Tuesday, June 27, 2017

Set size and paradox

Some people want to be able to compare the sizes of sets in a way that respects the principle:

  1. If A is a proper subset of B, then A ≤ B but not B ≤ A.

They do this in order to escape what they think are paradoxical consequences of the Cantorian way of comparing sizes. But from one paradox they fall into another. For the following can be proved without the Axiom of Choice:

  1. If there is a transitive and reflexive relation ≤ between sets of reals (or just countable sets of reals) that satisfies (1), then the Banach-Tarski Paradox holds.
And the Banach-Tarski Paradox is arguably more paradoxical than the paradoxes of infinity that (1) is supposed to avoid.

Anthropomorphism and theism

Sometimes theists are accused of anthropomorphism in their concept of God. But it is important to note that theists hold that God is the entity least like humans. Rocks are closer to us in intellectual capacity than God is. Amoebae are more like us in love than God is. Wet noodles resembles us in power more than God does. All creatures are more like one another than they are like God.

Of course, even if God is the entity least like humans, humans could be the entities most like God. But typical religious theists think even that is false: the angels are more like God than humans are.

None of this denies that there are particular (and controversial) theological views that may suffer from an undue anthropomorphism. I suspect certain motivations for taking God to be mutable to be like that.

Monday, June 26, 2017

Command ethics

I think one of the most powerful objections to divine command theory is MacIntyre’s question as to which divine attributes make it be the case that the obligatory is what God commands. It’s not God’s creating us: for imagine a naturalistic universe where a crazy scientist creates people—surely the crazy scientist’s commands do not constitute obligations. It’s not God’s being omnipotent—that just seems irrelevant. Omniscience also doesn’t seem to help. Etc.

Here’s a theory that just occurred to me which avoids this problem:

  • the obligatory is what is validly commanded by someone.

This is a command theory instead of a divine command theory. The difficulty with this theory is giving an account of a valid command that does not proceed by saying that a valid command is one that it is obligatory to obey. Perhaps, though, one could suppose that there is a fundamental property of non-derivative authority (actually, a relational property: non-derivative authority over x with respect to R) that some persons have. For instance, God has this property in a very broad and non-derivative way, but God might not be the only one (maybe parents have it with respect to children, and governments with respect to people). This theory solves the MacIntyre problem with divine command theory. And while there is a cost to having a primitive account of non-derivative authority, there is some reason to think that even if we grounded obligations in something other than commands, we might still have to take non-derivative authority to be primitive.

Of course, without God the command theory is just implausible: clearly there are ordinary obligations we have that do not come from the commands of other ordinary persons.

I certainly don’t endorse the theory. But it’s worth thinking about, and in particular it’s worth thinking whether it’s not superior to divine command theory.

Friday, June 23, 2017

The unknown mechanism of action of the IUD

A fellow philosopher just sent me this very interesting quote from an article in a reputable medical journal:
[I]f it was conclusively shown that the sole or principal mode of action [of the IUD] was to prevent the embryo from implanting, then this method, as in the case with emergency contraception, would be considered by the Roman Catholic church as causing an early abortion. As a result many agencies involved in the research, development or delivery of contraception prefer to leave the mechanism of action issue unresolved, which may explain why research into the contraceptive mechanisms of IUDs has been sparse in the last 20 years.

The quote’s invocation of politics fits with vague suspicions I had.

But in any case, I wonder whether leaving the “the mechanism of action issue unresolved” helps all that much morally. Suppose that prevention of implantation is morally on par with paradigmatic cases of killing an adult human. Now consider this story. You are a doctor on board a spaceship marooned on an alien planet. All your drugs have been destroyed but one of your patients is suffering severe pain. The aliens have a callous attitude to human life, but in exchange for a piece of fine art they offer you a drug. The aliens always tell the truth and they guarantee that the drug “terminates the pain.” But when you ask them about the mechanism by which it does so, they say: “Trade secret. It terminates the pain.” You try asking more general questions like: “Does it suppress pain signals in the brain?” They just say: “That would terminate the pain. It terminates the pain. Why ask more?” Then someone else in your crew asks: “Does it terminate the patient?” And the aliens say: “That would terminate the pain. It terminates the pain. Why ask more?”

The end result is that you have no idea whether the drug terminates the pain by suppressing the pain as such or by killing the patient. It is clear that in that case we should not use the drug, except as a last-ditch hope for a patient who is already dying. (I am not saying it is acceptable to kill someone who is already dying. But if someone is already dying, then one can tolerate a greater risk of unintended death.)

I am not saying, of course, that we need to find evidence against every crazy hypothesis. There is, after all, the hypothesis that ibuprofen works by annihilating the patient and calling in aliens that replace the patient with a pain-free simulacrum. The tiny but non-zero probability of that hypothesis should not keep us from using ibuprofen. But when we do not know how some drug or procedure works, and one of the serious hypotheses is that it works by killing someone, then that’s a problem.

Given the callousness of the aliens, the hypothesis that they are offering a euthanasia drug is a serious hypothesis. Likewise, the hypothesis that the IUD works primarily by preventing implantation is a serious hypothesis (see the suggestive evidence in the above-quoted paper). In both cases, then, unless we can find significant evidence against this serious hypothesis, the use of the drug or method is wrong (except perhaps in exceptional cases).

We rightly have a guilty-until-proved-innocent approach to medical interventions. Apart perhaps from exceptional cases (e.g., terminal ones), a medical intervention must be tested for its effects on the directly affected parties. The manufacturer's failure to gather data on the effects of the IUD on some of the directly affected parties, namely the embryos, means that the IUD has not been tested up to the morally required standards of testing medical interventions, and hence cannot be licitly used (apart perhaps from some exceptional cases), even absent the data that we have that is suggestive of fatal effects on those parties.

Abortifacient effects of contraception and the Principle of Double Effect

Suppose that a contraceptive has the following properties:

  • Fewer than 1% of users have a pregnancy annually.

  • At least 5% of users annually experience a cycle where the contraceptive fails to prevent fertilization but does prevent implantation.

I think there is good empirical reason to think there are such contraceptives on the market. But that’s a matter for another post. Here I want to look at just the ethics question. So let’s suppose that the above stipulated properties obtain, and in fact that they are known to obtain.

The cases where the contraceptive prevents implantation are cases where the contraceptive kills an early embryo: in short, they are cases where the contraceptive is being abortifacient. The question I want to address in this post is this: Could someone who thinks early embryos have whatever property (personhood, membership in the human race, the imago dei, the possession of the soul, etc.) that makes it paradigmatically wrong to kill adult human beings nonetheless defend the contraceptive on the grounds that the deaths due to implantation-prevention are just an unintended and unfortunate side-effect?

Basically, the defense being envisioned would invoke some version of the Principle of Double Effect, which allows for some actions that have a bad side-effect that isn’t intended as a means or as an end. Of course, Double Effect requires that there not be other reasons why the action is wrong. But let’s bracket the question—which I address at length in my One Body book—whether there are other reasons the contraceptive could be wrong to use, and just focus on the abortifacient effect.

We can ask the question from two points of view:

  1. Can the manufacturer justify the production of the contraceptive on the grounds that failures of implantation are just an unfortunate side-effect?

  2. Can the user justify the use on those grounds?

Regarding 1, here’s a thought. For the contraceptive to be competitive, it has to be highly effective. If one does not count the 5% of annual cases where fertilization occurs but implantation is prevented as part of the contraceptive’s effectiveness, then one can at most claim 95% effectiveness for the contraceptive. And that effectiveness would put the contraceptive significantly behind the most effective formulations of the pill. In fact, it will put it somewhat behind the results that can be achieved by Natural Family Planning by a well-prepared and well-motivated couple. So for commercial purposes, the manufacturer will have to be advertising 99% effectiveness. But one cannot with moral consistency claim 99% effectiveness while holding that 5% of that is an unfortunate side-effect. By claiming 99% effectiveness, one is putting oneself behind the mechanisms that one knows are being used to achieve that effectiveness.

Suppose that a manufacturer advertises an analgesic that is guaranteed to be 99% effective at pain relief. But suppose that 5% of the time, the analgesic kills the patient and 94% of the time it relieves pain non-fatally. Then indeed the analgesic relieves pain 99% of the time, since killing the patient stops the pain. But by holding out 99% effectiveness, the manufacturer is showing that that it is really intending this to be a pain-relief-cum-euthanasia drug rather than a mere pain-relief drug.

What about 2? As we saw from the case of the manufacturer, the user cannot intend 99% effectiveness while saying that the deaths of early embryos are unfortunate side-effects. But the user, unlike the manufacturer, can say: “From my point of view, this is about 94% effective, with a 5% likelihood of a fatal side-effect, which side-effect I don’t intend.”

There are two points I want to make here. First, Double Effect requires there to be no reasonable alternatives to the course of action. But there are methods of fertility control that do not cause implantation-failure, for instance Natural Family Planning, and some of these methods are not less effective when compared against the 94% figure. And one cannot with moral consistency compare these method against the 99% effectivness figure while holding out that 5% of that is an unfortunate side-effect one would like to avoid.

Finally, imagine a hypothetical male contraceptive pill that works by releasing genetically engineered sperm-eating viruses that has the following annual properties:

  • Fewer than 1% of female partners get pregnant.

  • But 5% of female partners get a fatal viral infection from it.

  • No men die.

Clearly, nobody would tolerate such a product. Both the manufacturer and the men using it would be accused of murder. Technically, it might not be murder if the deaths of the women were not intended, but the act would be closely akin to vehicular homicide through criminal negligence. Any Double Effect justification would have no hope of succeeding, because Double Effect requires that the unintended bads not be disproportionate to the intended goods. But a 5% annual chance of death is just not worth the contraceptive effect, especially when there are alternatives present. Indeed, even if the only alternative to using this nasty contraceptive were abstinence, which isn’t the case, surely total abstinence would typically be preferable to inducing a 5% annual chance of death (unless perhaps the woman were already suffering from a terminal disease).

Of course, my arguments are predicated on the assumption that killing an early embryo is morally on par with killing an adult. That's another argument.

Friday, June 16, 2017

Optimalism about necessity

There are many set-theoretic claims that are undecidable from the basic axioms of set theory. Plausibly, the truths of set theory hold of necessity. But it seems to be arbitrary which undecidable set-theoretic claims are true. And if we say that the claims are contingent, then it will be arbitrary which claims are contingent. We don’t want there to be any of the “arbitrary” in the realm of necessity. Or so I say. But can we find a working theory of necessity that eliminates the arbitrary?

Here are two that have a hope. The first is a variant on Leslie-Rescher optimalism. While Leslie and Rescher think that the best (narrowly logically) scenario must obtain, and hence endorse an optimalism about truth, we could instead affirm an optimalism about necessity:

  1. Among the collections of propositions, that collection of propositions that would make for the best collection of all the necessary truths is in fact the collection of all the necessary truths.

And just as it arguably follows from Leslie-Rescher optimalism that there is a God, since it is best that there be one, it arguably follows from this optimalism about necessity that there necessarily is a God, since it is best that there necessarily be a God. (By the way, when I once talked with Rescher about free will, he speculatively offered me something that might be close to optimalism about necessity.)

Would that solve the problem? Maybe: maybe the best possible—both practically and aesthetically—set theory is the one that holds of necessary truth.

I am not proposing this theory as a theory of what necessity is, but only of what is in fact necessary. Though, I suppose, one could take the theory to be a theory of what necessity is, too.

Alternately, we could have an optimalist theory about necessity that is theistic from the beginning:

  1. A maximally great being is the ground of all necessity.

And among the great-making properties of a maximally great being there are properties like “grounding a beautiful set theory”.

I suspect that (1) and (2) are equivalent.

Brute necessities and supervenience

There is something very unappealing about unexplained, i.e., brute, metaphysical necessities that are “arbitrary”. For instance, suppose that someone said that some constant in a law of nature had the precise value it does by metaphysical necessity. If that contant were 1 or π or something like that, we could maybe buy that. But if the constant couldn’t be put in any neat way, could not be derived from deeper metaphysical necessities, but just happened necessarily to be exactly 1.847192019... (in a natural unit system) for some infinite string of digits? Nah! It would be much more satisfactory to posit a theory on which that constant has that value contingently. “Arbitrariness” of this sort is evidence of contingency, though it is a hard question exactly why.

Here is an application of this epistemic principle. It seems very likely that any view on which mental properties supervene of metaphysical necessity on physical ones will involve brute metaphysical necessities that are “arbitrary”.

For instance, consider a continuum of physical arrangements, starting with a paradigmatic healthy adult human and ending with a rock of the same mass. The adult human has conscious mental properties. The rock does not. Given metaphysically necessary supervenience, there must be a necessary truth as to where on the continuum the transition from consciousness to lack of consciousness occurs or, if there is vagueness in the transition, then there must be a necessary truth as to how the physical continuum maps to a vagueness profile. But it is very likely that any such transition point will be “arbitrary” rather than “natural”.

Or consider this. The best naturalist views make mental properties depend on computational function. But now consider how to define the computational function of something, say of a device that has two numerical inputs and one numerical output. We might say that if 99.999% of the time when given two numbers the device produces the sum of the numbers, and there is no simple formula that gives a higher degree of fit, then the computational function of the device is addition. But just how often does the device need to produce the sum of the numbers to count as an adder? Will 99.99% suffice? What about 99.9%? The reliability cut-off in defining computational function seems entirely arbitrary.

It may be that there is some supervenience theory that doesn’t involve arbitrary maps, arbitrary cut-offs, etc. But I suspect we have no idea how such a theory would go. It’s just pie in the sky.

If supervenience theories appear to require “arbitrary” stuff, then it is reasonable to infer that any supervenience is metaphysically contingent—perhaps it is only nomic supervenience.

This line of argument is plausible, but to make it strong one would need to say more about the notion of the “arbitrary” that it involves.

Tuesday, June 13, 2017

Death, dignity and eternal life

One way to look at the difference between the deaths of humans and brute animals is to say that the death of a human typically deprives the human of goods of rational life that the brute animal is not deprived of. While it is indeed an important part of the evil of typical cases of death in humans that they are deprived of such goods, however, focusing on this leads to a difficulty seeing what is distinctively bad about the death of humans who are not deprived of such goods by death, say elderly humans who have already lost the distinctive goods of rational life.

Sure, one can say that the death of a human is the death of a being that normally has the goods of rational life. But it is unclear why the death of a being that normally has the goods of rational life but actually lacks them is worse than the death of a being that actually and normally lacks the goods of rational life.

(Of course, not everybody shares the normative view that there is something distinctively bad about the death of a human being even when the goods of rational life have already been lost. A significant number of people think that euthanasia in such cases is morally licit. But even among those who think that euthanasia in such cases is morally licit, I think many will still think that there is something particularly morally bad about killing such human beings against their clear prior wishes, and those may find something plausible about what I say below.)

How, then, do we explain the distinctive bad in the death of human beings, even ones that lack the distinctive goods of rational life? In the end, I think I would like to invoke human dignity here, but to a significant degree that’s just giving a name to the problem. Instead of invoking and trying to explain human dignity, I want to explore a different option, one that I think in the end will not succeed, but perhaps there is something in the vicinity that can.

Here is a hypothesis:

  • It is the nature of human beings to live forever and never die, but the nature of brute animals is to have a finite life.

If this is true, then death always constitutes a mutilation of the human being. It is what directly deprives the human being of the normative diachronic shape of its life. And killing a human mutilates the human being.

Objection 1: If a murderer didn’t kill her victim, the victim would still have died at some later point.

Response: The murderer is still the proximate cause of the victim’s not living forever. And such proximate causation matters. Suppose that my brother murdered Sally’s brother, and to avenge her brother, in true Hammurabic fashion, Sally seeks to kill me. When she finally comes upon me, I am already falling off a cliff. A moment before I would have hit the ground, Sally shoots and kills me. Sally has murdered me, a grave evil. She is the proximate cause of my death. And that matters, even though it would make little difference to my life if Sally hadn’t killed me.

Objection 2: Even if it is the nature of brute animals to have a finite life, it is not the nature of brute animals to die young. But it is not wrong to kill a brute animal when it is young, even though doing so mutilates the brute animal in much the same way that killing a human mutilates the human by causing her life to be finite if the hypothesis is true.

Response: Agreed: it does mutilate the brute animal to kill it when it is young. But to foreshorten the life of a human being from infinity to a finite amount is much worse—in a sense, infinitely worse—than to foreshorten the life of a brute animal from a longer finite length to a shorter finite length.

Objection 3: Christian faith holds that humans will be resurrected. Thus, killing a human being does not succeed in causing the human being to lose infinite life.

Response: Yes, but according to the hypothesis it is not only the nature of human beings to have an infinite future life but it is also the nature of human beings to have a death-free infinite future life.

Objection 4: Imagine an otherwise unremarkable shrub which has a very special nature: it is supposed to live forever, undying. Destroying this shrub would feel distinctively bad as compared to destroying an ordinary shrub, but still not bad in the same way that killing a human being is. Hence, reference to the normativeness of an infinite future life is not enough to explain the distinctive badness of killing humans.

Response: I think that this objection is decisive. Mere invocation of the normativeness of an infinite deathless life is not enough to solve the problem of the distinctive badness of human death. One still needs something like a story about the special dignity of human beings. But it might be that the hypothesis still helps: it multiplies the synchronic dignity of the human being by something like infinity. So less needs to be accomplished by the dignity part of the account.

Questions that interest me on norm institution and grounding

For any norm Nk that we institute, there is a prior norm Nk − 1 that specifies that when the acts of institution of Nk are performed, then Nk has such-and-such force.

On pain of a regress incompatible with the empirical facts of humanity’s finite past, any instituted norm must be grounded in an uninstituted norm. What are these uninstituted norms like?

Are they specific to our human nature or do they apply to all rational beings or are some of one sort and some of the other? Thinking about some issues in ethics, language, epistemology and decision theory has made me think that it is likely that at least some of the uninstituted norms are specific to human nature rather than to all rational beings.

Also, what types of norms are the uninstituted norms, and how do they relate to the types of norms that they ground? For instance, are instituted linguistic norms grounded in uninstituted linguistic norms or in some other kinds of norms, say moral ones?

For those of us who love theoretical simplicity, it would be a great joy if it turned out that all the uninstituted norms were of one type. If so, that type would be the moral. For, plausibly, no norm can ground an instituted norm that has greater force than itself, and moral norms have greater force than any others. In any case, either there are multiple types of uninstituted norms, or they are all moral. In the latter case all norms are moral or derive by institution from moral ones.

Note that the uninstituted norms need not be fundamental. There could be grounding relations between uninstituted norms. For instance, neither the moral norm not to torture the innocent nor the moral norm not to torture innocent blue-eyed people is instituted, but the latter (assuming it really counts as a norm, rather than an application or something like that) is clearly grounded in the former. If it turns out that, as I think, some uninstituted norms are specific to our human nature, it could still be the case that all the uninstituted norms that are specific to our human nature are grounded in a norm not specific to human nature—say, the universal norm to act in accordance with one’s nature.

Furthermore, there are norms that govern rational behavior as such and norms that do not govern rational behavior as such, such as the norm that two legs is good for humans and four legs is good for pigs. What grounding relationships are there between these? Are all the uninstituted norms of one sort or the other, or are they of both sorts?

There is material for interesting dissertations exploring questions like this. Of course, such questions have been explored in multiple contexts, but perhaps not quite in the above structure.

Monday, June 12, 2017

National self-defense

I think many of us have the intuition that it is permissible, indeed often morally required, for a decent country to defend itself against invaders when there is a reasonable hope of victory. The “decent” condition needs to be there: it was not permissible for Nazi Germany to defend itself against the Allies—they had the duty of surrendering. The “reasonable hope” condition needs to be there as well: if the consequence of fighting is nuclear attacks on all one’s cities, one should probably surrender.

If the Ruritanians invade Elbonia, a decent country, with the goal of killing all Elbonians, then at least if there is a reasonable chance of repelling the invaders, it is permissible for the Elbonians to defend themselves with lethal force. Only slightly less clearly, if the Ruritanians intend to cause no physical harm to Elbonians if the Elbonians surrender, but will wipe out Elbonian culture—they will forbid the use of the Elbonian language, ban the national pastime of painting intricate landscapes on pigeon feathers, and so on—then lethal self-defense is still likely to be permissible.

But what if the Ruritanians invade Elbonia simply in order to take away Elbonia’s sovereignty, so that if the Elbonians surrender, they lose sovereignty but nothing else? The Ruritanians won’t kill anyone, won’t disposs any individuals or corporations of their property, won’t interfere with any aspects of Elbonian culture, won’t conscript Elbonians into their military (the Ruritanians have an all-vounteer army), will not harm the Elbonian economical, educational and healthcare systems, etc. But they will take over national sovereignty. Moreover, the Elbonians are confident of this because the Ruritanians have a centuries-long record of expanding their empire on such terms, and many neighboring countries have lost their sovereignty but had no other losses. Furthermore, it is the Elbonians alone that are at issue. For geographic reasons, the Ruritanians are unable to expand any further, and so Elbonians in defending themselves cannot say that they doing so to protect other countries. And there are no other countries in the world capable of imperialism.

It is only permissible to wage war for the sake of a good that is proportionate to the great evils of war, after all. The question here is this: Is maintenance of national sovereignty worth the deaths—both Elbonian and Ruritanian—and manifold other harms of war?

I don’t know. A state is a valuable form of human community. The destruction of a state is prima facie a bad thing. But if the goods of culture and ordinary life are maintained, it does not seem to be a great bad. Suppose that there was no invasion, but the Elbonians voluntarily voted to join the Ruritanian Empire. Then while there would be some bad in the loss of the Elbonian state, it need not be a tragedy, and on balance it could even be for the good. It is, of course, gravely wrong for the Ruritanians to bludgeon the Elbonians into joining their Empire. But the good of sovereignty just might not be great enough for the Ruritanians to have a moral justification to resist to the death.

If this is right, then sometimes the mere fact that a war is one of just national self-defense is not enough to justify fighting. Do such perfectly clean cases occur? I doubt it: imperialist countries aren’t likely to be as nice as my hypothetical Ruritanians. However, one might have cases that are slightly less clean, where the expected damage to local culture is likely to be small relative to the expected harms of a protracted war, even if that war can be won by the defenders. Moreover, in real-life cases one needs to consider the value of policies that discourage future such attacks by this and other imperialist countries. If all small countries surrendered as soon as there was a Ruritanian-style invasion, then we could expect Ruritanians and others to mount a lot more invasions, which could indeed be harmful.

So our initial intuition about the permissibility of national self-defense is, I think, roughly right, though only roughly.

Thursday, June 1, 2017

Essences

Some properties that a thing has partially or wholly explain other properties the thing has or doesn’t have. For instance, my having a body partially explains my being in Waco and wholly explains my having a body or horns. Some properties that a thing has do not explain, even partially, what other properties the thing has or doesn’t have. Call such properties “explanatorily fundamental”.

So, here’s a theory. The primary essential properties of a thing are the explanatorily fundamental properties of the thing. The primary essential properties are both essential in the medieval explanatory sense and the contemporary modal sense (properties a thing cannot exist without).

What about the case of Christ, who is essentially divine and essentially human, and yet prior (in the order of explanation) to the incarnation was not human? Here’s what we could say: Divinity is the one and only primary essential property of Christ. But humanity is a secondary essential property. A secondary essential property of a thing is the sort of property that (a) is not a primary essential property of that thing, but (b) normally is the primary essential property of its possessor. In the case of Christ, his divinity is explanatorily prior to his humanity, but normally a thing’s humanity does not have any property of that thing explanatorily prior to it.

Tuesday, May 30, 2017

Drawers for small electronic components

With various ongoing projects, I've acquired a lot of small electronic components in little baggies. To store them, I designed a set of customizable plastic drawers that I could run off on my 3D printer. I am stingy, so I tried to reduce the amount of plastic that goes into them by making dividers thin and a grid-like pattern for the walls.


Location, causation and transsubstantiation

Here’s a fun thought experiment. By a miracle (say) I am sitting in my armchair in Waco but my causal interaction with my environment at the boundaries of my body would be as if I were in Paris. There is a region of space in Paris shaped like my body. When a photon hits the boundary of that region, it causally interacts with me as if I were in Paris: I have the causal power to act at a distance to reflect Parisian photons as if I were in that region in Paris. Alternately, that photon might be absorbed by me: I have the causal power to absorb Parisian photons. As a result, it looks to Parisians like I am in Paris, and as I look around, it looks to me like Paris is all around me. The same is true for other interactions. When my vocal cords vibrate, instead of causing pressure changes in Texan air, they cause pressure changes in chilly France. As I walk, the region of space shaped like my body in Paris that is the locus of my interaction with Parisians moves in the usual way that bodies move.

Furthermore, my body does not interact with the environment in Waco at all. Wacoan photons aimed at my body go right through it and so I am invisible. In fact, not just photons do that: you could walk right through my body in Waco without noticing. My body is unaffected by Texan gravity. It is simply suspended over my sofa. As I wave my hand, my hand does in fact wave in Texas, but does not cause any movement of the air in Texas—but in Paris, the region of space in which I interact with the Parisians changes through the wave, and the air moves as a result. When I eat, it is by means of Parisian food particles that come to be incorporated into my Wacoan body.

To me, to Wacoans and to Parisians it looks in all respects like I am in Paris. But I am in Waco.

Or am I? There is a view on which the causal facts that I’ve described imply that I am in Paris, namely the view that spatial relationships reduce to causal relationships. It is an attractive view to those like me who like reductions.

But this attractive view threatens to be heretical. Christ’s body is here on earth in the Eucharist, as well as in heaven in the more normal way for a body to be. But while the body is surely visible in heaven and interacts with Mary and any other embodied persons in heaven, it does not interact physically with anything on earth. Granted, there is spiritual interaction: Christ’s presence in the Eucharist is a means of grace to recipients. But that probably isn’t the sort of interaction that would ground spatial location.

There is, however, a way to modify the causal reduction of location that handles the case of the Eucharist. Actual causal interactions do not seem to be enough to ground location. The reduction very likely needs needs dispositional causal interactions that typically ground causal counterfactuals like:

  1. If Parisians were to shine a flashlight into that dark alley, they’d see me.

However, dispositions can be masked. For instance, sugar is still soluble even if God has promised to miraculously keep it from dissolving when it is placed in water. In such a case, the sugar still has the disposition to dissolve in water, but fails to ground the counterfactual:

  1. The lump would be dissolved were it placed in water.

We might, thus, suppose that when the Mass is being celebrated in Waco, Christ comes to have the dispositional causal properties that would ordinarily be contitutive of his being present in Waco, such as the disposition to reflect Texan photons, and so on. But by miracle, all these dispositions are masked and do not result in actual causal interaction. The unmasked dispositions are those corresponding to spiritual interaction.

Here’s an interesting lesson. The kind of causal-reductive view of location that I’ve just considered seems to be one of the least transsubstantiation-congenial views of location. But, nonetheless, the transsubstantiation can still be made sense of on that view when the view is refined. This gives us evidence that transsubstantiation makes sense.

And we can now go back to the story of my being in Waco while interacting in Paris. The story was underspecified. I didn’t say whether I have the dispositions that go with being in Waco. If I do, these dispositions are being miraculously masked. But they may be enough to make me count as being in Waco. So on the story as I’ve told it, I might actually be both in Waco and in Paris.

Final question: Can external temporal location be similarly causally grounded? (Cf. this interesting paper.)

Thursday, May 25, 2017

Can destruction be good for something?

It is good for a mouse to occupy a limited region of space: if a mouse were cat-sized, it would be incapable of excellent engagement in many of its characteristic behaviors (scurrying around in narrow passages). If time is relevantly like space, we would expect that there be things for which it is good that they occupy a limited interval of time--i.e., it is good for them to die, or at least good for them to die in a particular way. (It is good for a mouse to be spatially bounded--but only certain kinds of spatial bounds, those delimited by healthy skin and fur, are good for the mouse.)

One category of things whose destruction is a part of their flourishing is things whose purpose is to give rise to something else. For instance, sperm and egg are destroyed in giving rise to a zygote, and that it is their flourishing to be destroyed in this manner. But that's not the only category. It may be a part of the flourishing of a skin cell that it perish in order to make way for a newer skin cell. Both of these categories are subsumed in the category of things directed at the good of something other than themselves.

But I think human beings are not like that.

Tuesday, May 23, 2017

Natural Law decision theory

One of the things I’ve learned from the St Petersburg Paradox and Pascal’s Wager is that we are rationally required to have attitudes to risk that significantly discount tiny chances of benefits, rather than to maximize expected utility. This requirement is rational because failure to have such attitudes to risk makes one subject to two-person diachronic Dutch Books. But it is also clearly irrational to significantly discount large chances of benefits.

But where are the lines to be drawn? Maybe it’s not worth enduring an hour of sitting on an uncomfortable chair for a 1/101000 chance of any finite length of bliss, but enduring an hour of sitting in such a chair for a 45% chance of 1000 years of bliss is worthwhile. As long as we thought the decisions were to be made on the basis of expected utility, we could have said that the lines are to be non-arbitrarily drawn by multiplying probabilities and utilities. But that fails.

It is possible, I suppose, that there is a metaphysically necessary principle of rationality that says where the line of the negligibility of chances is to be drawn. Perhaps an hour in the uncomfortable chair for a 1/101000 chance of a finite benefit cannot possibly be worthwhile, but for a 1/106 chance of a large enough finite benefit it is worth it, and there is a cut-off precisely at π ⋅ 10−9. But the existence of any such a metaphysically necessary cut-off is just as implausible as it is to think that the constants in the laws of nature are metaphysically necessary.

(Vagueness is of no help. For even if the cut-off is vague, the shape—vague or exact—of the vagueness profile of the cut-off will still look metaphysically contingent.)

One could leave it to the individual. Perhaps rationality requires each individual to have a cut-off but where the cut-off lies is up to the individual. But rationality also places constraints on that cut-off: the person who is unwilling to sit in an uncomfortable chair for an hour for a 45% chance of 1000 years of bliss is irrational. (I deliberately made it 45%. The cut-off isn’t at 1/2, which would be satisfyingly non-arbitrary.) And where the constraints on the cut-off lie is itself something to be explained, and again it is implausible that it is metaphysically necessary.

In morals, we also have similar cut-off phenomena. It is morally wrong to put someone in prison for life for stealing an ordinary book, while a week of community service is morally permissible. Whence the cut-off? The problem in both cases comes from two features of the situation:

  1. We have a parameter that seems to have a normative force independent of our minds.

  2. That parameter appears to be contingent.

Utilitarianism provides an elegant answer, but no analog of that answer seems to apply in the rationality/risk case. Kantianism is out of luck. Divine command theory provides an answer, but one whose analogue in the case of rationality is quite implausible: it is irrational to be unwilling to sit in the uncomfortable chair for the 45% chance of the great benefit, rather than forbidden by God.

Natural Law, on the other hand, provides a framework for both the moral and the rational cases by saying that the parameter necessarily comes from our nature. Our nature is independent of our minds, and hence we do justice to (1). But while it is presumably not a contingent fact that we have the nature we do, it is a contingent fact that the persons that inhabit the world have the natures they do. Humans couldn’t have these normative risk or moral parameters other than they do, but there could easily have existed non-humans somewhat similar to us who did. The explanation is parallel to the Kripkean explanation of the seeming arbitrariness of water having two hydrogen atoms. Water couldn’t have had a different number of hydrogen atoms, but something similar to water could have had.

More and more, I think something like Natural Law is a powerful framework in normative areas outside of what is normally construe to be moral theory: in decision theory and epistemology. (I hedge with the “normally construe”, because I happen to think that both decision theory and epistemology are branches of moral theory.)

Wednesday, May 17, 2017

Could God be divinity?

Here's a plausible thesis:

  1. If it is of x's essence to be F, then Fness is prior to x.
This thesis yields a fairly standard argument against the version of divine simplicity which identifies God with the property of divinity. For if God is divinity, then divinity is prior to divinity by (1), which is absurd.

But (1) is false. For, surely:

  1. It is of a property's essence to be a property.
But propertyhood is a property, so it is of propertyhood's essence to be a property, and so propertyhood is prior to propertyhood if (1) is true, which is absurd. So, given (2), we need to reject (1), and this argument against the God=divinity version of divine simplicity fails.

What else might properties do?

Suppose that we think of properties as the things that fulfill some functional roles: they are had in common by things that are alike, they correspond to fundamental predicates, etc. Then there is no reason to think that these functional roles are the only things properties do. It is prima facie compatible with fulfilling such functional roles that a property do many other things: it might occupy space, sparkle, eat or think.

Can we produce arguments that the things that fulfill the functional roles that properties are defined by cannot occupy space, sparkle, eat or think? It is difficult to do so. What is it about properties that rules out such activity?

Here's one candidate: necessity. The functional roles properties satisfy require properties to exist necessarily. But all things that occupy space are contingent. And all things that sparkle or eat also occupy space. So no property occupies space, sparkles or eats. (Yes, this has nothing to say about thinking.) Yeah, but first of all it's controversial that all properties are necessary. Many trope theorists think that typical tropes are both contingent and properties. Moreover, it may be that my thisness is a property and yet as contingent as I am. Second, it is unclear that everything that occupies space has to be contingent. One might argue as follows: surely, for any possible entity x, it could be that all space is vacant of x. But it does not follow that everything that occupies space has to be contingent. For we still have the epistemic possibility of a necessary being contingently occupying a region space. Christians, for instance, believe that the Second Person of the Trinity contingently occupied some space in the Holy Land in the first century--admittedly, did not occupy it qua God, but qua human, yet nonetheless did occupy it--and yet the standard view is that God is a necessary being. (Also, God is said to be omnipresent; but we can say that omnipresence isn't "occupation" of space, or that all-space isn't a region of space.)

So the modal argument isn't satisfactory. We still haven't ruled out a property's occupying space, sparkling or eating, much less thinking. In general, I think it's going to be really hard to find an argument to rule that out.

Here's another candidate: abstractness. Properties are abstract, and abstracta can't occupy space, sparkle, eat or think. But the difficulty is giving an account of abstracta that lets us be confident both that properties are abstract and that abstract things can't engage in such activities. That's hard. We could, for instance, define abstract things as those that do not stand in spatiotemporal relations. That would rule out occupying space, sparkling or eating--but the question whether all properties are abstracta would now be as difficult as the question whether a property can occupy space. Likewise, we could define abstract things as those that do not stand in causal relations, which would rule out sparkling, eating and thinking, but of course anybody who is open to the possibility that properties can do these activities will be open to properties standing in causal relations. Or we could define abstractness by ostension: abstract things are things like properties, propositions, numbers, etc. Now it's clear that properties are abstracta, but we are no further ahead on the occupying space, sparkling, eating or thinking front--unless perhaps we can make some kind of an inductive argument that the other kinds of abstracta can't do these things, so neither can properties. But whether propositions or numbers can do these things is, I think, just as problematic a question as whether properties can.

All in all, here's what I think: If we think of the Xs (properties, propositions, numbers, etc.) as things that fulfill some functional roles, it's going to be super-hard to rule out the possibility that some or all Xs do things other than fulfilling these functional roles.

For more related discussion, see this old contest.

Tuesday, May 16, 2017

Pascal's Wager and the bird-in-the-hand principle

My thinking about the St Petersburg Paradox has forced me to reject this Archimedean axiom (not the one in the famous representation theorem):

  1. For any finite utility U and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.
Roughly speaking, one must reject (1) on pain of being subject to a two-player Dutch Book. But rejecting (1) is equivalent to affirming:
  1. There is a finite utility U and a non-zero probability ϵ > 0, such that no gamble that offers a probability ϵ of getting some finite benefit is better than certainty of U.
With some plausible additional assumptions (namely, transitivity, and that the same non-zero probability of a greater good is better than a non-zero probability of a lesser one), we get this bird-in-the-hand principle:
  1. There is a finite utility U and a non-zero probability ϵ > 0, such that for all finite utilities V, the certainty of U is better than a probability ϵ of V.
Now, Pascal's Wager, as it is frequently presented, says that:
  1. Any finite price is worth paying for any non-zero probability of any infinite payoff.
By itself, this doesn't directly violate the bird-in-the-hand principle, since in (3), I said that V was finite. But (4) is implausible given (3). Consider, for instance, this argument. By (3), there is a finite utility U and a non-zero probability ϵ > 0 such that U is better than an ϵ chance at N days of bliss for every finite N. A plausible limiting case argument suggests that then U is at least as good as an ϵ chance at an infinite number of days of bliss, contrary to (4)--moreover, then U+1 will be better than an ϵ chance at an infinite number of days of bliss. Furthermore, in light of the fact that standard representation theorem approaches to maximizing expected utility don't apply to infinite payoffs, the natural way to argue for (4) is to work with large finite payoffs and apply domination (Pascal hints at that: he gives the example of a gamble where you can gain "three lifetimes" and says that eternal life is better)--but along the way one will violate the bird-in-the-hand principle.

This doesn't, however, destroy Pascal's Wager. But it does render the situation more messy. If the probability ϵ of the truth of Christianity is too small relative to the utility U lost by becoming a Christian, then the bird-in-the-hand principle will prohibit the Pascalian gamble. But maybe one can argue that little if anything is lost by becoming a Christian even if Christianity is false--the Christian life has great internal rewards--and the evidence for Christianity makes the probability of the truth of Christianity not be so small that the bird-in-the-hand principle would apply. However, people's judgments as to what ϵ and U satisfy (2) will differ.

Pleasantly, too, the bird-in-the-hand principle gives an out from Pascal's Mugger.

Friday, May 12, 2017

More on St Petersburg

I’ve been thinking about what assumptions generate the St Petersburg paradox. As stated, the paradox depends on the assumption that we should maximize expected utility, an assumption that will be rejected by those who think risk aversion is rational.

But one can run the St Petersburg paradox without expected utility maximization, and in a context compatible with risk aversion. Suppose finite utilities can be represented by finite real numbers. Assume also:

  1. Domination: If a betting portfolio B is guaranteed to produce at least as good an outcome as A no matter what, then B is at least as good as A.

  2. Archimedeanism: For any finite utility U and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.

  3. Transitivity: If C is better than B and B is at least as good as A, then C is better than A.

(Note: For theistic reasons, one might worry about Construction when the Vi are very negative, but we can restrict Construction to positive finite utilities if we add the assumption in Archimedeanism that V can always be taken to be positive.)

For, given these assumptions, one can generate a gambling scenario that has only finite utilities but that is better than the certainty of any finite utility. Proceed as follows. For each positive integer n, let Vn be any finite utility such that probability 1/2n of Vn is better than certainty of n units of utility (this uses Archimedeanism; the apparent use of the Axiom of Choice can be eliminated by using the other axioms, I think) and Vn ≥ Vn − 1 if n > 1. Toss a fair coin until you get heads. Let your payoff be Vn if it took n tosses to get to heads.

Fix any finite utility U. Let n be a positive integer such that U < n. Then the gambling scenario offers a probability of 1/2n of getting at least Vn, so by Domination, Transitivity and the choice of Vn, it is better than U.

And the paradoxes in this post apply in this case, too.

If we have expected utility maximization, we can take Vn = 2n and get the classic St Petersburg paradox.

Given the plausibility of Domination and Transitivity, and the paradoxes here, it looks like the thing to reject is Archimedeanism. And that rejection requires holding that there is a probability ϵ so small and finite utility U so large that no finite benefit with that probability can outweigh U.

Wednesday, May 10, 2017

Teleology and the direction of time

It would be depressing to think that one will never swim as fast as one is swimming today. But it would uplifting to think that that one has never swum as fast as one is swimming today.

I used to think the direction of time was defined by the predominant direction of causation. That may be the case, but if one takes humanistic cases like the above as central, one might think that perhaps the predominant direction of teleology is a better way to define the direction of time. Of course, telê are there to be achieved, and so the direction of teleology needs to fit well with the direction of causation, at least in the case of things that concern us. Moreover, there is some reason to think that teleology is behind all causation—causation aims at an effect.

Certamen machine

My kids are involved in a Classics oriented quiz game called Certamen at school. These involve teams and buttons and a machine that determines the order in which buttons were pressed. Surprisingly, these machines seem to cost a ridiculous $500 and up, despite seeming to be quite a simple thing: 12 buttons, display which order the buttons are pressed in, lock out fellow team members once one member of a team has pressed it.

So I offered my kids' school to design and build one for them as a fun summer project for me and an opportunity for my kids to learn to solder. I ordered about $60 of parts, mostly from Aliexpress, centered on an Arduino Mega (I haven't done any Arduino-based programming, but I've used the Arduino toolchain with an ESP8266 before). The parts have started to come in, including the Mega, so I've started writing some code and prototyping. According to my oscilloscope, the quick and dirty polling code I have gets a worst-case detection speed of 0.1 milliseconds, which should be good enough for a quiz game. (I continue to be grateful to the Austin guy who gave had an oscilloscope for sale for $50 on Craigslist, but when I wanted to buy it, gave it to me for free because he liked the sorts of things I was going to use it for.)

I am a bit nervous about signal problems over the three five-meter CAT6 cables (the most expensive single parts of the project) from the control box to the buttons, but I ordered some capacitors for noise suppression, and once my RJ45 jacks come in, I can do some testing.


Monday, May 8, 2017

Good-bye, (Aristotelian) matter

Of course, there are material things like oaks and people, and it’s distinct from immaterial things like angels. But for a long time I’ve been wondering why my fellow Aristotelians think that there is matter, a component of material things. In the process of reflection, I have given up on matter as a fundamental ontological category. Of course, for theological and common-sense purposes, I need to have the concept of a material substance, but here I hope there is some reduction, such as that a material substance is a substance that has at least one geometric property. My Aristotelianism now inclines to be more like Leibniz’s than like the historical Aristotle’s or Aquinas’s. Material substances, on my view, are much like Leibniz’s monads; they are like Aristotle’s gods or Aquinas’s angels, plus whatever properties or causal powers are needed for them to count as material. I am my own form, and in this form there inhere accidents.

What philosophical work does matter play, particularly in Aristotelian theories?

  1. Many Aristotelians say that something remains through substantial change, namely matter.

The persistence of matter through substantial change is said to do justice to the intuition that the corpse is the remains of the living creature: that there is something in the corpse that was in the living creature. But it is notoriously difficult to remain faithful to the Aristotelian emphasis that identity always comes from form and allow that anything in the corpse is identical to anything in the prior living body. Absent a solution to this, the Aristotelian has to say that there is one bunch of matter prior to death, a bunch of matter informed by the form of the living body, and a different bunch of matter after death, informed by the forms of the substances making up the corpse. But that does not do justice to the common-sense intuition.

In the vicinity, too, there is the question of why it is that the corpse is physically like the living body. But this is not to be accounted for by matter, but by accidents such as shape, mass and color. Accidents are possessed by substances. Either accidents can or cannot survive the destruction of their underlying substance. If they can, then we have an explanation of why the corpse is physically like the living body. If they cannot, then adding that there is matter in both—and even that it is the same matter—does not help: we simply have to bite the bullet and say that the accidents of the living body have the power to cause similar accidents in the corpse.

  1. Matter may play a role in diachronic identity.

But since immaterial substances like angels can persist over time, matter isn’t needed to solve the problem of diachronic identity. Moreover, the problem of diachronic identity seems to me, as a four-dimensionalist, to be a pseudoproblem (see also this]). It is no more a problem how the same thing can exist in 2017 and in 2018 than it is a problem how someone can exist in the room and in the hall—just put a leg in each, and you’ll see how. Matter does nothing to help with the latter problem, since presumably it isn’t the same chunk of matter that’s in the room as in the hall. So, why should matter help with the former?

  1. Matter may play a role in problems of material composition.

Matter may also play a role in some specific solutions to the problem of material composition. One might, for instance, identify the lump with the matter and the statue with the substance composed of it, or the lump with one thing made of the matter and the statue with another thing made of the same matter, and then explain away the commonality of many properties, like mass, by the identity of matter. But either the statue and the lump have numerically the same accident of mass or they do not. If they do, then since accidents inhere in substances, not in matter, the commonality of matter doesn’t do any work. If they do not, then the commonality of matter doesn’t seem to have done much—we still have to explain why the two have an exactly similar accident of mass, given that they have numerically distinct ones.

What matter does do, I think, is help differentiate the classic statue–lump case from the horse–ghost case where Bucephalus’s ghost happens to walk right through the living Seabiscuit, in such a way that the ghost horse and the living horse happen to occupy exactly the same space. For we can say that the ghost case is a case of merely spatial colocation, while the statue–lump case is a case of having the same matter. And intuitively there is a difference between the two cases. Interestingly, though, this isn’t the material composition problem that matter usually gets invoked to solve. And since I don’t believe in statues, or in any other entities that could plausibly be thought to make there be two entities of one chunk of matter, this does little for me.

  1. Isn’t hylo-morphism the distinctively Aristotelian solution to the mind-body problem?

Sure. But, even more than the classic Aristotelian solution, my view is a dissolution to the mind-body problem rather than a solution. The form of course affects the accidents that constitute and shape our embodiment. All of this is due to the nexus—ontological, teleological and causal—that exists between the substance and its accidents (both substance–accident and accident–accident). It’s not a case of one thing moving another: it is just the common story of the form affecting the accidents and the accidents affecting one another.

And, yes, of course I agree with the Council of Vienne that the soul is the form of the body. On my view, talk of the soul is talk of the substance qua form and apart from the accidents constituting its materiality, and the substance qua form is a base for all the accidents which constitute us as having bodies. So, the soul is the form of the body.

  1. Physics talks of matter.

Sure, but physics probably doesn’t have a fundamental distinction between matter and energy, I think.

Anyway, I don’t deny that there is matter in the sense of substances that are so configured as to count as material. Quite possibly, where you have a heap of sand, you have a heap of material substances, and hence matter. (But perhaps not: perhaps fundamental physical reality is just a handful of fields.)


All in all, I just see little if any benefit to matter. And there is much mystery about it. Ockham’s razor cuts it away.

Unless, of course, we come to some philosophical problem that can’t be solved without matter, or can’t be solved as well without it…

A way to argue against Strong AI

  1. Strong AIs are finite persons who are implemented by software. (Definition.)

  2. The correct theory of personal identity for Strong AIs would be a version of the psychological theory.

  3. Necessarily, the same theory of personal identity applies to all possible finite persons.

  4. We are finite persons.

  5. So, if Strong AIs are possible, a version of the psychological theory of personal identity applies to us.

  6. But the psychological theory of personal identity is false.

  7. So, Strong AIs are impossible.

Of course, the hard part is to argue for (6), since (6) is so widely accepted.

Friday, May 5, 2017

How not to defend penal substitution

Consider the standard problem for penal substitution views:
  • How is it that an innocent person's suffering harsh treatment removes the guilt of this guilty?
This is just a quick remark. Here is how not to solve the problem: Don't invoke God's sovereignty or power to claim that God can transfer guilt and punishment at will. For if God can transfer guilt and punishment at will, then God could transfer the guilt and punishment to a tree. But wouldn't it be better that a tree should be harshly punished for eternity (say, constantly have its bark ripped off as it grows back) than that Christ suffer?

Thursday, May 4, 2017

Parsers

Somehow, I find writing parsers and interpreters one of the most satisfying computer programming activities I've done. I've done this a couple of times in my life, sometimes from scratch and sometimes using a tool like bison. Maybe it's because the resulting linguistic adeptness that the computer shows--even in the case of a very simple language--is somehow impressive. It's fun, for instance, to write a parser that translates a formula like "x^3*y-y^3*x" into a LISP-like representation ["-",["*",["^","x",3],"y"],["*",["^","y",3],"x"]], and that can then interpret the representation given values for x and y. Most recently, I had the fun of doing this in the OpenSCAD 3D design language, to enable passing formulas to functions/modules. This was kind of challenging for me as I'm not very comfortable with functional languages.

What Galileo should have said

The big theological problem that Galileo's opponents had for Galileo wasn't the (not very convincing) biblical arguments that the sun moves and the earth stands still, but a theological objection to Galileo's inference from (a) the greater simplicity of the Copernican hypothesis over its competitors and (b) the fact that the hypothesis fits the data to (c) the truth of the Copernican hypothesis. The theological objection, as I understand it, was that Galileo was endangering the doctrine of divine omnipotence, since if there is an omnipotent God, he can just as easily have made true one of the less simple hypotheses that fit the data. (And, indeed, an earth-centered system can be made to fit the data just as well as a sun-centered one if one has enough epicycles.)

What Galileo should have said is that his argument does not, of course, establish the Copernican hypothesis with certainty, but only as highly probable, and that his argument had the form of the well-established theological argument ex convenientia, or from fittingness: "It was fitting for God to do it, God was able to do it, so (likely) God did it." Such arguments were widely given in the Middle Ages for theological views such as the immaculate conception of Mary. The application is that it is fitting for God to do things in the more elegant Copernican fashion, an omnipotent God was able to do things in such wise, and so (likely) God did it. Not only would the argument form have been one that Galileo's interlocutors would have been familiar with and friendly towards, but Galileo would have the dialectical advantage that he could not be reasonably said to be challenging divine omnipotence if his own argument depended on it. (Maybe Galileo did say something like this. I've seen the use of the argumentum ex convenientia in astronomy attributed to Kepler. Maybe Kepler got it from Galileo.)

And, to be honest, I think that all science is essentially founded on arguments ex convenientia. Which are good arguments.

Tuesday, May 2, 2017

Grounding accidents in substances

Consider this plausible principle:

  1. x partially grounds y if and only if there are cs that fully ground y and x is one of the cs.

But now consider this plausible-sounding Aristotelian claim:

  1. The substance (or its form or its essence—the details won’t matter) partially grounds each of its accidents.

Note that the grounding here is not full. For if my substance fully grounded my accident of sleepiness, then my substance would be metaphysically sufficient for my sleepiness, and I would be always sleepy, which is fortunately not the case.

So, by 2, my sleepiness is partly grounded by my substance (i.e., me?), and merely partly. By 1, then, it follows there are other things, beside my substance, such that my sleepiness is fully grounded by my substance and those other things. What are those other things? Is it other accidents of me? If so, then the problem repeats for them. Or is it something beyond my substance or accidents? But what would that be?

I am inclined to think that the solution to this problem is to reject 1. Somehow, 1 is reminiscent to me of the false view that:

  1. x indeterministically causes y only if there are cs that deterministically cause y and x is one of the cs.

Compositional and non-compositional trope theories

There are two kinds of trope theories: Those on which the tropes are parts of the particular object—call these “compositional” trope theories—and those on which the relation between the object and its tropes is not a whole-to-part relation. Compositional trope theories have an initial advantage over non-compositional ones: they have no need to introduce a new relation to join objects to their tropes.

But this is only an apparent advantage. Consider this old argument. Assume compositional trope theory. Suppose my toe is blue. Then its blueness trope is a part of the toe, which is in turn a part of me, and so the blueness trope is a part of me. Hence I am blue.

Of course, the compositionalist has an answer to this argument: there are two different kinds of parthood here. The toe is, as the medievals would say, an integral part of me. And the blueness trope is a non-integral part of the toe. Transitivity holds for integral parts. It may or may not hold for non-integral parts, but it certainly doesn’t hold across types of parthood: if y is an integral part of x and z is a non-integral part of y, it does not follow that y is any kind of part of x.

But notice now that the compositionalist has lost the main advantage over the non-compositionalist. The compositionalist’s initial advantage was not having to introduce a new kind of relation over and beyond the familiar composition relation. But the familiar composition relation was the one between wholes and integral parts, and our compositionalist now has to introduce a new relation over and beyond that. Granted, it is a new relation of the same type as the familiar one. But this actually makes the compositionalist’s theory more complicated. For now the compositionalist has two relations, integral composition and non-integral composition, plus a new relation type, composition. But the non-compositionalist need only have two relations, integral composition and the object-to-trope relation. These two relations don’t need to have a new relation type to fall under. In other words, the non-compositionalist has only one mystery in her theory—what is the object-to-trope relation—while the compositionalist has two mysteries—what is the object-to-trope relation and what is the type composition.

The same point applies more generally to compositional ontologies versus relational ontologies.

Rapid cell replacement: A failed argument against materialism

I thought I had a nice argument against materialism, but it didn’t work out. Still, it’s fun to think about the argument and why it doesn’t work.

Start with this plausible thesis, which seems at least naturally necessary:

  1. If any cell in a human body blinks out of existence and a new cell, exactly like the one before, blinks into existence sufficiently quickly in the same orientation, then the result would not interrupt the human’s life or any train of consciousness.

Now imagine that very, very quickly one-by-one every cell in my body blinks out of existence and is replaced by a new cell formed by a coincidental quantum fluctuation. Moreover, suppose each replacement happens sufficiently quickly in the sense of (1), and indeed so quickly that all of the replacements are done in less than the blink of an eye. Applying claim (1) billions of times, I conclude that neither my existence nor my train of consciousness would be interrupted by this process.

But if materialism is true, the resulting entity would have insufficient causal connection to me to be me. Thus, if materialism is true, I would have to cease to exist as a result of these rapid replacements. But it seems this would violate (1) at some point. (Moreover, the resulting being would not be the product of natural selection, so on evolutionary functionalist theories, the being would not have mental states. Furthermore, in any case, its brain states would not have the kinds of connections with the external world that give rise to content according to the best materialist theories, so its thoughts would be largely contentless.)

But the argument I just gave doesn’t work. First, (1) is false in the case of a human zygote, since the destruction of one’s only cell would kill one. What made (1) plausible was the thought that we had many cells, and the replacement of any one of them with a randomly produced cell would make no difference. So, (1) needs to be modified to remain plausible:

  1. If any cell in a human body consisting of many cells blinks out of existence and a new cell, exactly like the one before, blinks into existence sufficiently quickly in the same orientation, then the result would not interrupt the human’s life or any train of consciousness.

But now it no longer follows that a quick cell-by-cell replacement would have to keep me alive. For here is a possible hypothesis: For a replacement cell to come to be a part of the body, it has to come to be sufficiently causally intertwined with the rest of the body. This takes some time. It could well be that if the cells are replaced one by one in less than the blink of an eye, the new cells don’t have time to become intertwined with the rest of the body. Thus, the body comes to have fewer and fewer cells as the gradual replacement process continues. If the replacement process were to stop, pretty quickly the replacement cells would come to be causally intertwined with the veteran cells, and would come to be a part of the body. But it doesn’t stop. As a result, eventually the process leads to a state where I don’t have “many” cells in my body, and hence (2) becomes inapplicable.

What if, on the other hand, the replacement is done more slowly, so that there is time for cells to causally intertwine and become a part of the body? Then there need be no problem for materialism, because now the resulting entity does have a sufficient causal connection to me to be me.

There is, of course, a vagueness problem for the materialist: When do I cease to exist in the process? But that's another argument. I think typical materialists who think that they exist cannot escape vague existence.

Monday, May 1, 2017

Desire-belief theory and soft determinism

Consider this naive argument:

  1. If the desire-belief theory of motivation is true, whenever I act, I do what I want.
  2. Sometimes in acting I do what I do not want.
  3. So the desire-belief theory is false.

Some naive arguments are nonetheless sound. (“I know I have two hands, …”) But that’s not where I want to take this line of thought, though I could try to.

I think there are two kinds of answers to this naive argument. One could simply deny (2), espousing an error theory about what happens when people say “I did A even though I didn’t want to.” But suppose we want to do justice to common sense. Then we have to accept (2). And (1) seems to be just a consequence of the desire-belief theory. So what to can one say?

Well, one can say that “what I want” is used in a different sense in (1) and (2). The most promising distinction here seems to me to be between what one wants overall and what one has a desire for. The desire-belief theorist has to affirm that if I do something, I have a desire for it. But she doesn’t have to say that I desire the thing overall. To make use of this distinction, (2) has to say that I act while doing what I do not overall want.

If this is the only helpful distinction here, then someone who does not want to embrace an error theory about (2) has to admit that sometimes we act not in accord with what we overall want. Moreover, it seems almost as much a truism as (2) that:

  1. Sometimes in acting freely I do what I do not want.

On the present distinction, this means that sometimes in acting freely, I do something that isn’t my overall desire.

But this in turn makes soft determinism problematic: for if my action is determined and isn’t what I overall desire, and desire-belief theory is correct, then it is very hard to see how the action could possibly be free.

There is a lot of argument from ignorance (the only relevant distinction seems to be…, etc.) in the above. But if it can be all cashed out, then we have a nice argument that one shouldn’t be both a desire-belief theorist or a soft-determinist. (I think one shouldn’t be either!)

Friday, April 28, 2017

Saying with possible worlds what can't be said with box and diamond

The literature contains a number of examples of a modal claim that can be made with possible worlds language but not in box-diamond language. Here is one that occurred to me that is simpler than any of the examples I’ve seen:

  • Reality could have been different.

Very simple in possible worlds language: There is a non-actual world. (Note: This doesn’t work on the version of Lewis’s modal realism that allows for duplicate worlds. All the worse for that version.) But no box-diamond statement expresses (*). One can, of course, say that there aren’t any unicorns but could be, which implies (*), but that’s not the same as saying (*).

Fun with St Petersburg

Consider any game, like St Petersburg where the expected payoff is infinite but the prizes are guaranteed to be finite. For instance, a number x is picked uniformly at random in the interval from 0 to 1 not inclusive, and your prize is 1/x.

Suppose you and I independently play this game, and we find our winnings. Now I go up to you and say: “Hey, I’ve got a deal for you: you give me your winnings plus a million dollars, and then you’ll toss a hundred coins, and if they’re all heads, you’ll get one percent of what I won.” That’s a deal you can’t rationally refuse (assuming I’m dead-set against your negotiating a better one). For the payoff for refusing is the finite winnings you have. The payoff for accepting is −1000000 + 2−100⋅0.01⋅(+∞) = +∞.

Wow!

Now let’s play doubles! There are two teams: (i) I and Garibaldi, and (ii) you and Delenn. The members of each team don’t get to talk to each other during the game, but after the game each team evenly splits its winnings. This is what happens. The house calculates two payoffs using independent runs of our St Petersburg style game, w1 and w2. I am in a room with you; Garibaldi is in a room with Delenn. I and Delenn are each given w1; you and Garibaldi are each given w2. Now, by pre-arrangement with Garibaldi, I offer you the deal above: You give me a million, and then toss a hundred coins, and then you get one percent of my winnings if they’re all heads. You certainly accept. And Garibaldi offers exactly the same deal to Delenn, and she accepts. What’s the result? Well, the vast majority of the time, the Pruss and Garibaldi team ends up with all the winnings (w1 + w2 + w1 + w2 = 2w1 + 2w2), plus two million, and the you and Delenn team end up out two million. But about once in 2100 runs, the Pruss and Garibaldi team ends up with 1.99w1 + 1.99w2, plus two million, while you and Delenn end up with 0.01w1 + 0.01w2 − 2000000.

And, alas, I don’t see a way to use Causal Finitism to solve this paradox.

Thursday, April 27, 2017

Materiality and spatiality

I’ve been fond of the theory that materiality is just the occupation of space. But here is a problem for that view.

I have argued previously that we should distinguish between the internal space (or geometry) of an object and external space. Here is quartet of considerations:

  • Imagine a snake one light-year in length out in empty space arranged in a square. Then imagine that God creates a star in the middle of the square. The star instantly disturbs the geometry of space and makes the distances between parts on opposite sides of the square be different from what they previously where. But this does not make any intrinsic change to the snake until physical influence can reach the snake from the star, which will take about 1/8 of a year (the sides of the square will be 1/4 light-years, so the closest any part of the snake is to the center is 1/8 light years). The internal geometry of the snake differs from the external one.

  • We have no difficulty imagining a magical house whose inside is larger than its outside.

  • Christ in the Eucharist has very different (larger!) internal size and geometry from the external size and geometry of where he is Eucharistically located.

  • Thought experiments about time travel and the twin paradox suggest that we should distinguish internal time from external time. But space is like time.

Now, if internal and external space can come apart so much, then it is plausible that an object could have internal space or geometry in the absence of any connection to external space. Furthermore, if a material object ceased to have an occupation relation to external space but retained its internal geometry, it would surely still be material. Only a material object can be a cube. But a cubical object could remain a cube in internal geometry even after losing all relation to external space. But if so, then materiality is not the occupation of external space.

In fact, even independently of the above considerations about internal and external space, it just doesn’t seem that objects are material in virtue of a relation to something beyond them—like external space.

So, it seems, objects aren’t material in virtue of the occupation of external space. Could they be material in virtue of the occupation of internal space? Not substances! A substance does not occupy its internal space. It has that internal space, and is qualified by it, but it seems wrong to say that it is in it in the sense of occupation. (Perhaps the proper parts of material substances do occupy the substance’s internal space.) But some substances, say pigs or electrons, are material. So materiality isn’t a function of the occupation of internal space, either. And unless we find some third sort of space, we can’t say that materiality is a function of the occupation of space.

Perhaps, though, we can say this. Materiality is the possession or occupation of space. Then material substances are material by possessing internal space, and the proper parts of material substances are material by occupying the substance’s internal space. On this view, the materiality of me and my heart are analogically related—a fine Aristotelian idea.

But I have a worry. Point particles may not exist, but they seem conceivable. And they would be material. But a point particle doesn’t seem to have an internal space or geometry. I am not sure what to say. Perhaps, a point particle can be said to be material by occupying external space (in my proposed account of materiality, I didn’t specify that the space was internal). If so, then a point particle, unlike a square snake, would cease to be material if it came to be unrelated to external space. Or maybe a point particle does have an internal zero-dimensional space. It is hard to see what the spatiality of this “space” would consist in, but then we don’t have a good account of the spatiality of space anyway. (Maybe the spatiality of an internal space consists in a potentiality to be aligned with external space?) And, finally, maybe point particles that are points both externally and internally (particles that have non-trivial internal geometry but that are externally point-like aren’t a problem for the view) either aren’t material or aren’t possible.

Wednesday, April 26, 2017

Surviving furlessness and inner earlessness

If we are animals, can we survive in a disembodied state, having lost all of our bodies, retaining only soul or form?

Here is a standard thought:

  1. Metabolic processes, homeostasis, etc. are defining features of being animals.

  2. In a disembodied state, one cannot have such processes.

  3. Something that is an animal is essentially an animal.

  4. So something that is an animal cannot survive in a disembodied state.

But here’s a parody argument:

  1. Fur and mammalian inner ear bones (say) are defining features of being mammals.

  2. In a furless and internally earless state, one cannot have such structures.

  3. Something that is a mammal is essentially a mammal.

  4. So something that is a mammal cannot survive in a furless and internally earless state.

I think 5-7 are no less plausible than 1-3. But 8 is clearly false: clearly, it is metaphysically possible to become a defective mammal that is furless and internally earless.

The obvious problem with 5, or with the inferences drawn from 5, is that what is definitory of being a mammal is being such that one should to have fur and such-and-such an inner ear. The same problem afflicts 2: why not say that being such that one should have these processes and features is definitory of being a mammal.

Person is not a natural kind

  1. God is not a member of any natural kind.

  2. If person is a natural kind, then every person is a member of a natural kind.

  3. God is a person.

  4. So, person is not a natural kind.

Monday, April 24, 2017

Do God's beliefs cause their objects?

Consider this Thomistic-style doctrine:

  1. God’s believing that a contingent entity x exists is the cause of x’s existing.

Let B be God’s believing that I exist. Then, either

  1. B exists in all possible worlds

or

  1. B exists in all and only the worlds where I exist.

(Formally, there are other options, but they have no plausibility. For instance, it would be crazy to think B exists in some but not all the worlds where I exist, or in some but not all the worlds where I don’t exist.)

Let’s consider (3) first. This, after all, seems the more obvious option. God’s beliefs are necessarily correct, so in worlds where I don’t exist, God doesn’t believe that I exist, and hence B doesn’t exist. Then, B is a contingent being that causes my existing. Now apply the Thomistic principle to this contingent being B. It exists, so God believing that B exists is the cause of B’s existing. Let B2 be God’s believing that B exists. Since B2 causes B, B2 must be distinct from B, as causation cannot be circular. Furthermore, if (3) is the right option in respect of B and me, then an analogue for B2 and B should hold: B2 will exist in all and only the worlds where B exists. The argument repeats to generate an infinite regress of divine believings: Bn is God’s believing that Bn − 1 exists and Bn causes Bn − 1. This regress appears vicious.

So, initial appearances aside, (3) is not the way to go.

Let’s consider (2) next. Then B exists in some possible world w1 where I don’t exist. Now, at w1, God doesn’t believe that I exist, since necessarily God’s beliefs are correct. This seems to be in contradiction to the claim that B exists at w1. But it is only in contradiction if it is true at w1 that B is God’s believing that I exist. But perhaps it’s not! Perhaps (a) the believing B exists at the actual world and at w1 but with different content, or (b) B exists at w1 but isn’t a believing at w1.

Let’s think some more about (2). Let w2 be a world where only God exists (I am assuming divine simplicity; without divine simplicity, it might be that in any world where God exists, something else exists—viz., a proper part of God). Then by (2), B exists at w2. But only God exists at w2. So, God is identical to B at w2. But identity is necessary. Thus, God is actually identical to B. Moreover, what goes for B surely goes for all of God’s believings. Thus, all of God’s believings are identical with God.

It is no longer very mysterious that God’s believing that I exist is the cause of my existence. For God’s believing that I exist is identical with God, and of course God is the cause of my existence.

The difficulty, however, is with the radical content variation. The numerically same mental act B is actually a believing that I exist, while at w2 it is a believing that I don’t exist. Furthermore, if truthmaking involves entailment, we can no longer say that B truthmakes that God believes that I exist. For B can exist without God’s believing that I exist.

All this pushes back against (1). But now recall that I only called (1) a “Thomistic-style” doctrine, not a doctrine of St. Thomas. The main apparent source for the doctrine is Summa Theologica I.14.8. But notice some differences between what Aquinas says and (1).

The first is insignificant with respect to my arguments: Thomas talks of knowledge rather than belief. But (1) with knowing in place of believing is just as problematic. Obviously, it can’t be a necessary truth that God knows that I exist, since it’s not a necessary truth that I exist.

The second difference is this. In the Summa, Aquinas doesn’t seem to actually say that God’s knowledge that x exists is the cause of x’s existence. He just says that God’s knowledge is the cause of x’s existence. Perhaps, then, it is God’s knowledge in general, especially including knowledge such necessary truths as that x would have such-and-such nature, that is the cause of x’s existence. If so, then God’s knowledge would be a non-determining cause of things—for it could cause x but does not have it (and, indeed, in those worlds where x does not exist, it does not cause x). This fits well with what Aquinas says in Article 13, Reply 1: “So likewise things known by God are contingent on account of their proximate causes, while the knowledge of God, which is the first cause, is necessary.”

Maybe. I don’t know.

Thoughts on theistic Platonism

Platonists hold that properties exist independently of their instances. Heavy-weight Platonists add the further thesis that the characterization of objects is grounded in or explained by the instantiation of a property, at least in fundamental cases. Thus, a blade of grass is green because the blade of grass instantiates greenness (at least assuming greenness is one of the fundamental properties).

Heavy-weight Platonism has a significant attraction. After all, according to Platonism (and assuming greenness is a property),

  1. Necessarily (i) an object is green if and only if (ii) it instantiates greenness.

The necessary connection between (i) and (ii) shouldn’t just be a coincidence. Heavy-weight Platonism explains this connection by making (ii) explain or ground (i). Light-weight Platonism, which makes no claims about an explanatory connection between (i) and (ii), makes it seem like the connection is a coincidence.

Still, I think it’s worth thinking about some other ways one could explain the coincidence (1). There are three obvious formal options:

  1. (ii) explains (i)
  2. (i) explains (ii)
  3. Something else explains both (i) and (ii).

Option (2) is heavy-weight Platonism. But what about (2) and (3)? It’s worth noting that there are available theories of both sorts.

Here’s a base theory that can lead to any one of (2)–(4). Properties are conceptions in the mind of God. Furthermore, instantiation is divine classification: x’s instantiating a property P just is God classifying x under conception P. It is natural, given this base theory, to affirm (3): x’s instantiating greenness just is God’s classifying x under greenness, and God classifies x under greenness because x is green. Thus, x instantiates greenness because x is green.

But, interestingly, this base theory can give other explanatory directions. For instance, Thomists think that God’s knowledge is the cause of creation. This suggests a view like this: God’s classifying x under greenness (which on the base theory just is x’s instantiating greenness) causes x to be green. On this view, x is green because x instantiates greenness. If the “because” here involves grounding, and not just causation, this is heavy-weight Platonism, with a Thomistic underpinning. Either way, we get (2).

And here is a third option. God wills x to be green. God’s willing x to be green explains both x’s being green and God’s classifying x as green. The latter comes from God’s willing as an instance of what Anscombe calls intentional knowledge. This yields (4).

So, interestingly, a theistic conceptual Platonism can yield any one of the three options (2)–(4). I think the version that yields (3)—interestingly, not the Thomistic one—is the one that best fits with divine simplicity.

Thursday, April 20, 2017

Are we in a computer simulation?

Do we live in a computer simulation?

Here’s a quick and naive thought. We would expect most computer simulations to be of pretty poor quality and limited in scope. If we are in a simulation, the simulation we are in is of extremely high quality and of great scope. That’s not what we would expect on the simulation hypothesis. So, probably, we don’t live in a computer simulation.

But the following argument is pretty convincing: 1. If materialism is true, then probably a computer simulation of a brain can think (since the best materialist theory of mind is functionalism). 2. If a computer simulation of a brain can think, then most thinkers live inside computer simulations.

So, the argument that we don’t live in a computer simulation gives us evidence against materialism.

Animals

Suppose that somewhere in the galaxy there is a planet where there are large six-legged animals with an inner supportive structure, that evolved completely independently of any forms of life on earth and whose genetic structure is not based on DNA but another molecule. What I said seems perfectly possible. But it is impossible if animals are simply the members of the kingdom Animalia, since the six-legged animals on that planet are neither DNA-based nor genetically connected to the animalia on earth.

On the other hand, the supposition that somewhere (maybe in another universe) there is water that does not have H2O in it is an impossible one. So is the supposition that there are horses without DNA.

So the kind animal is disanalogous to the kinds water and horse. The kind water is properly identified with a chemical kind, H2O, and the kind horse is properly identified with a biological species, Equus ferus. But the kind animal does not seem to be properly identified with any biological kind.

One can have DNA-based animals and non-DNA-based animals. If the Venus fly-trap evolved the ability to move from place to place following its prey, it would be an animal, but still a member of Plantae. Animals are characterized largely functionally, albeit not purely functionally, but also in reference to the function of their embodiment—there cannot be any animals that are unembodied.

Is animal a genuine natural kind? Or is it a non-natural kind, constructed in the light of our species’ subjective interests? I don’t know. I take seriously, though, the possibility that there is an "Aristotelian" philosophical categorization that goes across biological categories.