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.