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.

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:

• Pythagoras tree
• Dragon curve
• Space fill (rules from here)
• Sierpinski's triangle
• plant (from Wikipedia)

Axiom:
Rules:

	→
	→
	→
	→
	→
	→

Actions:

	→
	→
	→
	→
	→
	→

Preamble:
Iterations:
Show transformed text:

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.

Original:

Minecraft renderings:









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

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!

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.

I contributed to all the evils of the world

1. If doing A would have foreseeably been a contribution to decreasing the probability of an evil E, and I culpably did not do A, then I contributed to E.
2. Praying more for the good of all would have foreseeably been a contribution to decreasing the probability of each individual evil E in the world.
3. I culpably failed to pray more for the good of all.
4. So, I contributed to each individual evil in the world.

Mea culpa.

Elegance and stipulation

Depending on metaphysics, wholes depend on their parts or the parts depend on the wholes. But nothing depends on itself: that would be a vicious circularity. So nothing is a part of itself. On my own preferred story about parts, they are modes of wholes. But perhaps apart from God, nothing is a mode of itself. So, again, nothing is a part of itself (we shouldn't say that God is a part of himself, except trivially if everything is a part of itself).

Yet contemporary usage in mereology makes each thing a part of itself. One is free to stipulate how one wishes. If "part" is the ordinary notion, the contemporary mereologist can stipulate that parthood* is a disjunction of parthood and identity, i.e.,

1. x is a part* of y if and only if x is a part of y or x=y.

However, while one can stipulate how one wishes, one wouldn't expect a disjunctive stipulation to cut reality at its joints.

Why does this matter? Well, one of the interesting questions about parts is what axioms of mereology are true. We have several criteria for what makes a plausible axiom. It's supposed to be intuitive in itself, it's supposed to not lead to paradox, but it's also supposed to be elegant. It seems, however, that one can always ensure the elegance of any axioms with stipulation (just stipulate a zero-place predicate that says that the conjunction of the axioms is true). So it seems we want axioms to be elegant when expressed in terms that cut nature at the joints. In mereology, this would mean that we want axioms to be elegant when expressed in terms of proper parthood* (since proper parthood* is just parthood, the joint-carving natural concept) rather than in terms of parthood*.

This is a bit problematic. For it seems that the standard axioms of mereology get some of their prettiness by using the overlap relation:

2. Oxy iff x and y have a part* in common.

But the overlap relation is a nasty disjunctive mess when expressed in terms of proper parthood*:

3. Oxy iff x=y or x is a proper part* of y or y is a proper part* of x or x and y have a proper part* in common.

This suggests that much of the apparent elegance of the axioms of classical mereology may be spurious. They end up being a mess when you rewrite them in terms of parthood rather than parthood*.

I think the above negative conclusion about the elegance of the axioms of classical mereology is premature, and buys into a mistaken way to measure the elegance of the axioms of a theory. The mistake is to think that one rewrites all the axioms in what Lewis calls "perfectly natural" terms, and then looks at how brief the result is. Mathematicians frequently think that some set of axioms--say, group axioms--are quite "elegant and natural" even when rewriting the axioms in terms of the set membership relation ∈ produces a mess, as it generally does. (Just think of what a mess is produced when anything using the ordered pair (x,y) is rewritten using the set {{x},{x,y}}, and how just about everything in mathematics uses functions and hence ordered pairs.)

One can indeed make any set of axioms brief by careful choice of stipulations. But in some cases the stipulation will itself be very messy (the extreme case is where one replaces all the axioms with a single zero-place predicate) and in other cases there will be many stipulations. But if one can make a set of axioms brief by making a small number of relatively simple stipulations, that is impressive.

A theory can, thus, be elegant even if it is messy and long when all the axioms are written out in perfectly natural terms to the extent that the theory can be elegantly generated from an elegantly small set of elegant stipulations. Classical mereology can satisfy this elegance condition on theories even if I am right that the natural concept of parthood does not allow for proper parts. One just makes the fairly elegant (it's just a disjunction of two natural conditions) disjunctive stipulation (1), and then uses this stipulated notion of parthood* to elegantly stipulate a notion of overlap by means of (2), and then elegantly formulates the rest of the theory in terms of these.

The suggestion I am making is that we measure the complexity of a theory in terms of the brevity of expression in a language that has significant higher-order generative resources that, nonetheless, start with perfectly natural terms. These generative resources allow, in particular, for multiple levels of stipulation. We philosophers have a tendency to simply ignore stipulative definitions. But they do matter. If one takes classical mereology and rewrites the axioms in terms of (proper) parthood, one gets a mess; but the hierarchical stipulative structure of the classical theory is a part of the theory. Furthermore, the generative resources should also allow one to see an axiom schema as simpler and better unified than the sum total of the individual axioms falling under the schema. An axiom schema is not just the sum of the axioms falling under it.

This approach would also let one compare the complexity two different higher-level scientific theories, say in geology or organic chemistry, and say that one is simpler than the other even if both are equally intractable messes when fully expanded out in the vocabulary of fundamental physics. And one can do this even if one does not know how to make the needed stipulations--nobody knows how to define "tectonic plate" in the terminology of fundamental physics, but we can suppose the stipulation to have been made and proceed onward. All this makes it easier to be a reductionist about higher-level theories (I'm not happy about this, mais c'est la vie).

None of this should be news at all to those who are enamoured of computational notions of complexity.

One deep question here is just what generative resources the language should have.

And another deep question should be asked. When we formulate axioms by careful use of stipulation or axiom schemata, what we are really doing is describing the axioms in higher level terms: we are describing a set of sentences formulated in lower level terms. Patterns in reality are sometimes most aptly described not by first-order sentences in fundamental terms, but by describing how to generate those first-order sentences (say, as instances of a schema, or as the result of filling out a sequence of stipulations). We should then ask: How can such patterns be explanatory? I think that if such patterns are explanatory, if they are not mere coincidence, then in an important way reality is suffused with logos, in both of the main sense of the word (language and rationality).

There are, I think, three main options here. One is that we create this reality with our language. Realism forbids that. The second is that we are living in a computer simulation. But this explains the linguistic-type patterns only in contingent reality. But the axioms of mereology or of set theory are not merely contingent. The third is a supernaturalist story like theism, panentheism or pantheism.

A way of thinking about parthood

Take as primitive a "metaphysical component of" relation. Thus, accidents and essences are metaphysical components of their substances. I am interested in a family of accounts of parthood on which

1. x is a part of y if and only x is a metaphysical component of y and F(x) (and maybe G(x)).

In other words, to be a part just is to be a metaphysical component and to be the right sort of thing (and, maybe, for the thing you're a component of to be the right sort of thing). In other words, the relation of parthood would be defined in terms of the relation of being a metaphysical component (which, I suspect, is just the "mode of" or "accident or essence of" relationship) and something that isn't a relation between the part and whole.

Presentism, temporally extended events and Weak Supplementation

Suppose I've been practicing tennis for half an hour, and at this moment I am hitting the ball. Then there are two present events: my practice, P, and my hit, H. Of these events, H is a part of P. But H is distinct from P. After all, P started about half an hour before H. Hence H is a proper part of P. If the Axiom of Weak Supplementation is true, P has to have some proper part K that doesn't overlap H. But H contains all that is present in P. So, K is not present. Thus, there is a non-present event, and hence presentism is false. Assuming, of course, Weak Supplementation, which is the weak point of this argument.

I myself think that Weak Supplementation and Presentism are both false. The argument gets half-way: at least one of the two is false. (There is also the issue that the argument supposes a realism about events.)

Presentism, open future and spoken sentences

Assume:

1. Both presentism and open future are true,

a not uncommon combination. Next, plausibly:

2. It is an essential feature of a sentence token that it has the number of words it does.

Suppose I am now saying a sentence, and have so far uttered the four words "The sky is blue". Let S be my sentence token. Then:

3. There is no fact whether the sentence I am now saying is four words long.

For whether it is four words long depends on what I will go on to say, and that depends on my free will, and so by open future, there is no fact about it. But

4. It is a fact that the sentence I am now saying is S.

So:

5. There is no fact whether S is four words long.

But necessities are never open, and what essential features an object has (if it exists) is a matter of necessity. Hence (5) contradicts (2).

There is a host of premises one can use in place of (2). For instance, it seems to be an essential feature of a spoken sentence token that it ends with a particular sound, or that it has such-and-such grammatical form in such-and-such a language.

Of balloons and transubstantiation

Our three-dimensional space is curved, say, like the surface of a balloon--except that the surface of a balloon is two-dimensional while space is three-dimensional.

Now imagine you have an inflated balloon. Draw two circles, an inch in diameter, on opposite sides, one red and one blue. Put your left thumb in the middle of the red circle and your right thumb in the middle of the blue circle. Press the thumbs towards each other, until they meet, with two layers of rubber between them. The balloon now looks kind of like a donut, but with no hole all the way through. Imagine now that you press so hard that the two layers of rubber between your thumbs coalesce into a single layer of rubber.

Now the single layer of rubber between your thumbs is at the center of the red circle and at the center of the blue circle. We can think of each circle as defining a place, and the coalesced rubber inside it is found in both of these places.

Replace the red circle with a drawing of a church and the blue circle with a drawing of heaven. The same coalesced layer of rubber is both inside (a drawing of) a church and inside (a drawing of) heaven. Suppose now that the rubber is infinitely thin, and that there is a space that coincides with this rubber, and little two-dimensional people, animals, plants and other objects inhabiting this space, much as in Abbott’s novel Flatland . Suppose that the pictures of the church and heaven are replaced with two-dimensional realities. Then the space of the church and the space of heaven literally overlap, so that there is a place that is located in both. An object found in that place will be literally and physically located both in the church and in heaven. In one sense, that object is physically located in two places at once. In another sense, it is located in a single place, but that single place is simultaneously located both in heaven and in the church.

There is no serious additional conceptual difficulty in three-dimensional space curving in on itself similarly.

(This is largely taken from a forthcoming piece by Beckwith and Pruss.)

If the future is open, it is never true that one is saying the truth

Given an open future, it is only true once one has already spoken that one says/said a particular sentence. For as long as one is still speaking, there is no fact of matter about how the sentence will end. It might end in an emphatic "--not!" So no utterance is true while it is being made. It can only be true after a decent pause. This is implausible, so we should reject the open future.

Plagiarism and a repeat invitation

I am occasionally asked whether I am not afraid that someone will steal ideas from my blog and publish them. I'm not. If the ideas get published by someone else, that saves me the trouble of writing them up myself. Hopefully they will give credit where credit is due and it won't be theft.

Moreover, I invite anybody competent who wants to coauthor a paper with me by starting with the ideas in a post, working out the details and writing up a first draft. (Check with me first before getting to work, though.) In the philosophical profession, coauthored papers count pretty much the same as single-authored, so plagiarizing would involve unnecessary risk for very minor benefit.