Thursday, August 25, 2016

Syntax and semantics

One of the things that I've been puzzled by for a long time is the distinction between syntax and semantics. Start with this syntactically flawed bit of English:

  1. I am swimming a hamburger.
It is syntactically flawed, because "to swim" is an intransitive verb, and a sentence that applies an intransitive verb to a subject and an object is ungrammatical, just as an atomic sentence in First Order Logic that applies a unary predicate to two arguments is ungrammatical. This is a matter of syntax. But now consider this more complicated bit of language:
  1. Let xyzzing be eating if the temperature is more than 34 degrees and let it be swimming otherwise. I am xyzzing a hamburger.
My second sentence makes perfect sense when the temperature is 40 degrees, but is ungrammatical in exactly the same way that (1) is when the temperature is 30 degrees. Its grammaticality is, thus, semantically dependent.

One might object that the second sentence of (2) is syntactically correct even when the temperature is 30 degrees. It's just that it then has a semantic value of undefined. This move is similar to how we might analyze this bit of Python code:

def a(f): print(f(1,2))
def g(x,y): x+y
def h(x): 2*x
a(g if temperatureSensor()>34 else h)
This code will crash with
TypeError: () takes exactly 1 argument (2 given)
when the temperature sensor value is, say, 30. But the behavior of a program, including crashing, is a matter of semantics. The Python standard (I assume) specifies that the program is going to crash in this way. I could catch the TypeError if I liked with try/except, and make the program print "Sorry!" when that happens instead of crashing. There is no syntactic problem: print(f(1,2)) is always a perfectly syntactically correct bit of code, even though it results in a TypeError if it's called with f having only one argument.

I think the move to say that it is the semantic value of the second sentence of (2) that depends on temperature, not its grammaticality, is plausible. But this move allows for a different way of attacking the distinction between syntax and semantics. Once we've admitted that the second sentence of (2) is always grammatical but sometimes has the undefined value, we can say that (1) is grammatically correct, but always has the semantic value of undefined, and the same is true for anything else that we didn't want to consider grammatically correct.

One might then try to recapture something like the syntax/semantics distinction by saying things like this: an item is syntactically incorrect in a given context provided that it's not a priori that its semantic value in that context is undefined. This would mean that (2) is syntactically correct, but the following is not:

  1. Let xyzzing be eating if Fermat's Last Theorem is false and let it be swimming otherwise. I am xyzzing a hamburger.
For it's a priori that Fermat's Last Theorem is true. I think, though, that a syntax/semantics distinction that distinguishes (2) from (3) is too far from the classical distinction to count as an account of it.

It may, however, be the case that even if there is no general distinction between syntax and semantics, in the case of particular languages or families of languages one can draw a line in the send for convenience of linguistic analysis. But nothing philosophically or semantically deep should rely on that line.

Wednesday, August 24, 2016

Inculpably acting through culpable ignorance

It is widely held that:

  1. Doing the wrong thing while inculpably ignorant that it's wrong is itself inculpable.
  2. Doing the wrong thing while culpably ignorant that it's is culpable, assuming the other conditions for culpability are met (freedom, etc.).
I think (1) is true but (2) is false. I think that not only does inculpable ignorance excuse, but so does culpable ignorance. (Assuming, of course, that it's real ignorance: one can lie to oneself that one is ignorant when in fact one knows.)

Start with this case. Sally was inculpably ignorant of the wrongness of targeting civilians in just wars. Like many Americans, she was raised to think that the bombing of Hiroshima and Nagasaki were morally permissible, since the bombings saved many lives by ending the war early. One morning, while an undergraduate, she culpably spent an extra five minutes on Facebook before going to her ethics class. As a result, she culpably showed up five minutes late (being late to class isn't always morally wrong, but being late without sufficiently good reason disturbs others' learning and is morally wrong, and I assume this is a case like that). Consequently, she missed the discussion of double effect and the distinction between strategic and terror bombing. Had she heard the discussion, she would have known that it's wrong to target civilians. Since she is culpable for lateness to her ethics class, her ignorance of the wrongness of the kind of terror bombing that Hiroshima and Nagasaki were subjected to is wrong. Years later, incurring no further culpability, she is still ignorant. But then one day there is a just war, and she is a drone pilot asked to target civilians in a situation relevantly similar to Hiroshima and Nagasaki. She does so, believing that it's her duty to do so.

Had Sally refused to follow orders, she would have been culpable for violating her conscience--and indeed, very seriously culpable since her bombing saved many lives by ending the war early (I am assuming that this was the case in Hiroshima and Nagasaki). But in fact, Sally acted wrongly: she committed mass murder. She did so in ignorance, but her ignorance was culpable, since she was culpable for being late to the class that would have cured her of her ignorance.

Given (1), had double effect not been discussed in class that morning when she spent too much time on Facebook, she would have been entirely inculpable for mass murder. It seems implausible that whether Sally is culpable for mass murder depends on what in fact went on in a class that she missed. Furthermore, culpability shouldn't depend on arcane counterfactuals. But it could be quite an arcane counterfactual whether Sally would have learned that it's wrong to target civilians in a just war. It might have depended on fine details of just how persuasive the professor was, what effect Sally's presence in the class would have had on the mode of presentation, etc.

Moreover, it seems implausible that Sally is culpable for mass murder because of her culpability for the peccadillo of being five minutes late to class. The intuition behind (1) is that you don't get culpability out of inculpability. You likewise shouldn't get mass-murder-level culpability out of a peccadillo. But this last argument is a little fast. For while "Sally is culpable for mass-murder" misleadingly suggests that Sally has great culpability. If we accept (1), we should accept a parallel principle that the degree to which one is culpable for a wrong act done in ignorance is no greater than one's degree of culpability for the ignorance. As a result, we might say that Sally is culpable for mass-murder, but the degree of guilt is at a level corresponding to being five minutes late to class (without, I assume, any reasonable expectation that those five minutes would result in ignorance about mass murder).

Very well. Let's suppose that five milliturps are the level of guilt corresponding to the lateness to class. Maybe the level of guilt for the mass murder would have been a gigaturp per victim, if Sally had known that such bombing is wrong. So the suggestion we are now exploring for saving (2) is that Sally's level of guilt for an ignorant bombing run is capped at five milliturps, no matter how many victims there are. (There is something odd about having slight guilt for something so big, but I don't think we should worry about the oddity.) Very well. Consider now two scenarios. In the first one, Sally goes on a single bombing run that she knows will claim 10,000 civilian victims. In the second, she goes on two bombing runs, which will claim 5,000 civilian victims each. On the capping suggestion, in the first scenario, Sally acquires five milliturps of guilt for her bombing run. In the second scenario, she acquires five milliturps of guilt for the first bombing run, too. That's already a little strange: we would expect less culpability with fewer victims. But it gets worse. In the second bombing run, the capping view will also assign five milliturps. As a result, in the second scenario, Sally incurs a total of ten milliturps of guilt. And that seems just wrong: it shouldn't matter that much how the victims are divided up. Furthermore, the intuition being the principle that culpability for an ignorant act can't exceed the culpability for the ignorance is, I think, violated when a multiplicity of ignorant acts exceeds in total culpability the culpability for the ignorance.

We might try a modified capping principle: The culpability for all acts coming from culpable ignorance is capped in total. This has the odd result, however, that in the second scenario, Sally is five-milliturps-guilty for the first run, but not at all guilty for the second, having already reached her culpability cap. At this point it seems much more reasonable simply to suppose that all of Sally's guilt is the initial five milliturps for being late to class. She doesn't acquire a second five milliturps for her bombing runs.

It may seem to be an insult to the memory of the victims that Sally manages to murder them without incurring any guilt. But, for what it's worth, it seems to me to be less of an insult to suppose that she is innocent of the murder than to suppose that she is pecadillo-level guilty for it, as on the capping views.

Tuesday, August 23, 2016

Optical and emotional illusions

It's a pleasant and innocent pastime to look at optical illusions, planning to be initially pulled to error but then to overcome. On the other hand, it's not innocent to invite certain kinds of emotional illusions, to pursue a line of thought that one plans to excite in oneself an unjust scorn for someone or a feeling of class superiority, even if one plans and reasonably expects to overcome these mistaken emotions afterwards. Similarly, it can be a valuable exercise to take what one knows to be a piece of pseudoscientific reasoning and put oneself in the shoes of the reasoner, try to feel the force of that reasoning from the inside, as long as one is confident that one won't be finally taken in. But to do this with faulty moral reasoning seems deeply problematic: it is a bad thing to read Mein Kampf or watch Birth of a Nation while putting oneself in the author's or director's shoes, trying to feel the force of the moral convictions from the inside, even if one is confident that in the end one won't be taken in.

Likewise, there need be nothing wrong with reading science fiction or fantasy that presents a world with laws of nature different from ours and to engage in the willing suspension of disbelief. It may even be fine when the world has a different mathematics from ours--to read, for instance, a story about a message encoded in π, a message that, we suppose, isn't there (at least not where the story says it is). But to engage in the willing suspension of disbelief when reading fiction that presents a morally different world--say a world where enslaving the weak is actually right (and not just seen as right)--is much more problematic.

Ever since I met it in Plato's Protagoras, I've been attracted to the idea that emotions are a kind of perception, akin to visual perception. But the above disanalogies need to be taken into account. I see two ways of doing this. The first is to say that emotion differs frmiom the senses qua perception. Perhaps, for instance, the senses present things as prima facie, something that needs to be weighed further by reason, while emotions present things as ultima facie. I doubt that that works, but maybe some approach along those lines works. The other is to say that the difference has to do with content. We might say, inspired by Robert Roberts, that emotions have as their subject matter evaluative matters of concern to one qua evaluate matters of concern to one. Maybe this makes the pursuit of emotional illusion problematic.

But is pursuit of all emotional illusion problematic? While it would be wrong to pursue a feeling of class superiority, would it be wrong to pursue a feeling of class inferiority, for instance to better feel compassion for people who have been socialized into such a feeling? I am inclined to think that even pursuit of a feeling of class inferiority is morally problematic. That's a feeling no one should have, and it is contrary to self-respect to feel it.

Monday, August 22, 2016

Partial location, quantum mechanics and Bohm

The following seems to be intuitively plausible:

  1. If an object is wholly located in a region R but is not wholly located in a subregion S, then it is partially located in RS.
  2. If an object is partially located in a region R, then it has a part that is wholly located there.
The following also seems very plausible:
  1. If the integral of the modulus squared of the normalized wavefunction for a particle over a region R is 1, then the particle is wholly located in the closure of R.
  2. If the integral of the modulus squared of the normalized wavefunction for a particle over a region R is strictly less than one, then the particle is not wholly located in the interior of R.
But now we have a problem. Consider a fundamental point particle, Patty, and suppose that Patty's wavefunction is continuous and the integral of the modulus squared of the wavefunction over the closed unit cube is 1 while over the bottom half of the cube it is 1/2. Then by (3), Patty is wholly contained in the cube, and by (4), Patty is not wholly contained in the interior bottom half of the cube. By (1), Patty is partially located in the closed upper half cube. By (2), Patty has a part wholly located there. But Patty, being a fundamental particle, has only one part: Patty itself. So, Patty is wholly located in the closed upper half cube. But the integral of the modulus squared of the wavefunction over the closed upper half cube is 1−1/2=1/2, and so (4) is violated.

Given that scenarios like the Patty one are physically possible, we need to reject one of (1)-(4). I think (3) is integral to quantum mechanics, and (1) seems central to the concept of partial location. That leaves a choice between (2) and (4).

If we insist on (2) but drop (4), then we can actually generalize the argument to conclude that there is a point at which Patty is wholly located. Either there is exactly one such point--and that's the Bohmian interpretation--or else Patty is wholly multilocated, and probably the best reading of that scenario is that Patty is wholly multilocated at least throughout the interior of any region where the modulus squared of the normalized wavefunction has integral one.

So, all in all, we have three options:

  • Bohm
  • massive multilocation
  • partial location without whole location of parts (denial of (2)).
This means that either we can argue from the denial of Bohm to a controversial metaphysical thesis: massive multilocation or partial location without whole location of parts, or we can argue from fairly plausible metaphysical theses, namely the denial of massive multilocation and the insistence that partial location is whole location of parts, to Bohm. It's interesting that this argument for Bohmian mechanics has nothing to do with the issues about determinism that have dominated the discussion of Bohm. (Indeed, this argument for Bohmian mechanics is compatible with deviant Bohmian accounts on which the dynamics is indeterministic. I am fond of those.)

I myself have independent motivations for embracing the denial of (2): I believe in extended simples.

Thursday, August 18, 2016

Degrees of location?

If collapse versions of quantum mechanics are right, then objects typically don't have location simpliciter. Instead, they have a wavefunction the square of whose modulus describes the probability that the object will collapse to a given location. Perhaps right after a collapse, the objects have a single definite location, but the single definite location doesn't last beyond that moment.

Suppose we take all this seriously as metaphysics. I think there are several options. The first is that we should take the wavefunction, or the square of its modulus, as providing the whole story about an object's location. In that case, it is rarely if ever correct to say that an object has a particular location. Instead, one should say that objects have their locations to various degrees. (This degreedness of location is different from the way in which we can say that a person who has one leg in a room is to a lesser degree in the room than someone who has an arm and a leg in it.) Location, at least as exhibited in the actual world, is a degreed property.

The second option is that an object is wholly in a location when and only when the wavefunction assigns unit probability to its being there. This has the odd consequence that if a point particle is wholly in a region R, then it is also in every punctured region of the form R−{x}, since the integral of the modulus squared of the wavefunction over R and over R−{x} will be the same. But this means that the particle is wholly absent from every point of the region R, even while wholly present in the region R. That seems problematic.

A third option is that being wholly located is metaphysically primitive, and there is a law of nature that makes it be the case that when the integral of the modulus squared of the (normalized) wavefunction of a particle over a region R is 1, and the region R is "nice" (e.g., equals the interior of its closure), the particle is wholly in R.

I like the first option most...

Inside and outside

In The Last Battle, C. S. Lewis sketches a picture of heaven which is like an onion, with multiple layers, but with the inside of each layer bigger than the outside.

We can get a two-dimensional model by imaging a spherical space with an even bigger bubble sticking out of the sphere in one area.  A two-dimensional being could seamlessly transition from the original area to the bubble area. And of course we can enhance this by supposing bubbles on bubbles, larger and larger. The result would look like a snowman.

But even in the single bubble case, there is the question of the sense in which the bubble area counts as the inside and the rest as the outside. After all the bubble area is the larger one.

I think scenarios like C. S. Lewis's make us realized that the distinction between inside and outside may be rather arbitrary.

This reminds me of the joke about the mathematician who was given a rope and told he could have as much land as he could enclose. He made a small circle of rope around himself and said: "I stipulate that I am on the outside."

I'm probably not a brain in a vat

This is very naive but has only occurred to me:

  1. If I were a brain in a vat, I'd expect my experiences to be simple or not very orderly (glitchy); but if I were an ordinary human being as I seem to be, the experiences I would expect would be like that.
  2. My experiences are complex, continuous and very orderly.
  3. So, probably, I am an ordinary human being rather than a brain in a vat.
Why believe premise (1)? Well, it's hard to hook up all the nine or so senses to simulated data of great complexity. Furthermore, my experiences have diachronic order and complexity over decades. This could be produced by fake memories, but fake memories would likely be hard to impose.

This argument is specific to brains in vats. It might not apply to other sceptical hypotheses.

Tuesday, August 16, 2016

A strategy for arguing against physicalism

Here's an interesting argument schema:

  1. A single particle makes no definite difference to whether something has F.
  2. F is not vague.
  3. I definitely have F
  4. A single particle definitely does not have F
  5. So, I am not merely made of particles.
The inference goes something like this: If I am merely made of particles, one could just take away the particles one by one. If F is not vague, there will be a point at which F will definitely disappear by (4). But a single particle makes no difference to having F, so we must reject the assumption that I am merely made of particles.

The challenge in this argument schema is to find Fs that satisfy (1)-(4) (and typically (4) will be uncontroversial). Here are some plausible candidates:

  • consciousness
  • being a moral agent
  • rights (variants: being an end rather than a means; being such that it is wrong to intentionally kill one if one does not deserve it)
  • representation of the world (intentionality)
  • a teleological directedness to knowledge/virtue/etc.
Given a number of candidates for F we can run this meta-argument:
  1. At least one of these candidates satisfies (1)-(4).
  2. So, I am not merely made of particles.
And (6), being a large disjunction, will be probable.

Sunday, August 14, 2016

Virtue and mistaken conscience

Being fully virtuous is compatible with doing some things that are wrong. A juror, call her Alice, while acting in the best conscience, send an innocent person to prison, say because enough witnesses for the prosecution are particularly effective liars. It can even be the case that sending the innocent person to prison is done out of virtue and further contributes to virtue.

But now suppose Bob is a juror brainwashed through no fault of his own into thinking that members of some ethnic group should be found guilty whether or not they really are guilty, and that Bob voted to convict. He may well be acting in good conscience. But Bob is a vicious person, even if, I shall suppose, not culpably so. (If this case is possible, that creates trouble for claim (4) here.) Moreover, even though the only way for him to avoid incurring guilt is to unjustly vote to convict (for then he is inculpable, but if he voted to acquit, he would have been culpable for violating conscience), by voting to convict she contributes to her vice.

It is natural to distinguish the cases of Alice and Bob by noting that Alice's wrongful action comes from ignorance of non-moral matters while Bob's comes from ignorance of moral matters.

But that's not quite the right distinction. For instance, the question whether the accused person was in fact innocent may itself hinge on some moral question. Imagine that a perfectly truthful witness testified that either vegetarianism is not morally required or the accused was holding a knife, and this witness refused to say which disjunct is true. If Alice mistakenly (let's suppose) thinks that vegetarian is morally required, she could thereby come to an error about whether the accused committed the crime, on the basis of a mistake about a moral question.

Furthermore, there is a third case. Consider Carla, a good doctor who needs to make a decision whether to perform some procedure. The moral issues are quite unclear, and Carla cannot figure them out on her own. But Carla has good reason to trust her hospital's ethics committee. She acts in accordance with the committee's recommendation, even though in this case the committee is mistaken. Carla acts wrongly. Moreover, her wrong action comes from a mistake about moral matters, indeed a mistake about the specific moral matter at hand. But Carla's action need not (though this may depend on details of the case) be incompatible with full virtue--morality can be complex, and even a fully virtuous person may be unable to figure out all the intricacies of cooperation in evil or triple effect, say. Given enough complexity in the case, Carla may be sufficiently isolated from the wrongmaking features of her action that she does not become morally worse by acting wrongly.

So if we want to draw the distinction between a type of ignorance of what is to be done that detracts from virtue and a kind that does not, that distinction is not to be drawn by distinguishing between ignorance about moral matters and ignorance about non-moral matters, even if to get out of the vegetarianism case we refine this to be a distinction between ignorance about the morality of the matter at hand and other kinds of ignorance.

So how do we draw the distinction? I don't know.

Saturday, August 13, 2016

Physicalism, character and condemnation

The following argument is valid:

  1. (Premise) Necessarily, it is unjust to condemn a person for something that she is in no way responsible for.
  2. (Premise) Necessarily, it is not unjust to condemn a person for having a gravely wicked character when she in fact has a gravely wicked character.
  3. (Premise) If physicalism is true, it is possible for a person to have a gravely wicked character that she is in no way responsible for.
  4. It is impossible for a person to have a gravely wicked character that she is in no way responsible for. (By 1 and 2)
  5. So, physicalism is not true. (By 3 and 4)
Of the three premises, (3) is clearly true. If physicalism is true, a gravely wicked character is simply a function of the arrangement of matter, and particles in the brain of a good person could just randomly quantum tunnel into positions that constitute a gravely wicked character. That leaves premises (1) and (2). I am pretty confident of (1). And (2) has a certain plausibility to it.

Still, I am not really all that confident of (2). Part of my lack of confidence has to do with Christian intuitions about not condemning others. But those intuitions may not be relevant, since (2) concerns justice, while the Christian duties of forgiveness and non-condemnation are grounded in charity, and a desire to oneself be forgiven by God, rather than in justice to the wicked. Still, I am not sure of (2).

The quantum tunneling argument I gave for (3) in fact established a stronger claim than (3): it established the claim that if physicalism is true, it is causally possible for a human person to be gravely wicked without any responsibility for that. This means that we can weaken (1) and (2) by replacing "person" with "human person" and "Necessarily" with "Causally necessarily". I don't know if this does much to make (2) more plausible.

Whatever the merits of the argument, I think it is an independently really interesting question whether (4) is true.

Fun with L-systems

I haven't done much with javascript embedded in HTML before, but I had some fun today before and after our graduation ceremony (congratulations, Clifton, Dan and Karl!). For information about L-systems, see Wikipedia. Edit the following to your satisfaction. Feel free to view the source of this post, and I hereby release this post and its source code into the public domain.
If you click on "Go" with the default settings, you'll get a Koch snowflake. Here are some other systems to explore:
Show transformed text:

Wednesday, August 10, 2016

Calvinism and the Problem of Evil

Two of our former Baylor graduate students, David Alexander and Daniel Johnson, have put together what looks like a very interesting anthology on the problem of evil as connected with Calvinism. Some authors are Calvinists but at least one (myself) is a critic of Calvinism. The authors are: Daniel Johnson, Greg Welty, Heath White, James Bruce, David Alexander, Paul Helm, Hugh McCann, Alexander Pruss, James Anderson, Christopher Green, Matthew Green and Anthony Bryson.

Random dithering of images

I wanted to wrap a rectangular texture of, say, the earth around a sphere in Minecraft to make a 3D image (using RaspberryJamMod and Python). The problem was that my color palette would be limited to Minecraft blocks, and not all blocks would be appropriate--with my son's help, I selected a subset of 82 that would work well for general purpose image rendering. So I needed to reduce the color in the texture. One could just choose the nearest color available for each point in the image, but that would lose a lot of detail. The standard family of techniques to solve this is dithering. However, most dithering algorithms like Floyd-Steinberg or ordered dithering are designed for flat two-dimensional images.

One could come up with a 3D version of one of these algorithms, but I went for a different tack: random dithering. Random dithering isn't much used these days, because it is thought to produce really bad results. But while that would no doubt be true with a two-color palette, it doesn't seem to be true with a larger palette, like my Minecraft 82 block palette. The method I used was to add to each color channel a random perturbation, with distribution either uniform or a cut-off Gaussian, and the results were gratifying. Not quite as good as Floyd-Steinberg, but close.

The original is on the right. "Gaussian X/Y" means a perturbation with sigma X, cut off at -Y and Y. "Uniform X" means a perturbation uniform over the interval [-X,X].

And here's how it looks wrapped on an egg (uniform 20, I think):

Actually, on this cartoon stuff, the dithering is hardly needed. A photograph benefits more from the dithering. It's a dung beetle I photographed outside of our house some years ago.


Minecraft renderings:

In both cases, uniform 20 and Gaussian 20/30 seem good enough. Source code here.

Tuesday, August 9, 2016

Attempted murder is not an attempt to murder

Alice falsely believes that killing her husband Bob would be morally right (say, because Bob committed adultery). She shoots Bob, trying to hit him in the head, but misses completely and Bob escapes. Alice has committed attempted murder. But while she attempted to kill Bob, she did not attempt to murder Bob. For it was her intention to rightfully kill Bob rather than to murder him.

Therefore, attempted murder is not an attempt to murder. Speaking very carefully, we should say that Alice committed an attempted murder but did not attempt a murder. What she attempted was a killing, a killing that would have been a murder had she succeeded.

While the point is particularly clear in the case where the attempted murderer believes the killing to be right, the point also goes through in cases where the attempted murderer knows the killing would be a murder. Suppose Chuck wants to inherit an estate from his uncle Dave. Chuck knows full well that killing Dave would be a murder, and he attempts to kill Dave to gain the estate. Unless Chuck is especially malevolent, Chuck's intention is that Dave should die rather than that Dave should wrongfully die. After all, whether Dave's death is wrongful or not does not affect Chuck's inheritance (as long as Chuck doesn't get caught, that is). Thus Chuck did not intend that Dave be murdered, but only that he be killed.

It seems likely, thus, that in typical cases of attempted murder there was no attempt at murder, but only an attempt at a killing, a killing that the malefactor did or did not know to be a murder.

The point goes through for other misdeeds. An attempt at theft is typically an attempt to take something, but not typically an attempt to thieve. An attempt to lie is typically an attempt to convince of p, but not typically an attempt to convince of a (subjective or objective) falsehood (the crooked car dealer attempts to convince you that the car runs well, and that's all--she isn't trying to convince you of a falsehood as such).

Roughly, it seems that we call an action "an attempt at M", where "M" is a morally loaded description, provided that the agent is attempting to N, where "N" is a morally unloaded description, and where the N would be an M were the agent to succeed. But that's only a rough characterization. Here's a weird case. Erin has just picked up an alien weapon and is attempting to kill Frank, an innocent person, with that weapon. Unbeknownst to Erin, the weapon is a smart raygun that only fires at people whom it is just to kill (e.g., it checks whether the killing would be a part of a just war). Then Erin has committed attempted murder, even though had her attempt to kill succeeded, she would have been engaging in a just killing rather than a murder. I don't know how to characterize attempted murder to get out of counterexamples like this. An interesting ethics project for a graduate student!

Monday, August 8, 2016

A consideration against Weak Supplementation

The Axiom of Weak Supplementation (WS) says that if y is a proper part of x, then there is a part of x that doesn't overlap y. Standard arguments against WS adduce possible counterexamples. But I want to take a different tack. Proper parthood seems to be a primitive relation or a case of a primitive relation (the proper metaphysical component relation seems a good candidate; cf. here). Moreover, this relation does not involve any entities besides the two relata--it's not like the relationship of siblinghood, which holds between people who have a parent in common.

But if R is a primitive binary relation that does not involve any entities besides the two relata, then it is unlikely that the obtaining of R between two entities should non-trivially entail the existence of a third entity. (By "non-trivially", I want to rule out cases like this: everything trivially entails the existence of any necessary being; if mereological universalism is true, then the existence of any two entities trivially entails the existence of their sum.) But if WS is true, then existence of two entities in a proper parthood relationship non-trivially entails the existence of another part. Hence, WS is unlikely to be true.