Multiple levels of multiple realizability

We could have sophisticated beings who reason about the world via numerical Bayesian credences. But we could also have sophisticated beings who reason in some other way—indeed, we are such beings. And there is one sophisticated being who reasons about the world via omniscience. This suggests that reasoning and agency are multiply realizable at multiple levels, including:

1. brain/mind architecture

2. algorithms implementing general reasoning and representation strategy

3. general reasoning and representation strategy.

Each level is an abstraction from the previous. So now we have a very deep question: Is there a fourth level that abstracts from the third, to get the concept of reasoning as such? Or are the various general reasoning and representation strategies unified analogically, say by similarity to some primary case? And if so, what is the primary case? Omniscience? Logical omniscience plus numerical Bayesianism?

A pessimistic thought about epistemic rationality

The more I think about relatives of the Doomsday Argument and my insect argument, the more I become suspicious of both the self-sampling and the competing self-indication assumptions.

Both assumptions require one to assign non-zero probabilities to metaphysically impossible hypotheses about where I am located in spacetime, such as the hypothesis that I was born in the 19th century, the hypothesis that I am a non-human or the hypothesis that it is now a Wednesday. It is usual in the discussion of these hypotheses not to worry much about such issues of metaphysical impossibility. The thought is that we are doing epistemology, not metaphysics.

Moreover, it seems reasonable to assign a credence 1/10 to the proposition that the hundredth digit of π is 3 when one hasn’t calculated that digit, even though one knows that the proposition is either necessarily true or necessarily false.

Perhaps my Aristotelian meta-epistemology can help, though. What if the right way to assign credences is not some abstract “rational” way to do so, but rather the human way—the way that our human nature calls us on us to? Our human nature specifies how we should function within a certain broad range of conditions. But outside of that range, human nature may not specify how we should function. Our nature specifies normal human locomation in earth gravity, but specifies nothing about what normal human locomation out in space should be like. Likewise, our nature specifies normal human credential behavior in many circumstances, but need not specify human credential behavior in outlandish cases like Doomsday.

Of course this raises the very hard question of which cases are within the range of cases where our nature specifies credential behavior and which are not.

Super-simple fractal terrain generator

Here's a very simple algorithm for generating random terrains: Start with a equilateral triangle in the x-y plane. Add a uniformly and symmetrically distributed random z-offset to each vertex. Bisect each resulting edge and add a random z-offset at the newly added point, half of the magnitude of the random offsets earlier. Repeat several times.

The algorithm is no doubt known, but some quick searches for terrain generation algorithms didn't turn it up, so I am posting for people's convenience.

There are some artifacts at internal triangle boundaries that better algorithms presumably don't have, but the algorithm is super simple to implement, and because it is based on triangles it directly makes a triangular mesh. Here is some code which does this, starting with a hexagon divided into six equilateral triangles, and putting out an STL file.

Are the priors of subjective Bayesianism subjective?

Visual and auditory perception are not subject to rational evaluation. Nobody perceives visually or auditorily in a rational or irrational way. Nonetheless, perception is subject to evaluation. One’s perceptual faculties could function superlatively, adequately or inadequately. The mere fact that they are not subject to rational evaluation does not imply subjectivism about their functioning.

But now consider a Bayesian view on which:

1. Our priors are not subject to rational evaluation.

That view is known in the literature as “subjective Bayesianism”. But if we take seriously the lesson from perception, we should be sceptical of the inference from (1) to:

2. Our priors are merely subjective.

I have to confess to not taking this point seriously in the past, having been misled by the phrase “subjective Bayesianism” and by things I heard from subjective Bayesians.

What might a theory look like on which our priors are subject to evaluation but not rational evaluation? We could take our priors to be a kind of “probabilistic perception” of patterns in the world, a perception that is genetically and/or socially mediated. Such perceptions can be better or worse, just as the person who is looking at a horse and their visual system classifies it as 95% likely to be cat and 5% likely to be a horse is doing less well perceptually than one whose system makes the opposite classification. For instance, someone who has a prior close to 1 for the law of gravitation being an inverse 3.00001th power law is doing less well than someone who has a moderately high prior for it it being an inverse cube law and a moderately high prior for it being an inverse square law.

But if we take the perception analogy seriously, we get this question: What are we “perceiving” with our priors? Maybe something like facts about the sorts of laws worlds like ours have?

Probabilistic perception

We could imagine critters whose perceptual system works as follows: When they have an object in their visual field, instead of the perceptual system delivering the presence of a dog, it delivers something like:

• dog:0.93, coyote:0.03, wolf:0.03, deer:0.01.

There are probably many interesting questions to ask about critters with a perceptual system like that. But I want to briefly muse about three.

Question 1: Can we redescribe the perceptual system of these critters so that at base what we have are just attitudes to propositions or properties pairs or something like that?

Answer: I am not sure. Some options fail. For instance, while it may be true that the critter in my example is having a disjunctive perception of a dog-or-coyote-or-wolf, that doesn’t capture all the information in its perceptual system—it doesn’t capture the much greater probability of its being a dog.

Alternately, one could say that the critter has four perceptions of different strengths: a 0.93 strength perception as of a dog, a 0.03 strength perception as of a coyote, a 0.03 strength perception as of a wolf and a 0.01 strength perception as of a deer. But that doesn’t quite capture what’s going on, at least not if we read the story as I intended it. The critter takes dog, coyote, wolf and deer to be alternative hypotheses for what is in front of it, not to be four different perceptions. The story that breaks up the perception into four perceptions of different strengths fails to distinguish the story I intend from a story where the animal might be all four (it’s only a posteriori that we know there are no dog-coyote-wolf-deer).

Maybe we could say that the critter’s perceptual system also delivers something more complicated:

• only-dog:0.93, only-coyote:0.03, only-wolf:0.03, only-deer:0.01.

That will get out of the alternativeness worry, but I am sceptical that it needs to be like that. One could just see the four options, and not see that the probabilities involved force them to be exclusive (because the probabilities add up to one). This is even more plausible if the probabilities are qualitative or interval-based.

Nor will it do to say that one perceives that there is a 0.93 probability of a dog, a 0.03 probability of a coyote, and so on. For these probabilities are not objective facts out there. They are, I suppose, measures of what credence the critter should have in each hypothesis if there is no further data available. We need not suppose that the critter has the degree of self-reflectiveness that would be needed to perceive these measures of hypothetical credence as such.

So maybe a reduction to more familiar perception stories is possible, but I think there is some reason to be sceptical.

Question 2: What is it for this perceptual state to be veridical?

Answer: A necessary condition, of course, would have to be that what is present is a dog, coyote, wolf or deer. But there is room for much Gettiering. Maybe it’s a wolf dressed up as a sheep dressed up as a wolf. Then the perception isn’t in the right way, and we don’t have veridicality. But what if it’s a dog that recently went to the pet salon and was made up to look more wolf-like? Then maybe it’s veridical. Maybe. I just don’t know.

I have a suspicion that once we have such probabilistic deliverances of perception, the in-the-right-way problem of characterizing veridicality not only becomes epistemically intractable—it may already be that in standard theories of perception—but the whole concept of veridicality, apart from the necessary condition that one of the alternative hypotheses be true, may break down.

Question 3: Are we always such critters? We could, after all, take the ordinary perception of a dog to be just a limiting case like “dog:0.999999, something weird:0.000001” or even “dog:1”. Should we do that in every case?

Answer: Phenomenologically, the answer seems negative. But phenomenology can mislead about such things. But as long as it’s a live hypothesis that we might be such critters, we may need to be cautious about claims like that perception is a propositional attitude (see Question 1) or that there is a viable concept of veridicality (see Question 2).

And the apparent possibility of critters whose perception always works like this should make us cautious as to the kinds of claims we make in epistemology.

Diversity of goods, heaven and theodicy

Alice was tortured for weeks, but she remained loyal to the true and the good. Alice’s moral victory over her torturers was of great value. Let’s take it for granted that this situation represents something that is on balance a great good for Alice (and for the world). But suppose that God was choosing between Alice’s moral victory, on the one hand, and Alice doing something else that was virtuous, worthwhile but not painful—perhaps with great singlemindedness throwing herself into producing a great work of art. One might well make the judgment that while Alice’s moral victory was a great good, given the horrendous cost to Alice, it would on balance have been better for God to have steered her life away from the suffering and towards a good that comes without much pain.

I am sceptical of this judgment, but for the sake of the argument let’s grant it. Nonetheless, I think the assessment should change if one adds to the above a story about an infinite heavenly afterlife. Here is why. The judgment was that while there was great value in Alice’s moral victory, it would have been good to substitute a painless but valuable achievement for it.

But what if, instead, the question was this:

• Is it better for Alice to have the painful moral victory plus a hundred painless but valuable achievements, or just the hundred painless but valuable achievements?

If we grant the initial judgment that Alice’s moral victory was of great value, then we need to say that the first option is on balance better. The life with the painful victory and hundred painless achievements not only exhibits the additional good of the painful victory, but also exhibits the higher-order value of a diversity of types of goods.

Now ask this question:

• Is it better for Alice to have the painful moral victory plus an infinite number of painless but valuable achievements, or just the infinite number of painless but valuable achievements?

It sure seems like the first option is the better one. But now when we ask the initial question, whether God shouldn’t have given Alice a painless achievement instead, in the context of a theory of God that includes an infinite happy afterlife, that is in fact what the question comes to. The additional painless achievement would not add much to the infinitely many painless achievements in heaven. But the painful achievement adds something different in kind.

And when we add to the story that in the afterlife Alice (as well as her friends, likely many in number) will be able to enjoy, infinitely many times, the memory of her moral victory, without the memory of her suffering being itself a source of suffering (for, I take it, there is no suffering in heaven), it sure seems worth it.

But what if instead Alice cracked under torture, thereby losing the good? Well, now how well the story works depends on other questions. If we have Molinism, then it doesn’t work very well: given Molinism, God can foresee that Alice would crack, and so the value that there would be in her victory is irrelevant. But given simple foreknowledge (or open theism, but that’s a heretical option) God’s decision whether to put Alice in that situation can only be based on chances. For all we know, the chance of Alice’s cracking under torture, given the grace that God gave her, was not very high, and so the significant chance of the great goods of having a diversity in the types of goods one experiences and of having an infinite number of reminiscences of that diversity was worthwhile. Or, at least, we have little reason to think it wasn’t.

Internalism, externalism and Bayesianism

Maybe a Bayesian should be a hybrid of an internalist and an externalist about justification. The internalist aspect would come from correct updating of credences on evidence, internalistically conceived of. The externalist aspect would come from the priors, which need to be well adapted to one's epistemic environment in such a way as to lead reasonably quickly to truth in our world and maybe also in a range of nearby worlds.

This seems a natural way to think about the internalist and externalist question by means of the analogy of designing a Bayesian artificial intelligence system. The programmer puts in the priors. The system is not "responsible" for them in any way (scare quotes, since I don't think computers are responsible, justified, etc--but something analogous to these properties will be there)--it is the programmer who is responsible. Nonetheless, if the priors are bad, the outputs will not be "justified". The system then computes--that is what it is "responsible" for. It seems natural to think of the parts that the programmer is responsible for as the externalist moment in "justification" and the parts that the system is "responsible" for as the internalist moment. And if we are Bayesian reasoners, then we should be able to say the same thing, minus the scare quotes, and with the programmer replaced by God and/or natural selection and/or human nature.

The problem of priors

Counterfactuals about scientific practice reveal some curious facts about our prior probabilities. Our handling of experimental suggests an approximate flatness in our prior distributions of various constants (cf. this). But the flatness is not perfect. Suppose we are measuring some constant k in a law of nature, a constant that is either dimensionless or expressed in a natural unit system, and we come back with 2.00000. Then we will assign a fairly high credence to the hypothesis that k is exactly 2. But any kind of continuous prior distribution will assign zero prior to k being exactly 2, and the posterior will still be zero, so our prior for 2 must have been non-zero and non-infinitesimal. But for most numbers, the prior for k being that number must be zero or infinitesimal, or else the probabilities won’t add up to 1.

More generally, our priors favor simpler theories. And they favor them in a way that is tuned (finely or not). If our prior for k being exactly 2 were high, then we wpould believe that k = 2 even after a measurement of 3.2 (experimental error!). If our prior were too low, then we wouldn’t ever conclude that k = 2, no matter how many digits after the “2.” we measured to be zero.

There are is now an interesting non-normative question about the priors:

• Why are human priors typically so tuned?

There is, of course, an evolutionary answer—our reasoning about the world wouldn’t work if we didn’t have a pattern of priors that was so tuned. But there is a second question that the evolutionary story does not answer. To get to the second question, observe that our priors ought to be so tuned. Someone whose epistemic practices involve the rejection of the confirmation of scientific theories on the basis of too strong a prejudice for simple theories (“There is only one thing, and it’s round—everything else is illusion”) or too weak a preference for simple theories (“There are just as many temperature trends where there is a rise for a hundred years and then a fall for a hundred years as where there is a rise for two hundred years, so we have no reason at all to think global warming will continue”) is not acting as she ought.

So now we have this normative question:

• Why is it that our priors ought to be so tuned?

These give us the first two desiderata on a theory of priors:

1. The theory should explain why our priors are tuned with respect to simplicity as they are.

2. The theory should explain why our priors should be so tuned.

Here is another desideratum:

3. The theory should exhibit a connection between priors and truth.

Next, observe that our priors are pretty vague. They certainly aren’t numerically precise, and they shouldn’t be, because beings with our capacity couldn’t reason with precise numerical credences in the kinds of situations where we need to.

4. The theory should not imply that our having those priors we should requires us to always have numerically precise priors.

Further, there seems to be something to subjective Bayesianism, even if we should not go all the way with the subjective Bayesians. Which we should not, because then we cannot rationally criticize the person who has too strong or too weak an epistemic preference for simple theories.

5. The theory should not imply a unique set of priors that everyone should have.

Next, different kinds of agents should have different priors. For instance, agents like us typically shouldn’t be numerically precise. But angelic intellects that are capable of instantaneous mathematical computation might do better with numerically precise priors. Moreover, and more controversially, beings that lived in a world with simpler or less simple laws shouldn’t be held hostage to the priors that work so well for us.

6. The theory should allow for the possibility that priors vary between kinds of agents.

And then, of course, we have standard desiderata on all theories, such as that they be unified.

Finally, observe the actual methodology of philosophy of science: We observe how working scientists make inferences, and while we are willing at times to offer corrections, we use the actual inferential practices as evidence for how the inferential practices ought to go. In particular, we extract the kinds of priors that people have from their epistemic behavior when it is at its best:

7. The theory should allow for the methodology of inferring what kinds of priors we ought to have from looking at actual epistemic behavior.

Subjective Bayesianism fails with respect to desiderata 2 and 3, and if it satisfies 1, it is only by being conjoined with some further story, which decreases the unity of the story. Objective Bayesianism fails with respect to desiderata 5 and 6, and some versions of it have trouble with 4. Moreover, to satisfy 1, it needs to be conjoined with a further story. And it’s not clear that objective Bayesianism is entitled to the methodology advocated in 7.

What we need is something in between subjective and objective Bayesianism. Here is such a theory: Aristotelian Bayesianism. On general Aristotelian principles, we have natures which dictate a range of normal features with an objective teleology. For instance, the nature of a sheep specifies that they should have four legs in support of quadrapedal locomotion. Moreover, in Aristotelian metaphysics, the natures also explain the characteristic structure of beings with that nature. Thus, the nature of a sheep is not only that in virtue of which a sheep ought to have four legs, but also has guided the embryonic development of typical sheep towards a four-legged state. Finally, in an Aristotelian picture, when things act normally, they tend to achieve the goals that their nature assigns to that activity.

Now, in my Aristotelian Bayesianism, our human nature leads to characteristic patterns of epistemic behavior for the telos of truth. From the patterns of behavior that are compatible with our nature, one can derive constraints on priors—namely, that they be such as to underwrite such behavior. These priors are implicit in the patterns of behavior.

We can now take the desiderata one by one:

1. Our priors are tuned as they are since our development is guided by a nature that leads to epistemic behavior that determines priors to be so tuned.

2. Our priors ought to be so tuned, because all things ought to act in the way that their nature makes natural.

3. Natural behavior is teleological, and our epistemic behavior is truth-directed.

4. The the priors we ought to have are back-calculated from the epistemic behaviors we ought to have, and our behaviors cannot have precise numbers attached to them in such a way as to yield precise numerical priors.

5. Nothing in the theory requires that unique priors be derivable from what epistemic behavior is characteristic. Typically, in Aristotelian theories, there is a range of normalcy—a ratio of length of legs to length of arms between x and y, etc.

6. Different kinds of beings have different natures. Sheep ought to have four legs and we ought to have two. We are led to expect that different kinds of agents would have different appropriate priors. Moreover, animals tend to be adapted to their environment, so we would expect that in worlds that are sufficiently different, different priors would be appropriate.

7. Since beings have a tendency towards acting naturally, the actual behavior of beings—especially when they appear to be at their best—provides evidence of the kind of behavior that they ought to exhibit. And from the kind of epistemic behavior we ought to exhibit, we can back-calculate the kinds of priors that are implicit in that behavior.

This post is inspired by Barry Loewer saying in discussion that I was Kantian because I think there are objective constraints on priors. I am not Kantian. I am Aristotelian.

An unimpressive fine-tuning argument

One of the forces of nature that the physicists don’t talk about is the flexi force, whose value between two particles of mass m₁ and m₂ and distance r apart is given by F = km₁m₂r and which is radial. If k were too positive the universe would fall apart and if k were too negative the universe would collapse. There is a sweet spot of life-permissivity where k is very close to zero. And, in fact, as far as we know, k is exactly zero. :-)

Indeed, there are infinitely many forces like this, all of which have a “narrow” life-permitting range around zero, and where as far as we know the force constant is zero. But somehow this fine-tuning does not impress as much as the more standard examples of fine-tuning. Why not?

Probably it’s this: For any force, we have a high prior probability, independent of theism, that it has a strength of zero. This is a part of our epistemic preference for simpler theories. Similarly, if k is a constant in the laws of nature expressed in a natural unit system, we have a relatively high prior probability that k is exactly 1 or exactly 2 (thought experiment: in the lab you measure k up to six decimal places and get 2.000000; you will now think that it’s probably exactly 2; but if you had uniform priors, your posterior that it’s exactly 2 would be zero).

But his in turn leads to a different explanatory question: Why is it the case that we ought to—as surely we ought, pace subjective Bayesianism—have such a preference, and such oddly non-uniform priors?

Flatness of priors

I. J. Good is said to have said that we can know someone’s priors by their posteriors. Suppose that Alice has the following disposition with respect to the measurement of an unknown quantity X: For some finite bound ϵ and finite interval [a, b], whenever Alice would learn that:

1. The value of X + F is x where x is in [a, b], where
2. F is a symmetric error independent of the actual value of X and certain to be no greater than ϵ according to her priors, and
3. the interval [x − ϵ, x + ϵ] is a subset of [a, b]

then Alice’s posterior epistemically expected value for X would be x.

Call this The Disposition. Many people seem to have The Disposition for some values of ϵ, a and b. For instance, suppose that you’re like Cavendish and you’re measuring the gravitational constant G. Then within some reasonable range of values, if your measurement gives you G plus some independent symmetric error F, your epistemically expected value for G will be probably be equal to the number you measure.

Fact. If Alice is a Bayesian agent who has The Disposition and X is measurable with respect to her priors, then Alice’s priors for X conditional on X being in [a, b] are uniform over [a, b].

So, by Good’s maxim about priors, someone like the Cavendish-like figure has a uniform distribution for the gravitational constant within some reasonable interval (there is a lower bound of zero for G, and an upper bound provided by the fact that even before the experiment we know that we don’t experience strong gravitational attraction to other people).

Going from 2D drawings to 3D printing

I wanted make a 3D-printable Valentine's day card for my wife, with an inflated red heart on a white background, so I spent perhaps too much time playing with algorithms to "inflate" a 2D drawing of a heart into a 3D polyhedron that I can load into OpenSCAD. Here's the card I ended up with.

After Valentine's, I still worked on refining the Python code that did the inflation. The code is now an easy to use Inkscape extension, which adds the ability to save to an inflated SCAD or STL file. The official repository is here.

The final algorithm I settled on is a non-linear scheme that sets the height of the inflation of a 2D image at a given point in the image x by approximating the L^p norm (E(T_x^p))^1/p of the exit time T_x of a random walk started at x. For further adjustment, you can replace T_x with min(T_x,K) where K is exponentially distributed, which flattens the inflation in inner regions. The code could use a lot of optimization (using pypy instead of cpython improves runtimes by a factor of 10, but Inkscape only bundles python) as on my laptop the code takes about 45 seconds with default settings on one of my simple test images.

While my original Valentine's day card used p=1, I have since found that p=2 produces more nicely rounded output.

Total and average epistemic and pragmatic utilities

The demiurge flipped a fair coin. If it landed heads, he created 100 people, of whom 10 had a birthmark on their back. If it landed tails, he created 10 people, of whom 9 had a birthmark on their back. You’re one of the created people and the demiurge has just apprised you of the above facts.

What should your credence be that you have a birthmark on your back?

This seems a plausible answer:

• Answer A: (1/2)(10/100)+(1/2)(9/10)=1/2

Let’s think a bit about Brier scores, considered as measures of epistemic disutility. If everybody goes for Answer A, then the expected total epistemic disutility will be:

• TD(A) = (1/2)(100)(1/2)² + (1/2)(10)(1/2)² = 13.75

That’s not the best one we can do. It turns out that the strategy that minimizes the expected total epistemic disutility will be:

• Answer B: 19/110

which yields the expected total disutility:

• TD(B) = 7.9.

The same 19/110 answer will be optimal with any other proper scoring rule. Moreover, what holds for proper scoring rules also holds for betting scenarios, and so the strategy of going for 19/110, if universally adopted, will make for better total utility in betting scenarios. In other words, we have both an epistemic utility and a pragmatic utility argument for the strategy of adopting 19/110.

On the other hand, the 1/2 answer will optimize the expected average epistemic and pragmatic utilities in the population. But do we want to do that? After all, we know from Parfit that optimizing average pragmatic utilities can be a very bad idea (as it leads to killing off of those who are below average in happiness).

Yet the 1/2 answer has an intuitive pull.

An argument that insects are not conscious

Suppose insects are conscious. There are at least about a billion insects per human being. So, if insects are conscious, we should be surprised to find ourselves not being an insect. But if insects are not conscious, there is no surprise there. So, it seems, observing that we are not insects gives us very strong evidence that insects are not conscious.

But this just doesn’t seem to be a good argument… Perhaps the self-sampling thesis—the thesis that we should count ourselves as randomly selected from among observers—needs to be restricted to intelligent and not merely conscious observers? But isn’t that restriction ad hoc? If we're doing such restricting, maybe we should restrict even more finely, say to observers at our exact level of intelligence?

Contraception, liturgy and self-giving

Alice has a paper due the day after Thanksgiving. She’s already gotten all the extensions she can, and she can’t get it done except by working through Thanksgiving. She is thinking of not going to the big Thanksgiving dinner that her grandfather organizes every year, even though it brings together relatives she hasn’t heard from for a long time, has much warm family fellowship, and great food. But then she has an idea: “It’s better to attend distractedly than not at all. The table is big and my laptop is small, so I can easily put my laptop beside a plate, and then I can write all the way through dinner and finish my paper. And I’m good at multitasking, so I can still have an ear out for interesting bits of conversation, and occasionally I can put a forkful of food in my mouth or make a friendly remark to someone. It would be permissible for me to skip the dinner completely, and this is better than skipping it.”

Bob has a major exam on Wednesday. It is his habit to attend Mass daily, both for the spiritual benefits and because there is an incredible organist. He could skip Tuesday Mass, but reasons much as Alice does: “If I skip Mass, I get none of the spiritual and musical benefits. I’ll just bring my tablet, sit in the back pew so the bright screen doesn’t disturb anybody, study hard and I’ll at least get some of the benefits of Mass. After all, there is nothing wrong with my skipping Tuesday Mass, and this is better.”

Alice is being obtuse about human relationships and Bob doesn’t understand the kind of participation the Mass requires. There are some activities that one should give oneself pretty completely to—or not do them at all.

What if Bob says something like this? “But I go to Mass on many days when I’ve already spent hours working hard, and I’m really exhausted, and barely able to pay any attention to what the priest says. There is nothing morally wrong with attending Mass on days like that. But today I’m still fresh, and multitasking today I can participate at least as well as singletasking on a bad day.” And Alice can say something very similar—after all, very tired people can go to Thanksgiving dinner, too.

But that’s still not an excuse. For when one goes to Thanksgiving dinner or Mass, one should give oneself to it as much as one can (within some reasonable limit of what counts as “enough”). Both Alice and Bob are going to be deliberately withholding themselves from participation. But on the days when they attended while really tired, they weren’t doing that—they were giving what they could (it would be different if Bob ran a marathon in order to be too tired to follow the Gospel reading!).

Now, consider a common response to John Paul II’s argument that contraception is wrong because it deliberately blocks the total self-giving in sex. “Granted, contraception blocks an aspect of the union as one body. But a partial union is better than no union at all, and a couple is morally permitted to refrain from union for good reasons.” But that’s like Alice’s and Bob’s initial argument. And there is a case that can be made that sex is a liturgical kind of act, akin to Thanksgiving dinner or the Mass, and that in these kinds of liturgical acts one can’t participate while blocking an aspect of one’s participation—one needs to give one’s all, or not at all. It is better not to have sex at all than to have it while blocking one’s participation.

And then there is the riposte: “But the Catholic Church says it’s permissible to have sex while infertile. And contracepted sex has in it everything that infertile sex does.” But that riposte is just like Bob’s suggestion that studying at Mass with his tablet still leaves him as much (or more!) function as attending Mass on the days when he is really tired. Yes, that’s true, but it misses the liturgical meaning of deliberately distracting oneself with the tablet.

If it is objected that sex isn’t analogous to Thanksgiving dinner or the Mass (though I think it is), we could think about the case of Carl who is a professional movie reviewer. His wife would like to have sex with him, but he needs to watch and review a boring movie by tomorrow. So he sets up a laptop by the bed, and unites with his wife while watching the movie. Ugh! It would be better not to have sex at all.

The consent norm for sexual activity is insufficient

Consider the thesis that consent is the only norm of sexual activity. Of course, this does not imply the crazy claim that every consensual sexual act is permissible. Some consensual sexual acts violate promises, or constitute the neglect of some non-sexual responsibility (e.g., sex while driving), or just have sufficiently bad consequences for one or more people. Rather, the thesis can be taken to say that consent is the only norm of sexual activity as sexual, that it is the only distinctively sexual norm.

The thesis is still false. To see this, we will need a distinction between things that are very wrong and things that are wrong but not very wrong. Then:

1. Every case of coitus without consent is a case of rape.
2. Every case of rape is gravely wrong as a sexual act.
3. There is a case of coitus which is wrong as sexual but not gravely wrong.
4. So, there is a case of coitus which is not rape but is wrong as sexual. (2 and 3)
5. So, there is a case of coitus which is wrong as sexual even though there is consent. (1 and 4)

(When I say that a case of coitus is wrong, I mean that at least one party responsible for the coitus is in the wrong. That party could be one of the participants in coitus, but need not be: a rapist does not actually have to participate in the act of coitus, but could instead force two other people to engage in coitus with themselves.)

I think premise 3 is very plausible. It would be quite surprising if sexual wrongness of coitus only came in grave and not-at-all varieties, with nothing in between. But I can also offer an argument for premise 3 (I’ve used this argument in a previous post which gave a similar but perhaps less clear argument) assuming that consent is the only norm of sexual activity—the target of my argument obviously can’t dispute that.

We imagine a continuum of cases of coitus, where at one extreme there clearly is no consent and at the other extreme there clearly is consent.

(For instance, it could be a set of cases where a party threatens an adverse consequence if coitus is not engaged in: at one end, the consequence is torture and at the other end it’s a minor expression of minor displeasure. Accepting coitus as an alternative to torture is not consent. Accepting coitus as an alternative to witnessing a minor expression of minor displeasure can be consent (assuming that minor displeasure is all there is; obviously, minor displeasure from a tyrant could have further adverse consequences—including torture and death).)

Assuming consent is the only norm of sexual activity, there is no sexual wrong at the consent end of the continuum and there is grave sexual wrong by (1) and (2) at the no-consent end of the continuum. Given continuous variation in cases, we would expect continuous variation in wrongdoing. So if at one end we have grave sexual wrong and at the other end no sexual sexual wrong, somewhere in the middle there should be a case of non-grave sexual wrong, which is what premise (3) says.

Note how the enthusiastic consent alternative to the consent norm nicely escapes the argument. For the proponent of the enthusiastic consent norm case can agree to (2) but say that there are some non-grave sexual wrongs. These non-grave sexual wrongs could, for instance, include some of the cases where there is consent but the consent is insufficiently enthusiastic.

Pragmatically speaking, this is a risky argument to use in teaching. The problem is that a student might try to get out of the argument by denying premise (2) which, given the rape problem on many campuses, would be very bad. On the other hand, if students have a sufficiently strong commitment to (2), this argument could have positive consequences for campus sexual culture by getting them to realize that minimally-valid consent is not enough for permissibility (even if by definition it is enough to make the act not be a case of rape).

Philosophically, there is a technical weakness in that the notion of a sexually wrong act is a bit foggy. I think one can reformulate the argument by dropping the “sexual” qualifier in the argument but specializing to cases where there is no promise breaking, there are no bad non-sexual consequences, etc. But it’s hard to explicate the “etc.”