Two more counterexamples to utilitarianism

It’s an innocent and pleasant pastime to multiply counterexamples to utilitarianism even if they don’t add much to what others have said. Thus, if utilitarianism is true, I have to do so. :-)

Suppose you capture Hitler. Torturing him to death would appal many but, given fallen human nature, likely significantly please hundreds of millions more. This pleasure to hundreds of millions could far outweigh the pain to one. Moreover, even of those appalled by the torture, primarily only Nazis and a handful of moral saints would actually feel significant displeasure at the torture. For being appalled by an immoral action is not always unpleasant except to someone with saintly compassion—indeed there is a kind of pleasure one takes in being appalled. Normally in the case of counterexamples to utilitarianism one worries about making people more callous, the breakdown of law and order, giving a bad example to others, and so on. But the case of Hitler is so exceptional that likely the negative effects from a utilitarian point of view would be minimal if any.

One might think that an even better thing to do from the utilitarian point of view would be to kill Hitler painlessly, and then mark up his body so it looks like he was tortured to death, and publically lie about it.

Yet it is wrong to torture even Hitler, and it is wrong to lie that one has done so (especially if only for public pleasure).

Bailey's Priority Principle

Andrew Bailey formulated and defended the Priority Principle (PP), that we think our thoughts in a primary rather than inherited way. His main argument for PP is a two-thinkers argument: if I think my thoughts in an inherited way, then something else—the thing I inherit the thoughts from—thinks them as well, but there aren’t two thinkers of my thoughts. While this argument is plausible, I think it skirts around the main intuition behind the PP. That intuition is that there is something implausible about us being thinkers in a derivative way. This intuition, however, is quite compatible with there being something that derives its thoughts from us, but not so Bailey’s argument, which (unless I am missing something) equally rules out the hypothesis that we inherit our thoughts and the hypothesis that our thoughts are inherited by something else.

Is there a way to argue for PP in concert with this intuition, namely to argue that whether or not there are two thinkers of my thoughts, I am their primary thinker? Such an argument would also escape the following apparent counterexample. Social organizations can have thoughts, derivative in a complex way from their members’ thoughts. But now suppose I join a club, and everyone else resigns membership. Then the club’s opinion on matters relavant to the club’s subject matter comes to be inherited from me. So now there are two thinkers, the club and me, though I am the primary one. This case (which to be fair I am not completely sure of) is a counterexample to Bailey’s argument but not to its conclusion.

My students came up with two closely related arguments, which we might put something like this. First, among our thoughts are intentions. If these are derivative, we are puppets of the primary intender, contrary to our freedom. Second, some of our thoughts are deliberate. It is a contradiction in terms that we think deliberately and yet our deliberate thought is inherited from a prior deliberate thinker—puppetry is incompatible with deliberativeness.

These arguments do not directly show that we are always primary thinkers, so they immediately imply only a weaker version of the PP (WPP), namely that sometimes we think non-derivatively. WPP is still interesting. For instance, it rules out standard perdurantist theories on which we inherit all our thoughts from our temporal parts. Furthermore, WPP makes PP moderately likely: for it is plausible that if there is any thought-inheritance it always goes in the same direction.

That said, maybe there is some reason to accept WPP without PP. Here is one kind of case. Possessing a concept is, perhaps, a way of thinking. But given some moderate semantic externalism, sometimes we possess a concept—say, of a quark—by inheriting it from an expert. Or suppose that the extended mind thesis is true, so that we count as knowing some things because they recorded on our devices. Maybe electronic devices don’t have knowledge, so this isn’t exactly knowledge inheritance. But imagine that you train a parrot to remember all your credit card numbers (a foolish idea) and you carry the parrot with you always. Now you inherit the knowledge of the numbers (under some description common between you and the parrot, definitely not “credit card number”) from the parrot. I am dubious of the extended mind thesis, but there is no need to stick one’s neck out. WPP does justice to many of our intuitions.

Correction to "Goodman and Quine's nominalism and infinity"

In an old post, I said that Goodman and Quine can’t define the concept of an infinite number of objects using their logical resources. Allen Hazen corrected me in a comment in the specific context of defining infinite sentences. But it turns out that I wasn’t just wrong about the specific context of defining infinite sentences: I was almost entirely wrong.

To see this, let’s restrict ourselves to non-gunky worlds, where all objects are made of simples. Suppose, further, that we have a predicate F(x) that says that an object x is finite. This is nominalistically and physicalistically acceptable by Goodman and Quine’s standards: it states a physical feature of a physical object, namely its size qua made of simples. (If the simples all have some finite amount of energy with some positive minimum, F(x) will be equivalent to saying x has a finite energy.)

Now, this doesn’t solve the problem by itself. To say that an object x is finite is not the same as saying that the number of objects with some property is finite. But I came across a cute little trick to go from one to the other in the proof of Proposition 7 of this paper. The trick transposed to the non-gunky mereological setting is this. Then following two statements are equivalent in non-gunky worlds satisfying appropriate mereological axioms:

1. The number of objects x satisfying G(x) is finite.

2. There is a finite object z such that for any objects x and y with G(x) and $G(y), if x ≠ y, then x and y differ inside z (i.e., there is a part of z that is a part of one object but not of the other).

To see the equivalence, suppose (2) is true. Then if z has n simples, and if x is any object satisfying G(x), then all objects y satisfying G(x) differ from x within these n simples, so there are at most 2ⁿ objects satisfying G(x). Conversely, if there are finitely many satisfiers of G, there will be a finite object z that contains a simple of difference between x and y for every pair of satisfiers x and y of G (where a simple of difference is a simple that is a part of one but not the other), and any two distinct satisfiers of G will differ inside z.

I said initially that I was almost entirely wrong. In thoroughly gunky worlds, all objects are infinite in the sense of having infinitely many parts, so a mereologically-based finiteness predicate won’t help. Nor will a volume or energy-based one, because we can suppose a gunky world with finite total volume and finite total energy. So Goodman and Quine had better hope that the world isn’t thoroughly gunky.

Property inheritance

There seems to be such a thing as property inheritance, where x inherits a property F from y which has F in a non-derivative way. Here are some examples of this phenomenon on various theories:

1. I inherit mass from my molecules.

2. A person inherits some of their thoughts from the animal that constitutes the person.

3. A four-dimensional whole inherits its temporary properties from its temporal parts.

These are all cases of upward inheritance: a thing inheriting a property from parts or constituent. There can, however, be downward inheritance.

4. When a whole has the property of belonging to you, so do its parts, and often the parts inherit the property of being owned from the whole, though not always (you can buy a famous chess set piece by piece).

There may also be cases of sideways inheritance.

5. A layperson possesses the concept of a quark by inheritance from an expert to whom they defer with respect to the concept.

There seems to be some kind of a logical connection between property inheritance and property grounding, but the two concepts are not the same, since x’s possession of a property can be grounded in y’s possession of a different property—say, a president’s being elected is grounded in voters’ electing—while inheritance is always of the same property.

It is tempting to say:

6. An object x inherits a property F from an object y if and only if x’s having F is grounded in y’s having the same property F.

That’s not quite right. For if p grounds q, then p entails q. But this bundle of molecules’ having mass may not not entail my having mass, since it might be a contingent feature of the bundle that they are my molecules, so there is a possible world where the bundle exists and has mass, but I don’t (if only because I don’t exist). It seems that what we need in (6) is something weaker than grounding. But partial grounding seems too weak to plug into an account of property inheritance. Consider my property of knowing something. One of my pieces of knowledge is that you know something. So my knowing something is partially grounded in your knowing something, but I do not think that this counts as property inheritance. (Suppose one bites the bullet and says that my knowing something is inherited from you. Then, oddly, I have the property of knowing something both by inheritance and not by inheritance—inherited and non-inherited property possession are now compatible. I don’t know if that’s right, but at least it’s odd.)

I think we can at least say:

7. An object x inherits a property F from an object y only if x’s having F is grounded in y’s having the same property F.

But I don’t know how to turn this into a necessary and sufficient condition.

Dualism, humans and galaxies

Here is a mildly interesting thing I just noticed: given dualism, we cannot say that we are a part of the Milky Way galaxy. For galaxies, if they exist at all, are material objects that do not have souls as parts.

Hachette v. Internet Archive

I am not a lawyer, but I love constructing counterexamples. I’ve been thinking about the Hachette v. Internet Archive. The Archive scanned a bunch of books they owned, and then lent the scans to users on the Internet, making sure that for each physical book, only one scan was lent at a time. The courts ruled that this was copyright infringement.

I imagine a sequence of cases for a library (the Internet Archive is officially a library in California):

1. A user comes to the library and reads a book in the ordinary way.

2. The book is delicate and valuable, so the library puts the book in a metal box with a window, with delicate robotically controlled page flippers controlled by buttons outside the box. The user reads the book through the window while flipping pages with the buttons.

3. Same as 2, but the user wears glasses.

4. Same as 2, but the user lives across the street from the library, and the librarian has placed the box in the library window so pointed that the user, and the user alone, can read the book via an ordinary refracting telescope, with the user having buttons connected to the page flippers via long wires.

5. Same as 4, but the telescope is digital: it has an optical sensor connected electronically to a screen (basically, a CCTV system).

6. Same as 5, but the optical sensor is inside the library while the digital telescope’s screen is in the user’s home.

7. Same as 6, but the user can be arbitrarily far away, because wires are very long.

8. Same as 7, but instead of custom wiring for the connection between the sensor and the screen and the user’s button’s and the page flippers, a TCP/IP protocol over the Internet is employed.

9. Same as 8, but to reduce wear and tear on the book, the sensor caches the images, so that if the user chooses to jump to a page that has already been viewed, the flippers do not need to operate. The cache is deleted at the end of the session.

10. Same as 9, but the cache is not deleted at the end of the session, but is kept for the next session with the same user.

11. Same as 10, but the cache is kept for the next user. Only one user can access the book at once.

12. Same as 10, but a full cache is generated for all the pages once and for all users. Only one user can operate the system at once.

13. Same as 11, but the whole cache is copied to the user’s device and removed once the loan period expires.

Here, 12 is pretty much what the Archive was doing when it was letting users download books for a period, and 11 was what they were doing when it was letting users view the books via a browser.

If 11 and 12 are not allowed, at what point do things become impermissible?

If the worry is about there being copying, then there is already copying at 5: the electrical data from the sensor is copied to the screen. If the user flips through the book, the copying is of the book as a whole, though the copies are constantly deleted. But it seems to me (who am not a lawyer) that we shouldn’t make a significant distinction between a digital and an analogue telescope. Moreover, even viewing by eye involves copying. As soon as a page of a book is exposed to light, a large stream of copies of the data in the book appear in the air as patterns of light. Whether these copies are in the air or in glass (as in the case where glasses or an analogue telescope is used) does not seem significant. Is it significant if the data is in electrons rather than photons, as in 5?

Perhaps the worry is about non-evanescent copies. That sounds reasonable. When a book is exposed to light, the copies that are immediately made are evanescent (though very large in quantity), and likewise if a sensor and a screen arrangement (e.g., CCTV) is used. Thus, 1-8 might be distinguished from 9-12, and maybe the caching introduced at 9 is the problem.

However, the Internet and other electronic devices already have caching built in at various levels, so there is already some “hidden” caching introduced at 9, so the existence of caching doesn’t seem that significant. It seems like caching is just an efficiency improvement that does not significantly affect the normative issues.

Dignity, ecosystems and artifacts

1. If a part of x has dignity, x has dignity.

2. Only persons have dignity.

3. So, a person cannot be a proper part of a non-person. (1–2)

4. A person cannot be a proper part of a person.

5. So, a person cannot be a proper part of anything. (3–4)

6. If any nation or galaxy or ecosystem exists, some nation, galaxy or ecosystem has a person as a proper part.

7. So, no nation, galaxy or ecosystem exists. (5–6)

Less confidently, I go on.

8. If tables and chairs exist, so do chess sets.

9. If chess sets exist, so do living chess sets.

10. A living chess set has persons as proper parts. (Definition)

11. So, living chess sets do not exist. (4,10)

12. So, tables and chairs don’t exist. (8–9,11)

All that said, I suppose (1) could be denied. But it would be hard to deny if one thought of dignity as a form of trumping value, since a value in a part transfers to the whole, and if it’s a trumping value, it isn’t canceled by the disvalue of other parts. (That said, I myself don’t quite think of dignity as a form of value.)

Pairs

As a warmup to his arguments against the existence of ordinary objects, Trenton Merricks argues against the existence of pairs of gloves.

Here’s another argument against pairs of gloves. I recently bought a pack of 200 nitrile gloves. How many pairs am I buying? Intuitively, there were a hundred pairs in the box. But if so, then we have have an odd question: For which distinct gloves of x and y in the box, do x and y in the box constitute a pair? If they all do, then there are 200⋅199/2 = 19,900 pairs in the box, while sure we would feel ripped off if the box said “19,900 pairs”.

Well, we might say this, starting at the top of the box: the first and second gloves are a pair, the third and fourth are a pair, and so on. But now suppose that something went wrong in the packing, and only 199 gloves went into the box (maybe that actually happened—I didn’t count). Then the box has 49 pairs, plus one more glove. But which of the gloves is the extra? Is it the bottom one, the top one, or some one in the middle? There seems to be no answer here.

Moreover, sometimes I only use one glove at a time. If so, then there is a 50% chance that at this point the next two gloves from the box that I put on aren’t actually a pair, and so when I put them on, I am not actually putting on a pair of gloves.

Perhaps, you say, all these difficulties stem from the fact that nitrile gloves do not have a left and right distinction. But suppose they did, and I got sent a messy box with 100 left gloves and 100 right gloves. Now, if every left glove and every right glove make a pair, there are 100⋅100 = 10,000 pairs, but it would be clearly a rip-off to label the box “10,000 pairs”: clearly, there would be 100 pairs. But now we would once again have the insuperable question of which left glove with which right glove makes a pair.

Maybe the problem disappears if one buys things by the single pair, as the “true pairs” are the ones one buys? I doubt it. If you saw me walking around today, you’d have said I was wearing a pair of black running shoes. But what happened was this: Some years back, I bought a pair of running shoes. The stitching on the right shoe gave out all too soon, and I patched it with a punctured bike inner tube (I save inner tubes that are themselves too far gone to keep patching, as they are useful for various projects), and wore it for another couple of months, but eventually gave in and got a second pair of the same make, model, size and color. After a year or two, I noticed that the left shoe on my newer pair was now more worn than the left shoe on my older pair (I didn’t throw the first pair out). And you can guess what I did: I started wearing the right shoe from the newer pair with the left shoe from the older pair. And that’s what I was wearing today. So, if the true pairs are as purchased, you would have been objectively wrong if you thought you saw me wearing a pair of shoes today: I was wearing two half-pairs. But this is absurd.

One might say: shoes become a pair when customarily worn together. But how many days do I need to wear them together for them to become a pair? And what if I bought two pairs of shoes of the same sort, and every morning randomly chose which left one and which right one to wear?

Perhaps the problems afflicting pairs don’t afflict more tightly bound artifacts. But I suspect it’s largely just a difference in vividness of the problem.

Continuous variation

Some arguments against restricted composition—the view that some but not all pluralities compose a whole—are based on the idea that a feature that cuts reality at the joints, such as composition, cannot be vague, and that if composition is restricted, one can have a continuous series of cases from a case of composition to a case of having lack of composition.

But now suppose I owe you ten dollars. Then there is a continuous series of cases where the amount I pay you ranges from zero to $20. The properties wrong, right and supererogatory cut nature at the joints. But as my payment moves from $9.99 to $10.00, it switches from wrong to right, and as it hits $10.01, it switches from merely right to supererogatory. So, one can have a case where the presence of joint-cutting features depends on something that varies continuously. And there is no vagueness: if I pay less than $10, I definitely wrong you; if I pay $10 or more, I definitely do right.