Measuring rotational speed with a phone and an LED

Over the weekend, I was having fun with using an LED as a photodiode, and hooking it up to my oscilloscope. This can be used to measure the speed of a drill (just stick a reflective spot on a matte chuck and use a flashlight). I was going to make an Instructable on measuring rotational speeds of various objects, but my son told me that most people don't have an oscilloscope. But then I found you can just connect the LED to the microphone input on a phone and use a free oscilloscope app, and use that to measure rotational speed. And so I made an Instructable that doesn't need an oscilloscope.

The argument from vagueness

Here's an argument inspired by Plantinga's argument from counterfactuals:

1. The meaning of a word is wholly determined by the decisions of language users.
2. The meaning of "bald" is not wholly determined by the decisions earthly language users.
3. Therefore, there is a non-earthly language user whose decisions at least partly determine the meaning of "bald".

The argument for (2) is this:

4. In any hypothetical sequence to whose last member "bald" does not apply and to whose first it does, there is a transition point in the sequence, i.e., a member to whom "bald" applies but to whose successor it does not.
5. The points in a hypothetical sequence at which "bald" does or does not apply are wholly determined by the meaning of "bald".
6. There are hypothetical sequences where the decisions of earthly language users do not determine the transition point.
7. So, (2) is true.

The argument for (6) is simply to exhibit a series of people, with someone completely bereft of hair on one end, and someone with a full head of hair on the other, with very slight transitions. Clearly our decisions and those of our ancestors do not determine where the transition point is. Claim (5) seems very plausible.

That leaves (4). But that's a matter of logic for any fixed sequence, as a standard argument for epistemicism points out. For suppose there is no transition point. Then:

• not ("bald" applies to x_n and "bald" does not apply to x_n+1)

is true for n=1,...,N where N is the number of items in the series. Given the fact that "bald" applies to x₁, we can then conclude by classical logic that "bald" applies to x₂, and to x₃, and so on up to x_N, contrary to assumption.

And the best candidate for the non-earthly language user is God. For any finite language user, say an alien who gave us language, would be in the same boat: its decisions would be insufficient to determine all meaning.

Stomp rockets out of magazines

Here's my new and improved Instructible on recycling magazines into stomp rockets.

Intentions, tryings and Double Effect

Bob buys a lottery ticket, hoping to win but knowing that it's exceedingly unlikely.

Suppose Bob wins. We can't say that his winning is an unintended side-effect in the sense involved in the Principle of Double Effect. But it is also odd to say that he intended to win, given that he knows how exceedingly unlikely it is. The phrase "hoping to win"much more apt than "intending to win." Likewise, it doesn't seem right to say that winning was a part of Bob's plan. He'd have to be crazy to plan on winning. Nonetheless, winning is something he aimed at, and his action would have been a failure—an expected failure—if he didn't win.

I intend to post this post, and posting this post is a part of my action plan. Bob's relationship to winning only differs quantitatively from my relationship to posting this post. In both cases, there is probability of success somewhere between 0 and 1. In my case, it's close to 1. In Bob's case, it's close to 0. Neither of us can disclaim responsibility upon success. Both of us have our hearts set upon the goal, and our action is defective if it doesn't reach that goal. The difference is that Bob expects it to be defective while I expect mine to be successful (at least in respect of posting—whether it will be successful in respect of philosophical progress is a different question).

There is a yet third kind of case, that of "stretch goals". Suppose Sally buys a lottery ticket in order to support the government activities that the lottery funds, while at the same time still hoping to win (perhaps she plans to donate any winnings to the state, and thereby support the same government activities even more). If Sally wins, again that's not an unintended side-effect of the Double Effect sort. Winning is indeed something she aims at, something she has heart set on. But it's a stretch goal: if she doesn't accomplish it, her action need not be a failure in any way. It is even more awkward to say that Sally intends to win, or that winning is part of her action plan, than it is to say these things about Bob.

Both Bob and Sally are trying to win, but neither is intending to win. The difference between them is that if Bob doesn't win, his action fails, but if Sally doesn't win, his action doesn't need to fail in any way.

All this means that the traditional formulation of the Principle of Double Effect in terms of effects that are intended and effects that are not is incomplete.

I think we do a bit better, then, to formulate Double Effect not in terms of what one is intending, but in terms of what one is trying to do. The classical formulation tells us something like this:

1. An action expected to have an evil effect can be permissible when and only when one is intending a proportionate good and one does not intend the evil effect (either as a means or as an end).

Of course, when the action is expected to have an effect, the distinction between what one intends and what one tries for disappears. But we should extend the principle:

2. An action that has a chance of an evil effect can be permissible when and only when one is trying for a proportionate good and one is not trying for the evil effect (either as a means or as an end).

A bonus of (2) is that while some have claimed that merely instrumental goals are not intended, thereby destroying the distinction that Double Effect is about, it is obvious that an agent is trying to make these goals happen. Whatever we say about whether the terror bomber is intending to do, it's clear that he's trying to kill innocent people.

I also think that talking in terms of trying instead of intending has the benefit of further de-psychologizing the notion and avoiding the inner-speech objection to Double Effect (which says that one ends up justifying actions simply by thinking about them differently). It is even more obvious that the moral worth of an action depends on what one was trying to do than that it depends on what one was intending.

Now my own preferred reformulation of Double Effect is even more radical than (2): it replaces intention with accomplishment. I think (2) is a step along the path to that reformulation, since trying is more intimately linked to accomplishments than intending is (pace what I say about intention in that paper). If something is an accomplishment of mine, I tried to bring it about under some description. But I needn't have intended it under any description, as the cases of Bob and Sally show.

Reasons for non-disclosure

Until today I thought that non-disclosure was only justified in reference to our sinful condition. The psychologist doesn't disclose her patients' problems because sinful humans are likely to treat her patients wrongly if they know about the problems. And so on.

But I was mistaken. First, there are cases not referring to our present sinful condition but a potential future sinful condition. For instance, even an unfallen human can be swayed by temptation, as the story of the tree of knowledge of good and evil shows, and a person can be tempted by the disclosure of benefits.

Second, there are cases where it is good to fail to disclose information either because the order of disclosure is important or because because it is better that the information be discovered by someone on her own. This is an important part of sound pedagogy, and this does not seem to be an aspect of the Fall. God did not, as far as we know, disclose Pythagorean Theorem to Adam and Eve before the Fall, and it was better that humans discover it on their own.

"Finite chance"

The phrase "finite chance" (see Google) seems to be consistently used to mean a a nonzero chance, or maybe a chance that is neither zero nor one. The phrase is very commonly used in the longer phrase "small but finite chance" (oddly, Google has more hits for the longer phrase).

Yet zero is as finite a number as you can get! So what is going on? Maybe people are implicitly thinking in terms of something like von Neumann's log odds (log p/(1−p)), where probability zero is represented by −∞ and probability one by +∞? In that case, "finite probability" would indeed mean what Bayesians call "non-extreme probability", i.e., a probability strictly between zero and one.

By the way, it seems to me that when we connect probability with evidence it is natural to think in the von Neumann way (the force of new evidence will be additive then), while if we connect it with statistical expectations it is natural to think in the classical way.

The ability to do otherwise and brainwashing

Consider cases where an agent is brainwashed into having to choose A by having a set of desires implanted that are sufficiently strong to motivate her to choose A. Here's a rather rough argument:

1. In these brainwashing cases, there is no ability to do otherwise.
2. The relevant difference between these brainwashing cases and cases of agents in deterministic worlds is the history by which the agent came to have those desires.
3. The ability to do otherwise is independent of history.
4. So the relevant difference between brainwashing cases and cases of agents in deterministic worlds does not make a difference for the ability to do otherwise.
5. So agents in deterministic worlds are unable to do otherwise.

Of coure, if we replace "ability to do otherwise" by "freedom", the compatibilist, and many an incompatibilist as well, will dispute (3). But surely your ability to do otherwise depends only on how the world is now, not on how it used to be.

Basically, the point is that while compatibilists can perhaps get out of manipulation arguments by insisting that history makes a difference between cases of brainwashing and cases of determinism, since history makes no difference for the ability to do otherwise, manipulation arguments succeed for the ability to do otherwise, even if they fail for freedom.

There have been two kinds of compatibilists. The Humean compatibilist, well represented by Lewis, have held that determinism is compatible with the ability to do otherwise. The Frankfurtian compatibilist instead insisted that freedom does not require the ability to do otherwise. If my simple argument succeeds, compatibilists must be of the Frankfurtian sort.

Fictional characters, heaven and the multiverse

One of the minor sadnesses of life is when you finish a work of fiction and then you miss a character from there, wishing for more interaction with that character (some examples in my own case: Gandalf, Twoflower, Lucy Pevensie, Sherlock Holmes, Pan Wolodyjowski, Elizabeth Bennet, JC Denton, Inspector Gently, and the Moomins). It's not so much that you want to meet that character in real life (my first thought was that I wanted to meet the character, but then I realized that I just wouldn't click with all of them). But you want something like eternal fictional life for the character (to be distinguished from fictional eternal life, which at least the characters created by authors who believe in eternal life are presumed to have even if this is not mentioned, just as they are presumed to have spleens even if this is not mentioned).

In heaven all tears are wiped away, and presumably this includes the minor ones. So how is the minor sadness of missing a fictional character met? One possibility is that all that is engaging about any person, real or fictional, is his or her way of participating in God. Thus the beatific vision of God will supply the reality that the character is a shadow of.

But although the beatific vision we hope to receive after death even before the resurrection of the body will give us a bliss fulfilling our deepest desires, there is something fitting to our nature to also receive back our bodies. Likewise, then, there is something fitting to our nature to also receive back contact with fictional characters.

Let's speculate. Does this mean that further episodes in their lives will continue to be fictionally created—either by their author or by oneself—ad infinitum? Maybe: these episodes might be set in an infinite afterlife, or they might would-have-been episodes in parallel universes. But there may be a way in which such extension could betray the finitude and integrity of the author's creation, even when in-story the character has eternal life (as Lucy Pevensie clearly does). Though this is definitely one option. Another option is that even the finite earthly life of any real person has infinite thickness, infinite depth of participation in God. If so, then one might enjoy interaction with the character by coming to a deeper and deeper appreciation of the character. Another option is that we might stick to the canonical works created on earth, but have the ability to re-enjoy these works even more deeply than the first time (say, by reaching back in memory to them).

An even more daring option is that we might be living in a very large multiverse and we might meet the real people of whom the characters were shadows. But I am not sure that this is what we really want--I think in at least some of the cases (JC Denton?) we want more of the fictional interaction, rather than a meeting with a real-life person like the character.

There are interesting parallels between this set of issues and the issue of losing a pet.

I suppose the one thing we can with confidence about questions like is that way in which our tears--minor in this case, major in other cases--will be wiped away will be surprising...

The identity of the act of creation

God is three persons and God has created the universe. How many acts of creation are there here? There seem to be three options:

1. Each person of the Trinity performs his own distinct act of creation.
2. The persons of the Trinity jointly perform an act of creation, and no one person of the Trinity performs an act of creation.
3. Each person of the Trinity performs the one numerically same act of creation.

Option 3 is a special case of the doctrine of the identity of divine activities ad extra. I will argue for option 3 by arguing against options 1 and 2.

Since a divine act of creation is efficacious, option 1 implies three individually efficacious creative acts overdetermining the creation of the universe. Then if we attempt to secure reference to God as the one who has performed the act of creation, we fail since there is more than one act of creation, just as we fail if we attempt to secure reference to a place as the north pole of the moon of Mars, since Mars has two moons. But arguably identifying God as the creator either of the universe as a whole or of some aspect of it is central among the ways in which our ancestors gained reference to God. I suppose one could try to rescue our ancestors' reference to God by saying that they ended up ambiguously referring to the three persons. But if so, then it seems that we should say, if we use the word "God" as they did, that there really are three Gods, just as if our ancestors stipulated "Tyrolia" to be the north pole of the moon of Mars, then we should say there are two Tyrolias.

Option 1, thus, leads to some form of atheism or of tritheism.

Option 2 has the unacceptable consequence that the Creed is wrong when it says "I believe in God the Father almighty, the creator of heaven and earth."

That leaves option 3.

Spatializing time

Would it not be strange to accuse biologists of equinizing sharks because they say that horses and sharks are organisms ontologically on par with each other. Of course, both sharks and horses are organisms. Of course, they are ontologically on par. (If biological reductionism holds, they both reduce to particles. If biological anti-reductionism holds, neither reduces to particles.) And the similarities don't end there. They both have DNA, they reproduce sexually, they are both chordates, and so on. Nonetheless, they are obviously different in ways that do not mark an ontological difference, and the biologist is interested in such differences as well as in the similarities.

Eternalists get accused of spatializing time, because they are claimed to hold that time is a dimension ontologically on par with and akin to spatial dimensions. Now, first of all, an eternalist need not think time is a dimension ontologically on par with spatial dimensions. She could, for instance, be an absolutist about spatial relations and a relationalist about temporal ones, or vice versa. She could think that spatial relations are constituted by degrees of interaction (things that tend to interact more are therefore closer together), while temporal relations are primitive. Or she could think that spatial relations are primitive, while temporality is constituted by facts about the causal nexus. All if this is compatible with eternalism. So eternalists certainly do not need to take time to be ontologically on par with space. Of course, they will take time to be akin to space insofar as they hold that being now rather than then no more marks an ontological difference in an object than being here rather than there. But that's just one similarity, a similarity compatible with much ontological dissimilarity.

But let's even grant that we are dealing with an eternalist who thinks the temporal dimension is ontologically on par with the spatial ones. Still, as the case of horses and sharks shows, being ontologically on par is compatible with much significant difference. The biologist doesn't equinize sharks or sharkify equines. Likewise, an oscilloscope and a hammer are ontologically on par, and they are both kinds of tools, but saying that neither oscilloscopifies hammers nor hammerizes oscilloscopes. The differences are important and hard to miss.

The same is true for space and time. Persons' lives are strung out through time in a way that they are not strung out through space: they show significant temporal development but no analogous spatial development, and we are vastly thinner spatially than temporally. Time has a direction connected both with the increase of entropy and causation, while space is isotropic. Even in Relativity Theory, which treats space and time as a unified manifold, the temporal component gets counted completely differently in the metric: the square of the distance between two spacetime points in a flat space is equal to dx²+dy²+dz²−dt²: the time difference crucially gets a minus sign in the signature, a fact that has vast physical consequences. These are vast differences.

A standard four-dimensionalist analysis of change is that change consists of being one way at one time and another way at another. (It's hard to deny that this is necessary and sufficient for change1) This account is accused of making change be too much like the variation in landscape along a spatial axis. But that accusation assumes that on the four-dimensionalist analysis there is no significant difference between temporal and spatial variation. But if there is a significant difference between time and space, something that we saw is quite compatible with eternalism (and very hard to deny!), the accusation falls flat. Saying that temporal and spatial variation on eternalism is the same is like saying that there is no difference between imprisoning an innocent and a guilty person, because both are imprisonments. They are both imprisonments, but one is of an innocent and the other of a guilty person. Likewise, both temporal and spatial variation are variations, but one is a temporal variation and the other a spatial variation. Change is temporal variation.

Two kinds of tools

I picked up this beauty on Saturday from a generous person in Austin who was selling it on Craigslist, but gave it to me for free when it became clear that I'd be actually using it rather than reselling it. (The image on screen is a one-shot capture of the electricity generated by a DC motor when you set it spinning by hand and then let it slow down. Surprisingly linear down-slope, by the way.)

Anyway, thinking about this led me to a curious distinction between two kinds of tools. A tool is used for affecting something. We can distinguish tools into:

• Tools designed to affect minds.
• Tools designed to affect the extra-mental world.

An oscilloscope, a calculator, measuring tape, a book, binoculars and an anti-depressant are all tools designed to produce mental effects, of a particularly calibrated sort, whether by leading to beliefs about the results of measurements, or certain kinds of perceptions, or the like. On the other hand, a bulldozer, a vacuum cleaner, a test-tube and a roof are all tools designed to affect the extra-mental world. Of course, the affecting of the mind in the case of the first kind of tool might in some instance only be a means to affecting the extra-mental world (you might read a book about how to fix a car), while the affecting of the extra-mental world in the case of the second kind of tool might in some instance only be a means to affecting the mental world (the test-tube is used to contain chemicals in order to find out something). Nonetheless, the direct intended effect of the tools is, at least in the primary intended application, as stated.

Fun with ecological simulations

This week and last I'm having fun using AgentCubes to teach programming to gifted middle schoolers (the link is to the Frogger activity, but you can close the video and make whatever you like). One of the activities was designing a simple ecological simulation. It's very easy to set something up where there are, say, cows and grass, and the cows eat and reproduce, while the grass reproduces. But it's hard to tweak the parameters (reproduction rates, movement speeds, hunger thresholds) in a way that makes the simulation stable, with the population neither going out of control nor collapsing.

Here's a very simple simulation, with sexual reproduction (red bulls and white cows), and some immortal snakes that symbolize other dangers thrown in. But eventually the cow population explodes, destroys the grass, and we're left with just the immortal snakes.

When thinking about the problems that natural selection needs to find solutions to, it is easy for non-biologists like me to think primarily about individual immediate challenges: how to find a mate, how to reproduce, how to avoid predators, etc. But there is also the problem of avoiding unstable ecosystems. And these problems seem to me to be in one sense more difficult to find natural selection solutions to: it is only after a number of generations that one can evaluate whether the problem has been solved, and so the evolutionary process must be slower and there is the danger that variations that are ecologically beneficial in the long term might have enough short-term unfortunate consequences that they be selected against. Nothing new to biologists, no doubt, but I hadn't realized this.

More on fungibility and naturalism

In an earlier post, I argued against materialism on the grounds that persons are non-fungible but material objects are fungible or at least persons are non-derivatively non-fungible, while material objects are at best derivatively non-fungible.

Here's a pathway to arguing that if naturalism is true, then at least some persons are fungible. Since no persons are fungible, it follows that naturalism is false.

Start with the thought that:

1. Something wholly composed of fungible parts is fungible.

If this is right, and material objects are composed of elementary particles, then all material objects are fungible since elementary particles are fungible. And that's all we need for our argument.

But (1) may not be quite right. After all, arguably, the Mona Lisa is (derivatively) non-fungible, but all the elementary particles making it up are. There would be no loss if we replaced the particles of the Mona Lisa one by one. The non-fungibility of the Mona Lisa is grounded in the non-fungibility of the arrangement of the parts: If suddenly the Mona Lisa was burnt up, but by coincidence the particles in the ashes and smoke arranged themselves in an exactly similar arrangement, something of value would be lost. There is something special here about the arrangement.

What makes the arrangement of the Mona Lisa's particles special is the specialness of the artistic process that produced that arrangement. This suggests:

2. Something wholly composed of fungible parts arranged by a fungible process is fungible.

A fungible process is one such that it is value-relevant whether it is replaced by an exact copy. The painting of the Mona Lisa is like that. Given (2), it is very plausible that things composed of fungible parts are at best derivatively non-fungible, with their non-fungibility derived from that of the process of generation.

Now you or I perhaps did have our parts get arranged by a non-fungible process: our parents' loving union. But even persons produced by in-vitro fertilization had their parts arranged by our biological parents' bodies through their gametes, and the process of gamete production in a person is arguably non-fungible.

However, at least one person—namely, a first human person—has no person as a biological parent, on pain of an infinite regress. If theism is true, that person may still be the product of a non-fungible process of creation by a (divine) person. But naturalism rules out not only dualism but also theism. A naturalist who does not believe in an infinite past will have to hold that there is a first person who is in no way produced by a person. And there it seems that the process producing that first person is fungible—it plausibly doesn't matter value-wise which of two exactly similar brute animals mated with a brute animal to produce a person. (If it is responded that primates like those we descend from are themselves non-fungible, then just take the argument further back in our evolutionary past.)

Extinction, creationism and presentism

An intuition a lot of people have is:

1. The extinction of a species is a very bad thing.

On the other hand, extinction is central to the evolutionary process. Some species go extinct, making room for others, and thereby producing a greater diachronic biodiversity. Diachronic biodiversity is a very good thing, and the production of this diversity (wholly or at least to a significant degree) by natural evolutionary processes is a very good thing. This suggests:

2. If species at least typically arise by evolutionary processes, (1) is false.

What can we say given (2)? Well, we could argue:

3. Species at least typically arise by evolutionary processes. (Scientifically known fact)
4. Therefore, the extinction of a species is not a very bad thing. (By 2 and 3)

I am inclined to go for this. To soften the counterintuitive consequence, we might note that what is particularly bad is extinctions where no new species are likely to evolve to fill the niche, and the kind of environmental degradation that we want to oppose not only leads to the extinction of species but stands in the way of the evolution of new species that fill the niche. Though that's an empirical question, and I don't know if it's so.

Another move is to argue:

5. Both (1) and (2) are true.
6. Therefore, species do not arise by evolutionary processes, even typically. (By 5)
7. If species do not arise by evolutionary processes, creationism is true. (Since creationism is the best alternative to evolution.)
8. So, creationism is true. (By 6 and 7)

A yet different move is to deny (2). My thinking behind (2) was based on the value of diachronic biodiversity. But perhaps diachronic biodiversity is only as valuable as I think it is if presentism is false. It is only if the past organisms in extinct species really exist, even if pastly so, that they contribute in a valuable way to biodiversity. So one might replace (2) by:

9. If species at least typically arise by evolutionary processes and presentism is false, (1) is false.

And then one might argue:

10. Claims (1) and (3) are true.
11. Therefore, presentism is true. (By 9 and 10)

So I think we have three main options:

• Deny that extinction is a very bad thing.
• Deny evolution and affirm creationism.
• Affirm presentism.

I should note that in (1), I am thinking of on-balance badness rather than just intrinsic badness.

A quick argument for tropes

1. Every thought is a trope of a thinker.
2. There are thoughts.
3. So, there are tropes.

Fungibility, persons and materiality

This seems plausible:

1. All purely material objects are fungible.
2. No persons are fungible.
3. So, no persons are purely material objects.

Maybe that's not quite right. One might think that some objects care about (a colleague gave the examples of the Mona Lisa and Grandpa's Bible) are non-fungible. But I think it's plausible that material objects are at most derivatively non-fungible, deriving their non-fungibility from the non-fungibility of people. Thus:

4. No purely material object is non-derivately non-fungible.
5. Every person is non-derivatively non-fungible.
6. So, no person is a purely material object.

Presentism

I explained presentism to my 11-year-old daughter. I told her that according to presentism past and future events aren't real and reality is three-dimensional. She found this view scary. It made her think we live in something like a "flat world", something akin to a "two-dimensional" world. I take it her worry was that this impoverished the world, in much the way that denying a spatial dimension would. Her emotional reaction to presentism is much like mine is: presentism contracts the world to something way too thin.

My daughter then connected this with Zeno's paradox of the arrow. I think her thought might have been something like this: The eternalist can say that movement is what happens in virtue of the arrow being in different places at different times. But according to the presentist, the arrow is where it is, and that's that: that's all of reality. So presentism denies real change (which is ironic since presentists are largely motivated by the idea of saving change).

Now all this isn't entirely fair to the presentist. The presentist does not deny that the arrow was elsewhere and will be elsewhere. Still, "was" and "will be" are operators akin to modal ones like "can be". The fact that the arrow was elsewhere is related to the fact that the arrow is here in something like the way that the fact that the arrow could be elsewhere is related to that fact. Being in different places at different times ends up being akin to one's position being contingent. And that doesn't seem to do justice to the reality of motion. This is all suggestive, though it's probably not much of a knockdown argument.

Some issues with causal decision theory

Let U be utility, and let H_i be all the epistemically open causal hypotheses. To evaluate the value of an option A, causal decision theory says we should calculate the weighted sum:

• V₁(A)=Σ_iE(U|H_i&A)P(H_i).

Problem: But what if one of the causal hypotheses is incompatible with option A? For instance, H₂ might be the hypothesis that one is brainwashed into not choosing A. In that case, P(H_i&A)=0 and E(U|H_i&A) is apt to be undefined.

The natural solution is to modify the sum (1) to include only those hypotheses H_i such that P(H_i&A)>0, and renormalize the sum to compensate. For instance, if P(H_i&A)>0 for 1≤i≤m and P(H_i&)=0 for m<i≤n, then we should calculate the value of option A at:

• V₂(A)=a⁻¹Σ_i=1^mE(U|H_i&A)P(H_i)

where a=Σ_i=1^mP(H_i) is our normalization factor. And now we make decisions in the straightforward way: we choose the option that has the highest V₂-style value.

But this turns out to betray the core intuitions of causal decision theory. Suppose there are two equally likely causal hypotheses: H₁ says you're free to choose between pizza and falafel and H₂ says you're brainwashed into eating falafel. Suppose you prefer falafel to pizza. But of course your future is bleak if you're brainwashed into eating falafel. Wonderful as falafel is, eating falafel at every meal is going to be miserable. Now, V₂(pizza) includes in the sum only the term for hypothesis H₁, since H₂ is incompatible with pizza. Thus, V₂(pizza) is the value of eating pizza. But V₂(falafel) includes in the sum terms for both hypotheses H₁ and H₂. And since half of the weight of that sum will correspond to H₂, and on H₂ we have the misery of being brainwashed into falafel for the rest of our lives, the theory based on V₂ requires us to choose pizza, lest it turn out that we were brainwashed into eating falafel. But that's exactly the sort of silliness that causal decision theory was created to eliminate: your present decision whether to eat falafel or not makes not a whit of difference to whether you've been brainwashed. To go for pizza here is to act like an evidential decision theorist.

So our simple modification of V₁ to V₂ solves the problem of V₁ being undefined, but at the price of betraying causal decision theory intuitions.

There is, however, another modification. When choosing between some options, say pizza and falafel, we should define the value by only considering in our sums the hypotheses on which all options are causally possible. Interestingly, this means that the value of an option depends on which contrast class of options we are considering: the value of option A_j as chosen from between A₁,...,A_k will in general depend on what the options are. Thus, we should write the value as:

• V₃(A_j;A₁,...,A_k)=a⁻¹Σ_i=1^mE(U|H_i&A_j)P(H_i),

where it is assumed that H₁,...,H_m are the hypotheses that are compatible with each of A₁,...,A_k and a=Σ_i=1^mP(H_i).

The fact that the value of an option in general depends on what other options are in view will be a controversial but not fatal consequence.

Another interesting consequence is that if all the causal hypotheses are deterministic, then the value V₃ will be undefined. Thus, decisions presuppose the possibility of indeterminism. It's plausible that an argument can be made from this for incompatibilism, an argument well worth exploring.

Here, however, is a puzzle. Suppose that hitherto your preferences have been that you liked meatballs a little more than falafel which in turn you liked a little more than pizza (with transitivity). There are now two causal hypotheses each with probability 1/2: according to H₁ you have had no intervention, but according to H₂ you've been brainwashed against eating pizza and your brain response to falafel has been modified so that you will enjoy falafel far more than any food you've ever had. You are now choosing between falafel, meatballs and pizza. The V₃ calculation tells you to consider only those hypotheses compatible with all three options, i.e., to consider only hypothesis H₁. So you will go for meatballs. But surely that's a mistake. Falafel is a better option than meatballs, since if you weren't brainwashed against pizza, meatballs are only slightly better, while if you were brainwashed against pizza, falafel is far better. When evaluating falafel, you do need to take the possibility of H₂ into account.

So maybe the whole approach that fixes causal decision theory by restricting the list of causal hypotheses is wrong? Maybe instead we should restrict outcomes, only considering those outcomes that are caused by one's choice. Thus, in our falafel-pizza story, you simply don't count the disvalue of being brainwashed, since that doesn't causally depend on your decision, when evaluating the utilities. Unfortunately, it's not so simple, since surely we can come up with cases where there are subtle interactions between prior conditions, such as brainwashing, and one's decision. I don't know what to do. But fortunately I don't believe in these kinds of decision theories.

In-vitro fertilization and marriage

Traditional sexual norms say that non-marital sex is impermissible. Those who think in-vitro fertilization (IVF) is permissible but who want to hold on to this norms now need to decide:

• Is (voluntary[note 1]) reproduction outside of marriage permissible?

It would be odd, I think, to say that premarital sex is impermissible but premarital reproduction is permissible. First, the main natural law reasons for thinking premarital sex is impermissible involve the reproductive potential of sex. Second, it seems that children bind a couple together much in the way that sex does.

Suppose, then, that the rule that sex needs to be within marriage extends to reproduction. This leads to interesting questions at the beginning and end of a marriage.

End: Suppose one member of a married couple is about to die. Can that spouse give consent to IVF if the IVF would have to occur after death?

It would be in principle permissible (though often prudentially inadvisable) for a married couple to have sexual relations even if they somehow foresee that (a) fertilization will likely occur in a few days but (b) the man will die before fertilization occurs. By the same token, if IVF is permissible, it might be permissible for the couple to give consent to IVF during the marriage, even though the actual reproduction occurs after death (and hence after the end of the marriage).

Beginning: Suppose the couple's gametes are already available to medical professionals prior to their marriage (say, due to some kind of surgery). Is it permissible for an unmarried couple to give their authorization for the union of the gametes on the understanding that the medical professionals will only unite the gametes after the couple is married?

If this happens, the child will not be in any way a fruit of the marriage, since no marital action—not even the giving of consent—is involved in the reproduction. The connection between the child and the marriage would be merely temporal. This would not do justice to the connection between reproduction and marriage. (One can also come up with an argument for this conclusion by combining the Beginning and End scenarios.)

If this is right, then the crucial thing for the extension of the traditional sexual norm to IVF would be the provision of consent: it is this that must occur during marriage in order that the child be the fruit of the marriage.

But this in turn emphasizes once again the way that in non-coital reproduction the essential involvement by the couple is simply the provision of consent. And that troubles me, even if I do not yet have a fully worked out argument against IVF on this basis (though I do have other arguments against IVF here).

A difference between coital and non-coital reproduction

Non-coital reproduction (at least if it is to satisfy standard medical ethics rules) such as in-vitro fertilization requires the couple's consent, but does not require any specifically reproductive activity by the couple other than the giving of consent. Coital reproduction, on the other hand, requires the couple's consent, and more: it requires that the couple engage in coitus.

This may seem mistaken: After all, doesn't non-coital reproduction require the couple to provide gametes? Indeed, non-coital reproduction requires the couple's gametes. But the provision of the gametes does not require any reproductive action on the part of the couple besides the provision of consent. First, the gametes might be surgically extracted and that requires no activity on the part of the couple beside consent. Second, the gametes might be available to medical professionals due to earlier non-reproductive interventons, say because a cancerous ovary was removed.

And what about pregnancy? Isn't that an activity, even if not per se voluntary? Yes, it is an activity, but it is one that occurs after reproduction has already occurred. Once the gametes have fused into a new organism, reproduction has taken place.

Thus in non-coital reproduction, any reproductive activity by the couple besides the mere provision of consent is inessential. Thus, non-coital reproduction can be entirely outsourced: the couple need only be the source of gametes (some will say even this is not necessary, but I deny that the couple would be reproducing if their gametes are not used), but do not need to do anything to provide them.

This is a difference. Is it a morally significant difference? I think so, but I can't quite put my finger on it right now. A permissible form of reproduction just doesn't seem to me to be the sort of thing that could be outsourced without changing its essential nature.

First cause arguments of a Goedelian sort

We say that a proposition p precludes a proposition q provided that p and q cannot both be true. We say that x is purely good provided that x is good and there is no defect in x.

1. Necessarily, if x causes y, then it is impossible that y exists without x existing. (Follows from essentiality of origins.)
2. S5.
3. Being essentially the cause of every pure good other than perhaps oneself is a perfection.
4. If x is purely good and P is a perfection, then that something has P does not preclude that x exists and x is purely good and something has P.
5. Something is purely good. (For instance, a photon.)

Let x be the purely good thing. By (3) and (4), possibly x exists and x is purely good and something is essentially the cause of everything other than itself that is purely good. Call that something y. Then in some world w, y is the cause of x. By (1) and S5, y is actually the cause of x. By S5, y is also actually essentially the cause of every purely good thing other than itself. So:

6. There is something that is essentially the cause of every purely good thing other than perhaps itself.

We can run the argument without essentiality of origins with a tweak. Simply modify (3) to start "Being essentially the essential cause...", where the essential cause of something is a cause without which it cannot exist.

Whitaker's Words for Kindle

My wife asked me to get a Latin dictionary for my daughter's Kindle, so I dusted off the source files for my PalmOS Whitaker's Words dictionary, modified them a little and generated this dictionary. Enjoy!

Driving Roombas and other IR vehicles over WiFi

I've lately been having fun trying to get lots of the devices in the house to talk to each other. There is something gratifying in using an infrared transmitter from a broken helicopter, an old phone and a laptop to control a Roomba. :-) Here are instructions.

From tropes to the Trinity

Suppose that each cat has its own catness trope, each dog has its own dogness trope, and so on: each thing has its own essence trope. Thus, whenever we have two cats, we have two individuals—understood as bare particulars, bundles, substances, composite wholes, or in some other way—and two catnesses. Now, the question comes: When we say "There are two cats", is the content that

1. There are two individuals each of which is a cat, or that
2. There are two catnesses?

Whenever one is true, so is the other. Moreover, both statements are pretty natural. On a reference magnetism semantics on which the contents of our assertions are determined by charity plus naturalness, the choice between (1) and (2) will be a close one. In fact, it may be so close that it may be indeterminate whether "There are two cats" means (1) or (2). If naturalness favors either reading, it seems to favor (2) slightly, I think. So the choice between (1) and (2) will be a close one, and the answer will be either indeterminate or in favor of (2).

Likewise, does "Felix" refer to the individual or the catness? If the former, then "Felix sits" has the content that this individual has a sitting trope, and if the latter, then "Felix sits" has the content that this catness is coinstantiated with a sitting trope. Again, both candidates are pretty close to as natural. So again, the question whether names refer to individuals or their essence tropes will be a close one on reference magnetism, and maybe the answer will be indeterminate.

Suppose now that by a miracle there came to be two cat individuals that had the very same catness trope. Why not, after all? There doesn't appear to be anything logically contradictory about the supposition. After all, Siamese twins may share a heart. Why can't they share a trope as well?

So now you assign names, Felix and Tiger, and you say: "Felix is not Tiger." While it may have been indeterminate, or at least was close, whether ordinary cat names referred to catnesses or individuals, in the case at hand there is no indeterminacy or closeness. Charity now requires that at least these two names refer to the individuals, not the shared catness, since there is but one shared catness.

But while it is clear that we should say that Felix is not Tiger, it is less clear whether we should say that there are two cats. It is tempting to argue that Felix is a cat, Tiger is a cat, Felix and Tiger are two, so there are two cats. Certainly, there are two each of which is a cat. But are there two cats? Remember that it was indeterminate or close whether in general "There are two cats" referred to a duality of individuals or a duality of catnesses. If it should turn out to have in general referred to a duality of catnesses, then we should say "There is one cat". But even if it was indeterminate whether "There are two cats" refers to a duality of individuals or catnesses, we might reasonably in this very exceptional case settle on duality of catnesses. There is also a significant consideration in favor of describing the case by saying "There is one cat": it lets one say that there is exactly one catness trope per cat.

But now suppose we have three individuals, the Father, the Son and the Holy Spirit, who have one divinity trope. Then charity will make us say that the Father, the Son and the Holy Spirit are three individuals. Should we say that they are three Gods or that they are one God? If in ordinary cases we take counting to go with essence tropes, then we unambiguously have to go for the "one God" reading. If in ordinary cases, counting is indeterminate between individuals and their essence tropes, then we might in the case at hand simply reasonably resolve the ambiguity by speaking in the "one God" way, which then lets us say, as appears right, that there is exactly one divinity trope per God.

I am not defending this exact theory of the Trinity. One needs to be very cautious talking of individuals that have divinity due to divine simplicity. But I think something like the above is Aquinas' story.