We have four jobs in philosophy or closely adjacent areas at Baylor, with most of the deadlines coming in mid-October:
Sometimes one talks of humans as having a higher value than other animals, and hence it being appropriate to treat them better. While humans do have a higher value, I don't think this is what justifies favoring them. For to treat something well is to bestow value on them. But it is far from clear why the fact that x has more value than y justifies bestowing additional value on x rather than on y. It seems at least as reasonable to spread value around, and preferentially treat y.
A confusing factor is that we do have reason to preferentially treat those who have more desert, and desert is a value. But the reason here is specific to desert, and does not in any obvious way generalize to other values.
I don't deny that we should treat humans preferentially over other animals, nor that humans are more valuable. But these two facts should not be confused. Perhaps we should treat humans preferentially over other animals because humans are persons and other animals are not--but this is a point about personhood rather than about value. I am inclined to think we shouldn't argue: humans are persons, personhood is very valuable, so we should treat humans preferentially. Rather, I suspect we should directly argue: humans are persons, so we should treat humans preferentially, skipping the value step. (To put it in Kantian terms, beings with dignity are valuable, but what makes them have dignity isn't just that they are valuable.)
Over the last couple of days I have realized that the laws of physics are rather more complex than they seem. The lovely equations like G = 8πT and F = Gmm′/r2 (with a different G in the two equations) seem to be an iceberg most of which is submerged in the icy waters of the foundations of mathematics where the foundational concepts of real analysis and arithmetic are defined in terms of axioms.
This has a curious consequence. We might think that F = Gmm′/r2 is much simpler than F = Gmm′/r2 + Hmm′/r3 (where H is presumably very, very small). But if we fill out each proposal with the foundational mathematical structure, the percentage difference in complexity will be slight, as almost all of the contribution to complexity will be in such things as the construction of real numbers (say, via Dedekind cuts).
Perhaps, though, the above line of thought is reason to think that real analysis and arithmetic are actually fundamental?
According to Hume, for one to be responsible for an action, the action must flow from one’s character. But the actions that we praise people for the most include cases where someone breaks free from a corrupt character and changes for the good. These cases are not merely cases of slight responsibility, but are central cases of responsibility.
A Humean can, of course, say that there was some hidden determining cause in the convert’s character that triggered the action—perhaps some inconsistency in the corruption. But given determinism, why should we think that this hidden determining cause was indeed in the agent’s character, rather than being some cause outside of the character—some glitch in the brain, say? That the hidden determining cause was in the character is an empirical thesis for which we have very little evidence. So on the Humean view, we ought to be quite skeptical that the person who radically changes from bad to good is praiseworthy. We definitely should not take such cases to be among paradigm cases of praiseworthiness.
On a "Humean" Best System Account (BSA) of laws of nature, the fundamental laws are the axioms of the system of laws that best combines brevity and informativeness.
An interesting consequence of this is that, very likely, no amount of
advances in physics will
suffice to tell us what the fundamental laws are: significant advances
in mathematics will also be needed. For suppose that after a lot of
extra physics, propositions formulated in sentences p1, ..., pn
are the physicist’s best proposal for the fundamental laws. They are
simple, informative and fit the empirical data really well.
But we would still need some very serious mathematics. For we would need to know there isn’t a simpler collection of sentences {q1, ..., qm} that is logically equivalent to {p1, ..., pn} but simpler. To do that would require us to have a method for solving the following type of mathematical problem:
in the case of significantly non-trivial sentences s.
We might be able to solve (1) for some very simple sentences. Maybe there is no simpler way of saying that there is only one thing in existence than ∃x∀y(x=y). But it is very plausible that any serious proposal for the laws of physics will be much more complicated than that.
Here is one reason to think that any credible proposal for fundamental laws is going to be pretty complicated. Past experience gives us good reason to think the proposal will involve arithmetical operations on real numbers. Thus, a full statement of the laws will require including a definition of the arithmetical operations as well as of the real numbers. To give a simplest formulation of such laws will, thus, require us to solve the problem of finding a simplest axiomatization of the portions of arithmetic and real analysis that are needed for the laws. While we have multiple axiomatizations, I doubt we are at all close to solving the problem of finding an optimal such axiomatization.
Perhaps the Humean could more modestly hope that we will at least know a part of the fundamental laws—namely the part that doesn’t include the mathematical axiomatization. But I suspect that even this is going to be very difficult, because different arithmetical formulations are apt to need different portions of arithmetic and real analysis.
Say that a function P : F → [0,1] where F is a σ-algebra of subsets of Ω is chanceable provided that it is metaphysically possible to have a concrete (physical or not) stochastic process with a state space of the same cardinality as Ω and such that P coincides with the chances of that process under some isomorphism between Ω and the state space.
Here are some hypotheses ones might consider:
If P is chanceable, P is a finitely additive probability.
If P is chanceable, P is a countably additive probability.
If P is a finitely additive probability, P is chanceable.
If P is a countably additive probability, P is chanceable.
A product of chanceable countably additive probabilities is chanceable.
It would be nice if (2) and (4) were both true; or if (1) and (3) were.
I am inclined to think (5) is true, since if the Pi are chanceable, they could be implemented as chances of stochastic processes of causally isolated universes in a multiverse, and the result would have chances isomorphic to the product of the Pi.
I think (3) is true in the special case where Ω is finite.
I am skeptical of (4) (and hence of (3)). My skepticism comes from the following line of thought. Let Ω = ℵ1. Let F be the σ-algebra of countable and co-countable subsets (A is co-countable provided that Ω − A is countable). Define P(A) = 1 for the co-countable subsets and P(A) = 0 for the countable ones. This is a countably additive probability. Now let < be the ordinal ordering on ℵ1. Then if P is chanceable, it can be used to yield paradoxes very similar to those of a countably infinite fair lottery.
For instance, consider a two-person game (this will require the product of P with itself to be chanceable, not just P; but I think (5) is true) where each player independently gets an ordinal according to a chancy isomorph of P, and the one who gets the larger ordinal wins a dollar. Then each player will think the probability that the other player has the bigger ordinal is 1, and will pay an arbitrarily high fee to swap ordinals with them!
Here are three plausible theses:
You’re only culpable for a morally wrong choice determined by a relevantly abnormal mental state if you are culpable for that mental state.
A mental state that determines a morally wrong choice is relevantly abnormal.
You are not culpable for anything that is prior to the first choice you are culpable for.
Given these theses and some technical assumptions, it follows that:
For suppose that you are blameworthy for some choice and determinism holds. Let t1 be the time of the first choice you are culpable for. Choices flow from mental states, and if determinism holds, these mental states determine the choice. So there is a time t0 at which you have a mental state that determines your culpable choice at t1. That mental state is abnormal by (2). Hence by (1) you must be culpable for it given that it determines a wrong choice. But this contradicts (3).
The intuition behind (1) is that abnormal mental states remove responsibility, unless either the abnormality is not relevant to the choice, or one has responsibility for the mental state. This is something even a compatibilist should find plausible.
Moreover, the responsibility for the mental state has to have the same valence as the responsibility for the choice: to be culpable for the choice, you must be culpable for the abnormal state; to be praiseworthy for the choice, you must be praiseworthy for the abnormal state. (Imagine this case. To save your friends from a horrific fate, you had to swallow a potion which had a side-effect of making you a kleptomaniac. You are then responsible for your kleptomania, but in a praiseworthy way: you sacrificed your sanity to save your friends. But now the thefts that come from the kleptomania you are not blameworthy for.)
Premise (2) is compatible with there being normal mental states that determine morally good choices, as well as with there being normal mental states that non-deterministically cause morally wrong choices (e.g., a desire for self-preservation can non-deterministically cause an act of cowardice).
What I find interesting about this argument is that it doesn’t have any obvious analogue for praiseworthiness. The conclusion of the argument is a thesis we might call culpability incompatibilism.
The combination of culpability incompatibilism with praiseworthiness compatibilism (the doctrine that praiseworthiness is compatible with determinism) has some attractiveness. Leibniz cites with approval St Augustine’s idea that the best kind of freedom is choosing the best action for the best reasons. Culpability incompatibilist who are praiseworthiness compatibilists can endorse that thesis. Moreover, they can endorse the idea that God is praiseworthy despite being logically incapable of doing wrong. Interestingly, though, praiseworthiness compatibilism makes it difficult to run free will based defenses for the problem of evil.
Suppose there is a 75% chance that I have done a specific wrong thing yesterday. (Perhaps I have suffered from some memory loss.) What should be my attitude? Guilt isn’t quite right. For guilt to be appropriate, I should believe that I’ve done a wrong thing, and 75% is not high enough for belief.
Guilt does come in degrees, but those degrees correlate with the degrees of culpability and wrongness, not with the epistemic confidence that I actually did the deed.
If I am not sure that I’ve done something, then a conditional apology makes sense: “Due to memory loss, I don’t know if I did A. But if I did, I am really sorry.” Maybe there is some conditional guilt feeling that goes along with conditional apology. But I am not sure there is such a feeling.
However, even if there is such a thing as a conditional guilt feeling, it presumably makes just as much sense when the probability of wrongdoing is low as when it is high. But it seems that whatever feeling one has due to a probability p of having done the wrong thing should co-vary proportionately to p.
Here’s an interesting possibility. There is no feeling that corresponds to a case like this. Feelings represent certain states of the world. The feeling of guilt represents the state of one’s having done a wrong. But just as we have no perceptual state that represents ultraviolet light, we have no perceptual state that represents probably having done a wrong. Other emotions do exist that have probabilistic purport. For instance, fear represents a chance of harm, and the degree (and maybe type: compare ordinary fear with dread!) of fear varies with the probability of harm.
While we can have highly complex cognitive attitudes, our feelings have more in the way of limitations. Just as there are some birds that have perceptual states that represent ultraviolet light, there could be beings that represent a probability that one did wrong, a kind of uncertain-guilt. But perhaps we don’t have such a feeling.
We get around limitations in our perceptual skills by technological means and scientific inference. We cannot see ultraviolet, but we can infer its presence in other ways. Similarly, we may well have limitations in our emotional attitudes, and get around them in other ways, say cognitively.
It would be interesting to think what other kinds of feelings could make sense for beings like us but which we simply don’t have.
A generous patron makes an offer to you. You are to pick out a positive integer n and you will get 2n units of value. You have the ability to pick out any positive integer at no cost to yourself (maybe you can engage in a supertask and name long numbers really fast).
You think about naming a million, but then a billion would pay so much better, and a billion and two is four times better! You agonize. And then you have a brilliant idea. You will randomize by choosing positive integer n with probability 2−n (say, by flipping a coin until you get heads and counting how many flips that took). Your expected payoff will be
That beats any specific number you could choose. So you go for it.
And, poof, you get 4. Regrets! You don’t want to stick to what the random choice gave you, as you’ll “only” get 24 = 16 units of value. Disappointing! So you try again. You choose another positive integer. Now it is, mirabile dictu, a billion and two. But you think: 21000000002 may be a lot, but infinity is more, and if you randomly choose another number, your expected payoff is ∞. So you randomly choose again. And whatever you get, you are dissatisfied.
We have an intuitive line as to where the suffering in animal’s life is so great compared to the goods in it that when we are able to do so, we euthanize animals when the suffering causes the value of the animal’s life to fall below that line. On the other hand, the life of an animal that falls above this line is a life that is a benefit to the animal.
It seems to me that this intuitive line could be a helpful discernment criterion for animal experimentation. Animals that are used for experiments are often bred for that purpose. Thus, they wouldn’t exist absent the practice of experimentation. It seems, hence, that experiments where the stresses on the animals make the animal’s life fall below this intuitive line are very easy to justify: the animals are benefitted by the practice, even if the experiments do impose some suffering on the animal. It seems plausible that such experiments could thus be justified by the intrinsic value of the knowledge gained for its own sake, or even by pedagogical benefits for students.
On the other hand, if the stresses in the animal’s life are such as to make their life fall below the line, then stronger justification is needed: the prospective benefits of the research need to be rather more significant.
I don’t know how good we are at discerning where that line goes. People with pets and farm animals do make hard decisions about this, though, so we seem to have some epistemic access to the line.
(I do think that it is permissible to be much more utilitarian about animal life than about human life. I certainly would not generalize what I say above to the case of humans.)
It seems surprising that space is three-dimensional. Why so few dimensions?
An anthropic answer seems implausible. Anthropic considerations might explain why we don’t have one or two dimensions—perhaps it’s hard to have life in one or two dimensions, Planiverse notwithstanding—but thye don’t explain why don’t have thirty or a billion dimensions.
A simplicity answer has some hope. Maybe it’s hard to have life in one and two dimensions, and three dimensions is the lowest dimensionality in which life is easy. But normally when we do engage in simplicity arguments, mere counting of things of the same sort doesn’t matter much. If you have a theory on which in 2050 there will be 9.0 billion people, your theory doesn’t count as simpler in the relevant sense than a theory on which there will be 9.6 billion then. So why should counting of dimensions matter?
There is something especially mathematically lovely about three dimensions. Three-dimensional rotations are neatly representable by quaternions (just as two-dimensional ones are by complex numbers). There is a cross-product in three dimension (admittedly as well as in seven!). Maybe the three-dimensionality of the world suggests that it was made by a mathematician or for mathematicians? (But a certain kind of mathematician might prefer an infinite-dimensional space?)
Conglomerability says that if you have an event E and a partition {Ri : i ∈ I} of the probability space, then if P(E∣Ri) ≥ λ for all i, we likewise have P(E) ≥ λ. Absence of conglomerability leads to a variety of paradoxes, but in various infinitary contexts, it is necessary to abandon conglomerability.
I want to consider a variant on conglomerability, which I will call independence conglomerability. Suppose we have a collection of events {Ei : i ∈ I}, and suppose that J is a randomly chosen member of I, with J independent of all the Ei taken together. Independence conglomerability requires that if P(Ei) ≥ λ for all i, then P(EJ) ≥ λ, where ω ∈ EJ if and only if ω ∈ EJ(ω) for ω in our underlying probability space Ω.
Independence conglomerability follows from conglomerability if we suppose that P(EJ∣J=i) = P(Ei) for all i.
However, note that independence conglomerability differs from conglomerability in two ways. First, it can make sense to talk of independence conglomerability even in cases where one cannot meaningfully conditionalize on J = i (e.g., because P(J=i) = 0 and we don’t have a way of conditionalizing on zero probability events). Second, and this seems like it could be significant, independence conglomerability seems a little more intuitive. We have a bunch of events, each of which has probability at least λ. We independently randomly choose one of these events. We should expect the probability that our randomly chosen event happens to be at least λ.
Imagine that independence conglomerability fails. Then you can have the following scenario. For each i ∈ I there is a game available for you to play, where you win provided that Ei happens. You get to choose which game to play. Suppose that for each game, the probability of victory is at most λ. But, paradoxically, there is a random way to choose which game to play, independent of the events underlying all the games, where your probability of victory is strictly bigger than λ. (Here I reversed the inequalities defining independence conglomerability, by replacing events with their complements as needed.) Thus you can do better by randomly choosing which game to play than by choosing a specific game to play.
Example: I am going to uniformly randomly choose a positive integer (using a countably infinite fair lottery, assuming for the sake of argument such is possible). For each positive integer n, you have a game available to you: the game is one you win if n is no less than the number I am going to pick. You despair: there is no way for you to have any chance to win, because whatever positive integer n you choose, I am infinitely more likely to get a number bigger than n than a number less than or equal to n, so the chance of you winning is zero or infinitesimal regardless which game you pick. But then you have a brilliant idea. If instead of you choosing a specific number, you independently uniformly choose a positive integer n, the probability of you winning will be at least 1/2 by symmetry. Thus a situation with two independent countably infinite fair lotteries and a symmetry constraint that probabilities don’t change when you swap the lotteries with each other violates independence conglomerability.
Is this violation somehow more problematic than the much discussed violations of plain conglomerability that happen with countably infinite fair lotteries? I don’t know, but maybe it is. There is something particularly odd about the idea that you can noticeably increase your chance of winning by randomly choosing which game to play.
Are there ways in which it would be better if axiology were different? Here’s a suggestion that comes to mind:
For surely it would be better for there to be more goods!
On the other hand, one might have this optimistic thought:
(Theists are particularly likely to think this, since they will likely think that the true axiology is grounded in the nature of a perfect being.)
We have an evident tension between (1) and (2).
What’s going on?
One move is to say that it makes no sense to discuss the value of impossible scenarios. I am inclined to think that this isn’t quite correct. One might think it would be really good if the first eight thousand binary digits of π encoded the true moral code in English using ASCII coding, even though this is impossible (I assume). Likewise, it is impossible for a human to know all of mathematics, but it would be good to do so.
The solution I would go for is that axiology needs to be kept fixed in value comparisons. Imagine that I am living a blessed life of constant painless joy, and dissatisfied with that I find myself wishing for the scenario where joyless pain is even better than painless joy and I live a life of joyless pain. If one need not keep axiology fixed in value comparisons, that wish makes perfect sense, but I think it doesn’t—unlike the wish about π or the knowledge of mathematics.
For years I would find myself periodically annoyed by shoelaces. Several times a day, I would have to engage in finicky fine-motor activity to tie my shoes. This made me a little angry, because I suspected that the reason why few adult shoes have alternate closures has to do with fashion rather than with any technological benefits of shoelaces (note, after all, that shoelaces come undone, as well as get caught in bike gears, so it's not all a matter of laziness), and I've always resented social pressures of fashion imposing burdens on us.
I've thought about this for a long time, and then recently finally decided to do something about it. I pulled out some cord locks (in the photo are some heavy duty cord locks that I salvaged from something years ago), pulled my shoelaces through them, and after a day or two of experimental use, I cut the shoelaces down, and knotted them above the cord locks. No more regular annoyance and anger at society's fashion choices!
To fasten, I just grab the cord lock with one hand, and pull the permanent knot with the other. To unfasten, I just grab the cord lock and pull it to the knot. At any time, I can easily adjust tension in either direction without untying. It doesn't come loose. It doesn't get stuck in bike gears. It's not quite as instantaneous as I had imaged, but it is pretty fast.
It has some minor down sides. Eventually a cord lock will break down--though I don't know if this will be sooner than the shoe. At the length of lace I settled for (a little shorter than in this photo), the shoes don't loosen quite as far for removal as I might ideally prefer. And one would probably need to cut the laces to launder the shoes, but I don't launder my shoes.
Philoponus says:
When Democritus said that the atoms are in contact with each other, he did not mean contact, strictly speaking, which occurs when the surfaces of the things in contact fit on [epharmazousōn] one another, but the condition in which the atoms are near one another and not far apart is what he called contact. For no matter what, they are separated by void. (67A7)
This odd view would lead to three difficulties. First, the loveliness of the Democritean system is that everything is explained by atoms pushing each other around, without any mysterious action at a distance, without any weird forces like the love and strife posited by other Greek thinkers. But if two atoms are moving toward each other, and they must stop short of touching each other, it seems that we have some kind of a repulsion at a “near” distance. Second, the atomists thought everything happened of necessity. But why should two atoms heading for each other stop at distance x apart rather than distance x/2 or x/3, say? This seems arbitrary. And, third, what reason would Democritus have to say such a strange thing?
One solution is to simply say Philoponus was wrong about Democritus (cf. this interesting paper). One might, for instance, speculate that Democritus said something about how there will always be interstices of void when atoms meet, much like the triangle-like interstices when you tile the plane with circles in a hexagonal pattern, because their surfaces do not perfectly match like jigsaw pieces would, and Philoponus confused this with the claim that there is void between the atoms.
But I want to try something else. There is a famous problem—discussed by Sextus Empiricus, the Dalai Lama (!) and a number of people in between—about how impenetrable material objects can possibly touch. For if they touch, their surfaces are either separated by some distance or not.If their surfaces are separated, they don’t really touch. If their surfaces are not separated, then the surfaces are in the same place, and the objects have penetrated each other (albeit only infinitesimally) and hence they are not really impenetrable.
Suppose now that we think that Democritus was aware of this problem, and posited the following solution. Atoms occupy open regions of space, ones that do not include any of their boundaries or surfaces. For instance, atoms of fire, which are spherical, occupy the set of points in space whose distance to the center is strictly less than a radius r: the boundary, where the distance to the center is exactly r, is unoccupied. If two spherical atoms, each of radius r, come in contact, the distance between their centers is 2r, but the point exactly midway between their centers is not occupied by either atom. There is a single point’s worth of void there.
This immediately solves two of the three problems I gave for the void-between-atoms view. If I’m right, Democritus has very good reason to posit the view: it is needed to avoid the problem of interpenetration of surfaces. Furthermore, the arbitrariness problem disappears. Atoms heading for each other stop precisely when their boundaries would interpenetrate if they had boundaries in them. They stop at distance zero. There is no smaller distance they could stop at. The two spherical atoms stop moving toward each other when there is exactly one point of void between them: any more and they could keep on moving; any less is impossible.
We still have the problem of mysterious action at a distance requiring some force beyond mere contact. But Democritus might think—I don’t know if he would be right—that action at zero distance is less mysterious than action at positive distance, and on the suggestion I am offering the distance between objects that are touching is zero. There is a point’s (or a surface of points, if say we have two cubical atoms meeting with parallel faces) worth of distance, and that’s zero. Impenetrability at least explains why the atoms can’t go any further towards each other, even if it does not explain why they deflect each other’s motion as they do (which anyway, as we learn from Hume’s discussion of billiard balls, isn’t easy). So the remaining problem is reduced.
It wouldn’t surprise me at all if this was in the literature already.
