the kids. My son asked to be taken for a bike ride. The thought flashed into my head: “If I go, I probably won’t be home when my wife comes back with the groceries, and hence I won’t be able to help with unloading them.” There are three possible attitudes I could have with respect to this observation:

1. I shouldn’t take my son for a bike ride now.

2. Not being able to help my wife is an unfortunate side-effect of taking my son for a bike ride.

3. Being able to get out of helping my wife is a reason to take my son for a bike ride.

In cases (2) and (3), the foreseen effects are the same. There are no deontic issues (I didn’t promise my wife to be home). But clearly if I take attitude (3), and hence intend not to be there when my wife comes back, I am being a bad husband, while if I go for (1) or (2), my behavior is defensible. (In fact, I never got around to taking my son for the bike ride.)

What is this?

Consider the black item to the right here on your screen. Is it a token of the Latin alphabet letter pee, the Greek letter rho or the Cyrillic letter er? The question cannot be settled by asking which font, and where in the font, the glyph is taken from, because I drew the drawing in Inkscape rather than using any font, precisely to block such an answer. Nor will my intentions answer the question, since I drew the thing precisely to pose such a philosophical question rather than to express any one of the three options.

There are two interesting questions here. The first is an ontological one. Is a token on screen something different from the pattern of light? If it's the same as the pattern of light, then there is at most one token, there being at most one relevant pattern of light (perhaps none, if our ontology doesn't include patterns of light), though this token is a token of pee, and a token of rho and a token of er. If a token is not identical with a pattern of light, then we might as well keep on multiplying entities, and say that there is a pattern of light and three tokens, of pee, rho and er, respectively, with the first entity constituting the latter three.

The second one is a philosophy of language one. What determines whether or not the pattern of light is or constitutes a token of, say, rho? Is it my intentions? If so, then indeed we have tokens of pee, rho and er, as making these was my intention, but we do not have a token of the Coptic letter ro or a token of the letter qof in 15th century Italian Hebrew cursive, since I didn't think of these when I was doing the drawing. Is it the linguistic context? But then it's not a token of any letter, since a displayed png file in an analytic philosophy post is not a the kind of linguistic context that determines a token.

Or is it that the pattern of light is or constitutes tokens of all the letters it geometrically matches, whether or not it was intended as such? If so, then we also have a letter dee (just turn your screen). But now suppose a new alphabet is created, and it contains a letter that looks just like the drawing. It would be odd to say that if a new language were created on another planet this instantly would multiply the entities on earth (at the speed of light? faster?). So it seems that on this view, we should say that the pattern of light is or constitutes tokens of all the letters in all the alphabets that will ever exist. But future actions shouldn't affect how many things there now are. So on this view, we should be even more pluralistic: the pattern of light is or constitutes tokens of all the letters in all possible alphabets.

We thus have two questions: one about ontology and one about what is being tokened. Both questions have parsimonious and profligate answers. The parsimonious answer to the ontology question is that there is one thing, which can be a token of multiple things. The profligate one is that we have many tokens. The parsimonious answers to the language question are that intentions and/or context determines what's been tokened. The profligate answer has an infinite amount of tokening.

We probably shouldn't combine the two profligate answers. For then on your screen there are infinitely many physical things, all co-located (and some perhaps even with the same modal profile). That's too much.

That still leaves three combinations. I think there is reason to reject the combination of ontological profligacy with parsimony on the philosophy of language side. The reason is that tokens get repurposed. Consider a Russian who has a Scrabble set and loses an er tile. She then buys a replacement pee tile, as it looks pretty much the same (I looked at online pictures--both have value 1 and look the same). Then it seems that a new entity, a token of er, comes into existence if we have ontological profligacy and linguistic parsimony. Does a mere intention to use the tile for an er what magically creates a new physical object, a token? That seems not very plausible.

That leaves two combinations:

• ontological and linguistic parsimony
• ontological parsimony and linguistic profligacy.

Bestowing harms and benefits

A virtuous person happily confers justified benefits and unhappily bestows even justified harms. Moreover, it is not just that the virtuous person is happy about someone being benefitted and unhappy about someone being harmed, though she does have those attitudes. Rather, the virtuous person is happy to be the conferrer of justified benefits and unhappy to be the bestower even of justified harms. These attitudes on the part of the virtuous person are evidence that it is non-instrumentally good for one to confer justified benefits and non-instrumentally bad for one to bestow even justified harms. Of course, the bestowal of justified harms can be virtuous, and virtuous action is non-instrumentally good for one. But an action can be good for one qua virtuous and bad for one in another way—cases of self-sacrifice are like that. Virtuously bestowing justified harms is a case of self-sacrifice on the part of the virtuous agent.

When multiple agents are necessary and voluntary causes of a single harm, the total bad of being a bestower of harm is not significantly diluted between the agents. Each agent non-instrumentally suffers from the total bad of bestowing harm, though the contingent psychological effects may—but need not—be diluted. (A thought experiment: One person hits a criminal in an instance of morally justified and legally sentenced corporal punishment while the other holds down the punishee. Both agents are equally responsible. It makes no difference to the badness of being the imposer of corporal punishment if instead of the other holding down the punishee, the punishee is simply tied down. Interestingly, one may have a different intuition on the other side—it might seem worse to hold down the punishee to be hit by a robot than by a person. But that’s a mistake.)

If this is right, then we have a non-instrumental reason to reduce the number of people involved in the justified imposition of a harm, though in particular cases there may also be reasons, instrumental and otherwise, to increase the number of people involved (e.g., a larger number of people involved in punishing may better convey societal disapprovat).

This in turn gives a non-instrumental reason to develop autonomous fighting robots for the military, since the use of such robots decreases the number of people who are non-instrumentally (as well as psychologically) harmed by killing. Of course, there are obvious serious practical problems there.

Intending material conditionals and dispositions, with an excursus on lethally-armed robots

Alice has tools in a shed and sees a clearly unarmed thief approaching the shed. She knows she is in no danger of her life or limb—she can easily move away from the thief—but points a gun at the thief and shouts: “Stop or I’ll shoot to kill.” The thief doesn’t stop. Alice fulfills the threat and kills the thief.

Bob has a farm of man-eating crocodiles and some tools he wants to store safely. He places the tools in a shed in the middle of the crocodile farm, in order to dissuade thieves. The farm is correctly marked all-around “Man-eating crocodiles”, and the crocodiles are quite visible to all and sundry. An unarmed thief breaks into Bob’s property attempting to get to his tool shed, but a crocodile eats him on the way.

Regardless of what local laws may say, Alice is a murderer. In fulfilling the threat, by definition she intended to kill the thief who posed no danger to life or limb. (The case might be different if the tools were needed for Alice to survive, but even then I think she shouldn’t intend death.) What about Bob? Well, there we don’t know what the intentions are. Here are two possible intentions:

1. Prospective thieves are dissuaded by the presence of the man-eating crocodiles, but as a backup any that not dissuaded are eaten.

2. Prospective thieves are dissuaded by the presence of the man-eating crocodiles.

If Bob’s intention is (1), then I think he’s no different from Alice. But Bob’s intention could simply be (2), whereas Alice’s intention couldn’t simply be to dissuade the thief, since if that were simply her intention, she wouldn’t have fired. (Note: the promise to shoot to kill is not morally binding.) Rather, when offering the threat, Alice intended to dissuade and shoot to kill as a backup, and then when she shot in fulfillment of the threat, she intended to kill. If Bob’s intention is simply (2), then Bob may be guilty of some variety of endangerment, but he’s not a murderer. I am inclined to think this can be true even if Bob trained the crocodiles to be man-eaters (in which case it becomes much clearer that he’s guilty of a variety of endangerment).

But let’s think a bit more about (2). The means to dissuading thieves is to put the shed in a place where there are crocodiles with a disposition to eat intruders. So Bob is also intending something like this:

3. There be a dispositional state of affairs where any thieves (and maybe other intruders) tend to die.

However, in intending this dispositional state of affairs, Bob need not be intending the disposition’s actuation. He can simply intend the dispositional state of affairs to function not by actuation but by dissuasion. Moreover, if the thief dies, that’s not an accomplishment of Bob’s. On the other hand, if Bob intended the universal conditional

4. All thieves die

or even:

5. Most thieves die

then he would be accomplishing the deaths of thieves if any were eaten. Thus there is a difference between the logically complex intention that (4) or (5) be true, and the intention that there be a dispositional state of affairs to the effect of (4) or (5). This would seem to be the case even if the dispositional state of affairs entailed (4) or (5). Here’s why there is such a difference. If many thieves come and none die, then that constitutes or grounds the falsity of (4) and (5). But it does not constitute or ground the falsity of (3), and that would be true even if it entailed the falsity of (3).

This line of thought, though, has a curious consequence. Automated lethally-armed guard robots are in principle preferable to human lethally-armed guards. For the human guard either has a policy of killing if the threat doesn’t stop the intruder or has a policy of deceiving the intruder that she has such a policy. Deception is morally problematic and a policy of intending to kill is morally problematic. On the other hand, with the robotic lethally-armed guards, nobody needs to deceive and nobody needs to have a policy of killing under any circumstances. All that’s needed is the intending of a dispositional state of affairs. This seems preferable even in circumstances—say, wartime—where intentional killing is permissible, since it is surely better to avoid intentional killing.

But isn’t it paradoxical to think there is a moral difference between setting up a human guard and a robotic guard? Yet a lethally-armed robotic guard doesn’t seem significantly different from locating the guarded location on a deadly crocodile farm. So if we think there is no moral difference here, then we have to say that there is no difference between Alice’s policy of shooting intruders dead and Bob’s setup.

I think the moral difference between the human guard and the robotic guard can be defended. Think about it this way. In the case of the robotic guard, we can say that the death of the intruder is simply up to the intruder, whereas the human guard would still have to make a decision to go with the lethal policy in response to the intruder’s decision not to comply with the threat. The human guard could say “It’s on the intruder’s head” or “I had no choice—I had a policy”, but these are simply false: both she and the intruder had a choice.

None of this should be construed as a defence in practice of autonomous lethal robots. There are obvious practical worries about false positives, malfunctions, misuse and lowering the bar to a country’s initiating lethal hostilities.

The sharpness of the Platonic realm

I feel an intellectual pull to a view that also repels me. The view is that all contingent vague truths are grounded in contingent definite truths and necessary vague truths. For instance, that Jim is bald might be grounded in a contingent definite truth about the areal density of hair on his scalp and a necessary vague truth that anyone with that areal density of hair is bald.

On this view, any vague differences between possible worlds are grounded in definite differences between possible worlds.

But the view also repels me. I have the Platonic intuition that the realm of necessary truth should be clean, unchanging, sharp and definite. Plato would be very surprised to think that fuzziness in the physical world is grounded in fuzziness in the Platonic realm.

Epistemicism, of course, nicely reconciles the Platonic intuition about necessary truths with the intellectual pull of the grounding claim. For it is no surprise that there be things in the Platonic realm that are not accessible to us. If vagueness is merely epistemic, then there is no difficulty about vagueness in the Platonic realm.

Knowledge of vague truths

Suppose that we know in lottery cases—i.e., if a lottery has enough tickets and one winner, then we know ahead of time that we won’t win. I know it’s fashionable to deny such knowledge, but such denial leads either to scepticism or to having to say things like “I agree that I have better evidence for p than for q, but I know q and I don’t know p” (after all, if a lottery has enough tickets, I can have better evidence that I won’t win than that I have two hands).

Suppose also that classical logic holds even in vagueness cases. This is now a mainstream assumption in the vagueness literature, I understand.

Finally, suppose that once the number of tickets in a lottery reaches about a thousand, I know I won’t win. (The example can be modified if a larger number is needed.) Now for each positive natural number n, let T_n be the proposition that a person whose height is n microns is tall but a person whose height is n−1 is not tall. At most one of the T_n propositions is true, since anybody taller than a tall person is tall, and anybody shorter than a non-tall person is short. Moreover, since there is a non-tall person and there is a tall person, classical logic requires that at least one of the T_n is true.

Hence, exactly one of the T_n is true. Now, some of the T_n are definitely false. For instance, T_1000000 is definitely false (since someone a meter tall is definitely not tall) and T_2000000 is definitely false (since someone a micron short of two meters tall is definitely tall). But if anything is vague, it will be vague where exactly the cut-off between non-tall and tall lies. And if that is vague, then in the vague area between non-tall and tall, it will be vague whether T_n is true. That vague area is at least a millimeter long (in fact, it’s probably at least five centimeters long), and since there are a thousand microns to the millimeter, there will be at least a thousand values n such that T_n is vague.

Moreover, these thousand T_n are pretty much epistemically on par. Let n be any number within that vague range, and suppose that in fact T_n is false. Then this is a lottery case with at least a thousand tickets. So, if in the lottery case I know I didn’t win, in this case I know that T_n is false.

Hence, some vague truths can be known—assuming that we know in lottery cases and that classical logic holds.

Of course, as usual, some philosophers will want to reverse the argument, and take this to be another argument that we don’t know in lottery cases, or that classical logic doesn’t hold, or that there is no vagueness.

Doing things fast

I was thinking about deadlines--papers and exams to grade--and realized that doing things fast is a similar kind of challenge to making things small. Companies try to fit phone electronics into as spatially thin a region of spacetime as possible, while runners try to fit a run of a particular distance into as temporally thin a region of spacetime as possible. (And while sometimes small spatial and temporal size has "utilitarian value", as in the case of getting my grades in, in the phone and running cases, the reasons are mainly of the aesthetic variety.)

Vague propositions

Suppose Jim says, in English, “2+2=4”. Then:

1. What Jim said is such that it is contigent that it is true, because it is contingent that “4” means four rather than five

but:

2. What Jim said is a necessary truth, because it cannot but be true that 2+2=4.

Here the apparent contradiction is resolved by disambiguating “what Jim said” between the uttered sounds and the expressed meaning.

But when talking about vagueness, this straightfoward point can be a bit less clear. Suppose that it’s vaguely true that “4” in Jim’s dialect means four, rather than five, and Jim says “2+2=4” (and suppose that all the other relevant stuff is definite). Then:

3. What Jim said is vaguely true, because it’s vaguely true that “4” is four.

4. What Jim said is not vaguely true, because what Jim said is definitely true or definitely false, depending on what “4” means.

Again, make the same move as in (1)-(2): in (3), “what Jim says” is the uttered sounds or words and in (4) it’s the proposition.

This line of thought suggests one of two possibilities. Either, propositions are never vague, or there are two interestingly different kinds of vagueness. If propositions are never vague, then in the proposition sense of “what was said” it is never correct to say that what was said is vague. That’s a bit counterintuitive, but some counterintuitive things are true.

But if some propositions are vague, then it seems that we have two interestingly different kinds of vagueness an utterance could suffer from. It could be vague which non-vague proposition an utterance expresses or it could be definite which vague proposition an utterance expresses—or one could have combinations, as when it’s vague which vague proposition is expressed. In the case above, I claimed that it was vaguely the case that Jim expressed the non-vague proposition that 2+2=4. But presumably if there are vague propositions, there will be one that has the kind of vagueness that makes the non-vague propositions that 2+2=4 and that 2+2=5 be its admissible precifications.

So now we would have this interesting question: What determines whether Jim’s case was a case of vaguely expressing a non-vague proposition or non-vaguely expressing a vague proposition or some combination? Maybe there is a good answer to this question, but I have some doubts. In light of these doubts, I think that the proponent of vague and non-vague propositions should say is something like this. There are at least three senses of “what was said”: the sounds or words (and that makes for two, but I won’t be interested in this distinction in this post), the non-vague proposition and the vague proposition. What Jim said is vaguely true in the first and third sense, but not in the second. This is sufficiently complicated that one might prefer to go back to the less intuitive option, that in the proposition sense “what was said” is never vague.

I am dreadfully confused.

Actions that are gravely wrong for qualitative reasons

Some types of wrongdoing vary in degree of seriousness from minor to grave. Stealing a dollar from a billionaire is trivially wrong while stealing a thousand dollars from someone poor is gravely wrong. A poke in the back with a finger and breaking someone’s leg with a carefully executed kick can both be instances of battery, but the former is likely to be a minor wrong while the latter is apt to be grave.

On the other hand, there are types of wrongdoing that are always grave. An uninteresting (for my purposes) case is where the gravity is guaranteed because the description of wrongdoing includes a grave-making quantitative feature as in the case of “grand theft” or “grevious bodily harm”. The more interesting case is where for qualitative reasons the wrongdoing is always grave. For instance, murder and rape. There are no trivial murders or minor rapes.

Of course, even if a type of act is always seriously wrong, the degree of culpability might be slight, say due to lack of freedom or invincible ignorance. Think of someone brainwashed into murder, but who still has a slight sense of moral discomfort—although her action is gravely wrong, she may be only slightly culpable. My interest right now, however, is in the degree of wrongness rather than of culpability.

We can now distinguish types of wrongdoing that are always grave for qualitative reasons from those that are always grave merely for quantitative reasons. Here is a fairly precise characterization: if W is a type of wrongdoing that is always grave for qualitative reasons, then there is no sequence of acts, starting with a case of W, and with merely quantitative differences between the acts, such that the sequence ends with an act that isn’t grave. Grand theft and grevious bodily harm are examples of types of wrongdoings that are always grave merely for quantitative reasons.

On the other hand, it is intuitively plausible that murder and rape are not gravely wrong for merely quantitative reasons. If this intuition is correct, then we get some very interesting substantive consequences. In the case of rape, I’ve explored some relevant issues in a past post, so I want to focus on murder here.

The first consequence of taking murder to be always gravely wrong for qualitative reasons is that there is no continuous scale of mental abilities (whether of first or second potentiality) that takes us from people to lower animals. An unjustified killing of a lower animal is only a minor wrong (take this to constrain what “lower” means). If there were a continuous scale of mental abilities from people to lower animals, then murder would be gravely wrong only for quantitative reasons: because the victim’s mental abilities lie on such-and-such a position on the scale. So once we admit that murder is gravely wrong for qualitative reasons, we have to suppose a qualitative gap in the spectrum of mental abilities. This probably requires the rejection of naturalism.

A second consequence is that if killing a consenting adult in normal health is murder—which it is—then euthanasia is gravely wrong. For variation in health and comfort is merely quantitative, and one cannot go from a case of murder to something that isn’t gravely wrong by merely quantitative variation, since murder is always gravely wrong for qualitative reasons.

I suspect there are a number of other very interesting consequences of taking murder to be gravely wrong for qualitative reasons. I think these consequences will motivate some people to give up on the claim that murder is gravely wrong for qualitative reasons. But I think we should hold on to that claim and accept the consequences.

Love and reasons

Humans are fundamentally loving beings. This is more fundamental than their being rational, because the nature of reasons, and hence of rationality, is to be accounted for in terms of the nature of love.

A sketchy approximation to a love-based account of external reasons is this:

• A fact F is an external reason for ϕing if and only if F partially grounds ϕing being in some respect loving towards something or someone or not ϕing being in some respect unloving towards something or someone.

• A plurality of facts is a conclusive external reason for ϕing if and only if the plurality grounds its being unloving not to ϕ.

If I am right that love has the three fundamental aspects of benevolence, appreciation and union, these probably also provide the three basic kinds of reasons. There are reasons to do good and to prevent bad: these come from the benevolence aspect. There are reasons to, e.g., admire and be grateful that come from appreciation. Interestingly, I think appreciation also provides reasons for things like criticism and punishment. In criticism and punishment we appreciate someone or something qua someone or something that ought to do better: we appreciate nature over actual activity. And finally there is union, which needs to be appropriate to the love (I develop this at greater length in One Body).

Internal reasons are occurrent beliefs that are in some sense about what there is external reason to do and that enter into the right way into choice. These beliefs come in a broad variety, and are not always explicitly about reasons as such.

3D-printable cookie cutters with Inkscape and OpenSCAD

We thought that our 4-year-old would enjoy a Pikachu cookie cutter for Christmas, but I didn't like the existing designs on Thingiverse. So I wrote a Python script, eventually packaged into an Inkscape extension, that generates a 3D-printable OpenSCAD file from a color-coded SVG path file. Instructions are here.

  

A Trinitarian structure in love

In One Body, I identified three crucial aspects in every form of love: benevolence, appreciation and unity. But I did not have an argument that there are no further equally central aspects. I still don’t.

But I now have some suggestive evidence: There is a Trinitarian structure to these three aspects. The Father eternally conferring his divine nature—the nature of being the Good Itself—on the Son and, through the Son, on the Holy Spirit. The Son in turn eternally and gratefully contemplates the Father. And the Holy Spirit joins Father with Son. This makes for benevolence, appreciation and unity, respectively, all perichoretically interconnected. That there are only three Persons in the most blessed Trinity is thus evidence that these three aspects are what love is at base.

No-collapse interpretations without a dynamically evolving wavefunction in reality

Bohm’s interpretation of quantum mechanics has two ontological components: It has the guiding wave—the wavefunction—which dynamically evolves according to the Schrödinger equation, and it has the corpuscles whose movements are guided by that wavefunction. Brown and Wallace criticize Bohm for this duality, on the grounds that there is no reason to take our macroscopic reality to be connected with the corpuscles rather than the wavefunction.

I want to explore a variant of Bohm on which there is no evolving wavefunction, and then generalize the point to a number of other no-collapse interpretations.

So, on Bohm’s quantum mechanics, reality at a time t is represented by two things: (a) a wavefunction vector |ψ(t)⟩ in the Hilbert space, and (b) an assignment of values to hidden variables (e.g., corpuscle positions). The first item evolves according to the Schrödinger equation. Given an initial vector |ψ(0)⟩, the vector at time t can be mathematically given as |ψ(t)⟩ = U_t|ψ(0)⟩ where U_t is a mathematical time-evolution operator (dependent on the Hamiltonian). And then by a law of nature, the hidden variables evolve according to a differential equation—the guiding equation—that involves |ψ(t)⟩.

But now suppose we change the ontology. We keep the assignment of values to hidden variables at times. But instead of supposing that reality has something corresponding to the wavefunction vector at every time, we merely suppose that reality has something corresponding to an initial wavefunction vector |ψ₀⟩. There is nothing in physical reality corresponding to the wavefunction at t if t > 0. But nonetheless it makes mathematical sense to talk of the vector U_t|ψ₀⟩, and then the guiding equation governing the evolution of the hidden variables can be formulated in terms of U_t|ψ₀⟩ instead of |ψ(t)⟩.

If we want an ontology to go with this, we could say that the reality corresponding to the initial vector |ψ₀⟩ affects the evolution of the hidden variables for all subsequent times. We now have only one aspect of reality—the hidden variables of the corpuscles—evolving dynamically instead of two. We don’t have Schrödinger’s equation in the laws of nature except as a useful mathematical property of the U_t operator described by the initial vector). We can talk of the wavefunction U_t|ψ₀⟩ at a time t, but that’s just a mathematical artifact, just as m₁m₂ is a part of the equation expressing Newton’s law of gravitation rather than a direct representation of physical reality. Of course, just as m₁m₂ is determined by physical things—the two masses—so too the wavefunction U_t|ψ₀⟩ is determined by physical reality (the initial vector, the time, and the Hamiltonian). This seems to me to weaken the force of the Brown and Wallace point, since there no longer is a reality corresponding to the wavefunction at non-initial times, except highly derivatively.

Interestingly, the exact same move can be made for a number of other no-collapse interpretations, such as Bell’s indeterministic variant of Bohm, other modal interpretations, the many-minds interpretation, the traveling minds interpretation and the Aristotelian traveling forms interpretation. There need be no time-evolving wavefunction in reality, but just an initial vector which transtemporally affects the evolution of the other aspects of reality (such as where the minds go).

Or one could suppose a static background vector.

It’s interesting to ask what happens if one plugs this into the Everett interpretation. There I think we get something rather implausible: for then all time-evolution will disappear, since all reality will be reduced to the physical correlate of the initial vector. So my move above is only plausible for those no-collapse interpretations on which there is something more beyond the wavefunction.

There is also a connection between this approach and the Heisenberg picture. How close the connection is is not yet clear to me.

Material conditionals and quantifiers

From:

1. Every G is H

it seems we should be able to infer for any x:

2. If x is G, then x is H.

This pretty much forces one to read “If p, then q” as a material conditional, i.e., as q or not p. For the objection to reading the indicative conditional as a material conditional is that this leads to the paradoxes of material implication, such as that if it’s not snowing in Fairbanks, Alaska today, then it’s correct to say:

3. If it’s snowing in Fairbanks today, then it’s snowing in Mexico City today

even if it’s not snowing in Mexico City, which just sounds wrong.

But if we grant the inference from (1) to (2), we can pretty much recover the paradoxes of material implication. For instance, suppose it’s snowing neither in Fairbanks nor in Mexico City today. Then:

4. Every truth value of the proposition that it’s snowing in Fairbanks today is a truth value of the proposition that it’s snowing in Mexico City today.

So, by the (1)→(2) inference:

5. If a truth value of the proposition that it’s snowing today in Fairbanks is true, then a truth value of the proposition that it’s snowing today in Mexico City is true.

Or, a little more smoothly:

6. If it’s true that it’s snowing in Fairbanks today, then it’s true that it’s snowing in Mexico City today.

It would be very hard to accept (6) without accepting (3). With a bit of work, we can tell similar stories about the other standard paradoxes. The above truth-value-quantification technique works equally well for both the true⊃true and the false⊃false paradoxes. The remaining family of paradoxes are the false⊃true ones. For instance, it’s paradoxical to say:

7. If it’s warm in the Antarctic today, it’s a cool day in Waco today

even though the antecedent is false and the consequent is true, so the corresponding material conditional is true. But now:

8. Every day that’s other than today or on which it’s warm in the Antarctic is a day that’s other than today or on which it’s cool in Waco.

So by (1)→(2):

9. If today is other than today or it’s warm in the Antarctic today, then today is other than today or today it’s cool in Waco.

And it would be hard to accept (9) without accepting (7). (I made the example a bit more complicated than it might technically need to be in order not to have a case of (1) where there are no Fs. One might think for Aristotelian logic reasons that that case stands apart.)

This suggests that if we object to the “material conditional” reading of “If… then…”, we should object to the “material quantification” reading of “Every F is G”. But many object to the first who do not object to the second.

Are we all seriously impaired?

When I taught calculus, the average grade on the final exam was around 55%. One could make the case that this means that our grading system is off: that everybody’s grades should be way higher. But I suspect that’s mistaken. The average grasp of calculus in my students probably really wasn’t good enough for one to be able to say with a straight face that they “knew calculus”. Now, I think I was a pretty rotten calculus teacher. But such grades are not at all unusual in calculus classes. And if one didn’t have the pre-selection that colleges have, but simply taught calculus to everybody, the grades would be even lower. Yet much of calculus is pretty straightforward. Differential calculus is just a matter of ploughing through and following simple rules. Integral calculus is definitely harder, and exceling at it requires real creativity, but one can presumably do decently just by internalizing a number of heuristics and using trial and error.

I find myself with the feeling that a normal adult human being should be able to do calculus, understand basic Newtonian physics, write a well-argued essay, deal well with emotions, avoid basic formal and informal fallacies, sing decently, have a good marriage, etc. But I doubt that the average adult human being can learn all these things even with excellent teachers. Certainly the time investment would be prohibitive.

There are two things one can say about this feeling. The first is that the feeling is simply mistaken. We’re all apes. A 55% grade in calculus from an ape is incredible. The kind of logical reasoning that an average person can demonstrate in an essay is super-impressive for an ape. There is little wrong with average people intellectually. Maybe the average human can’t practically learn calculus, but if so that’s no more problematic than the facts that the average human can’t practically learn to climb a 5.14 or run a four-minute mile. These things are benchmarks of human excellence rather than of human normalcy.

That may in fact be the right thing to say. But I want to explore another possibility: the possibility that the feeling is right. If it is right, then all of us fall seriously short of what normal human beings should be able to do. We are all seriously impaired.

How could that be? We are, after all, descendants of apes, and the average human being is, as far as we can tell, an order of magnitude intellectually ahead of the best non-human apes we know. Should the standards be another order of magnitude ahead of that?

I don’t think there is a plausible naturalistic story that would do justice to the feeling that the average human falls that far short of where humans should be at. But the Christian doctrine of the Fall allows for a story to be told here. Perhaps God miraculously intervened just before the first humans were conceived, and ensured that these creatures would be significantly genetically different from their non-human parents: they would have capacities enabling them to do calculus, understand Newtonian physics, write a well-argued essay, deal well with emotions, avoid fallacies, sing decently, have a good marriage, etc. (At least once calculus, physics and writing are invented.) But then the first humans misused their new genetic gifts, and many of them were taken away, so that now only statistically exceptional humans have many of these capacities, and none have them all. And so we have more geneticaly in common with our ape forebears than would have been the case if the first humans acted better. However, in addition to genetics, on this story, there is the human nature, which is a metaphysical component of human beings defining what is and what is not normal for humans. And this human nature specifies that the capacities in question are in fact a part of human normalcy, so that we are all objectively seriously impaired.

Of course, this isn’t the only way to read the Fall. Another way—which one can connect in the text of Genesis with the Tree of Life—is that the first humans had special gifts, but these gifts were due to miracles beyond human nature. This may in fact be the better reading of the story of the Fall, but I want to continue exploring the first reading.

If this is right, then we have an interesting choice-point for philosophy of disability. One option will be to hold that everyone is disabled. If we take this option then for policy reasons (e.g., disability accommodation) we will need a more gerrymandered concept than disability, say disability^*, such that only a minority (or at least not an overwhelming majority) is disabled^*. This concept will no doubt have a lot of social construction going into it, and objective impairment will be at best a necessary condition for disability^*. The second option is to say only a minority (or not an overwhelming majority) is disabled, which requires disability to differ significantly from impairment. Again, I suspect that the concept will have a lot of social construction in it. So, either way, if we accept the story that we are all seriously impaired, for policy reasons we will need a disability-related concept with a lot more social construction in it.

Should we accept the story that we are all seriously impaired? I think there really is an intuition that we should do many things that we can’t, and that intuition is evidence for the story. But far from conclusive. Still, maybe we are all seriously impaired, in multiple intellectual dimensions. We may even be all physically impaired.

The identity of countries and persons

Suppose Canada is dissolved, and a country is created, with the same people, in the same place, with the same name, symbols, and political system. Moreover, the new country isn’t like the old one by mere happenstance, but is deliberately modeled on the old. Then very little has been lost, even if it turns out that on the correct metaphysics of countries the new country is a mere replica of Canada.

On the other hand, suppose Jean Vanier is dissolved, and a new person is created, with the same matter and shape, in the same place, with the same name, apparent memories and character. Moreover, the new person isn’t like the old one by mere happenstance, but is deliberately modeled on the old. Then if on the correct metaphysics of persons the new person is a mere replica of Jean Vanier, much has been lost, even if Vanier’s loving contributions continue through the new person.

This suggests an interesting asymmetry between social entities and persons. For social entities, the causal connections and qualitative and material similarities across time matter much more than identity itself. For persons, the identity itself matters at least as much as these connections and similarities.

Perhaps the explanation of this fact is that for social entities there is nothing more to the entity than the persons and relationships caught up in them, while for persons there is something more than temporal parts and their relationships.

[Note added later: This was, of course, written before the revelations about Jean Vanier's abusiveness. I would certainly have chosen a different example if I were writing this post now.]

An Aristotelian picture of set theory

There are some sets we need just because of the fundamental axioms of set theory, whatever these are (ZF? ZFC?). Probably, we could satisfy the fundamental axioms of set theory with a collection of sets that in some sense is countable. But then we need to add some sets because the world is arranged thus and so. For instance, we may need to add a real number representing the exact distance between my thumbs in Planck units. (If the world is describable as a vector in a separable Hilbert space, all we need to add can be encoded as a single real number.) This is a very Aristotelian paper: the sets are an abstraction from the concrete reality of the world.

On this Aristotelian picture, what sets exist might well have been different had I wiggled my thumb. Perhaps, then, some of the non-fundamental axioms of set theory are contingent.

Against isotropy

We think of Euclidean space as isotropic: any two points in space are exactly alike both intrinsically and relationally, and if we rotated or translated space, the only changes would be to the bare numerical identities to the points—qualitatively everything would stay the same, both at the level of individual points and of larger structures.

But our standard mathematical models of Euclidean space are not like that. For instance, we model Euclidean space on the set of triples (x, y, z) of real numbers. But that model is far from isotropy. For instance, some points, like (2, 2, 2) have the property that all three of their coordinates are the same, while others like (2, 3, 2) have the property that they have exactly two coordinates that are the same, and yet others like (3, 1, 2) have the property that their coordinates are all different.

Even in one-dimension, say that of time, when we represent the dimension by real numbers we do not have isotropy. For instance, if we start with the standard set-theoretic construction of the natural numbers as

0 = ⌀, 1 = {0}, 2 = {0, 1}, 3 = {0, 1, 2}, ...
and ensure that the natural numbers are a subset of the reals, then 0 will be qualitatively very different from, say, 3. For instance, 0 has no members, while 3 has three members. (Perhaps, though, we do not embed the set-theoretic natural numbers into the reals, but make all reals—including those that are natural—into Dedekind cuts. But we will still have qualitative differences, just buried more deeply.)

The way we handle this in practice is that we ignore the mathematical structure that is incompatible with isotropy. We treat the Cartesian coordinate structure of Euclidean space as a mere aid to computation, while the set-theoretic construction of the natural numbers is ignored completely. Imagine the look of incomprehension we’d get from a scientist if one said something like: “At a time t₂, the system behaved thus-and-so, because at a time t₁ that is a proper subset of t₂, it was arranged thus-and-so.” Times, even when represented mathematically as real numbers, just don’t seem the sort of thing to stand in subset relations. But on the Dedekind-cut construction of real numbers, an earlier time is indeed a proper subset of a later time.

But perhaps there is something to learn from the fact that our best mathematical models of isotropic space and time themselves lack true isotropy. Perhaps true isotropy cannot be achieved. And if so, that might be relevant to solving some problems.

First, probabilities. If a particle is on a line, and I have no further information about it except that the line is truly isotropic, so should my probabilities for the particle’s position be. But that cannot be coherently modeled in classical (countably additive and normalized) probabilities. This is just one of many, many puzzles involving isotropy. Well, perhaps there is no isotropy. Perhaps points differ qualitatively. These differences may not be important to the laws of nature, but they may be important to the initial conditions. Perhaps, for instance, nature prefers the particles to start out at coordinates that are natural numbers.

Second, the Principle of Sufficient Reason. Leibniz argued against the substantiality of space on the grounds that there could be no explanation of why things are where they are rather than being shifted or rotated by some distance. But that assumed real isotropy. But if there is deep anisotropy, there could well be reasons for why things are where they are. Perhaps, for instance, there is a God who likes to put particles at coordinates whose binary digits encode his favorite poems. Of course, one can get out of Leibniz’s own problem by supposing with him that space is relational. But if the relation that constitutes space is metric, then the problem of shifts and rotations can be replaced by a problem of dilation—why aren’t objects all 2.7 times as far apart as they are? Again, that problem assumes that there isn’t a deep qualitative structure underneath numbers.

Universal countable numerosity: A hypothesis worth taking seriously?

Here’s a curious tale about sets and possible worlds: What sets there are varies between metaphysically possible worlds and for any possible world w₁, the sets at w₁ satisfy the full ZFC axioms and there is also a possible world w₂ at which there exists a set S such that:

1. At w₂, there is a bijection of S onto the natural numbers (i.e., a function that is one-to-one and whose range is all of the natural numbers).

2. The members of S are precisely the sets that exist at w₁.

Suppose that this tale is true. Then assume S5 and this further principle:

3. If two sets A and B are such that possibly there is a bijection between them, then they have the same numerosity.

(Here I distinguish between “numerosity” and “cardinality”: to have the same cardinality, they need to actually have a bijection.) Then:

4. Necessarily, all infinite sets have the same numerosity, and in particular necessarily all infinite sets have the same numerosity as the set of natural numbers.

For if A and B are infinite sets in w₁, then at w₂ they are subsets of the countable-at-w₂ set S, and hence at w₂ they have a bijection with the naturals, and so by (3) they have the same numerosity.

Given the tale, there is then an intuitive sense in which all infinite sets are the same size. But it gets more fun than that. Add this principle:

5. If two pluralities are such that possibly there is a bijection between them, then the two pluralities have the same numerosity.

(Here, a bijection between the xs and the ys is a binary relation R such that each of the xs stands in R to a unique one of the ys, and vice versa.) Then:

6. Necessarily, the plurality of sets has the same numerosity as the plurality of natural numbers.

For if the xs are the plurality of sets of w₁, then there will be a world w₂ and a countable-at-w₂ set S such that the xs are all and only the members of S. Hence, there will be a bijection between the xs and the natural numbers at w₂, and hence at w₁ they will have the same numerosity by (5).

So if my curious tale is true, not only does each infinite set have the same numerosity, but the plurality of sets has the same numerosity as each of these infinite sets.

We can now say that a set or plurality has countable numerosity provided that it is either finite or has the same numerosity as the naturals. Then the conclusion of the tale is that each set (finite and infinite), as well as the plurality of sets, has countable numerosity. I.e., universal countable numerosity.

But hasn’t Cantor proved this is all false? Not at all. Cantor proved that this is false if we put “cardinality” in place of “numerosity”, where cardinality is defined in terms of actual bijections while numerosity is defined in terms of possible bijections. And I think that possible bijections are a better way to get at the intuitive concept of the count of members.

Still, is my curious tale mathematically consistent? I think nobody knows. Will Brian, a colleague in the Mathematics Department, sent me a nice proof which, assuming my interpretation of its claims is correct, shows that if ZFC + “there is an inaccessible cardinal” is consistent, then so is my tale. And we have no reason to doubt that ZFC + “there is an inaccessible cardinal” is consistent. So we have no reason to doubt the consistency of the tale.

As for its truth, that's a different matter. One philosophically deep question is whether there could in fact be so much variation as to what the sets are in different metaphysically possible worlds.

From a principle about looking down on people to some controversial consequences

It’s wrong to look down on people simply for having physical or intellectual disabilities. But it doesn’t seem wrong to look down on, say, someone who has devoted her life to the pursuit of money above all else. Where is the line to be drawn? Whom is it permissible for people to look down on?

Before answering that question, I need to qualify it. I think that a plausible case can be made that it is not permissible for us to look down on anyone. The reason for that is that (a) we have all failed morally in many ways, (b) we would very likely have failed in many more had we been in certain other circumstances that we are lucky not to have been in, and (c) we are not epistemically in a position to judge that a specific other person’s failures are morally worse than our own would likely be in circumstances that it is only our luck (or divine providence) not to be in, especially when we take into account the fact that we know much less about other people’s responsibility than about our own. So I want to talk, instead, about when it is intrinsically permissible to look down on people—when it would be permissible if we were in a position to throw the first mental stone.

Let’s go back to the person who has devoted her life to the pursuit of money above all else. Suppose that it turns out that she suffered from a serious intellectual disability that rendered her incapable of grasping values. But her parents, with enormous but misguided rehabilitative effort, have managed to instill in her the grasp of one value: that of money. Given this backstory, it’s clear that looking down on her for pursuing money above all else is not relevantly different from looking down on her for having a disability. On the other hand, it still doesn’t seem wrong to look down on a person of normal intellectual capacities in normal circumstances who has devoted her life to the pursuit of money through making greedy choice after greedy choice.

This suggests a plausible principle:

1. It is only permissible to look down on someone if one is looking down on her for morally wrong choices she is responsible for and conditions that are caused by these choices in a relevant way.

If so, then it is wrong to look down on people for reasoning badly, unless this bad reasoning is a function of morally wrong choices they are responsible for. This has some interesting implications. It sure seems typically intrinsically permissible to look down on someone who reasons badly because she is trying to avoid finding out that she’s wrong about something. If this is right, then typically trying to avoid finding out that one is wrong is itself morally wrong. This suggests that typically:

2. We typically have a moral duty (an imperfect one, to be sure) to strive to avoid error.

Moreover, I think it is implausible to think that this moral duty holds simply in virtue of the practical consequences of error. Suppose that Sally has an esoteric astronomical theory that she isn’t going to share with anybody but you and you tell her that the latest issue of Nature has an article refuting the theory. Sally, however, refuses to look at the data. This seems like the kind of avoidance of finding out that one is wrong that it seems intrinsically permissible to look down on, even though it has no negative practical consequences for Sally or anybody else. Thus:

3. We typically have a moral duty (an imperfect one) to strive for its own sake to avoid error.

But the intrinsic bad in being wrong is primarily to oneself (there might be some derivative bad to the community, but this does not seem strong enough to ground the duty in question). Hence:

4. We have duties to self.

Thus, the principle (1), together with some plausible considerations, leads to a controversial conclusion about the morals of the intellectual life, namely (3), and to the controversial conclusion that we have duties to self.

Cambridge events and objects

Suppose Joe Shmoe died on February 17, 1982, sadly leaving no relatives or friends behind. Every year, on February 17, the anniversary of Shmoe's death occurs. No one marks it in any way. But it occurs, every year, invariably. It is what one might call a Cambridge event, whose occurrence does not mark any real change in the world.

Similarly, there seem to be Cambridge objects. Just as the anniversary is defined by a certain temporal distance, we can define an object by a certain spatial distance. For instance, let me introduce an object: my visual focus. My visual focus is a moving object a certain distance in front of my eyes--sometimes moving very fast (in principle, a visual focus could move faster than light!). My visual focus is a persisting object, unless I close my eyes (I am not sure whether it persists when I blink or just blinks out of existence). Curiously, my visual focus, while typically having a spatiotemporal location, could also exist outside of spacetime. Imagine that I am focused a meter ahead of my nose, and space has an edge. I walk towards that edge, unblinking and never refocusing, rapt in thought about ontology. Before my nose touches the edge of space, my visual focus will have moved beyond it! We can say that the visual focus is "a meter ahead of my face", but that isn't an actual place. So we cannot identify the visual focus with a whole made up of spacetime locations.

My brief remarks have taught you, I think, a little bit about how to talk about visual foci. You now know roughly when my, or your, visual focus exists. You know something about its persistence conditions. You know a little bit about what predicates apply to it. And there is a vast range of stuff that's as yet underdetermined, and could be determined in more than one way. For instance, how wide is the visual focus? Does it shift very quickly with saccades?

But of course it's also clear that there has to be a sense in which there really are no visual foci. Objects that can leave our spacetime so easily, that can move faster than light, and that are entirely outside us but are entirely grounded in our state just aren't really there. They are Cambridge objects instead of real ones, akin to Cambridge events, Cambridge properties and Cambridge changes.

This post is inspired by John Giannini's dissertation.

Philosophy as metaphysics: A very biased view

A Traveling Forms Interpretation of Quantum Mechanics

Paper is here.

Abstract: The Traveling Minds interpretation of Quantum Mechanics is a no-collapse interpretation on which the wavefunction evolves deterministically like in the Everett branching multiple-worlds interpretation. As in the Many Minds interpretation, minds navigate the Everett branching structure following the probabilities given by the Born rule. However, in the Traveling Minds interpretation (a variant by Squires and Barrett of the single-mind interpretation), the minds are guaranteed to all travel together--they are always found in the same branch.

The Traveling Forms interpretation extends the Traveling Minds interpretation in an Aristotelian way by having forms of non-minded macroscopic entities that have forms, such as plants, lower animals, bacteria and planets, travel along the branching structure together with the minds. As a result, while there is deterministic wavefunction-based physics in the branches without minds, non-reducible higher-level structures like life are found only in the branch with minds.

Ontological grounding nihilism

Some people are attracted to nihilism about proper parthood: no entity has proper parts. I used to be rather attracted to that myself, but I am now finding that a different thesis fits better with my intuitions: no entity is (fully) grounded. Or to put it positively: only fundamental entities exist.

This has some of the same consequences that nihilism about proper parthood would. For instance, on nihilism about proper parthood, there are no artifacts, since if there were any, they'd have proper parts. But on nihilism about ontological grounding, we can also argue that there are no artifacts, since the existence of an artifact would be grounded in social and physical facts. Moreover, nihilism about ontological grounding implies nihilism about mereological sum: for the existence of a mereological sum would be grounded in the existence of its proper parts. However, nihilism about ontological grounding is compatible with some things having parts--but they have to be things that go beyond their parts, things whose existence is not grounded in the existence and relations of their parts.

The direction of fit for belief

It’s non-instrumentally good for me to believe truly and it’s non-instrumentally bad for me to believe falsely. Does that give you non-instrumental reason to make p true?

Saying “Yes” is counterintuitive. And it destroys the direction-of-fit asymmetry between beliefs and desires.

But it’s hard to say “No”, given that surely if something is non-instrumentally good for me, you thereby have have non-instrumental reason to provide it.

Here is a potential solution. We sometimes have desires that we do not want other people to take into account in their decision-making. For instance, a parent might want a child to become a mathematician, but would nonetheless be committed to having the child to decide on their life-direction independently of the parent’s desires. In such a case, the parent’s desire that the child become a mathematician might provide the child with a first-order reason to become a mathematician, but this reason might be largely or completely excluded by the parent’s higher-order commitment. And we can explain why it is good to have such an exclusion: if a parent couldn’t have such an exclusion, she’d either have to exercise great self-control over her desires or would have to have hide them from their children.

Perhaps we similarly have a blanket higher-order reason that excludes promoting p on the grounds that someone believes p. And we can explain why it is good to have such an exclusion, in order to decrease the degree of conflict of interest between epistemic and pragmatic reasons. For instance, without such an exclusion, I’d have pragmatic reason to avoid pessimistic conclusions because as soon as we came to them, we and others would have reason to make the conclusions true.

By suggesting that exclusionary reasons are more common than I previously thought, this weakens some of my omnirationality arguments.

My new toy

I've acquired a 3D printer (a used DaVinci 1.0a, hacked by the previous user to have custom firmware), and I've been having fun with it. I still don't have the ideal printing parameters figured out (ABS works OK, but PLA is dodgy, because the printer wasn't designed for it--I had to add a heat sink to help it), but I'm learning how to design 3D solid objects.

I've been finding graphical 3D design tools like Sketchup and Fusion 360 highly unintuitive--maybe with more practice I can improve--but I've also come across OpenSCAD where one uses a simple programming language to code shapes, and that is much more intuitive to me. Last night I designed and printed a super-simple collimator box for the laser collimator for my telescope. Rotating, drawing and dragging faces would have been a big nuisance, but it was a simple bit of code, and it's easily customizable for other dimensions of laser.

Cessation of existence and theories of persistence

Suppose I could get into a time machine and instantly travel forward by a hundred years. Then over the next hundred (external) years I don’t exist. But this non-existence is not intrinsically a harm to me (it might be accidentally a harm if over these ten years I miss out on things). So a temporary cessation of existence is not an intrinsic harm to me. On the other hand, a permanent cessation of existence surely is an intrinsic harm to me.

These observations have interesting connections with theories of persistence and time. First, observe that whether a cessation of existence is bad for me depends on whether I will come back into existence. This fits neatly with four-dimensionalism and less neatly with three-dimensionalism. If I am a four-dimensional entity, it makes perfect sense that as such I would have an overall well-being, and that this overall well-being should depend on the overall shape and size of my four-dimensional life, including my future life. Hence it makes sense that whether I undergo a permanent or impermanent cessation of existence makes a serious difference to me.

But suppose I am three-dimensional and consider these two scenarios:

1. In 2017 I will permanently cease to exist.

2. In 2017 I will temporarily cease to exist and come back into existence in 2117.

I am surely worse off in (1). But if I am three-dimensional, then to be worse off, I need to be worse off as a three-dimensional being, at some time or other. Prior to 2117, I’m on par as a three-dimensional being in the two scenarios. So if there is to be a difference in well-being, it must have something to do with my state after 2117.

But it seems false that, say, in 2118, I am worse off in (1) than in (2). For how can I be better or worse off when I don’t exist?

The three-dimensionalist’s best move, I think, is to say that I am actually worse off prior to 2017 in scenario (1) than in scenario (2). For, prior to 2017, it is true in scenario (1) that I will permanently cease to exist while in (2) it is false that I will do so.

It can indeed happen that one is worse off at time t₁ in virtue of how things will be at a later time t₂. Perhaps the athlete who attains a world-record that won’t be beaten for ten years is worse off at the time of the record than the athlete who attains a world-record that won’t be beaten for a hundred years. Perhaps I am worse off when publishing a book that will be ignored than when publishing a book that will be taken seriously. But these are differences in external well-being, like the kind of well-being we have in virtue of our friends doing badly or well. And it is counterintuitive that permanent cessation of existence is only a harm to one’s external well-being. (The same problem afflicts Thomas Nagel’s theory that the badness of death has to do with unfinished projects.)

The problem is worst on open future views. For on open future views, prior to the cessation of existence there may be no fact of the matter of whether I will come back into existence, and hence no difference in well-being.

The problem is also particularly pressing on exdurantist views on which I am a three-dimensional stage, and future stages are numerically different from me. For then the difference, prior to 2017, between the two scenarios is a difference about what will happen to something numerically different from me.

The problem is also particularly pressing on presentist and growing block views, for it is odd to say that I am better or worse off in virtue of non-existent future events.

Of the three-dimensionalists, probably the best off is the eternalist endurantist. But even there the assimilation of the difference between (1) and (2) to external well-being is problematic.

Progress

I was doing logic problems on the board in class and thinking about rock climbing, and I was struck by the joy of knowing one's made progress on a finite task. You can be pretty confident that if you've got an existential premise and you've set up an existential elimination subproof then you've made progress. You can be pretty confident that if you've got to a certain position on the wall and there is no other way to be at that height then you've made progress. And there is a delight in being really confident that one has made progress.

Moreover, the value of the progress doesn't seem here to be merely instrumental. Even if in the end you fail, still having made progress feels valuable in and of itself. One can try to say that what's valuable is the practice one gets, or what the progress indicates about one's skills, but that doesn't seem right. It seems that the progress itself is valuable. Of course, it has to be genuine progress, not mere going down a blind alley (though recognizing a blind alley, in a scenario where there are only finitely many options, is itself progress).

The value of progress (as such) at a task derives from the value of fulfilling the task, much as the value of striving at a task derives from the value of fulfilling it. But in both cases this is not a case of end-to-means value transfer. Maybe this has something to do with the idea developed by Robert M. Adams of standing for a good. Striving and a fortiori progress are ways of standing and moving in favor of a task. And that's worthwhile even if one does not accomplish the task.

Realism and anti-reductionism

The ordinary sentence "There are four chairs in my office" is true (in its ordinary context). Furthermore, its being true tells us very little about fundamental ontology. Fundamental physical reality could be made out of a single field, a handful of fields, particles in three-dimensional space, particles in ten-dimensional space, a single vector in a Hilbert space, etc., and yet the sentence could be true.

An interesting consequence: Even if in fact physical reality is made out of particles in three-dimensional space, we should not analyze the sentence to mean that there are four disjoint pluralities of particles each arranged chairwise in my office. For if that were what the sentence meant, it would tell us about which of the fundamental physical ontologies is correct. Rather, the sentence is true because of a certain arrangement of particles (or fields or whatever).

If there is such a broad range of fundamental ontologies that "There are four chairs in my office" is compatible with, it seems that the sentence should also be compatible with various sceptical scenarios, such as that I am a brain in a vat being fed data from a computer simulation. In that case, the chair sentence would be true due to facts about the computer simulation, in much the way that "There are four chairs in this Minecraft house" is true. It would be very difficult to be open to a wide variety of fundamental physics stories about the chair sentence without being open to the sentence being true in virtue of facts about a computer simulation.

But now suppose that the same kind of thing is true for other sentences about physical things like tables, dogs, trees, human bodies, etc.: each of these sentences can be made true by a wide array of physical ontologies. Then it seems that nothing we say about physical things rules out sceptical scenarios: yes, I know I have two hands, but my having two hands could be grounded by facts about a computer simulation. At this point the meaningfulness of the sceptical question whether I know I am not a brain in a vat is breaking down. And with it, realism is breaking down.

In order for the sceptical question to make sense, we need the possibility of saying things that cannot simply be made true by a very wide variety of physical theories, since such things will also be made true by computer simulations. This gives us an interesting anti-reductionist argument. If the statement "I have two hands" is to be understood reductively (and I include non-Aristotelian functionalist views as reductive), then it could still be literally true in the brain-in-a-vat scenario. But if anti-reductionism about hands is true, then the statement wouldn't be true in the brain-in-a-vat scenario. And so I can deny that I am in that scenario simply by saying "I have two hands."

But maybe I am moving too fast here. Maybe "I have two hands" could be literally true in a brain-in-a-vat scenario. Suppose that the anti-reductionism consists of there being Aristotelian forms of hands (presumably accidental forms). But if, for all we know, the form of a hand can inform a bunch of particles, a fact about a vector or the region of a field, then the form of a hand can also inform an aspect of a computer simulation. And so, for all we know, I can literally and non-reductively have hands even if I am a brain in a vat. I am not sure, however, that I need to worry about this. What is important is form, not the precise material substrate. If physical reality is the memory of a giant computer but it isn't a mere simulation but is in fact informed by a multiplicity of substantial and accidental forms corresponding to people, trees, hands, hearts, etc., and these forms are real entities, then the scenario does not seem to me to be a sceptical scenario.

Accretion, excretion and four-dimensionalism

Suppose we are four-dimensional. Parthood simpliciter then is an eternal relation between, typically, four-dimensional entities. My heart is a four-dimensional object that is eternally a part of me, who am another four-dimensional object.

But there is surely also such a thing as having a part at a time t. Thus, in utero my umbilical cord was a part of me, but it no longer is. What does it mean to have a part at a time? Here is the simplest thing to say:

1. x is a part of y at t if and only if x is a part of y and both x and y exist at t.

But (1) then has a very interesting metaphysical consequence that only a few Aristotelian philosophers endorse: parts cannot survive being accreted by or excreted from the whole. For if, say, my finger survived its removal from the whole (and not just because I became a scattered object), there would be a time at which my finger would exist but wouldn’t be a part of me. And that violates (1) together with the eternality of parthood simpliciter.

This may seem to be a reductio of (1). But if we reject (1), what do we put in its place, assuming four-dimensionalism? I suspect we will have to posit a second relation of parthood, parthood-at-a-time, which is not reducible to parthood simpliciter. And that seems to be unduly complex.

So I propose that the four-dimensionalist embrace (1) and conclude to the thesis that parts cannot survive their accretion or excretion.

Dualist survivalism

According to dualist survivalism, at death our bodies perish but we continue to exist with nothing but a soul (until, Christians believe, the resurrection of the dead, when we regain our bodies).

A lot of the arguments against dualist survivalism focus on how we could exist as mere souls. First, such existence seems to violate weak supplementation: my souls is proper part of me, but if the body perished, my soul would be my only part—and yet it would still be a proper part (since identity is necessary). Second, it seems to be an essential property of animals that they are embodied, an essential property of humans that they are animals, and an essential property of us that we are humans.

There are answers to these kinds of worries in the literature, but I want to note that things become much simpler for the dualist survivalist if she accepts a four-dimensionalism that says that we are four-dimensional beings (this won't be endurantist, but it might not be perdurantist either).

First, there will be a time t after my death (and before the resurrection) such that the only proper part of mine that is located at t is my soul. However, the soul won’t be my only part. My arms, legs and brain are eternally my parts. It’s just that they aren’t located at t, as the only proper part of me that is located at t is my soul. There is no violation of weak supplementation. (We still get a violation of weak supplementation for the derived relation of parthood-at-t, where x is a part-at-t of y provided that x is a part of y and both x and y exist at t. But why think there is weak supplementation for parthood-at-t? We certainly wouldn’t expect weak supplementation to hold for parthood-at-z, where z is a spatial location and x is a part-at-z of y provided that x is a part of y and both x and y are located at z.)

Second, it need not follow from its being an essential property of animals that they are embodied that they have bodies at every time at which they exist. Compare: It may be an essential property of a cell that it is nucleated. But the cell is bigger spatially than the nucleus, so it had better not follow that the nucleus exists at every spatial location at which the cell does. So why think that the body needs to exist at every temporal location at which the animal does? Why can’t the animal be bigger temporally than its body?

Of course, those given to three-dimensional thinking will say that I am missing crucial differences between space and time.

Three strengths of desire

Plausibly, having satisfied desires contributes to my well-being and having unsatisfied desires contributes to my ill-being, at least in the case of rational desires. But there are infinitely many things that I’d like to know and only finitely many that I do know, and my desire here is rational. So my desire and knowledge state contributes infinite misery to me. But it does not. So something’s gone wrong.

That’s too quick. Maybe the things that I know are things that I more strongly desire to know than the things that I don’t know, to such a degree that the contribution to my well-being from the finite number of things I know outweighs the contribution to my ill-being from the infinite number of things I don’t know. In my case, I think this objection holds, since I take myself to know the central truths of the Christian faith, and I take that to make me know things that I most want to know: who I am, what I should do, what the point of my life is, etc. And this may well outweigh the infinitely many things that I don’t know.

Yes, but I can tweak the argument. Consider some area of my knowledge. Perhaps my knowledge of noncommutative geometry. There is way more that I don’t know than that I know, and I can’t say that the things that I do know are ones that I desire so much more strongly to know than the ones I don’t know so as to balance them out. But I don’t think I am made more miserable by my desire and knowledge state with respect to noncommutative geometry. If I neither knew anything nor cared to know anything about noncommutative geometry, I wouldn’t be any better off.

Thinking about this suggests there are three different strengths in a desire:

1. S_p: preferential strength, determined by which things one is inclined to choose over which.

2. S_h: happiness strength, determined by how happy having the desire fulfilled makes one.

3. S_m: misery strength, determined by how miserable having the desire unfulfilled makes one.

It is natural to hypothesize that (a) the contribution to well-being is S_h when the desire is fulfilled and −S_m when it is unfulfilled, and (b) in a rational agent, S_p = S_h + S_m. As a result of (b), one can have the same preferential strength, but differently divided between the happiness and misery strengths. For instance, there may be a degree of pain such that the preferential strength of my desire not to have that pain equals the preferential strength of my desire to know whether the Goldbach Conjecture is true. I would be indifferent whether to avoid the pain or learn whether the Goldbach Conjecture is true. But they are differently divided: in the pain case S_m >> S_h and in the Goldbach case S_m << S_h.

There might be some desires where S_m = 0. In those cases we think “It would be nice…” For instance, I might have a desire that some celebrity be my friend. Here, S_m = 0: I am in no way made miserable by having that desire be unfulfilled, although the desire might have significant preferential strength—there might be significant goods I would be willing trade for that friendship. On the other hand, when I desire that a colleague be my friend, quite likely S_m >> 0: I would pine if the friendship weren’t there.

(We might think a hedonist has a story about all this: S_h measures how pleasant it is to have the desire fulfilled and S_m measures how painful the unfulfilled desire is. But that story is mistaken. For instance, consider my desire that people not say bad things behind my back in such a way that I never find out. Here, S_m >> 0, but there is no pain in having the desire unfulfilled, since when it’s unfulfilled I don’t know about it.)

"Should know"

I’ve been thinking about the phrase “x should know that s”. (There is probably a literature on this, but blogging just wouldn’t be as much fun if one had to look up the literature!) We use this phrase—or its disjunctive variant “x knows or should know that s”—very readily, without its calling for much evidence about x.

• “As an engineer Alice should know that more redundancy was needed in this design.”

• “Bob knows or should know that his behavior is unprofessional for a librarian.”

• “Carl should have known that genocide is wrong.”

Here’s a sense of “x should know that s”: x has some relevant role R and it is normal for those in R to know that s under the relevant circumstances. In that sense, to say that x should know that s we don’t need to know anything specific about x’s history or mental state, other than that x has role R. Rather, we need to know about R: it is normal engineering practice to build in sufficient redundancy; librarians have an unwritten code of professional behavior; human beings normally have a moral law written in their hearts.

This role-based sense of “should know” is enough to justify treating x as a poor exemplar of the role R when x does not in fact know that s. When R is a contingent role, like engineer or librarian, it could be a sufficient for drumming x out of R.

But we sometimes seem use a “should know” claim to underwrite moral blame. And the normative story I just gave about “should know” isn’t strong enough for that. Alice might have had a really poor education as an engineer, and couldn’t have known better. If the education was sufficiently poor, we might kick her out of the profession, but we shouldn’t blame her morally.

Carl, of course, is a case apart. Carl’s ignorance makes him a defective human being, not just a defective engineer or librarian. Still a defective human being is not the same as a morally blameworthy human being. And in Carl’s case we can’t drum him out of the relevant role without being able to levy moral blame on him, as drumming him out of humanity is, presumably, capital punishment. However, we can lock him up for the protection of society.

On the other hand, we could take “x should know that s” as saying something about x’s state, like that it is x’s own fault if x doesn’t know. But in that case, I think people often use the phrase without sufficient justification. Yes, it’s normal to know that genocide is wrong. But we live in a fallen world where people can fall very far short of what is normal through no fault of their own, by virtue of physical and mental disease, the intellectual influence of others, and so on.

I worry that in common use the phrase “x should know that s” has two rationally incompatible features:

• Our evidence only fits with the role-based normative reading.

• The conclusions only fit with the personal fault reading.

Two senses of "decide"

Suppose:

1. Alice sacrifices her life to protect her innocent comrades.

2. Bob decides that if he ever has the opportunity to sacrifice his life to protect his innocent comrades, he’ll do it.

We praise Alice. But as for Bob, while we commend his moral judgment, we think that he is not yet in the crucible of character. Bob’s resolve has not yet been tested. And it’s not just that it hasn’t been tested. Alice’s decision not only reveals but also constitutes her as a courageous individual. Bob’s decision falls short both in the revealing but also in the constituting department (it’s not his fault, of course, that the opportunity hasn’t come up).

Now compare Alice and Bob to Carl:

3. Carl knows that tomorrow he’ll have the opportunity to sacrifice his life to protect his innocent comrades, and he decides he will make the sacrifice.

Carl is more like Bob than like Alice. It’s true that Carl’s decision is unconditional while Bob’s is conditional. But even though Carl’s decision is unconditional, it’s not final. Carl knows (at least on the most obvious way of spelling out the story) that he will have another opportunity to decide come tomorrow, just as Bob will still have to make a final decision once the opportunity comes up.

I am not sure how much Bob and Carl actually count as deciding. They are figuring out what would or will (respectively) be the thing to do. They are making a prediction (hypothetical or future-oriented) about their action. They may even be trying by an act of will to form their character so as to determine that they would or will make the sacrifice. But if they know how human beings function, they know that their attempt is very unlikely to be successful: they would or will still have a real choice to make. And in the end it probably wouldn’t surprise us too much if, put to the test, Bob and Carl failed to make the sacrifice.

Alice did something decisive. Bob and Carl have yet to do so. There is an important sense in which only Alice decided to sacrifice her life.

The above were cases of laudable action. But what about the negative side? We could suppose that David steals from his employer; Erin decides that she will steal if she has the opportunity; and Frank knows he’ll have the opportunity to steal and decides he’ll take it.

I think we’ll blame Erin and Frank much more than we’ll praise Bob and Carl (this is an empirical prediction—feel free to test it). But I think that’s wrong. Erin and Frank haven’t yet gone into the relevant crucible of character, just as Bob and Carl haven’t. Bob and Carl may be praiseworthy for their present state; Erin and Frank may be blameworthy for theirs. But the praise and the blame shouldn’t go quite as far as in the case of Alice and David, respectively. (Of course, any one of the six people might for some other reason, say ignorance, fail to be blameworthy or praiseworthy.)

This is closely to connected to my previous post.

Two senses of "intend"?

Consider these sentences:

1. Intending to kill the wolverine, Alice pulled the trigger

and:

2. Intending to get to the mall, Bob started his car.

If Alice pulls the trigger intending to kill the wolverine and the wolverine survives, then necessarily Alice’s action is a failure.

But suppose that Bob intends to get to the mall, starts his car, changes his mind, and drives off for a hike in the woods. None of the actions described is a failure. He just changed his mind.

If nanoseconds after the bullet leaving the muzzle Alice changed her mind, and it so happens the wolverine survived, it is still true that Alice’s action failed. Given her intention, she tried to kill the wolverine, and failed.

In the change of mind case, Bob, however, didn’t try to get to the mall. Rather, he tried to start to get to the mall, and he also started trying to get to the mall. His trying to start was successful—he did start to get to the mall. But it makes no sense to attribute either success or failure to a mere start of trying.

There seems to be a moral difference, too. Suppose that killing the wolverine and getting to the mall are both wrong (maybe the wolverine is no danger to Alice, and Bob has promised his girlfriend not to go to this mall). Then Alice gets the opprobrium of being an attempted wolverine killer by virtue of (1), while Bob isn’t yet an attempted mall visitor by virtue of (2)—only when he strives to propel his body through the door does he become an attempted mall visitor. Even if killing the wolverine and getting to the mall are equally wrong, Bob has done something less bad—for the action he took in virtue of (2) was open to the possibility of changing his mind, as bringing it to completion would require further voluntary decisions. What Bob did was still wicked, but less so than what Alice did.

Action (1) commits Alice to killing the wolverine: if the wolverine fails to die, Alice is still an attempted wolverine killer. But Bob has undertaken no commitment to visiting the mall by starting the car.

This suggests to me that perhaps “intends” may be used in different senses in (1) and (2). In (1), it may be an “intends” that commits Alice to wolverine killing; in (2), it may be an “intends” that only commits Bob to starting trying to visit the mall. In (1), we have an intending that p that constitutes an action as a trying to bring it about that p.