A consideration in favor of factory farming

In the US, the number of days per week that people in the under $25,000 income bracket (2012 data) consume meat is approximately the same as in higher income brackets. It seems very plausible to think that what makes this equality in the consumption of meat possible is the affordability of meat resulting from factory farming.

Suppose this is so and factory farming were eliminated. Then, there might be little change in the consumption of meat by people at the top of the income scale, as they could afford meat from small and expensive operations, but we would expect a significant decrease in the consumption of meat at the lower end of the income scale. Since people’s feelings of happiness and misery are largely tied to comparative evaluations, this inequality would be likely to lead to increased misery in those at the lower levels of the income scale who are already living lives of quiet desperation.

Moreover, observe that the impact that a pleasure has on a life intuitively depends on what other pleasures are available in life. Suppose I ceased to eat meat. But my own life is really great, and opportunities for pleasure abound. I have a wonderful family, a really fun job, access to Baylor’s incredible recreational facilities, books, video games, microcontrollers from Aliexpress, and enough leisure to enjoy all these. Losing regular access to the gustatory pleasures of meat would make only a small dent in my subjective wellbeing. (It would mostly be a nuisance: I would have to think harder how to fulfill my high caloric needs.)

But imagine that I am really poor. I am trying to support my family by holding down multiple low-paying jobs. There are few pleasures I have time for in my life and much stress. In that context, losing regular access to meat would take away one of the few pleasures in life—the pleasure of eating meat with a regularity that in the past mainly the rich could afford. Moreover, the pleasures of eating are often not just solitary pleasures but communal: I would lose sharing this pleasure with other family members living difficult lives.

In other words, the elimination of factory farming would have a highly unequal effect: the rich could still have their meat, and meat plausibly makes for a much smaller contribution to the well-being of the rich given all the other opportunities for pleasure available to them; but the poor would lose much of their access to one of the much smaller number of pleasures in their life, which would be a much greater loss.

Now, of course, an argument like this won’t justify every inhumane farming method in the name of making meat available to the poor. But it seems to me to be a serious argument in favor of some factory farming practices. Moreover, there is here a positive, albeit weak, argument in favor of even those of us who could afford meat farmed more humanely to eat factory farmed meat: in doing so, we contribute to the economies of scale that make meat affordable to those in lower income brackets to a historically unprecedented degree.

Are monads in space?

It is often said that Leibniz’s monads do not literally occupy positions in space. This seems to me to be a mistake, perhaps a mistake Leibniz himself made. Leibnizian space is constituted by the perceptual relations between monads. But if that’s what space is, then the monads do occupy it, because they stand in the perceptual relations that constitute space. And they occupy it literally. There is no other way to occupy space, if Leibniz is right: this is literal occupation of space.

Perhaps the reason it is said that the monads do not literally occupy positions in space is that an account that reduces position to mental properties seems to be a non-realist account of position. This is a bit strange. Suppose we reduce position to gravitational force and mass (“if objects have masses m₁ and m₂ and a gravitational force F between them, then their distance is nothing but (Gm₁m₂/F)^1/2”). That’s a weird theory, but a realist one. Why, then, should a reduction to mental properties not be a realist one?

Maybe that’s just definitional: a reduction of physical properties to mental ones counts as a non-realism about the physical properties. Still, that’s kind of weird. First, a reduction of mental properties to physical ones doesn’t count as a non-realism about the mental properties. Second, a reduction of some mental properties to other mental properties—say, beliefs to credence assignments—does not count as non-realism about the former. Why, then, is a reduction of physical to mental properties count as a non-realism?

Maybe it is this thought. It seems to be non-realist to reduce some properties to our mental properties, where “our” denotes some small subset of the beings we intuitively think exist. Thus, it seems to be non-realist to reduce aesthetic properties to the desires and beliefs of persons, or to reduce stones to the perceptual properties of animals. But suppose we are panpsychist as Leibniz is, and think there are roughly at least as many beings as we intuitively think there are, and are reducing physical properties to the mental properties of all the beings. Then it’s not clear to me that that is any kind of non-realism.

Leibniz's idealistic transsubstantiation

I’ve been thinking how much nicer Leibnizian idealism is than the Berkeleyan sort, because you get this nice dose of realism from unconscious perception.

For instance, in one of his letters to Des Bosses, Leibniz offers a neat idealistic account of transsubstantiation: the unconscious perception of the micro-structure of the bread and wine perishes and is replaced with the unconscious perception of the micro-structure of Christ’s body, while the conscious perception of the macro-structure of the bread and wine remains. Material substance is better identified with micro-structure than macro-structure, and the macro-structure is more accident-like, so this counts as a replacement of the material substances in the bread and wine with the material substance of Christ’s body and blood.

Clever! But I am not sure what Leibniz can do with issues about size. The phenomenal perception of the micro-structure of Christ’s body presumably covers a larger volume of perceptual space than the macro-structure of the host. But Christ’s body is supposed to be where the host is.

Leibniz doesn’t say that this account of transsubstantiation is good. He suggests it’s the best one that can be adopted by Jesuits who don’t believe in composite substances.

Leibniz and inter-monadic causation

Along with my graduate students, I was trying yesterday to figure out how Leibniz’s argument against inter-monadic causation works. There are two constrants on figuring this out:

1. Leibniz thinks intra-monadic causation happens.

2. Leibniz thinks God can exercise causation on monads.

Here is a somewhat a moderately interesting Aristotelian argument that may or may not be what Leibniz had in mind:

3. Inter-monadic causation is the causation of an accident of one substance by another substance.

4. Accidents are grounded in their substances.

5. If y is grounded in x, and z causes y, then either z causes x or z = x.

6. So, if substance z causes accident y of substance x, then either z causes x or z = x. (by 4, 5)

7. So, a distinct substance can only cause an accident in another substance if it causes that substance. (by 6)

Leibniz thinks that only God causes monads. Given this, it would follow from (7) that only God can cause an accident in a distinct substance.

One controversial premise in the argument is (5). But it seems to me to have some intuitive force. An official’s being elected is grounded in her getting a majority of the votes, say. But then the only way you can cause the official to be elected is by causing her to get a majority of the votes: i.e., you cause the grounded event (election) by causing the ground (majority vote).

Perhaps the big weakness in the argument is that (5) is most plausible for full grounding, while accidents seem to be only partly grounded in their substances. But the best argument that accidents are only partly grounded in their substances seems to be that full grounding necessitates: if x fully grounds y, then x’s existence or occurrence necessitates y’s; but accidents are not in general necessitated to exist by the existence of their substance. However, Leibniz does think that accidents are in general necessitate to exist by the existence of their substance—that is part of the “complete individual concept” idea. So Leibniz may think (4) is true even for full grounding. (Spinoza almost certainly does.)

Open theism and technical formal epistemology

If open theism is true and there is an infinite future afterlife full of free choices, then some of the puzzling cases involving non-measurable sets and probability that I like to discuss on this blog are faced by God. For any set A of sets of natural numbers, there is the proposition p_A that the set of days in heaven on which David will dance a jig is a member of A. But it seems likely that some sets A will be non-measurable relative to the relevant probability measure.

So, open theists should have motivation to work on highly technical formal epistemology. The more working on that, the merrier. :-)

Windows clip command

The Windows command-line clip command is really great. You can pipe text into it, and it puts it into the clipboard. I write most of my blog posts in a text editor, run them through a bash script that does

pandoc -S $1 | perl -pe 's|(.*?)|$1|g' | iconv -f utf-8 -t utf-16le | clip

and then just paste them right into blogger. Sometimes when I want to write an email to all my students, I run a python script that extracts the emails from the csv file on our class list server, pipe the output into clip, and then just paste it into my email.

Real questions about infinity and probability

One may have the impression that the kinds of questions I like to ask about infinity and probability, questions involving zero probability events and infinitesimals are all purely hypothetical. We don’t actually play games with infinitely many die rolls and the like.

This is a mistake. Here are five non-hypothetical questions that have problematic features dealing with infinity:

1. How epistemically likely is it that we live in a multiverse with exactly K universes (where K is finite or infinite, and at least 1)?

2. How epistemically likely is it that we live in a multiverse that includes at least one K-dimensional universe (where K is finite or infinite, but different from 4)?

3. How epistemically likely is it that there are exactly K objects in existence (where K is finite or infinite, and at least around 10⁸⁰)?

4. How epistemically likely is it that in the future I will roll a die infinitely often and each time get heads?

5. How epistemically likely is it that the first counterexample to Goldbach’s conjecture is between 10¹⁰⁰ and 10¹⁰¹?

Since the epistemic probability that we live in an infinite multiverse is non-zero, questions 1 and 2 have non-hypothetical bite. Question 3 obviously has bite. Likewise, question 4 has bite because the epistemic probability of an infinite afterlife is non-zero. Question 5 has bite because it is epistemically possible that Goldbach’s conjecture is false.

The Euthyphro

I’ve realized today that I read the Euthyphro dilemma differently from how some other people do. I think some people read it as meant to be a real dilemma—a real philosophical question—whether the gods love the holy because it’s holy or whether things are holy because the gods love them.

Maybe it is a real philosophical question, but I don’t think that’s how the text intends it. I suspect that Plato (along, I expect, with Socrates) just straightforwardly thinks:

1. The gods love the holy because it is holy.

2. If the holy were defined as what is loved by the gods, then the holy would be the holy because the gods love it.

3. There is no circularity in explanation. (Implicit premise)

4. So, the holy is not defined as what is loved by the gods. QED

Best explanation and sexual ethics

Consider three ethical claims about sexuality:

1. Rape is always wrong.

2. Incest is always wrong.

3. Bestiality is always wrong.

Take these claims in the strong sense: they hold genuinely always, no matter what the circumstances. Rape is wrong even if the victim is in a coma, is unharmed physically, permission is given by a proxy, and nobody (including the victim) ever finds out. Incest is wrong even between consenting adult relatives raised apart, with no chance of conception. Bestiality is wrong no matter whether the animal is aware of the event, and no matter how low on the evolutionary scale the animal falls or how much the animal wants the act. All these things are wrong even if much rides on them: they are wrong even to save multiple lives, including the life of the victim in case (1).

Now, although it is easy to find ethical views of sexuality that explain why rape, incest and bestiality are almost always wrong, it is hard to find coherent and well-developed views that explain why these are always wrong. But such views do exist. I know of two families of them: there are traditional natural law views and there are views like those of Karol Wojtyla which meld natural law with personalism (my One Body is in this category). However, these two families of views also entail highly controversial further prohibitions on unmarried sexuality, artificial contraception and same-sex sexual activity.

This yields an indirect inference to best explanation argument for the controversial further prohibitions: the best views we have that explain (1)–(3) also entail these further prohibitions.

Of course, one can try to turn the argument around. But I think generally speaking we have better epistemic access to what is forbidden than what is permissible, and so arguing from commonly accepted prohibitions to controversial prohibitions is better than arguing from commonly accepted permissions to controversial permissions.

I am not saying that those who deny the controversial prohibitions need to deny that (1)–(3) are exceptionlessly true to be consistent. I am just saying that they probably aren't going to have a good explanation for why (1)–(3) are exceptionlessly true.

An asymmetry between the theistic and atheistic modal ontological arguments

A simple version of the modal ontological argument goes as follows:

1. Necessarily: If there is a God, then necessarily there is a God. (Premise)

2. Possibly, there is a God. (Premise)

3. So, possibly necessarily there is a God. (By 1 and 2)

4. So, there is a God. (By 3)

It is well-known that there is a very similar argument for the opposite conclusion. Just replace (2) by the premise that possibly there is no God, and you can change the conclusion to read that there is no God. So it seems we have a symmetric stalement. Though, perhaps, as Plantinga has noted, we get to conclude from the arguments that the probability that God exists is 1/2, which when combined with other arguments for theism (or maybe with a particularly plausible version of Pascal’s Wager?) it could be useful.

However, interestingly, the symmetry is imperfect in a way that I haven’t seen mentioned in the literature. Consider this atheistic ontological argument:

5. If there is a God, then necessarily there is a God. (Premise)

6. Possible, there is no God. (Premise)

7. So, it’s not necessary that there is a God. (By 6)

8. So, there is no God. (By 5 and 7)

This argument differs from the theistic one in two ways. First, the atheistic argument can get away with premise (5) which is formally weaker (given Axiom T) than (1). This is not a big difference, since (5) is no more plausible than (1).

But there is a bigger difference. In the theistic argument, to derive (4) from (3) requires the somewhat controversial Brouwer Axiom of modal logic (which follows from S5). But the atheistic argument does not need any axioms of modal logic, besides the uncontroversial modal De Morgan equivalences behind the inference of (7) from (6).

My first thought on noticing this asymmetry was that the atheistic argument is somewhat superior to the theistic, at least when the audience isn’t sure of S5 (or Brouwer).

My second thought was that the atheistic argument is more subject to the objection that its possibility premise begs the question. For the conclusion follows more directly from the possibility premise, and that makes a question-beggingness objection a little bit more plausible.

I don’t know exactly what to think now.

Anyway, nothing earthshaking here. For those of us who think S5 is true, the differences are pretty small. But it’s worth remembering that the symmetry is imperfect.

More fun with non-measurability

Suppose an infinite collection of fair coins is going to be tossed. An outcome is then a specification of how each particular coin (maybe they are numbered) has landed. For any set of outcomes A, we can define this game:

• Game G_A: You toss the coins. If the outcome is in A, you get a dollar. Otherwise, you get nothing.

Here’s a way of putting the paradox of nonmeasurable sets. Assume the Axiom of Choice. Suppose that for every set A of outcomes you assign a (countably additive) probability P(A) between 0 and 1 (not inclusive) of winning the game.

Suppose you are perfectly rational. Then there is a set A of outcomes where you will behave in the following way. First, you agree to pay an initial amount of money to play G_A. After we have made the agreement, I offer you a special deal. For a certain extra increment of money and a certain particular coin C, after all the coins are tossed, regardless of how coin C has landed, I will give it an extra turn-over before we check whether you won (i.e., whether the outcome is in A). And you agree.

The paradoxical part is the “And you agree”. If the coins are fair, it should make no difference whether I give a coin an extra turn-over before you learn the outcomes (of course, with an unfair coin, it will in general make a difference). But for any probability measure on the collection of all outcomes of an infinite collection of coins, there will be a game G_A and a coin C where you will think it is more likely that you will win if you give C an extra turn-over.

The above remarks are just a restatement of the fact that given the Axiom of Choice, there is no (countably additive) probability measure on the set of all outcomes of an infinite collection of coin flips that is invariant under all individual coin reversals.

This trick need not work if the probability measure is only finitely additive: given the Axiom of Choice, there is a finitely measure invariant under all individual coin reversals (because the group generated by the coin reversals is Abelian and hence amenable).

Extended simples

1. It is possible to have a simple that exists at more than one time.

2. Four-dimensionalism is true.

3. So, temporally extended simples are possible. (By 1 and 2)

4. If four-dimensionalism is true, the time and space are metaphysically very similar.

5. So, probably, spatially extended simples are possible.

A reductive account of parthood in terms of causal powers

Analytic philosophers like to reduce. But not much work has been done on reduction of parthood. Here’s an attempt, no doubt a failure as most reductive accounts are. But it’s worth trying.

Suppose that necessarily everything has causal powers. Then we might be able to say:

1. x is a part of y if and only if every (token) causal power of x is a causal power of y.

Some consequences:

2. Transitivity

3. Reflexivity

4. If nothing other than x shares a token causal power with x, then x is mereologically simple and does not enter into composition. Plausibly nothing shares a token causal power with God, so it follows that God is mereologically simple and does not enter into composition.

How does this work for hard cases where parthood is controversial?

Suppose I lose a leg and get a shiny green prosthesis. If the prosthesis is a part of me, then the prosthesis’ power of reflecting green light is a power I have. It seems about as hard to figure out whether the power of reflecting green light is a power that I have as it is to figure out whether the prosthesis is a part of me. So here it is of little help.

Suppose I am plugged into a room-size heart-lung machine. Is the machine a part of me? Well, the machine has the power of crushing people by its weight. It seems intuitively right to say that by being plugged into that machine, I have not acquired the power of crushing people. So it seems that it’s not a part of me.

Is a fetus a part of the mother? Here, maybe the story is some help. The fetus eventually acquires certain powers of consciousness. These do not seem to be powers of the mother—she can be conscious while the fetus is awake. So, once consciousness is acquired, the fetus is not a part of the mother. But earlier, the fetus as the power to acquire these instances of consciousness, and the mother does not seem to, so earlier, too, the fetus does not seem to be a part of the mother. Here the story is of some help, maybe.

However, one doesn’t need all of (1) for some of the applications. The “only if” part of in (1) is sufficient for the heart-lung machine and pregnancy cases.

A quick argument against some materialisms

1. Any pretty simple component of us can be replacement by a functionally equivalent prosthesis that isn’t a part of us without affecting our mental functioning.

2. It is not possible to replace all our pretty simple components by prostheses that aren’t part of us without affecting our mental functioning.

3. Hence, we are not wholly constituted by a finite number of pretty simple components.

This argument tells against all materialisms that compose us from pretty simple components. How simple is “pretty simple”? Well, simple enough that premise 1 be true. A neuron? Maybe. A molecule? Surely. It doesn’t, however, tell against materialisms that do not compose us from pretty simple components, such as a materialism on which we are modes of global fields.

Arbitrariness, probability and infinitesimals

A well-known objection to replacing the zero probability of some events—such as getting heads infinitely many times in a row—with an infinitesimal is arbitrariness. Infinitesimals are usually taken to be hyperreals and there are infinitely many hyperreal extensions of the reals.

This version of the arbitrariness has an objection. There are extensions of the reals that one can unambiguously define. Three examples: (1) the surreals, (2) formal Laurent series and (3) the Kanovei-Shelah model.

But it turns out that there is still an arbitrariness objection in these contexts. Instead of saying that the choice of extension of the reals is arbitrary, we can say say that the choice of particular infinitesimals within the system to be assigned to events is arbitrary.

Here is a fun fact. Let R be the reals and let R^* be any extension of R that is a totally ordered vector space over the reals, with the order agreeing with that on R. (This is a weaker assumption than taking R^* to be an ordered field extension of the reals.) Say that an infinitesimal is an x in R^* such that −y < x < y for any real y > 0.

Theorem: Suppose that P is an R^*-valued finitely additive probability on some algebra of sets, and suppose that P assigns a non-real number to some set. Then there are uncountably different many R^*-valued finitely additive probability assignments Q on the same algebra of sets such that:

1. If P(A) is real if and only if Q(A) is real, and then P(A)=Q(A).

2. All corresponding linear combinations of P and Q are ordinally equivalent to each other, i.e., for any sets A₁, ..., A_n, B₁, ..., B_m in the algebra and any real a₁, ..., a_n, b₁, ..., b_m, we have ∑a_iP(A_i)<∑b_iP(B_i) if and only if ∑a_iQ(A_i)<∑b_iQ(B_i).

3. P(A)−Q(A) differ by a non-zero infinitesimal whenever P(A) is non-real.

Condition (ii) has some important consequences. First, it follows that ordinal comparisons of probabilities will be equally preserved by P and by Q. Second, it follows that both probabilities will assign the same results to decision problems with real-number utilities. Third, it follows that P(A)=P(B) if and only if Q(A)=Q(B), so any symmetries preserved by P will be preserved by Q. These remarks show that it is difficult indeed to hold that the choice of P over Q (or any of the other uncountably many options) is non-arbitrary, since it seems epistemic, decision-theoretic and symmetry constraints satisfied by P will be satisfied by Q.

Sketch of proof: For any finite member x of R^* (x is finite if and only if there is a real y such that −y < x < y), let s(x) be the unique real number such that x − s(x) is infinitesimal. Let i(x)=x − s(x). Then for any real number r > 0, let Q_r(A)=s(P(A)) + ri(P(A)). Note that s and i are linear transformations, from which it follows that Q_r is a finitely additive probability assignment. It is not difficult to show that (i) and (ii) hold, and that (iii) holds if r ≠ 1.

Remark 1: I remember seeing the s + ri construction, but I can’t remember where. Maybe it was in my own work, maybe in something by someone else (Adam Elga?).

Remark 2: What if we want to preserve facts about conditional probabilities? This is a bit trickier. We’ll need to assume that R^* is a totally ordered field rather than a totally ordered vector space. I haven’t yet checked what properties will be preserved by the construction above then.