Tuesday, December 12, 2017

Zero chance events

A standard thing in the philosophy of science to say such stochastic explanation questions is that one can given an answer in terms of the objective chance of the event, even when these chances are less than 1/2.

But consider the question: Why did this atom decay exactly at t1?

Here, the objective chance may well be zero. And surely that an event had zero chance of happening does nothing to explain the event. After all, that the decay at t1 had zero chance does not distinguish the atom’s decaying at t1 from the atom’s turning into a square circle at t1. And to explain something we minimally need to say something that distinguishes it from an impossibility.

Here, I think, the causal powers theorist can say something (even though I may just want to reject the presuppositions; see the Response to Objection 2, below). Stochastic systems have a plurality of causal powers for incompatible outcomes. The electron in a mixed-spin state may have both a causal power to have its spin measured as up and to have its spin measured as done. Normally, some of the causal powers are apt to prevail more than others, and hence have a greater chance than others. But even the weaker causal powers are there, and we can explain the event by citing them. The electron’s spin was measured as, say, up because it had a causal power to that outcome; had it been measured as, say, down, that would have been because it had a causal power to that outcome. We can give further detail here: we can say that one of these causal powers is stronger than the other. And the stronger causal power has, because it is stronger, a higher chance of prevailing. But even the weaker causal power can prevail, and when it does, we can explain the outcome in terms of it.

This story works just fine even when the chances are zero. The weaker causal power could be so weak that the chance associated with it has to be quantified as zero. But we can still explain the activation of the weaker causal power.

So, going back to the decay, we can say that the atom had a causal power to decay at t1, and that’s why it decayed at t1. That causal power was of minimal strength, and so the chance of the decay has to be quantified as zero. But we still have an explanation.

The causal powers story about the atom encodes information that the chances do not. The chances do not distinguish the atom’s turning into a square circle from the atom’s decaying exactly at t1. The causal powers do, since it has a power to decay but no power to turn into a square circle.

Objection 1: Let’s say that the atom has twice as high a chance of decaying over the interval of times [0, 2] as over the interval of times [0, 1]. How do we explain that in terms of causal powers, given that there are equally many (i.e., continuum many) causal powers to decay at precise times in [0, 2] as there are causal powers to decay at precise times in [0, 1]?

Response: It could be that just as the causal power story carries information the chance story does not, the chance story could carry information the causal power story does not, and both stories reflect aspects of reality.

Another story could be that there are causal powers associated with intervals as well as points of times, and the causal power to decay at a time [0, 2] is twice as strong as the causal power to decay at a time in [0, 1]. There are difficulties here, however, with thinking about the fundamentality relations between the powers associated with different intervals. I fear that there is no avoiding an infinite sequence of causal powers that violates causal finitism, and I am inclined to reject the possibility of exact decay times—and hence reject the explanatory question I started this post with. I don’t see much hope for a measurement of an exact time after all. But someone with other commitments about finitism could have a story.

Objection 2: This is just like a dormitive power explanation of opium making someone sleepy.

Response: Opium’s dormitive power is fundamental or not. If opium has a fundamental dormitive power, then the dormitive power explanation is perfectly fine. That’s just the kind of explanation we have to have at the fundamental level. If the dormitive power explanation is not fundamental, then the explanation is correct but not as informative as an explanation in terms of more fundamental things would be.

Likewise, the power to decay at t1 either is or is not fundamental. If it is fundamental, then the explanation in terms of the power is perfectly fine. If it is not, then there is a more fundamental explanation. But probably the more fundamental explanation will also involve minimal strength powers with zero activation chances, too.

Friday, December 8, 2017

Two explanatory stories in Natural Law

One of the most fundamental claims of classical Natural Law (NL), as I understand it, is that:

  1. The right exercise of our wills is precisely that which fullfills the proper functions of the will.

This claim is, I think, close to trivial. What is much less trivial is the further NL claim that the “fulfills the proper functions” explains the “right”. There are two (at least) ways of running this explanatory story:

A. To fulfill the proper function of the will is good for us, and it’s right to pursue what’s good for us.

B. It is directly true that the right is what fulfills the will’s proper function. Exercising the proper function of the will, like exercising any other natural faculty, of course good for us, but that isn’t what makes it right.

Story A makes the theory a form of eudaimonism, since it implies that what is good for us is generally to be pursued.

Story B does not claim that what is good for us is generally to be pursued, though it is compatible with that claim. Story B claims that one of the things that are good for us—the proper exercise of the will—is to be done, but it does not claim that other things good for us are to be pursued, and does not even claim that that one thing is to be pursued (for it is a different thing to do what is right and to pursue doing what is right). As far as it goes,

Story B is compatible with, say, total selflessness, the theory that the one thing to be pursued is the good of everybody else. To get total selflessness, all one needs is to supplement Story B with the theory that the proper function of our will is fulfilled precisely in the pursuit of the good of everybody else. Likewise, Story B is compatible with eudaimonism—one just needs to add that the pursuit of our good is what in fact fulfills our will. But it is also compatible with kakodaimonism, the theory that the one thing to be pursued is one’s own languishing. (One might think that it would be self-defeating to pursue one’s own harm if pursuit of one’s harm were the proper function of our wills, since the pursuit would fulfill one’s will and hence be good for one. But that would be to confuse the good pursued with the good of pursuit.)

In other words, Story B has much less in the way of normative ethics implications: it is very strictly a story about the meta-level.

There is reason to prefer Story A: it leads to a helpful normative ethics by itself.

There is reason to prefer Story B: the normative ethics that Story A leads to is a form of rational egoism.

I like Story B. But Story B must be supplemented with an account of what fulfills the will.

The answer to that is love.

From particular perfections to necessary existence

This argument is valid:

  1. Necessarily, any morally perfect being can morally perfectly deal with any possible situation.

  2. Necessarily, one can only morally deal with a situation one would exist in.

  3. So, necessarily, any morally perfect being is a necessary being.

That said, (1) sounds a bit fishy to me. One may want to say instead:

  1. Necessarily, any morally perfect being can morally perfectly deal with any possible situation in which it exists.

But that’s actually a bit weaker than we want. Imagine a being that can deal with one situation and only with it: the case where it has promised to eat a delicious cookie that is being offered to it. But imagine, too, that the being can only exist in that one situation. Then (4) is satisfied, but surely being able to fulfill a promise to eat a cookie isn’t enough for moral perfection. So we do actually want to strengthen (4). Maybe there is something in between (1) and (4) that works. Maybe there isn’t.

There are other arguments of the above sort that one can run, based on premises like:

  1. A maximally powerful being can weakly actualize any possibility.

  2. An epistemically perfect being can know any possible proposition.

  3. A rationally perfect being can rationally deal with any possible situation.

It is looking like moral perfection, maximal power, epistemic perfection and rational perfection each individually imply necessary existence.

If this is right, then we have an ontological argument:

  1. Possibly, there is a morally perfect or a maximally powerful or an epistemically perfect or a rationally perfect being.

  2. So, possibly there is a necessary being. (By arguments like above.)

  3. So, there is a necessary being.

I am not saying that this a super-convincing argument. But it does provide some evidence for its conclusion.

Thursday, December 7, 2017

Pro-life outreach to fellow Christians

At a recent pro-life event that I participated in, the question was asked the panel how to convince a pastor that one’s church should support the pro-life cause, notwithstanding pro-choice congregation members. An answer was offered by a panelist that talked well of standard texts of Scripture that have bearing on the humanity of the fetus.

A day after the event, one of the audience members told me that there was too much focus on the status of the fetus, because even if students are convinced that human life starts at conception, they still think that because of conflict between the rights of the fetus and the rights of the mother, abortion is permissible.

In light of this, it seems to me that a crucial part of pro-life outreach to fellow Christians—including but not just pastors—is to focus on more general texts about our duties towards the vulnerable and needy. While a major part of the debate over abortion is indeed focused on the moral status of the fetus, both motivationally and intellectually it seems really important to focus on a deep underlying assumption that we do not have much in the way of onerous duties towards others, unless we have voluntarily undertaken those duties. Yet the Gospel teaches that we do have such duties, duties binding under pain of eternal damnation. Thus in addition to a reliance on texts about the status of the unborn, one needs motivationally powerful texts like:

Then he will say to those at his left hand, ‘Depart from me, you cursed, into the eternal fire prepared for the devil and his angels; for I was hungry and you gave me no food, I was thirsty and you gave me no drink, I was a stranger and you did not welcome me, naked and you did not clothe me, sick and in prison and you did not visit me.’ Then they also will answer, ‘Lord, when did we see thee hungry or thirsty or a stranger or naked or sick or in prison, and did not minister to thee?’ Then he will answer them, ‘Truly, I say to you, as you did it not to one of the least of these, you did it not to me.’ And they will go away into eternal punishment, but the righteous into eternal life. (Matthew 25:41-46).

These texts make it clear that we have highly onerous duties towards others, duties we may have done nothing to acquire. It is very difficult to defend disconnection from the violinist while thinking about such texts.

But of course if we use such texts then we had better be sure that we live so that they do not condemn us, too. For they are indeed terrifying texts on many fronts. May God have mercy on all our souls!

Wednesday, December 6, 2017

Being a bad person and doing wrong

Until recently, I assumed everyone agreed to something like this principle:

  1. If performing an action constitutes you as a bad person, the action is morally wrong.

Virtue ethicists, of course, make this a biconditional that defines wrongness, but I would have assumed that just about everybody would agree that the conditional (1) is true.

But I am now thinking that (1) is not accepted as widely as I thought it is. What makes me think this is the way that Thomson’s violinist case resonates with so strongly with so many people, and presumably continues to do so even if one adds the necessary proviso that the violinist is one’s own minor child (otherwise it wouldn’t be applicable to typical cases of abortion). Yet it seems utterly obvious to me to that:

  1. If the violinist is your own minor child, disconnecting from the violinist makes you a bad parent and a bad person.

But one cannot consistently accept (1) and (2) and think it is morally permissible to disconnect from the violinist when the violinist is one’s own child.

I would love to see empirical data on whether people who find the violinist case compelling deny (1) or deny (2). Thomson herself probably denies (2).

Tuesday, December 5, 2017

More on omniscience

In an earlier post, I argued that the definition of omniscience as knowing every truth and believing nothing but truths is insufficient for omniscience because an omniscient being would also be certain, and knowledge of every truth does not guarantee certainty of every truth.

Here’s another thing that the definition leaves out. Normally, when we say that someone knows or believes p, we are talking about non-occurrent knowledge. We say things like: “Alice knows the atomic number of carbon”, even while Alice is not thinking about carbon. However, I think an omniscient being—one that enjoys the perfection of knowledge—will need to have occurrent knowledge of all truths. Moreover, the omniscient being will need to always be attending to every piece of that knowledge to a maximal degree. (It is not a perfection in us to attend to everything we think maximally, because for us attending to one thing often excludes attending to another. But that’s due to our imperfection.)

Symmetry and Thomson's violinist

I’ve been thinking about Thomson’s Violinist case. I should say about that case that it seems utterly obvious to me that in the case where the violinist is your child and you are in no long term danger from the connection, it’s a vicious failure of parental duties to disconnect.

But my current interest is not so much in figuring out the case itself, as trying to figure out why so many people find it compelling. To that end, I’ve been thinking about two symmetric cases.

Lifeboat: You, who are a really bad pianist, and a really bad violinist find yourselves drifting in a lifeboat in space, kidnapped and put there by the Music Lovers’ Society, to keep you both from performing publicly. The lifeboat is designed for one person, and the hyperspace engines don’t work with the mass of two people. Fortunately, your calculations show that in nine months the lifeboat drift will get you back to earth, and there is air, food and water enough for two for nine months. But it’s really uncomfortable. You both have to sit squished together on an uncomfortable chair, you’re away from your friends (though you can talk to them on hyperspace Skype whenever you like), from your job, etc. Waste disposal is handled hygienically but it’s a rather disgusting process under the circumstances. However, when the violinist is asleep, you could just push him out of the airlock, and then use the hyperspace engines to get back home in a day. Of course, the violinist could do the same to you.

Frankenkidney: Both you, who are an excellent pianist, and an excellent violinist are suffering from kidney failure. The Music Lovers’ Society kidnapped both of you and out of two malfunctioning kidneys made a single functioning frankenkidney. When you awake, you are taped to the violinist, with your abdomens touching. You know that where the abdomens are touching you each have a hole, and in that hole is that frankenkidney. You could wait nine months because that’s how long it takes for the lab to culture brand new kidneys for you and the violinist. Or you could pull the frankenkidney from the violinist’s body, put it in yours, and then have some straightforward surgery to close up the hole. Of course, the violinist could do the same to you.

I am thinking—perhaps too optimistically—that in these cases people would say: “You’re in the same boat as the violinist and just need to make the best of it.”

Notice that in terms of the consequences of your decision, as well as desert and contract, these cases are very much like the original violinist story. Your personal space is encroached on by a violinist who is innocent of the encroachment. You can end the encroachment at the expense of the violinist’s life.

But the cases are different from the original. In the original, the situation benefits the violinist and harms you. In the symmetric cases, either you are both harmed (Lifeboat) or both benefited (Frankenkidney). Moreover, in the original case, the violinist continues to derive a benefit from you without giving anything back. (I think that’s something disanalogous to the abortion case, by the way, since the life of one’s child is a benefit to one, even if one does not see it this way.)

However, I do not know that these differences about the flow of benefits and harms matter, given that neither you nor the violinist have any responsibility for being in the situation in any of the three cases. Suppose we take the Lifeboat case and add this to the story:

Lifeboat Supplement: After a few hours in the lifeboat, the violinist’s body’s thermoregulation has shut down and the lifeboat’s heating system is working poorly. Your body heat is enough to maintain a liveable temperature for the two of you in the lifeboat, and medicine can fix his problem once you get back to civilization, but if the violinist threw you out the airlock, he’d soon die of hypothermia. You'd do fine physically without him, though.

In the supplemented lifeboat story, there is a net flow of life-giving benefits from you to the violinist, just as in the original violinist case. But it would be absurd that as soon as the violinist’s body’s thermoregulation shuts down you can throw him out the airlock. Yet the resulting story is now very much like the original violinist story, I think.

My conjecture is that a central reason the violinist case seems compelling to so many has to do with the asymmetry between the two parties, and when one primes the thinking by starting with a more symmetric situation, as in the Lifeboat case, the intuitions change, and perhaps stay changed even if one adds an asymmetric supplement.

By the way, for another symmetric analogy, see Himma.

Monday, December 4, 2017

Omniscience, omnipotence and perfection

Recently, I’ve been worried about arguments like this:

  1. It is always more perfect to be able to do more things.

  2. Being able to do impossible things is a way of being able to do more things.

  3. So, a perfect being can do impossible things.

But I really don’t want to embrace 3.

It’s just occurred to me, though, that the argument 1-3 is parallel to the clearly silly argument:

  1. It is always more perfect to know more things.

  2. Knowing falsehoods is a way of knowing more things.

  3. So, a perfect being knows falsehoods.

Once we realize that among “more things” there could be falsehoods, it becomes clear that 4 as it stands is false, but needs to be restricted to the truths. But arguably what truths are to knowledge, that possibles are to power (I think this may be a Jon Kvanvig point, actually). So we should restrict 1 to the possibles.

Friday, December 1, 2017

Laws of nature and moral rules

There is a lot to be said for the Mill-Ramsey-Lewis (MRL) account of laws as the axioms of a system that optimizes a balance of informativeness and simplicity. But there are really serious problems. The deepest is that the MRL regularities seem to systematize but not explain.

Similarly, there is a lot to be said for rule utilitarianism, but it also suffers from really serious problems. The deepest is probably that it just does not seem to be a compelling moral reason to do something harmful that under normal circumstances it is beneficial.

The MRL account of laws and rule utilitarianism are similar and a number of the problems facing them are structurally similar. Most deeply, the MRL laws don’t move things physically and rule utilitarian rules don’t move us morally. But there are also structurally similar technical problems, such as the account of simplicity, the way in which simplicity is to be balanced with informativeness or beneficiality, the apparent influence of future facts on present laws or moral truths, etc.

It is interesting that many of the problems of both accounts can be solved by bringing in theism. For instance, one can get a theistic MRL account of laws by saying that laws are the divinely willed axioms of a system that optimizes a divinely defined balance of informativeness and simplicity. And one can get a theistic rule utilitarian account by saying that laws are the divinely commanded rules that optimize a divinely defined balance of beneficiality and simplicity.

(I myself would prefer not to go for something quite so simple on the moral side: I’d prefer to insert our natures to mediate between God and our duties.)

Thursday, November 30, 2017

Self-sacrifice and bigotry

Case 1: A child is drowning in a dirty pond. You can easily pull out the child. But you’ve got cuts all over your dominant arm and the water is full of nasty bacteria and medical help is a week away. If you go in the water to pull out the child, your arm will get infected, become gangrenous and in a week it will be amputated. There will be no social losses or gains to you.
Case 2: A child is drowning in a clean pond. You can easily pull out the child. But the child is a member of a despised minority group, and you will be ostracized by your friends and family for life for your rescue. There will be no physical losses or gains to you.

Here is my intuition. In both cases, it would be a good thing to rescue the child. But in Case 1, unless you have special duties (e.g., it’s your own child), you do not have a duty to rescue given the physical costs. In Case 2, however, you do have a duty to rescue, despite the social costs.

The difference between the two cases does not, I think, lie in its being worse to lose an arm than to be ostracized. Imagine your community has a rite of passage that involves swimming in the dirty pond with the cuts on your arm, and you’d be ostracized if you don’t. You might well reasonably judge it worthwhile—but still, I think, the intuition remains that in Case 2 you ought to pull out the child, while in Case 1 it’s supererogatory. So it seems then you might have a duty to undertake the greater sacrifice (facing social stigma in Case 2) without a duty to undertake the lesser sacrifice (amputation in Case 1). But for simplicity let’s just suppose that the harms to you in the two cases are on par.

Is it that physical harm excuses one from the duty to rescue the child but social harm does not? I don’t think so.

Case 3: A child is being murdered by drowning in a clean pond. You can easily pull out the child. But if you do, the murderer will punish you for it by transporting you away from your home community to a foreign community where you will never learn the difficult language and hence will not have friends.

We can set this up so the harm in all three cases is equal. But my intuition is that Case 2 is like Case 1: in both cases it is supererogatory to rescue the child but there is no duty.

In Cases 2 and 3 we have equal social harms, but I feel a difference. (Maybe you don’t!) Here’s one consideration that would explain the difference. That an action gains one the praise and friendship of bigots qua bigots does not count much in favor of the action, even if, and perhaps even especially if, such praise and friendship would make one’s life significantly more pleasant. Similarly, that an action loses one the friendship of bigots, and does so precisely through their bigotry, is not much of a consideration against the action. I say “not much”, because there might be instrumental gains and losses in both cases to be accounted for.

Here’s a second consideration. Perhaps if I refrain from doing something directly because doing it will lose me bigots’ friendship or gain me their stigma, I am thereby complicit in the bigotry. In Case 2, then, I need to ignore the direct loss of goods of social connectedness in considering whether to rescue the child. I need to say to myself: “When those are the conditions of their friendship, so much the worse for their friendship.” In Case 3, I have similar social losses, but I don't lose the friendship of bigots qua bigots, so the loss counts a lot more.

But note that one can still legitimately consider the instrumental harms from the loss of goods of social connectedness. Consider:

Case 4: A child is drowning in a clean pond, but you have a wound that will become gangrenous and force amputation absent medical help. You can easily pull out the child. But the child is a member of a despised minority group, and if you rescue the child, the only doctor in town will refuse to have anything to do with you. As a result, your wound will become gangrenous by the time you find another doctor, and you will require amputation.

I think in Case 4, you are permitted not to rescue the child, just as in Case 1.

Wednesday, November 29, 2017

Inductive evidence of the existence of non-spatial things

Think about other plausibly fundamental qualities beyond location and extension: thought, charge, mass, etc. For each one of these, there are things that have it and things that don’t have it. So we have some inductive reason to think that there are things that have location and things that don’t, things that have extension and things that don’t. Admittedly, the evidence is probably pretty weak.

Tuesday, November 28, 2017

Wronger and wronging

Here’s an interesting thing. An act doesn’t necessarily become any more wrong for wronging someone.

Alice and Bob respectively come across a derelict spaceship. Their sensors show that there is intelligent life aboard. Each blasts the respective spaceship as target practice. Bob’s sensors malfunctioned: there was no intelligent life on the ship he blasted. Alice’s sensors were just fine. Alice wronged the people she killed. Bob wronged no one, as there was no one there to be wronged. But what Bob did was no less wrong than what Alice did.

Note 1: Bob’s case differs from standard cases of attempted murder. For in standard cases of attempted murder, the intended victim is wronged.

Note 2: I am not claiming that Bob wrongs no one. Bob wrongs both God and himself. But Alice also wrongs God and herself, just as much as Bob does, and additionally wrongs the people she kills. That additional wronging doesn’t make her act wronger, though.

Note 3: One might argue that Bob and Alice wrong all the people who have the property that they might (epistemically? alethically?) have been on the ship. Sure, but what if there are no such people in Bob's case? Perhaps Bob, unbeknownst to himself, is alone in his universe.

An anti-Aristotelian argument for divine simplicity

The doctrine of divine simplicity fits comfortably with Aquinas’s Aristotelian framework. But it is interesting that anti-Aristotelianism also leads to divine simplicity.

  1. The proper parts are more fundamental than the whole. (Mereological anti-Aristotelianism.)

  2. Nothing is more fundamental than God.

  3. So, God has no proper parts.

Of course, as an Aristotelian I reject 1, so while I accept the conclusion of this argument, I can’t use the argument myself.

Monday, November 27, 2017


It’s notoriously hard to characterize the physical precisely enough to attack or defend physicalism. To attack physicalism, however, it is enough to attack a characterization broader than physicalism, and to defend physicalism, a narrower characterization will do.

Here’s a suggestion along the “broader” lines. We can characterize reductive physicalism over-broadly as:

  • Reductive first-orderism: All facts about the concrete (variants: contingent, spatiotemporal) features of the world reduce to first-order facts.

This may take in some theories other than what one intuitively counts as reductive physicalism, but if the object is ciriticism, that’s all we need.

Note how this characterization nicely shows how paradigm examples of magic would violate reductive physicalism: for paradigm examples of magic involve causation irreducibly by virtue of the meaning of a spell, gesture, etc., and meaning is a higher-order property. It also shows why irreducible Aristotelian teleology has no place in a reductive physicalist story: for teleological properties are second-order (I think).

Moreover, if we see reductive physicalism in the above way, it’s also easy to see that it’s false, by an argument of Leon Porter. For any first-order fact can be expressed in a first-order language. But, famously, the property of truth cannot be reduced to properties expressible in a first-order language (Tarski’s indefinability of truth; or, more simply, note that if you could express something equivalent to the property of truth in a first-order language, you could express the Liar Sentence in a first-order language). And some concrete objects, namely inscriptions, have this property of truth. Hence, some concrete objects have a property that cannot be expressed in first-order terms, contrary to reductive first-orderism.

Change in transubstantiation

The two main parts of the doctrine of transubstantiation that get philosophically discussed are that after consecration we have:

  • Real Presence: Christ's body and blood is really there.
  • Real Absence: bread and wine is no longer there.
But there may be another part: that the bread and wine change into the body and blood rather than simply being replaced by the body and blood. Certainly the Council of Trent uses the language of "conversion" of bread and bread wine, but it is not completely clear to me that they mean to define there to be something more than replacement. Aquinas talks unclearly (to me) of the substantial change as a kind of "order" in the two substances.

Besides the general puzzle of how change differs from replacement, there are at least two philosophical difficulties about the change. The first is that on some versions--not mine--of Aristotelian metaphysics, what makes substantial change be a change is the persistence of matter. But there is no matter persisting here (indeed, Aquinas' remark emphasizes this). The second is that what the bread and wine change into, namely Christ's body, is already there. But it seems that if x changes into y, then y doesn't exist prior to the change.

Leibniz considers a theory on which the bread and wine change into new parts of Christ's body. This solves the second problem, but at the expense of having to say that the bread changes into a mere part of Christ's body, which does not appear to be what the Church means. Trent does say that whole Christ comes to be present. I suppose one could have a hybrid theory on which the bread and wine change into new parts of Christ's body, and the rest of Christ's body then additionally comes to be present, but not by conversion. While I do not have decisive textual evidence, this does not seem to me to be what Trent means. And it is grotesque to think that Christ gets fatter at transubstantiation.

While it could well be that the Council doesn't mean anything beefy about the "conversion", and perhaps all it is an "order" between the two substances (cf. Aquinas), an order constituted by by non-coincidental replacement in the same location. That would simplify things metaphysically. But I want to try for something metaphysically thicker.

Here's the thought. On my Aristotelian metaphysics, nothing persists in substantial change. But when a change of substance x into substance y, a rather special causal power is triggered in x, the causal power of giving rise to y while perishing. The exercise of such a causal power is what makes it be the case that x has changed into y. There isn't any matter persisting in the change, so the first of the two philosophical problems with the Eucharistic change disappears. What about the second? Here's my suggestion. Normally, the existence of Christ's body at later times is caused by its existence at earlier times. But what if we say that the bread miraculously gets a special causal power, the power of causing Christ's body to exist just as the bread perishes? Then the existence of Christ's body after consecration will be causally overdetermined by two things: the bread's exercising that causal power and Christ's body exercising its ordinary causal power to make itself persist.

The bread in perishing is an overdetermining cause of the existence of Christ's body, and that is exactly how substantial change happens on my view. The main metaphysical difference here is that normally substantial change is not overdetermined, while here it is.