Faith and credence

Alice: I just saw a giraffe in my yard.
Bob: I always trust you about what's in your yard. So I think it's 55% likely there is a giraffe in your yard.

No, Bob doesn't trust Alice. If he trusted her, his credence that she's telling the truth would have been high.

I am not claiming that we always assign high credence in the assertions of someone we trust in a given matter. This dialogue is perfectly sensible.

Alice to Carla: I just saw a giraffe in my yard.
Bob to Dave: I always trust Alice about what's in her yard. I think I might have just overheard her saying that she saw a giraffe in her yard. So now I think it's 25% likely there is a giraffe in her yard.

In the second dialogue, the reason Bob's credence that there is a giraffe in Alice's yard is lowish has little to do with not trusting Alice about these matters. Rather, it is that he doesn't trust his hearing--he's far from sure that he heard her report a giraffe. I assume in the first dialogue, Bob is quite confident that Alice reported a giraffe--if he isn't, there is no problem.

Trust doesn't require high credence in the assertions of the person we trust. But:

1. If one trusts x with regard to p-type propositions, one assigns high credence to non-exclusive disjunctions like: p is true or x did not assert p.

When I started thinking about this, I also thought it required a high conditional probability P(p | Alice asserted p). But it doesn't require that. Suppose I trust Alice about mathematics and I hear her confidently say something that vaguely sounded like "The derivative of a sine function is a tangent." My unconditional probability that the derivative of a sine function is a tangent is very low (I can just see in my mind that the slope of a sine is bounded and a tangent is unbounded), but even my conditional probability on Alice's asserting it is very low. It's not that I actually don't trust Alice. Rather, it's that if she asserted that the derivative of a sine were a tangent, I would lose my trust in her mathematical knowledge. (It might be a bit more complicated. Trust might be compatible with accepting minor occasional slip-ups. So I might think it's one of those. So maybe even if she said this, I would be trusting her in general--but not in this circumstance.) And it's compatible with trust that there be possible circumstances where one would rationally stop trusting.

Now, here is a question that has had some discussion in the literature: Is it rationally possible to have explicit Christian faith (I am using "explicit" to distinguish from the kind of faith that an "anonymous Christian" might have) and assign only a modest (not at all high) credence to the proposition that God exists? I think that given fairly uncontroversial historical evidence, this can't happen. Here is why:

2. One has explicit Christian faith only if one trusts Jesus in central parts of his teaching.
3. The historical evidence clearly shows that Jesus existed and that a central part of his teaching is that God loves us.

Given the uncontroversial historical evidence, a rational person will accept with very high credence that a central part of Jesus's teaching is that God loves us. By (1) and (2), if she has explicit Christian faith, she will also assign a high credence to the disjunction that God loves us or Jesus didn't centrally teach that God loves us. Since the second disjunction is uncontroversially historically false, the credence will transfer to the first disjunct, and she will assign a fairly high credence to the claim that God loves us. But that God loves us obviously entails that God exists. So she will assign a fairly high credence to that, too. And hence her credence won't be modest (i.e., not at all high).

Interestingly, as far as arguments like this go, it might be possible to have faith in God while only assigning a modest credence to the existence of God. Someone who has faith in God will trust God. So she will assign a high credence to disjunctions like: God loves us or God didn't say God loves us. But while it's uncontroversial that Jesus said God loves us, it's controversial that God said God loves us, since it's controversial whether God exists, but the existence of Jesus is an uncontroversial historical matter (I understand that even the Soviet historians eventually stopped saying that there was no Jesus).

Do theists believe by faith in God that God exists?

Do theists typically believe by faith in God that God exists? Faith is much more than propositional belief. But someone who has faith in a person can believe propositions by faith. What does that mean? I want to start with this necessary condition:

1. x believes that p by faith in y only if x believes that p because x takes y to have assured her specifically that p.

To make the condition sufficient as well as necessary one would at least need to specify something that ensures that the the apparent assurance causes the belief in the right way.

But given (1), how could one believe that y exists by faith in y? One would have to believe that y exists because one took y to assure one specifically to that effect. But that would be rationally odd. Granted, I could hear a voice in the dark assuring "I exist", and I could first believe that The Voice is assuring me that it exists, and conclude from this that The Voice exists. But I wouldn't be concluding that The Voice exists because of the specific content of what was voiced, but simply because something was voiced. The connection between the assurance and the belief that The Voice exists is not a connection in the right way for belief by faith.

Granted, it is possible that the voice sounds so trustworthy that I first form the belief that the content of what was said is true, and then because of that I come to believe that The Voice exists. In that case, I would indeed be believing that The Voice exists and doing so by faith. But I would be ignoring an obvious logical inference from one's data and getting the conclusion of that inference by other means. So what we seem to learn from the case of The Voice is this:

2. Anybody who believes by faith in y that y exists is in a position to believe by obvious logical inference and not by faith that y exists.

And we would expect that often people in that position would go for the obvious logical inference.

But that doesn't quite answer the question I started with, namely whether theists typically believe by faith that God exists. For it could be that (2) is true, and that most people do in fact go for the obvious logical inference, but the voice of God assuring them of his existence is so powerful that in most cases the belief is overdetermined: they believe both by obvious logical inference from God's assurance and by faith.

There is a second complication. One might have faith in y under one description and believe that y exists under another description. For instance, suppose that The Voice in the dark says: "I am the brother you never thought you had." Then you might believe your brother exists by faith in The Voice. This model works well for Christianity. A Christian might well believe that God exists by faith in Christ, even though Christ is in fact God.

Does the model work outside of Christianity, say in Old Testament times? Well, the Voice/brother case suggests that it might work in cases of religious experience. But it seems implausible that most of the theists in Old Testament times were theists because they had a religious experience whose content included an assurance of God's existence. Maybe, though, one can introduce the notion of indirectly believing by faith, where you indirectly believe something by faith provided that you infer it from something that you (directly) believe by faith. To adapt a Plantinga example, God might give you a religious experience that God forgave you your sins; trust in the "inner voice" (i.e., in God, but you don't know that right away) leads you to believe by faith that God forgave you your sins; and then you conclude by logic that God exists.

I don't have an answer to the question I started with, whether theists typically believe by faith in God that God exists. But I have a story that would have to hold for the answer to be affirmative. Typical theists would either have to be in a rational overdetermination scenario or they would have to be in a position where the difference between two different ways of referring to God can be leveraged to make it rationally possible for them to first believe in an assurer, who happens to be God, and then in God as such.

A simple causal theory of the arrow of time

Typical causal theories of time say that the order of time is determined by the order of causal relationships between events in time. This tends to be a difficult theory to develop, if only because of the possibilities of simultaneous causation and time travel. But suppose with substantivalists that there really are moments (or intervals) of time. Then it is possible to have a very simple and elegant theory of the order of time:

1. Time u is prior to time v if and only if time u causes time v.

This theory is, I suppose, inspired by Tooley's idea that earlier points of spacetime cause later ones. It has no worries about the possibility of simultaneous causation. For even if there is simultaneous causation, there is no simultaneous causation between times, since distinct times can never be simultaneous (if u and v are times and they are simultaneous, they are the same time--and of course nothing can cause itself). Likewise, while there is some cost in denying time travel and backwards causation, one can accept time travel and backwards causation while denying that a later time can cause an earlier one.

There is also an interesting and slightly more complex variant:

2. Time u is prior to time v if and only if some event at u at least partially causes v.

This variant, too, is compatible with simultaneous and backwards causation between events--it just rules out simultaneous or backwards causation between an event and a time. It has the advantage that perhaps the dynamic evolution of times isn't just causally driven by earlier times, but by the events at those earlier times. For instance, if a time is a maximal spacelike hypersurface, it is very natural to think on the grounds of General Relativity that the distribution of matter at earlier times causes that hypersurface. We can, further, deem each time's existence to be an event that happens at that time. If we do that, then (2) becomes a generalization of (1).

Duties to siblings: A neglected topic in ethics

There is significant philosophical reflection on the parent-child relationship and the associated duties. But the sibling relationship is, as far as I know, largely neglected. But it's very interesting. Few have a choice whether to be a sibling. Many of us are already siblings from the first moment of our existence, and those who became siblings later were rarely consulted by their parents on whether they wanted to do so. Most of us who are siblings became siblings in childhood, and I suppose we could say that our parents had the authority to make us into siblings at that time. But one can become a sibling in adulthood, too.

Parenthood can be at least in part (and only in part, I've argued) ceded to another by adoption. But while Western culture historically does have siblingmaking (adelphopoiesis) rituals, these are merely the creation of a new sibling relationship rather than the transfer of the relationship. (One might think that adoption transfers the sibling relationship. I am not sure about that. But in any case, adoption is typically a decision by the parents.)

So not only do we typically become siblings with no initial choice, but we have no choice whether to remain siblings. This is made easier by the fact that in the ordinary course of things, duties to one's siblings are less onerous than duties to one's children. But that is only in the ordinary course of things. A stepmotherly nature--or a Providence that cares more about character than comfort--can throw us into circumstances where our duties to siblings are extremely onerous. (This also illustrates a comment from Mark Murphy that we should not expect moral burdens to be equally distributed.)

But what are the duties we have to our siblings? How do they change with the age of the siblings and other differences in circumstances? How are these duties spread among a multiplicity of siblings if there more than two?

Haecceitism and degrees of freedom

According to haecceitism as I shall understand it, there are vast numbers (probably infinitely many) possible worlds that are just like ours in all qualitative features but that differ in which particular entities fill which roles in the world. We should, however, prefer theories with fewer fundamental degrees of freedom. And haecceitism introduces many new fundamental degrees of freedom into the theory like the answer to "Who lived Einstein's life?"

This isn't an objection that haecceitism violates the Principle of Sufficient Reason. It might not. It might be that we can explain why Einstein rather than some other (actual or possible) person lived Einstein's life by supposing that the values of different individuals living a life are always incommensurable and that God freely chooses between these incommensurables. But even if (as I have argued) such a divine choice would be an explanation, it wouldn't be a very illuminating one. It would be a choice between vast (probably infinite) numbers of alternatives that are in an important sense on par. A theory that posits that is less attractive.

We all speak Human

I am attracted to this picture of language. Whether we are speaking Russian or Polish or Mandarin or English or Esperanto, we all speak subsets of one language, Human. Nobody understands much less speakers all of Human, just as nobody understands all of English. Here is a reason to think this. Among the rules governing speech, we have rules governing whether our utterances are to be interpreted as Russian or Polish or Mandarin or English or Esperanto. In some cases the rule is simply: "If the utterance makes sense as Polish but not as anything else, it's Polish." But sometimes that rule isn't good enough. Sometimes the same sequence of sounds (perhaps with slight differences in pronunciation and accent--but those need not determine the language that is being spoken) will make sense in Polish and in Russian. Typically, but not always, it will have a similar meaning. In those cases, the rule is something more contextual: "If we've just been speaking Polish, and this sounds like Polish, it's Polish." But you can also switch between the languages, as long as you make clear that you're doing so. There are, thus, linguistic rules governing the transition between the languages. This makes me think that all the languages are part of one big language, Human, much as the Olympics are one big game played between nations, containing subgames such as fencing or the pentathlon.

Are computer languages part of Human? I am not sure. They aren't languages primarily for communication between humans. I would say that they are part of Human insofar as they are being used to communicate with other people. But if we met aliens, their language wouldn't be a part of Human, even if it sounded just like Polish and had the same semantics. It would be truly a foreign language.

Junior and senior philosophy positions at Baylor

We have two full-time positions at Baylor starting fall 2017:

1. tenure-track assistant professor
2. senior position at the associate, full or distinguished professor level.

Area for both is open.

Write to me if you have questions about Baylor and Waco. If you're thinking of applying, you likely already know about the academic side of our Department, but I can answer those questions.

I think Waco is an amazingly great place to live. The costs of living are sufficiently low that we frequently have graduate students afford to buy houses (admittedly, not in the nicest of neighborhoods). The campus is beautiful and has good recreational facilities. I live across the street from campus, a five minute walk to the gym (free, with pool, 53ft climbing wall, exercise equipment), an eight minute walk to the marina on the Brazos river (free kayak, SUP board, canoe and sunfish rentals) and a twelve minute walk to the Department. There are great mountain-biking and hiking trails in Cameron Park, a really nice zoo, and a fine children's museum. Surprising numbers of people think Fixer Upper is a plus. :-) We are roughly equidistant between Austin and Dallas/Ft. Worth (about 100 miles from each).

Do stipulations change the language?

Technical and legal writing often contains stipulations. The stipulations change the meanings of words already in the language and sometimes introduce neologisms. It seems, however, that technical and legal writing in English is still writing in English. After all, the stipulations are given in English, and stipulation is a mechanism of the English language, akin to macros in some computer programming languages. But we can now suppose that there is a pair of genuinely distinct natural languages, A and B, such that the grammatical structure of A is a subset of the grammatical structure of B, so that if we take any sentence of A, we can translate it word-by-word or word-by-phrase to a sentence of B. Now we can imagine Jan is a speaker of B and as a preamble she goes through all the vocabulary of A and stipulates its meaning in B. She then speaks just like a speaker of A.

When Jan utters something that sounds just like a sentence of A, and means the same thing as the sentence of A, is she speaking B or A? It seems she is speaking B. Stipulation is a mechanism of B, after all, and she is simply heavily relying on this mechanism.

Of course, there probably is no such pair of natural languages. But there will be partial cases of this, particularly if A is restricted to, say, a technical subset, and if we have a high tolerance for artificial-sounding sentences of B. And we can imagine that eventually a human language will develop (whether "naturally" or by explicit construction) that not only allows the stipulation of terms, but has highly flexible syntax, like some programming languages. At this point, they will be able to speak their extensible language, but with one preamble sound just like speakers of French and with another just like speakers of Mandarin. But the language itself wouldn't be a superset of French or Mandarin. And eventually the preamble could be skipped. The language could have a convention where by adopting a particular accent and intonation, one is implicitly speaking within the scope of a preamble made by another speaker, a preamble that stipulated which accent and intonation counted as a switch to the scope of that preamble. Then all we would need to do is to have a speaker (or a family of speakers) give a French-preamble and another speaker give a Mandarin-preamble. As soon as any speaker of our flexible language starts accenting and intoning as in French or Mandarin, their language falls under the scope of the preamble. (The switch of accent and tone will be akin to importing a module into a computer program.) But it's important to note that the production of a preambles should not be thought of as a change in the language any more than saying "Let's call the culprit x" changes English. It's just another device within the old language.

What's the philosophical upshot of these thought experiments? Maybe not that much. But I think they confirm some thoughts about language that people have had already. First, the question of when a language is being changed and when one is simply making use of the flexible facilities of the original question is probably not well-defined. Second, given linguistic flexibility, the idea of context-free sentences and of lexical meaning independent of context is deeply problematic. Stipulative preambles are a kind of context, and any sentence can have its meaning affected by them. There might be default meanings in the absence of some marker, but the absence of a marker is itself a marker. Third, we get further confirmation of the point here that syntax is in general semantically fraught, since it is possible to make the choice of preamble be conditional on how the world is. Fourth, this line of thought makes more plausible the idea that in some important sense we are all speaking subsets of the same language (cf. universal grammar).

This post is based on a line of inquiry I'm pursuing: What can we learn about language from computer languages?

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. Obama equals.

It is syntactically flawed, because "to equal" is a transitive verb, and a sentence that applies an intransitive verb to a single argument is ungrammatical, just as an atomic sentence in First Order Logic that applies a binary predicate to one argument is ungrammatical. (I leave open the further question whether "Obama equals Obama" is grammatically correct; maybe the arguments of the English "equals" have to be quantities.) This is a matter of syntax. But now consider this more complicated bit of language:

2. Let xyzzing be sitting if the temperature is more than 34 degrees and let it be equalling otherwise. Obama xyzzes.

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))
def g(x,y): x+y
def h(x): 2*x
a(h if temperatureSensor()>34 else g)

This code will crash with

TypeError: <lambda>() takes exactly 2 arguments (1 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 politely print "Sorry!" when that happens instead of crashing. There is no syntactic problem: print(f(1)) is always a perfectly syntactically correct bit of code, even though it throws a TypeError whenever 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 a priori that its semantic value in that context is undefined. This would mean that (2) is syntactically correct, but the following is not:

3. Let xyzzing be sitting if Fermat's Last Theorem is false and let it be equalling otherwise. Obama xyzzes.

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 sand for convenience of linguistic analysis. But as a rule of thumb, nothing philosophically or semantically deep should rely on that line.

Now it's time to be a bit of a hypocrite and prepare my intermediate logic lecture, where instilling the classical distinction between syntax and semantics is one of my course objectives. But FOL is a special case where the distinction makes good sense.

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.

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.

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 R−S.
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:

3. 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.
4. 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.

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.

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:

6. At least one of these candidates satisfies (1)-(4).
7. So, I am not merely made of particles.

And (6), being a large disjunction, will be probable.

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.)