The first rule for the professor of higher faculties

From the Jesuit Ratio Studiorum of 1599:

It should be the set purpose of the teacher, both in his lectures as opportunity offers and on other occasions, to inspire his students to the love and service of God and to the practice of the virtues which He expects of them, for this is the sole purpose of all their activities.

Deep Thoughts XXXI

The adequate is good enough.

[If I wrote in a letter of recommendation that someone was an adequate candidate that would probably the kiss of death. But why? Putative explanation 1: It is a tautology that the adequate is good enough. However, it is only a tautology if the same context is held fixed throughout the sentence. Thus, someone might be adequate as a student, but not good enough for admission to a highly competitive program. Putative explanation 2: Letters of recommendation are overblown.]

No one but you yourself can reliably make you be evil

This argument for incompatibilism is inspired by an excellent paper by Patrick Todd that I just heard. I don't know if Patrick would endorse the argument I give, though.
Start with this principle:

1. No one but you yourself can reliably make you be evil.

Explanation is needed. Evil isn't just a bad here—it is a particularly serious kind of bad. Nor is being evil just a matter of having an evil character. For I could, through no fault of my own, be brainwashed into having an evil character, but that wouldn't make me be evil. If I were brainwashed into having a seriously bad character, my actions and my character would be worthy of condemnation, but I would be deserving of pity, and not the kind of condemnation that evil people deserve.
Now, people can cause you to be evil. For instance, they can present you with the temptation to do an evil, and if you fall prey to it your character becomes distorted and they have successfully caused you to be evil. But this temptation was either one that you were very likely to fall prey to or it is not on that you were very likely to fall prey to.
If it was a temptation that you were very likely to fall prey to, then you already had an evil character. For a character that makes one very likely to fall prey to a temptation to do an evil seems to be an evil character. So, the tempter did not make you have an evil character. This may seem to show that the tempter did not make you be evil, but that's not right—it leaves out one possibility, which is that previously you had an evil character but were not evil, because you were not sufficiently culpable for the evil character, but now that you've falled into this temptation, that made you be evil. But I think this can't be so. For if an evil character that you were not sufficiently culpable for made the evil action very likely, then you were not very culpable for the evil action—you were only somewhat culpable for it—and that isn't enough to make you be evil. So if the temptation was one that you were very likely to fall prey to, then either you were already evil, or else you lacked sufficient culpability, and you still lack sufficient culpability.
Oone might worry about boundary cases. Let's say you're pretty bad, but not quite evil. You're just one micromoriarty short of being evil. In that case, maybe, the tempter can produce a temptation such that very likely you'll take it, and then it'll push you over the edge, giving you that micromoriarty, and make you be evil. But I think it's not correct to say then that the tempter made you evil. The tempter only helped you a little bit—you already were almost all the way there.
On the other hand, suppose that the temptation was one you were not very likely to fall prey to. Then quite possibly you did become evil, but because you were not very likely to fall prey to the temptation, the tempter's method by which he made you evil wasn't a reliable method, and so we still do not have a counterexample.
One might have another worry about the argument. There may be some temptations that only a moral hero would have much chance at withstanding. Let's say that only a moral hero would have much chance at failing to betray her friend given some particularly nasty torture T. But we can imagine that if she betrays, she will acquire an evil character. So if you're not a moral hero, it will be very likely that the torture will make you betray, and hence will become evil. But I deny that in this case you will become evil—only your character will. The reason is that temptation that only a moral hero would have much chance at withstanding makes you only slightly culpable, and that isn't enough to make you be evil, unless you were already just a shade short of being evil.
What I said above about single temptations generalizes to long-term plans of temptation. If the plan is pretty sure to work, you already have an evil character, or else you don't become culpable when you fall prey to the plan.
Suppose that (1) is correct. Then we can have the following argument against compatibilism:

2. If compatibilism is true—i.e., if freedom is compatible with all one's mental life being determined—then by setting up appropriate environmental and genetic conditions, one can reliably make someone be evil.
3. Therefore, compatibilism is false. (By 1 and 2)

Epistemic self-sacrifice and prisoner's dilemma

In the fall, I attended a really neat talk by Patrick Grim which reported on several computer simulation experiments by Grim. Suppose you have a bunch of investigators who are each trying to find the maximum ("the solution to the problem") of some function. They search, but they also talk to one other. When someone they are in communication with finds a better option than their own, they have a certain probability of switching to that. The question is: How much communication should there be between investigators if we want the community as a whole to do well vis-a-vis the maximization problem?

Consider two models. On the Local Model (my terminology), the investigators are arranged around the circumference of a circle, and each talks only to her immediate neighbors. On the Internet Model (also my tendentious terminology), every investigator is in communication with every investigator. So, here's what you get. On both models, the investigators eventually communally converge on a solution. On the Internet Model, community opinion converges much faster than on the Local Model. But on the Internet Model the solution converged on is much more likely to be wrong (to be a local maximum rather than the global maximum).

So, here is a conclusion one might draw (which may not be the same as Grim's conclusion): If the task is satisficing or time is of the essence, the Internet Model may be better—we may need to get a decent working answer quickly for practical purposes, even if it's not the true one. But if the task is getting the true solution, it seems the Local Model is a better model for the community to adopt.

Suppose we're dealing with a problem where we really want the true solution, not solutions that are "good enough". This is more likely in more theoretical intellectual enterprises. Then the Local Model is epistemically better for the community. But what is epistemically better for the individual investigator?

Suppose that we have a certain hybrid of the Internet and Local Models. As in the Local Model, the investigators are arranged on a circle. Each investigator knows what every other investigator is up to. But the investigator has a bias in favor of her two neighbors over other investigators. Thus, she is more likely to switch her opinion to match that of her neighbors than to match that of the distant ones. There are two limiting cases: in one limiting case, the bias goes to zero, and we have the Internet Model. In the other limiting case, although she knows of the opinions of investigators who aren't her neighbors, she ignores it, and will never switch to it. This is the Parochial Model. The Parochial Model gives exactly the same predictions as the Local Model.

Thus, investigators' having an epistemic bias in favor of their neighbors can be good for the community. But such a bias can be bad for the individual investigator. Jane would be better off epistemically if she adopted the best solution currently available in the community. But if everybody always did that, then the community would be worse off epistemically with respect to eventually getting at the truth, since then we would have the Internet Model.

This suggests that we might well have the structure of a Prisoner's Dilemma. Everybody is better off epistemically if everybody has biases in favor of the local (and it need not be spatially local), but any individual would be better off defecting in favor of the best solution currently available. This suggests that epistemic self-sacrifice is called for by communal investigation: people ought not all adopt the best available solution—we need eccentrics investigating odd corners of the solution space, because the true solution may be there.

Of course, one could solve the problem like this. One keeps track of two solutions. One solution is the one that one comes to using the biased method and the other is the best one the community has so far. The one that one comes to using the biased method is the one that one's publications are based on. The best one the community has so far is the one that one's own personal opinion is tied to. The problem with this is that this kind of "double think" may be psychologically unworkable. It may be that investigation only works well when one is committed to one's solution.

If this double think doesn't work, this suggests that in some cases individual and group rationality could come apart. It is individually irrational to be intellectually eccentric, but good for the community that there be intellectual eccentrics.

My own pull is different in this case than in the classic non-epistemic Prisoner's Dilemma. In this case, I think one should individually go for individual rationality. One should not sacrifice oneself epistemically here by adopting biases. But in the classic Prisoner's Dilemma, one has very good reason to sacrifice oneself.

A dignity argument against most abortions

1. (Premise) If x has dignity, it is wrong to intentionally kill x primarily for the sake of a benefit to someone other than x.
2. (Premise) Elderly people whose minds are functioning very poorly have dignity.
3. (Premise) If elderly people whose minds are functioning very poorly have dignity, fetal humans have dignity.
4. Therefore, it is wrong to kill a fetal human primarily for the sake of a benefit to someone other than the fetus.

I think something broader than (1) is true—it's also wrong to kill an innocent for the sake of a benefit to x. But (1) will be less controversial. I think (3) is probably the most controversial premise. One argument for (3) is this:

5. (Premise) Dignity is either had by all humans or only by those who satisfy achievement-type conditions for personhood, such as being able to solve relatively sophisticated problems or communicate on a large variety of topics.
6. (Premise) Fetal humans are humans.
7. (Premise) If dignity is only had by those who satisfy achievement-type conditions for personhood, then elderly people whose minds are functioning very poorly do not have dignity.
8. Therefore, if elderly people whose minds are functioning very poorly have dignity, then dignity is had by all humans, and hence by fetal humans as well.

Alas, premise (2) may be somewhat controversial. Here is an argument for it.

9. (Premise) x can only suffer an indignity if x has dignity.
10. (Premise) Elderly people whose minds are functioning very poorly can suffer indignities (and often do).
11. Therefore, elderly people whose minds are functioning very poorly have dignity.

Horrendous evil and indignity

Many horrendous evils are horrendous largely because of horrendous indignity to the sufferer. Such "horrendous indignities" may seem to provide evidence against the existence of God. But on reflection, I think, they do not. For only a being with a dignity can suffer an indignity. It is no indignity for a rock to have mud poured over it. Making fun of a monkey does not harm the monkey. Moreover, only a being with great dignity can suffer a great indignity. Thus, that some beings suffer horrendous indignities entails that these beings have great dignity.

The evidence that many suffer horrendous indignities thus tells us that:

1. There are many finite beings with great dignity,
2. who suffer great indignities.

Now, is this better predicted by theism or by naturalism? Theism predicts (1), though it may not predict (2). Naturalism does not predict (1)—it could even be that naturalism is incompatible with (1) since perhaps great dignity requires being in the image of God; I do not know what it says about (2) (even conditionally on (1)). In any case, the existence of horrendous indignities is also a problem for naturalism, because the existence of beings of great dignity is a problem for naturalism.

Let us step back and ask if (2) is usually such a great problem given theism. We need distinguish "o-dignity", the innate "ontological" dignity of a being, from the "m-dignity" which is a manifestation of o-dignity. In (1) we are talking of o-dignity. Indignity, however, is not the opposite of o-dignity, but of m-dignity. The person who suffers an indignity still has o-dignity—if she didn't have it any more, she wouldn't be suffering an indignity, just as a rock cannot suffer an indignity because it lacks o-dignity. (One's pride can only be hurt when one has pride; otherwise, at worst one's former pride is hurt, and that's not a present hurt.) Thus manifest indignity as such highlights the o-dignity of the being suffering from the indignity. Only the evidently holy can be manifestly blasphemed.

In other words, manifest indignity is a kind of m-dignity. Manifest indignities are self-defeating—they highlight the dignity of that which they demean. (This may remind one of Hegel's master-slave dialectic and of the mockeries Christ suffered.) But horrendous indignities tend to be manifest. As such they paradoxically conduce to the manifestation of o-dignity, and hence there is reason for God to allow them to occur.

True kingship is most manifest when stripped, on the cross and with the side pierced.

Compatibilism and classical theism

Standard definitions of compatibilism say something like:

1. Compatibilism holds if and only if there is a world where there is determinism and at least one exercise of free will.

Standard definitions of determinism say something like:

2. Determinism holds at w if and only if for any time t in the history of w, and any world w* such that (a) the laws of w hold at w* and (b) w* exactly matches w at t, the worlds w and w* exactly match in the future of t.

If we define compatibilism and determinism as above, then classical theism entails compatibilism. According to classical theism, God is outside time, free and omnipotent. God could, then, create a world at which determinism holds, since determinism only concerns the beings that are in time, and hence the determinism would not apply to him. (A tricky issue is: Couldn't God always produce miracles, thereby making the right hand side of (2) be unsatisfied? Well, we could imagine that in the deterministic world, at every time, there is heard a divine promise to do no miracles.) And if he did this, then that would be a world where there is determinism and at least one exercise of free will—namely, God's exercise of free will.
I think this only shows that the standard definitions of (in)compatibilism are wrong. Instead of saying that determinism is incompatible with freedom, they should say that determinism is incompatible with beings like us having freedom.

Liar Paradox and being in a position to know

1. I am in a position to know the denial of (1).

Part I: Assume (1). Then I am in a position to know the negation of (1). But I can only be in a position to know something that's true, and if (1) is true, then its negation is not. So it seems we have a rock-solid argument against (1). Part II: But if we have a rock-solid argument against p, then we are in a position to know the denial of p. Hence I am in a position to know the denial of (1). But that's what (1) says, so (1) is true, after all.

One move that works here, but not in the original Liar Paradox, however, is that one say that Part II of the argument provides a defeater for the argument in Part I, and ensures that the argument in Part I does not put me in a position to know the denial of (1).

So the original Liar Paradox is more powerful. But there is still some paradoxicality here.

A-theory and worlds

According to the best A-theories (i.e., those that accept an Aristotelian view of propositions as changing in truth value), there is an objective and non-relational fact as to what time it is, a fact that won't obtain tomorrow. Assume this. Here is one way to think about this. Let w be the actual world. The actual world holds all the actually true facts, including presumably the fact that it is January 18, since it is indeed Tuesday. Moreover, there will be a world w* at which everything happens just as at w except that at w* it is some time t on January 19. World w* will be a world that we will inhabit at t, tomorrow.

On this view, at every time, we are in a different world. We will then have an earlier-than relation between worlds defined as follows: w is earlier than w* if and only if at w* it is true that w was actual. Assume the earlier-than relation is transitive. Say that two worlds are directly temporally related if and only if either they are identical or one is earlier than the other. We then get:

1. The future is closed if and only if direct temporal relatedness is transitive.

Suppose the future is closed—the best A-theory will say that (or so I claim). Then direct temporal relatedness is an equivalence relation, and for any world w, we can form the equivalence class T(w) of all the worlds directly temporally related to w.

We need one more thing in the formalism. We need a way to compare times between worlds that aren't directly temporally related. Thus, there is a simultaneity relation between worlds. Worlds w and w* are simultaneous provided that at both worlds it is the same time. This relation is also an equivalence relation, and we can let S(w) be the equivalence class of all worlds simultaneous with w.

Each world w is then a member of two orthogonal equivalence classes: T(w) which contains all the directly past and future worlds, and S(w) which contains all the simultaneous worlds. This provides resources for the formation of new modal operators, using one or the other of the equivalence relations as an accessibility relation.

Enough formalism. Maybe in a future post I will try to criticize the view.

Wiimote board

A colleague mentioned how nice it would be to have a SMART Board in one of our classrooms for when he teaches philosophical writing, so he could put student papers up and annotate them on screen.  But, my oh my, these SMART Boards are expensive.  They seem to start at around $1000.  I had vague recollections that I once saw that one could do something quite similar with a Wii Remote, and I told my colleague that I was pretty sure I could put together a solution for about $100.

So, I went home and searched the Internet.  The Wii remotes have cameras that track infrared points.  Johnny Chung Lee wrote free software that works like this: you get a pen with an infrared LED at the tip, point the Wii Remote camera at the screen, calibrate quickly, and then the pen operates the mouse.  Simple and cheap, though you still need software for annotating whatever you want.  There is also shareware Smoothboard software, for under $30, that is more polished and elaborate, allows using two Wii remotes in case one can't see the pen, and includes software that lets you annotate what's currently on the screen.  You don't need a Wii, just a Wii remote, which sells for $33.  And you need a Bluetooth adapter if your PC doesn't have one.  The infrared pens can be bought for less than $10, and if you use a single Wii remote, the project easily comes in under $100 (you may also need to buy a mounting bracket, or make your own).  With two Wii remotes, the project is a little over $100.

We have a Wii and I have a large collection of scrap materials, and that included an infrared LED, an AA battery holder and I had bought a bunch of momentary switches for a now-abandoned project (from Tayda Electronics, in Thailand--surprisingly, their shipping was really cheap, and their components are super cheap), so I quickly made a little infrared pen out of a plastic 35mm film canister, set up our video projector and ran the shareware software.  And, yes, it worked.  It was a bit fiddly to find positions in the room where the Wii remotes' cameras could see all of the screen, and the film canister often obscured the LED.  But it worked.

I also made a second generation infrared pen that made the LED stick out more, out of a piece of bamboo whose hollow was just the right size to take an AA battery.  I didn't try that with the projector, but it works really nicely with the big home laptop.  I eventually stood the Wii remote on my set of Harbor Freight helping hands, and it turns out I didn't need to use a second Wii remote.  It works nicely, except when the kids are using the other remote with the Wii as the Wii grabs the remote when I turn it on.

I was hoping the kids would enjoy it.  With the free driver software (which, granted, is not as polished and much more crashy than the shareware version--but I am cheap), it makes a great controller for Crayon Physics (you need to put Crayon Physics in a double-click erase mode) and works well with the kids' favorite Tux Paint as acceptable with World of Goo.  But surprisingly my daughter prefers the mouse.

I had a lot of fun with the project over the weekend.  I am not sure my own teaching would benefit from the setup.  I don't use Powerpoint very often, and when I do, I don't think I need to annotate on screen.  And if I did, I wouldn't mind doing it with a keyboard and mouse.

Basically, the whole thing is a modern take on a light pen, except that the light pen technology was tied to CRT displays.

An argument against a metaethical naturalism

Consider this metaethical naturalist view:

1. Every moral property is identical with a natural property.

Here is a simple argument against this. Let M be a very general moral property like having at least one obligation or not being morally guilty of anything (the argument doesn't work for all moral properties, but does work for these two). Then:

2. (Premise) For any natural property N, it is possible for there to be a being that lacks N but has M.
3. Therefore, M is not identical with any natural property.
4. (Premise) M is a moral property.
5. Therefore, there is a moral property that is not identical with a natural property.

The controversial premise is (2). One way to (2) is this. We can imagine a non-natural agent that lacks all natural properties but nonetheless has M. We can imagine non-material beings that have no energy, no charge, that do not occupy space and time, but that, nonetheless, have moral properties like M.

But there is, I think, an interesting response to the argument. Maybe a property P can be natural in a being x but not natural in a different being x. For instance, the property of being a cause might be a natural property of a physical event, but a non-natural property of a supernatural being. Thus, one might argue that our non-natural being x that has M but "lacks all natural properties" can still have P, because P might be natural in us, but non-natural in x.

If so, then (1) should be modified to:

6. Every moral property is identical with a property that is natural as found in beings like us.

Or, even more cautiously, acknowledging that there might be moral properties that a being like us cannot have, but that a supernatural being can have (e.g., if A is some action completely beyond our capabilities, then we cannot be obligated to do A, but a supernatural being that promised to do A can be obligated to do A):

7. Every moral property of a being like us is identical with a property that is natural as found in beings like us.

But (7) is subject to a worry. If the argument is right, then moral properties like being obligated to do something or not being guilty of anything can only be identical with those properties natural in us that a radically supernatural moral agent could also have. Those would be complexes of very general properties like being a cause, but not of properties like having a brain. This constrains the ingredients for a naturalist metaethics to a subclass of the natural properties—namely, those that radically supernatural moral agents could have—and thereby makes naturalist metaethics harder. And the idea that naturalness is relative to the being in which the property is found is going to be at least somewhat controversial.

The same argument applies in the case of mental properties.

The problem of the stone

I like to use the stone argument as a warm-up in a philosophy of religion class. But it's actually kind of tricky to use. Here's a natural way to put it:

1. Either God can or cannot make a stone he can't lift.
2. If God cannot make such a stone, then there is something God can't do.
3. If God can make such a stone, then there is something God can't do, namely lift the stone.
4. So, there is something God can't do.

But in this formulation, (3) can be easily rejected. It does not follow follow from God's merely being able to make such a stone that there is something God can't do, just as it doesn't follow from God's being able to make a unicorn that there is a unicorn. The correct conditional is:

5. If God does make such a stone, then there is something God can't do, namely lift the stone.

But if we replace (3) by (5) in the argument, the argument ceases to be valid.

This means that the stone argument isn't actually an argument against omnipotence. If all that was in view was omnipotence, one could say: "Sure, God can create such a stone. Were he to create it, he wouldn't be omnipotent. But he hasn't created such a stone and he is omnipotent." Rather, we should take the stone argument as an argument against essential omnipotence. And that makes the argument a little less suited for warm-up classroom use, because one has to introduce the notion of an essential property.

What I actually did in class today is I gave the argument in the invalid form. Alas, nobody caught the invalidity. Though, interestingly, one student was unsure of disjunction-elimination in general.

I also emphasized that the stone wasn't really a problem for omnipotence, but for particular attempts to define omnipotence. I think it's important to to distinguish those atheological arguments that are problems for theism from those that are problems for particular ways of defining theism. The inductive problem of evil is an argument against theism; the stone argument is only an argument against particular formulations.

Grammar, types and tokens

Question: Does grammar primarily govern the relations between word-types or those between word-tokens?

Answer: Grammar does not primarily govern the relations between word-tokens. In human spoken and written languages, there are are tokens corresponding to parts of sentence types like the subject or the predicate. Thus, a token of the sentence "Paris is full of snow" contains a token of "Paris" and a token of "is full of snow". But this is a mere accident of our languages. We can easily imagine languages where the grammatical parts of a sentence type do not correspond to physical parts of a sentence token. For instance, we could imagine that a language can only be spoken via Goedel numbering. In such a language, we can still have a complex grammar, and there will be tokens of sentences—e.g., Arabic numeral expressions of Goedel numbers—but there need be no tokens of individual words. We could, I suppose, stipulate that a word is tokened when a sentence containing it is tokened, but that only gives us acts of tokening and not tokens. And, ontologically, it is not clear that there would be a separate act of tokening for each of the parts—maybe one could just say the sentence as a whole, without thinking about the parts. (I am a coarse-grained action theorist.)

One can imagine languages where the only tokens are tokens of sentences, but where there is still a Montague grammar. But in such a language, the arguments of the functors do not correspond to tokens.

Since we want the phenomenon of grammar to be as uniform as we can make it across imaginable languages, we should not take grammar to govern the relations between tokens, or even potential tokens, because some languages just don't have enough of these.

But strictly speaking we should not take grammar to govern the relations between types. For in a language where there are no tokens corresponding to, say, individual nouns, but only sentence tokens, the grammar may still take account of nouns. But these nouns won't be types, because a type is the sort of thing that is supposed to have a token. Rather, in such a language we would introduce abstract entities to play the role of types, but these abstract entities wouldn't actually be types, since there would be no type-token relation defined for them. We could call these entities "linguistic items". The grammar of the language would then specify how linguistic items can combine into other linguistic items, in the standard Montague grammar way. And then some special, distinguished linguistic items—for instance, sentences—would have the additional property of being expressible by a token. And these linguistic items would also be types.

So in fact the answer to the question is "neither". Grammar governs the relations between linguistic items. But these items need be neither types nor tokens. (This undercuts Goodman-Quine attempts to do grammar at the token level.) Then there is something other than grammar, which we might call coding, which governs the relation between the special linguistic items that are expressible by a token and their tokens. And of course there will be semantics/pragmatics (I do not distinguish these, though of course most do).

So what are these linguistic items? One option, inspired by Rob Koons: Carefully delineated social practices. I am not sure this will work, but it might. Second option: Don't worry! Just do your grammar, coding and semantics/pragmatics in terms of linguistic items, and Ramseyfy. I also don't know if this will work, but it might.

Virtue and wasted life

The following argument is valid:

1. (Premise) No life lived virtuously can have been wasted.
2. (Premise) If God doesn't exist, a life lived virtuously can have been wasted.
3. Therefore, God exists.

Is it sound? Well, yes, if God exists. For if God exists, then (1) is true, and if God exists, then (2) is trivially true as its antecedent is false (my indicatives in arguments are material unless noted otherwise).

But of course the question is whether the argument is any good, at all useful towards giving someone reason to accept the conclusion. Well, I do find myself with a certain pull towards (1) and (2) independently of theism. Claim (1) just seems right to me. But if God doesn't exist, then it does seem quite possible for someone's central life pursuits to have been unsuccessful, despite these central life pursuits being virtuous.

However, I have the following worry. Maybe no life lived virtuously can have been wasted, because what it is to have wasted a life is to have failed at one's central pursuits or to have centrally pursued only vanities. But a virtuous person always has her own virtue as a central pursuit, and hence a virtuous person's life is never wasted, as one of her central non-vain pursuits—that of her own virtue—has been successful. Thus, even if God doesn't exist, a life lived virtuously couldn't have been wasted.

But I think that if theism were false, then a virtuous person might never centrally pursue her own virtue. For it could be that she is faced with needs more urgent than the pursuit of her own virtue—feeding a starving family, say—and so virtue could require her not to centrally pursue her own virtue. And if this is rigth, then (2) is non-trivially true. If God did not exist, there would be a possibility of a wasted virtuous life. It would be a life where one has virtue but does not pursue it as a central part of one's life, because virtue itself prohibits making the pursuit of virtue central.

If Christian theism is true, however, other duties will not be sufficient to shift the pursuit of virtue into something of secondary importance. For the Christian can have a trust in Providence that we will not go wrong by making our pursuit of union with God (which requires the pursuit of virtue) central to our lives.

This gives a second version of the argument:

4. (Premise) If theism is false, then a virtuous human being can be in circumstances such that she should assign only secondary importance to the pursuit of virtue.
5. (Premise) It is not possible for a human being to be in circumstances in which she should assign only secondary importance to the pursuit of virtue.
6. Therefore, theism is true.

I do not find the two arguments in this post deeply compelling. But I think they at least should somewhat raise the probability of theism for those for whom it is neither zero nor one.

Retinal images

Here's a nice way to get an idea just how much processing intervenes between retinal images and conscious perception. Unless you're reading this post through a screen reader or some other assistive technology, while you're reading the post, your eyes are moving in very fast saccades. So your retinal images are a mess. They are like a video produced by a camera that is waving around apparently randomly at high speed. But screen and the text on it looks to you as if it was basically still. You do not see the mess of retinal images with different orientations—they are all stitched together in complex post-processing into an image of something unmoving. Now, walk around while looking at some three solid and unmoving dimensional object in your environment. In addition to the shifts in retinal image produced by the eye motion, there are shifts due to head motion, due to the up-and-down rhythm of your walk, as well as the exposures of hidden surfaces. Yet the solid and unmoving object looks unmoving.

Of course, there are times when the post-processing fails—there are illusions of motion. For instance, because there is a background behind the laptop screen, and parallax ensures apparent relative movement of the laptop and the background, when I move my head, it does look like the laptop is moving relative to the background.

In any case, what we see does not look like what you get from a head mounted camera. And our retinal images are even jumpier than that, as the head mounted camera does not follow the eye-muscle saccades. We have some really quite amazing image stabilization.

The Principle of Sufficient Reason, now in paperback

Shame-free self-promotion: I was looking on Amazon, and it looks like my Principle of Sufficient Reason book is now available in paperback (oddly, rather less expensive than the Kindle edition), while Actuality, Possibility and Worlds can be preordered in hardback and paperback.

Deep Thoughts XXX

Only a professional can be unprofessional.

Saying

Consider this theory. To utter a sentence is to offer a description of a proposition. Sometimes, whether contingently or necessarily, no proposition meets the description. That is a case of nonsense. Sometimes more than one proposition meets the description. That is a case of vagueness (ambiguity is a case where the sentence's words fail to determine the proposition, but the sentence as a whole does—in agreement with how one might read Frege on tense, I take the context to be a part of the sentence or, in his terminology, the "expression"). Subintensional vagueness is when the propositions that meet the description necessarily have the same truth value. Intensional vagueness is when they possibly have different truth values. Extensional vagueness is when they actually have different truth values. I suspect that subintensional vagueness occurs all over the place.

How do these descriptions work? I think in a recursive way. For instance, the sentence "F(a)" describes a proposition that applies Fness to a. What does it mean to say that a proposition "applies" Fness to a? Well, we can say this: necessarily, a proposition that applies Fness to a is true if and only if a exists and has Fness. But this is not sufficient to determine the concept of application—after all, there are many propositions that satisfy this description, such as the proposition that God knows that a has Fness and the proposition that a has Fness or 2+2=5. We can lay down a few more conditions on application. A proposition that applies Fness to a is not going to be truthfunctionally complex if F is not truthfunctionally complex. (But truthfunctional complexity needs to be defined, and it is hard to do that.) The functor application from property-object pairs to propositions is natural. Maybe something can be said about explanatory priority.

But, on the present theory, there is little reason to think that filling out the above story will narrow down the notion of application, or of Fness for that matter, so far as to ensure that there is only one proposition that meets the description given by the sentence "F(a)". Similar points apply to truthfunctionally complex sentences. Thus, "s and u" describes a proposition which the output of the conjunction functor as applied to the propositions described by "s" and by "u". But we cannot give an unambiguous definition of the conjunction functor. So subintensional vagueness is everywhere.

Now we have a story to tell about the classic liar sentence: "This is a falsehood." Such a sentences attempts to describe a proposition that denies truth to itself. But there is no reason to suppose that there is such a proposition, and indeed there is a very good reason to suppose that there isn't—namely, that the supposition that there is such a proposition immediately leads to a logical contradiction (what better argument could one ask for?). (One might try Goedel numbering and diagonalization. But Goedel numbering works for sentences, not propositions, and because of subintensional vagueness, the correspondence between sentences and propositions is not one-to-one.)

The contingent liar is tougher, but perhaps some generalization of the solution will work. (It might help if some propositions are contingent beings.)

Sex and the definition of marriage

Marriage is primarily defined by a solemn commitment and perhaps some related auxiliary conditions, like a psychological and physical ability to at least minimally fulfill the commitment. Here is a question one may ask about this commitment:

1. Is there any positive sexual content to the marital commitment?

By "positive sexual content", I mean a commitment to engage in, or at least be ready to engage in, some specified or unspecified form of sexual activity with one's spouse.

Question 1 is of both theoretical and practical interest. If the answer to 1 is negative, then it is hard to resist the suggestion that there is nothing problematic about same-sex marriage. After all, if there is no positive sexual content to the commitment, then it seems that same-sex couples can make exactly the same defining commitment that opposite-sex couples can. Moreover, Scriptural and philosophical arguments about the wrongness of same-sex sexual activity cease to be directly relevant to the question of same-sex marriage, since given a negative answer to question 1, same-sex marriage does not imply same-sex sexual activity or a commitment thereto.

On the other hand, if the answer to Question 1 is positive, then a natural second question is:

2. Does the sexual content concern a particular kind of sexual activity, and, if so, what kind?

For instance, emotionally intense romantic hand-holding may count as a sexual activity. If there is no specific restriction as to the kind of sexual activity, a willingness and readiness to engage in emotionally intense romantic hand-holding will suffice. I suspect that if we answer Question 1 in affirmatively, we will want to place some restrictions on the sexual content in the answer to 2. If we go all the way to specifying that the relevant kind of sexual activity is coitus, then we have an argument against the existence of same-sex marriage: Marriage involves some positive commitment to coitus; same-sex couples do not in fact commit themselves to coitus (bracketing complicated questions about "sex-change" operations); therefore, same-sex couples do not marry. And since the state should not recognize as a marriage what is in fact not a marriage, the state should not recognize same-sex unions as marriages.

I don't want to address question 2 here. I want to focus on question 1.

Suppose we answer question 1 in the negative. Then there is a sub-question:

3. Is there any negative sexual content to the marital commitment?

The standard form of negative sexual content is a commitment not to engage in sexual activity with anyone else.

Suppose first that we answer both question 1 and question 3 in the negative. Then there is no sexual content to the marital commitment at all. What, then, is the content of the commitment? It is presumably something about a kind of intense friendship. It is something like a commitment to love, care for and cherish through thick and thin. But now we have a problem: This kind of commitment fails to distinguish marriage from other relationships. It would be deeply controversial to say that it is permissible for two siblings to marry. But it would not be deeply controversial to say that it is permissible for two siblings to solemnly commit to love, care for and cherish through thick and thin. Hence, to solemnly commit to this is not the same as marrying. Moreover, many parents do, though typically not solemnly (e.g., they rarely make vows), promise their children to be there for them no matter what, even after the child is grown up. And we would neither be very surprised nor morally troubled if an adult child reciprocated that commitment—and we certainly would not think that this was tantamount to a marital commitment. Nor were the Three Musketeers married to each other.

But perhaps the marital commitment includes a commitment to a certain kind of deep emotional sharing, a sharing that goes beyond that which close siblings unproblematically engage in. But just as a view on which the commitment has coitus in its content would exclude same-sex couples from marrying, a view on which the commitment has deep emotional sharing as its content would exclude persons who are not very emotional or not capable of deep emotional sharing from marrying. And the latter exclusion is more problematic. We have a cultural stereotype that many men are not interested in deep emotional sharing with their wives. But if marital commitment included a commitment to such sharing, it would be a consequence of this stereotype that either they aren't married to their so-called wives or they are unfaithful to their marital commitment. This is not a plausible consequence. And stereotypes aside, there surely are very large numbers of people who are not interested in deep emotional sharing, and yet marry. And when they marry, it is implausible to suppose that they commit themselves to the deep emotional sharing they are uninterested in.

Moreover, given that some siblings (especially identical twins) are very close, and yet not at all incestuously involved, and we could imagine that the siblings commit themselves to that closeness, it would be very difficult to require a marital commitment to an emotional closeness that goes beyond those cases of fraternal closeness without requiring a commitment to something that few married couples have or are even capable of.

Supposing a commitment to deep intellectual communion would be even worse at distinguishing the marital relationship from other relationships.

There does not, then, appear to be much hope of specifying in an entirely non-sexual way what the marital commitment is. The view that the answers to both Questions 1 and 3 are negative is untenable.

Suppose, howevere, we allow that the answer to Question 3 is positive but that to Question 1 is negative. On this view, the marital commitment contains on the positive side a commitment to a certain kind of deep friendship, and on the negative side a commitment to abstaining from sexual activity with anyone else. But if a certain kind of deep friendship didn't do the job of defining the content of the marital commitment, neither will adding a commitment to abstinence from sexual activity with others. After all, plausibly, one way of committing oneself not to engage in sexual activity with anyone other than one's spouse-to-be is to commit oneself not to engage in sexual activity with anyone at all. But, surely, if a commitment to deep friendship was not sufficient for a marital commitment, adding vows of general sexual abstinence (I almost said "vows of celibacy", but "celibacy" in the traditional sense of the word means abstinence from marriage) will not help.

Perhaps, though, this is unfair. Maybe the content of the commitment needs to be, at least semi-explicitly, that one will abstain from sexual activity with anyone else, and to commit oneself to something that entails this (such as committing oneself to total abstinence) will not do. But I think this won't help. Take the case of two siblings who promise to always be there for each other, to love and cherish one another. And then they break up their promise of general celibacy into two: "Nor will we ever engage in sexual activity with anyone else. And certainly not with one other (ugh!)." That would be weird, yet surely they would not become married just because they broke up their promise of general celibacy in this way. But once they so broke it up, they did in fact explicitly commit not to engage in sexual activity with anyone else.

Thus, if a commitment to some deep friendship won't do the job for the content of the marital commitment, adding a commitment to abstain from sexual activity with others will not help. Therefore, the answer to Question 1 is positive, whether or not the answer to Question 3 is positive or negative. A marital commitment must include some sexual content or else we will either exclude some obvious cases of marriage (e.g., people incapable of deep emotional sharing) or count as marriage what is clearly not (people committing non-maritally to one another) or both.

This is not enough to answer questions about the possibility of same-sex marriage. To answer those questions, Question 2 would need to be addressed. My view is that the only fully defensible answer to Question 2 involves coitus, and hence excludes same-sex marriage, but I am not arguing for that in this post.

Friendship and friendly love

Thesis 1: There is no special form of love that falls under the label "friendly love" or "the love characteristic of friendship". Every love is a friendly love.

To love someone involves appreciating the beloved, pursuing her good, and seeking some sort of union of common pursuit with her. If we have only one out of three then we do not have love, but something else, respectively like disinterested appreciation, benevolence or lust. Nor are two out of three enough. But if one has all three, one has friendly love. For friendship is multiform, and any common pursuit providing a genuine union can be made the object of a friendship.

One might try to distinguish "friendly love", however, by its mutuality. While one can have unrequited romantic love, one cannot have unrequited friendship. Friendship is essentially mutual. But this argument is invalid, since friendship is not the same as friendly love. Friendly love is the love characteristic of friendship. But it can exist without a friendship. If I am your false friend, but am a very good actor, we can have what from your point of view looks just like friendship. And your love does not fall short of friendly love—it is my love that does so. So, you have a friendly love, even though there is no friendship. Or consider cases where the friendship has been lost, because one party has slid into vice, but the other retains a friendly love, striving to rescue the backslider.

The distinction between friendly love and friendship is essential to Plato's Lysis. The Lysis begins by attempting to define a friend (philos--the noun) in terms of friendly loving (philein--the verbal form; I am suspecting that philia is ambiguous in the Greek between friendly love and friendship). We begin by rejecting the definition of a friend as someone whom one loves with friendly love or someone who loves one with friendly love, on the grounds that if the friendly love is reciprocated with hatred, we do not have a case of a friend. This argument requires that it be possible to have a friendly love that is reciprocated with hatred, and hence that it is possible to have a friendly love without friendship.

Thesis 2: Friendship is the right kind of mutuality in friendly love, i.e., in love.

I do not know how exactly to characterize this mutuality, though. Minimally, it requires that each should know of the other's friendly love, but more than that is needed.

A consequence of this is that appropriately mutual romantic love is a kind of friendship.

Conclusive evidence and confirmation

Fitelson proposes the following principle: "If E constitutes conclusive evidence for H₁, but E constitutes less than conclusive evidence for H₂ (where it is assumed that E, H₁ and H₂ are all contingent), then E favors H₁ over H₂."

The principle is false. You witness Jones being shot and after approaching you observe that he is dead. Let E be this evidence. Let H₁ be the hypothesis that Jones is dead. Let H₂ be the hypothesis that Jones has been killed. Then E is conclusive evidence for H₁ and less than conclusive evidence for H₂. (That you observed that Jones is dead entails H₁. But on one reading of "Jones being shot", E is compatible with the hypothesis that Jones was already dead when he was shot—we can say "He was shot after he died." And on any reading, E is compatible with Jones having died of some other cause, coincidentally.) But it is wrong to say that E favors the hypothesis that Jones is dead over the hypothesis that Jones was killed.

A derivation of the likelihood-ratio measure of confirmation

Let C_K(E,H) be the degree of confirmation that E lends H given background K. Here is a derivation of the likelihood-ratio measure. The derivation is, I think, more compeling than Milne's.
We need several assumptions. For simplicity, write P_K(A)=P(A|K) and P_K(A|B)=P(A|BK). Our first assumption is uncontroversial and everybody accepts it. (For simplicity, I shall also suppose throughout that we're working with events such that none of the relevant Boolean combinations have probability zero or one.)

1. C_K(E,H) is a continuous function of the probabilities P_K(−) where the blank can be filled in by any boolean combination of E and H.

Everybody in the measure of confirmation business accepts (1). We now need two more complex theses to get some interesting results. One is this:

2. If I is independent of all Boolean combinations of E, H and K, then C_K(IE,H)=C_K(E,H).

An event I like that is obviously irrelevant, and so E and IE confirm H equally. This should be uncontroversial, though it is sufficient to refute the Eells-Jeffrey measure. The next thesis is more controversial:

3. If E and F are events that are conditionally independent given HK as well as given (~H)K, then C_KE(F,H)=C_K(F,H).

This thesis says that independent evidence has the same evidential force no matter in which order it comes in. For instance, if you flip a coin twice to gather evidence for whether the coin is biased in favor of heads, and you get heads twice, each heads result provides exactly the same confirmation.
Now we get some substantive results. The first one is easy.
Theorem 1. If (1), then C_K(E,H) is a function solely of P_K(H), P_K(E|H) and P_K(E|~H), i.e., there is a function f such that C_K(E,H)=f(P_K(E|H),P_K(E|~H),P_K(H)).
This is because all the relevant Boolean combinations can be written in terms of these three probabilities.
I am omitting the proofs of the next couple of Theorems, except to note that obviously Theorem 4 follows from Theorems 2 and 3. I haven't written any of proofs out, but I am confident of theoremhood (maybe with some minor additional assumption). Of course, I could be wrong.
Theorem 2. If (1) and (2), then C_K(E,H) is a function solely of P_K(H) and the likelihood ratio P_K(E|H)/P_K(E|~H).
Observe that Theorem 2 refutes the Eells-Jeffrey likelihood-difference measure, given that (1) and (2) are so plausible.
Theorem 3. If (1) and (3), then C_K(E,H) is a function solely of the likelihoods P_K(E|H) and P_K(E|~H).
Theorem 4. If (1), (2) and (3), then C_K(E,H) is a function solely of the likelihood ratio P_K(E|H)/P_K(E|~H).
Therefore, given (1)-(3), C_K(E,H)=f(P_K(E|H)/P_K(E|~H)) for some function f. It is obvious that f must then be an increasing function (this needs some additional assumptions). If all that is of interest is the comparison of degrees of confirmation, this is all we need. But perhaps we want to combine degrees of confirmation. This could be done additively or multiplicatively, i.e.,

4. If E and F are conditionally independent given HK and (~H)K, then C_K(EF,H)=C_K(E,H)+C_KE(F,H)

or

5. If E and F are conditionally independent given HK and (~H)K, then C_K(EF,H)=C_K(E,H)C_KE(F,H).

Now we get two final results.
Theorem 5. Assume (1), (2), (3) and (4). Then there is a constant c such that C_K(E,H)=clog(P_K(E|H)/P_K(E|~H)).
Theorem 6. Assume (1), (2), (3) and (5). Then there is a constant c such that C_K(E,H)=(P_K(E|H)/P_K(E|~H))^c.
And for simplicity in both cases we should normalize by setting c=1.