Thursday, September 29, 2016

Role kinds

Some kinds of roles succeed in imposing norms on those in roles of that kind. For instance, friends should help each other because they are friends, and spouses should be faithful to each other because they are spouses. Other kinds of roles do not succeed in imposing any norms. If I hurt you, I cannot rationalize my action by saying that I did that because I was your enemy. That may be an explanation, but being an enemy imposed no norm on me. At most it imposes merely apparent norms (before Socrates, the Greeks thought you should treat your enemies badly--they were wrong). What makes the difference? What gives some roles the genuine normative power they have?

Here is a natural law hypothesis I am attracted to. There are some natural human roles, and they each impose norms on those who fill them. I've in effect argued that spouse is one of those roles. Some other plausible examples: parent, child, friend, authority, subject of authority. Our nature specifies a potentiality to such roles, and gives them their normative power. There is a classificatory hierarchy between the natural roles. Spouse is a sub-role of friend, for instance. (An interesting and controversial question: are husband and wife natural sub-roles of spouse? If so, there will be further norms to being a husband and to being a wife.) And then all roles that have normative power are either natural roles or sub-roles specialized on the scaffolding of one or more natural roles, inheriting all their normative power from the natural roles. For instance, the roles of president and monarch are socially constructed sub-roles of authority, and their normative power over those in the role entirely comes from the role of authority. What about the normative power of the role over other people? That I suspect actually comes from the other people having the roles of citizen or subject, respectively, which are both sub-roles of the natural role of subject of authority. Being a monarch spouse is, on the other hand, a constructed sub-role of two different roles: monarch and spouse. (Think here of object oriented languages with multiple inheritance.) And while spouse is natural monarch is a constructed sub-role of authority.

In the above, I was talking about roles considered as general types, like spouse or parent or monarch. These types have tokens: spouse of Bill, parent of Joey, monarch of Canada. One can think of these token roles as also sub-roles, specializations of the role. An interesting question: is there any token role that is natural? That would be a token role whose normative force comes not just from the type role that it is a token of, as when being a spouse of Bill gets its normative force from being a spouse of someone-in-general. I think one plausible case is when the role is with respect to God. Being a subject of God may be a natural role. (What about friend of God? Perhaps that, too, but there the relevant nature may be a grace-nature.)

We can ask some interesting structural questions. Is there a highest level natural role? Perhaps being human or being a person. I have in the past speculated that it might be friend, but I now think that's mistaken, because friend roles are tied to particular individuals, while some of the other roles are not: an authority need not change qua authority when subjects are replaced by others (through conception, death and migration), but a friend does change in respect of friendship when friends come and go.

And how is this all tied to love? I suspect like this. Love isn't itself a role. But the roles determine which form one's love should take. Maybe in fact that is how they exercise their normative force, and that is what explains why there can't be a natural role such as enemy.

Wednesday, September 28, 2016

Cerebrums, animalism and teleology

Suppose you are essentially an animal. If your cerebrum were transplanted into a vat and the rest of your body—including, of course, the brain-stem—were to maintain circulation, nutritive functioning, muscle tone and so on, where would you go? Would you go with the cerebrum in the vat, with the rest of the body, or would you be just plain dead?

Here’s a line of thought. There are more primitive animals that don’t have a cerebrum, but still have a circulatory system, a nutritive system, etc. Thinking about these animals makes on think that the survival of an animal has to do with maintenance of the lower level homeostatic functions. So, we go with the parts of the body responsible for such things.

But an Aristotelian animalist can resist the analogy to primitive animals on teleological grounds. For instance, our circulatory system’s physical resemblance to the circulatory systems of primitive animals misses out on a crucial metaphysical difference: our circulatory system has the support of the life of the mind as its central telos, and it supports the life of the mind by supporting the cerebrum. The teleological structure of primitive animals and human animals is different: functions that are close to the teleological center of the life of a primitive animal are further from the teleological center of human life. It may be the case that when an animal is divided, it goes with the parts that are teleologically more central. If so, then in the initial thought experiment, you would go with the cerebrum.

[By the way, this post represents a new workflow. I am using John MacFarlane pandoc, writing the post as a text file, and then running a script that does pandoc -S filename | iconv -f utf-8 -t utf-16le | clip and pasting it in. This should make math less painful to type.]

Pleasure and pain are discrete

Alice, Bob and Chuck each come into existence at 1 o'clock.

  • Alice lives for one hour. She feels continuous and unchanging morally innocent pleasure during that hour with no pain.
  • Bob lives for two hours. During the first hour his experiences are exactly like Alice's during the second hour, these experiences re-run.
  • Chuck has the same internal stream of subjective experiences as Bob, but is accelerated by a factor of two relative to external time, so he lives only for one hour.

Now, let's add some axioms about hedonic value:

  1. If x and y have the same internal stream of subjective experiences, though perhaps at different external rates, their lives are hedonically equally.
  2. If x and y live during the same period of external time, and at each moment experience the same pleasure or pain, their lives are hedonically equal.
  3. If x and y live hedonically equal lives, and y and z live hedonically equal lives, then x and z live hedonically equal lives (hedonic equality is transitive).
  4. The same pleasant experience lived twice is hedonically better than when lived once.
Note that (4) needs to be carefully understood. Of course, a longer stint of a pleasant experience can get boring. But if one experiences boredom, that's not the same experience then.

Now, we have a contradiction. For by (1), Chuck and Bob's lives are hedonically equal. But by (2), Alice's and Chuck's lives are hedonically equal. Here's why. Take any time t between 1 and 2 o'clock, i.e., any time during the lives of Alice and Chuck. Because the pleasure is constant during that hour-long period, Alice's pleasure at t is the same as her pleasure at (say) 1:30. And for the same reason, Chuck's pleasure at t is the same as his pleasure at (say) 1:15. But Chuck's state at 1:15 is the same as Bob's state at 1:30, since Chuck lives the same life that Bob does, but twice as fast. And Bob's state at 1:30 is the same as Alice's state at 1:30. So, Chuck's pleasure at t is equal to Alice's pleasure at t, and hence by (2) Alice's and Chuck's lives are hedonically equal. Hence, by transitivity, Alice's and Bob's lives are hedonically equal. And this contradicts (4).

Assuming our hedonic axioms (1)-(4) are correct, the story about Alice, Bob and Chuck leads to a contradiction. So what's wrong with the story? I think it's the assumption that it's possible for pleasure to be continuous. Instead, I submit, temporally extended pleasure has to be discrete, made up of a finite number of pieces of pleasure. These pieces might be instantaneous or temporally undivided but extended. And of course the argument can be run with pain in place of pleasure as well.

Tuesday, September 27, 2016

Saturday, September 24, 2016

Pursuit of victory

I wonder if it's rational to choose to play a game precisely in order to win. Winning is a practice-internal goal. Does this goal make sense when one isn't already decided on playing the game? Of course people do choose to play in order to win. But I wonder if those aren't cases where the victory is a means to something else, like money, fame or satisfaction?

Friday, September 23, 2016

A Copenhagen interpretation of classical mechanics

One can always take an indeterministic theory and turn it deterministic in some way or other while preserving empirical predictions. Bohmian mechanics is an example of doing that with quantum mechanics. It's mildly interesting that one can go the other way: take a deterministic theory and turn it indeterministic. I'm going to sketch how to do that.

Suppose we have classical physics with phase space S and a time evolution operator Tt. If the theory is formulated in terms of a constant finite number n of particles, then S will be a 6n-dimensional vector space (three position and three momentum variables for each particle). The time evolution operator takes a point in phrase space and says where the system will be after time t elapses if it starts at that point. I will assume that there is a beginning to time at time zero. The normal story then is that physical reality is modeled by a trajectory function s from times to points of S, such that Tt(s(u))=s(u+t).

Our indeterministic theory will instead say that physical reality is modeled by a (continuous) sequence of probability measures Pt on the phase space S for times t≥0. These probability measures should be thought of as something like a physical field, akin to the wavefunction of quantum mechanics--they represent physical reality, and not just our state of knowledge of it. Mirroring the consciousness-causes-collapse version of the Copenhagen interpretation of quantum mechanics, we now say this. If from time u (exclusive) to time t+u (inclusive) no observation of the system was made, then Pt+u(A)=Pt(Tu−1[A]). I.e., the probability measure is just given by tracking forward by the time-evolution operator in that case.

On the other hand, suppose that at time t an observation is made. Assume that observations are binary, and correspond to measurable subsets of phase space. Intuitively, when we observe we are checking if reality is in some region A of phase space. (It's easy to generalize this to observations having any countable number of possible outcomes.) Suppose Pt* is the value that Pt would have had there been no observation at t by the no-observation evolution rule. Then I suppose that with objective chance Pt*(A) we observe A and with objective chance 1−Pt*(A) we observe not-A, with the further supposition that if one of these numbers is zero, the corresponding observation physically cannot happen. Then the probability measure Pt equals the conditionalization of Pt* on the observation that does in fact occur. In other words, if we observe A, then Pt(B)=Pt*(B|A) and otherwise Pt(B)=Pt*(B|not-A). And then the deterministic evolution continues as before until the next observation.

As far as I can see, this story generates the same empirical predictions as the original deterministic classical story. Also note that while in this story, collapse was triggered by observation, presumably one can also come up with stories on which collapse is triggered by some other kind of physical process.

So what? Well, here's one thought. Free will is (I and others have argued) incompatible with determinism. One thought experiment that people have raised is this. If you think free will incompatible with determinism, and suddenly the best physics turned out to deterministic, what would you do? Would you deny free will? Or would you become a compatibilist? Well, the above example shows that there is a third option: give an indeterministic but empirically adequate reinterpretation of the physics. (Well, to be honest, this might not entirely solve the problem. For it might be, depending on how the details work out, that past observations narrow down the options for brain states so much that they become deterministic. But at least there would be hope that one wouldn't need to give up on libertarianism.)

The above way of making free will compatible with physical determinism is functionally similar to Kant's idea that our free choices affect the initial conditions of the universe, but without the freaky backwards-like (not exactly backwards, since the noumenal isn't in time) causation.

Here's another thought. Any indeterministic theory can be reinterpreted as a deterministic multiverse theory with traveling minds, while maintaining empirical adequacy. The multiverse traveling minds theory allows for causal closure of a deterministic physics together with robust alternate-possibilities freedom. Combining the two reinterpretations, we could in principle start with a deterministic physics, then reinterpret it in a Copenhagen way, and then impose on top of that the traveling minds interpretation, thereby gaining an empirical equivalent theory with robust alternate-possibilities freedom and no mental-to-physical causation. I bet a lot of people thought this can't be done.

Thursday, September 22, 2016

More on competitive sports and other games

I wonder how psychologically feasible it would be to generally engage in competitive sports or other games with one's intention being that the one's competitor win against as strong an opposition as possible. This is not all that difficult to achieve when competing with one's child: one may want the child to beat one, and to beat one when one is playing at one's best. The psychological difficulty is that one's intention that one's competitor win may well weaken one's playing. If one could play excellently with such an intention, wouldn't it be a laudable way to play?

To be as strong an opposition as possible, it would help to have the intention to win. I wonder if it would be possible to have two clearly logically incompatible ends at the same time: (a) that my competitor win against as strong an opposition as possible and (b) that I win. This isn't as problematic as intending p and not p at the same time. Maybe you can't do that, because any action that furthers not p impedes p. But actions that promote (b) can promote (a) by making the opposition as strong as possible, and vice versa. So it might be that incompatible ends like (a) and (b) can be both held together, though it is uncomfortable to do so.

Competitive sports

We think of competitive team sports as involving two groups of people, with cooperation within each group but competition between the groups. However, there is a better picture. We can think of the two teams as part of a larger cooperating group, which is subdivided into two subgroups. The two subgroups cooperate with each other for the goods that the sport achieves. The means by which the two subgroups cooperate for the goods of the sport is competition, much as when lawyers for two sides (normatively speaking) cooperate for the sake of truth and justice by competitively each giving the best rendition of one side of the case. Central among the goods in the sport case will presumably be athletic excellence (I am grateful to Dan Johnson for pointing out this good to me), but there will be other goods such as health, fun, entertainment of others, etc.

Of course, something similar happens in competitive individual sports: the individuals cooperate with each other in order that they achieve the goods of the sport.

From this high vantage point, all competitive sports--as well as other games--are a cooperative human activity. I think one can feel this particularly well when one wants to play a sport or another kind of game and an opponent becomes only available after some difficulty. There is a gratitude one has to the opponent for making the game possible.

Yet, paradoxically, the cooperation can involve each pursuing an incompatible end: their own victory. But ideally each pursues that end because the pursuit (but not necessarily achievement) of that end is what makes the joint goods possible.

The meaning of life

The meaning of life is a contingent constant of the story about the same as the particles.

The state of the basic sense of the following options are responsible for an infinite sense of evil is a member of the probability of the fact that the above argument for the sentence for the probability that what is a table of the second sense of the above theory of a lot of the particles in the way that the problem of the subject of the probability of the responsibility is probably the second problem of moral states of a sentence is that it is a non-empty actions of P(A)=P(A) is a property of an argument for the virtue of a controversial and more about the conditional to the constraints of the best ordinary and more probability of the content of the conclusion of the case of the healthy of a positive sex in the state in A is the interesting to the action to the property of the person who does not allow that the answer to include the heart with the ...

What's that? Well, I had some fun running 6mb worth of my blog posts through this character-based recurrent neural network trainer which is based on this. I then followed an online suggestion and prompted it with "The meaning of life is " and let it generate text mimicking my posts (temperature = 0.4). I find the first sentence kind of interesting. What's cool is that the system starts out without any knowledge of language. It works character by character, eventually figuring out how to make sequences of characters that look like words, how to punctuate, capitalize, insert HTML formatting, etc. The grammar often leaves something to be desired, and it has a tendency to get stuck generating giant sentences with lots of clauses (guess whose writing taught it that?).

Some other quotations, with the temperature value listed (the higher the temperature, the more randomness in the output):

If this is something like the same as the proposition that p is true that the moral reason to be sufficient to do any necessity of the probability that it is the problem of the same probability that the principle and sex and the probability of the same reason to do the reason to be a difference between the problem of the probability of the problem of the same explanation of a sentence is a concept of the probability to the problem of the probability that the probability of a proposition that the contradiction is that the same thing that is the same thing to say that the probability that the proposition that the concept of a property of the proposition p to the probability that it is true and the argument is the argument is that the same thing in the above existence is that the other conditions are not the probability of the same probability of the state of the same as the probability that the same sentence that are not true and the same token, we can also be a stronger than an object of B is a proposition that the probability of the same time [0.3]
The problems think that a promise of the predicates are not human beings and interesting assumption that the presentist stands the correct conscience can be in Case, the strangers are more conversion of the world, not true, for short where P(BK(x1 be the only simple condition to be a physical probability of the like right. </li></ol> where the only quite a very organism is measurable acts should insisted to exist. [0.7]
A relations are 1/2)=(√X2)=/titiely, at all view is that when I said because the person is the substance "p.

Whether I fill out that by the following decided the borning and God wrong, which can presuppose on indeed more pothing" was clearly open the explanan of ohn suggests that they are surprising how we learned lacks effort, if Q; <0) (A>), where this society (e.g., generally distinguish science is said to see that they should say the sake that generates it that each would freely-valiel was intrinsically basically good response holding worlds x as one stating chasted to the following problems, when as the chosen biological speaking only: [1.0]

Wednesday, September 21, 2016

Quantum mechanics and points in space

There are two different pictures of space: space is made of points or space is made of regions. I will argue that quantum mechanics naturally suggests the latter view.

Consider a single-particle system. Its quantum state can be representated by a wavefunction Ψ, which is a square-integrable complex-value function. This seems to go nicely along with the idea that there is such a thing as space, and each point in space has the property of having such-and-such a value of the wavefunction Ψ. (And in a multi-particle system, tuples of points are related to a value.) But that misses a subtlety. While a square-integrable function Ψ represents a quantum state, any two square-integrable functions Ψ1 and Ψ2 that agree outside of a set of measure zero are taken to represent the same quantum state. The measure of a (set consisting of a) single point is going to be zero. So there is no a physical fact of the matter as to the value of the wavefunction is a particular point.

This seems to me to cohere a little better with a view on which space is built up out of extended regions rather than points. While there will be no fact of the matter as to what "the" value of the wavefunction is at a point x, for any extended (at least in the sense of being nonzero-measure) but bounded region R of space, say a ball or cube, there will be a fact about what the average value of the wavefunction over R is (functions that are square-integrable are locally integrable). Moreover, one can recover the value of the quantum state from the values of such averages over, say, all balls. (If space is potentially subdivisible but not actually subdivided, some of these balls will be potential regions of space, and the average of the wavefunction over such a ball may be a dispositional property--the average it would have if space were divided so as to have that ball as a region.)

This is not a knock-down argument against views on which space is made of points. One could say that space is made of points but deny that quantum states have values at single points. Or one could say that wavefunctions that differ on a set of zero measure represent different in principle empirically indistinguishable quantum states. The latter is, I think, unattractive. We should avoid positing an infinite number of empirically unobservable degrees of freedom in physics.

Tuesday, September 20, 2016

The problem of sleep

Consider this natural law argument:

  1. Rational functioning is a basic good.
  2. One may never intentionally act against a basic good.
  3. In intending to fall asleep, one intends to stop rational function (i.e., thought).
  4. Therefore, it is wrong to intend to fall asleep.
One could, I suppose, embrace the conclusion and say something like this: At night, we foresee but do not intend sleep. At night we lie down in bed, accepting but not intending the evil of sleep, much like a person who foresees death might lie down to face death in comfort. But this just won't explain all our practices. First of all, we often lie down and close our eyes to sleep hours before we would expect sleep to overtake us were we to stay up. It seems clear that we lie down and close our eyes in order to accelerate the sleep process. And sometimes, with good reason, we may take medication to help us fall asleep. To condemn such practices would be highly counterintuitive. In fact, one might take the anti-sleep argument as a reductio ad absurdum of natural law reasoning, which appears to be committed to premises (1) and (2).

It is tempting to dismiss the argument by saying that we need sleep to be rational. But that doesn't touch the argument. There are circumstances where the only way to survive is by killing an innocent person--but the end does not justify such a means. Likewise, if (1)-(3) are true, even if the only way we can maintain rational functioning is by sleeping, such a means is impermissible.

Aquinas discusses the question whether sex can be permissible in light of the fact that sex involves such an "excess of pleasure" that "it is incompatible with the act of understanding" (he attributes the latter claim to Aristotle). His answer is that sex can be done in accordance with reason, and what is done in accordance with reason is not sinful. He then says: "For it is not contrary to virtue, if the act of reason be sometimes interrupted for something that is done in accordance with reason, else it would be against virtue for a person to set himself to sleep." Unfortunately, Aquinas doesn't tell us which premise of the anti-sleep argument is false. It is not even clear that he has the same argument clearly in mind. In the case of sex, after all, the hampering of rational function looks like a side-effect (it's interesting that Aquinas doesn't just use Double Effect here) which need not be intended, while in sleep the lack of thought seems central.

For years I've struggled with the anti-sleep argument (but lost no sleep over it). I have two responses. Both of them leave (1) and (2) intact, but query (3). The first response is that in intending to fall asleep one intends to put off one's rational functioning rather than to stop it. A philosopher who leaves his office to walk around the beautiful campus intends that his rational functioning occur outdoors rather than in his office. Likewise, one might intend that one's rational functioning occur in the morning rather than late at night. And the reasons can be similar. The rational functioning outdoors or in the morning is likely to be fresher than in the office or late at night. The analogy here is strongest if one accepts a B-theory of time (and in fact, it may be an argument for a B-theory of time that it makes it easier to justify sleep).

The second answer is that sleep is not actually a cessation of rational function. It is very plausible that unconscious mental processes occur during asleep (it is clear that brain processes do!)--and an important part of sleep involves consciousness anyway. Sleep seems to be an important part of our rational functioning rather than an interruption. Clearly it is not an action against a basic good to switch from one kind of rational functioning to another, say turning one's mind from practical to abstract matters.

A difficulty with the second answer is that some people may not know that rational function continues in sleep. Yet surely such ignorance doesn't make it wrong to fall sleep. I agree. But we can also say that such a person may not intend the cessation of rational functioning. She may simply intend sleep, a particular natural human organic process. And if I am right that sleep is not constituted by a cessation of rational function, then we cannot even say that she "implicitly" acts against rationality or anything like that.

So, the anti-sleep argument fails, and natural lawyers can sleep with a sound conscience.

Monday, September 19, 2016

More on comparing infinities

Some people don't want to say that there are just as many even natural numbers as natural numbers. But suppose that you and I will spend eternity singing numbers in harmony. You will sing every natural number in sequence: 1, 2, 3, ..., with a long pause for applause in between. And while you sing n, I will sing 2n. We will vary the speed of our singing to ensure that we take equal amounts of time. Clearly:

  1. The number of natural numbers = the number of your performances.
  2. The number of your performances = the number of my performances.
  3. The number of my performances = the number of even natural numbers.
  4. So, the number of natural numbers = the number of even natural numbers.
Premises (1)-(3) are obviously true, and I don't understand what "the same number" relation could mean if it's not transitive.

Friday, September 16, 2016

Mathematics without proof

My 11-year-old complained to me that his mathematics teacher tells them things without proof. This made me realize that the sorts of things that he mentioned as given without proof--say, the distributive law and maybe some facts about prime factorization (maybe the Fundamental Theorem of Arithmetic? I can't remember)--were things that somehow no one ever showed me a proof of, either, despite getting an undergraduate degree in mathematics and then a PhD. So I can't just say: "Hold on, one day they will give you the proof of this."

Wednesday, September 14, 2016

Does the size of an organism matter morally?

One might with pull a small plant from one's garden with little thought. But one wouldn't do that to a full grown tree. Of course it's harder to pull out a tree, but that doesn't seem to be all that's going on. The tree seems more significant.

Part of that is that the tree has been growing for a longer time. Temporal size definitely seems to matter. We would think a lot harder about cutting down a tree that hundreds of years old rather than one that's five years old. (Interestingly, we tend to have the opposite judgment in the case of people: it is perfectly understandable when an older person lays down their life for a child. Maybe this is because people have an irreplaceability that plants do not.)

But what about pure spatial size? Does that matter? I once thought about this case. We kill insects for minor reasons. But would we do that if the insects were our size? I thought at the time that we would have more hesitation to kill the large insects for minor reasons (we might not hesitate on self defense), but that this was an irrational bias.

But I now think there might be a justification to thinking of spatially larger organisms as having more value. The larger organisms have more cells, and that makes for a complex system, just like a castle made of ten thousand Legos is more complex, other things being equal, than one made of a thousand.

In the case of people, I guess we will have a duty of justice to bracket reasons arising from the number of cells. So we shouldn't save the fatter person just because he has more cells.

But what about dogs, say. Is it really the case that if a Chihuahua and a Great Dane are drowning, other things being equal we should try to save the Great Dane?

Maybe the differences due to the number of cells are on a logarithmic scale, and hence are only significant given an order of magnitude difference? But a Great Dane is an order of magnitude heavier than a Chihuahua, and so I'd guess it has an order of magnitude more cells.

Maybe the moral difference requires several orders of magnitude? Or maybe it runs on a loglog scale?

Or maybe I'm barking up the wrong tree and spatial size doesn't matter morally at all.

If size doesn't matter morally at all, we have a nice argument that the parts of a substance are never substances. For if the parts of a substance are ever substances, the cells of a multicellular organism will surely qualify. But if the cells are substances, then they are living substances. But surely an order of magnitude difference in the number of living substances destroyed makes a moral difference.