Anti-reductionism and supervenience

In the philosophy of mind, those who take anti-reductionism really seriously will also reject the supervenience of the mental on the non-mental. After all, if a mental property does not reduce to the non-mental, we should be able to apply a rearrangement principle to fix the non-mental properties but change the mental one, much as one can fix the shape of an object but change its electrical charge, precisely because charge doesn’t reduce to shape or shape to charge. There might be some necessary connections, of course. Perhaps some shapes are incompatible with some charges, and perhaps similarly some mental states are incompatible with some physical arrangement. But it would be surprising, in the absence of a reduction, if fixing physical arrangement were to fix the mental state.

Yet it seems that in metaethics, even the staunchest anti-reductionists tend to want to preserve the supervenience of the normative on the non-normative. That is surprising, I think. After all, the same kind of rearrangement reasoning should apply if the normative properties do not reduce to the non-normative ones or vice versa: we should be able to fix the non-normative ones and change the normative ones at least to some degree.

Here’s something in the vicinity I’ve just been thinking about. Suppose that A-type properties supervene on B-type properties, and consider an A-type property Q. Then consider the property Q^B of being such that the nexus of all B-type properties is logically compatible with having Q. For any Q and B, having Q^B is necessary for having Q. But if Q supervenes on B-type properties, then having Q^B is also sufficient for having Q. Moreover, Q^B seems to be a B-type property in our paradigmatic cases: if B is the physical properties, then Q^B is a physical property, and if B is the non-normative properties, then Q^B is a non-normative property. (Interestingly, it is a physical or non-normative property defined in terms of mental or normative properties.)

But now isn’t it just as weird for a staunch anti-reductionist to think that there is a non-normative property that is necessary and sufficient for, say, being obligated to dance as it is for a staunch anti-reductionist to think there is a physical property that is necessary and sufficient for feeling pain?

Supervenience and natural law

The B-properties supervene on the A-properties provided that any two possible worlds with the same A-properties have the same B-properties.

It is a widely accepted constraint in metaethics that normative properties supervene on non-normative ones. Does natural law meet the contraint?

As I read natural law, the right action is one that goes along with the teleological properties of the will. Teleological properties, in turn, are normative in nature and (sometimes) fundamental. As far as I can see, it is possible to have zombie-like phenomena, where two substances look and behave in exactly the same way but different teleological properties. Thus, one could have animals that are physically indistinguishable from our world’s sheep, and in particularly have four legs, but, unlike the sheep, have the property of being normally six-legged. In other words, they would be all defective, in lacking two of their six legs.

This suggests that natural law theories depend on a metaphysics that rejects the supervenience of the normative. But I think that is too quick. For in an Aristotelian metaphysics, the teleological properties are not purely teleological. A sheep’s being naturally four-legged simultaneously explains the normative fact that a sheep should have four legs and the non-normative statistical fact that most sheep in fact have four legs. For the teleological structures are not just normative but also efficiently causal: they efficiently guide the embryonic development of the sheep, say.

In fact, on the Koons-Pruss reading of teleology, the teleological properties just are causal powers. The causal power to ϕ in circumtances C is teleological and dispositional: it is both a teleological directedness towards ϕing in C and a disposition to ϕ in C. And there is no metaphysical way of separating these aspects, as they are both features of the very same property.

Our naturally-six-but-actually-four-legged quasi-sheep, then, would differ from the actual world’s sheep in not having the same dispositions to develop quadrapedality. This seems to save supervenience, by exhibiting a difference in non-normative properties between the sheep and the quasi-sheep.

But I think it doesn’t actually save it. For the disposition to develop four (or six) legs is the same property as the teleological directedness to quadrapedality in sheep. And this property is a normative property, though not just normative. We might say this: The sheep and the quasi-sheep differ in a non-normative respect but they do not differ in a non-normative property. For the disposition is a normative property.

Perhaps this suggests that the natural lawyer should weaken the supervenience claim and talk of differences in features or respects rather than properties. That would allow one to save a version of supervenience. But notice that if we do that, we preserve supervenience but not the intuition behind it. For the intuition behind the supervenience of the normative on the non-normative is that the normative is explained by the non-normative. But on our Aristotelian metaphysics, it is the teleological properties that explain that actual non-normative behavior of things.

Properties, relations and functions

Many philosophical discussions presuppose a picture of reality on which, fundamentally, there are objects which have properties and stand in relations. But if we look to how science describes the world, it might be more natural to bring (partial) functions in at the ground level.

Objects have attributes like mass, momentum, charge, DNA sequence, size and shape. These attributes associate values, like 3.4kg, 15~kg m/s north-east, 5C, TTCGAAAAG, 5m and sphericity, to the objects. The usual philosophical way of modeling such attributes is through the mechanism of determinables and determinates. Thus, an object may have the determinable property of having mass and its determinate having mass 3.4kg. We then have a metaphysical law that prohibits objects from having multiple same-level determinates of the same determinable.

A special challenge arises from the numerical or vector structure of many of the values of the attributes. I suppose what we would say is that the set of lowest-level determinates of a determinable “naturally” has the mathematical structure of a subset of a complete ordered field (i.e., of something isomorphic to the set of real numbers) or of a vector space over such a field, so that momenta can be added, masses can be multiplied, etc. There is a lot of duplication here, however: there is one addition operator on the space of lowest-level momentum determinates and another addition operator on the space of lowest-level position determinates in the Newtonian picture. Moreover, for science to work, we need to be able to combine the values of various attributes: we need to be able to divide products of masses by squares of distances to make sense of Newton’s laws of gravitation. But it doesn’t seem to make sense to divide mass properties, or their products, by distance properties, or their squares. The operations themselves would have to be modeled as higher level relations, so that momentum addition would be modeled as a ternary relation between momenta, and there would be parallel algebraic laws for momentum addition and position addition. All this can be done, one operation at a time, but it’s not very elegant.

Wouldn’t it be more elegant if instead we thought of the attributes as partial functions? Thus, mass would be a partial function from objects to the positive real numbers (using a natural unit system) and both Newtonian position and momentum will be partial functions from objects to Euclidean three-dimensional space. One doesn’t need separate operations for the addition of positions and of momenta any more. Moreover, one doesn’t need to model addition as a ternary relation but as a function of two arguments.

There is a second reason to admit functions as first-class citizens into our metaphysics, and this reason comes from intuition. Properties make intuitive sense. But I think there is something intuitively metaphysically puzzling about relations that are not merely to be analyzed into a property of a plurality (such as being arranged in a ball, or having a total mass of 5kg), but where the order of the relata matters. I think we can make sense of binary non-symmetric relations in terms of the analogy of agents and patients: x does something to y (e.g. causes it). But ternary relations that don’t reduce to a property of a plurality, but where order matters, seem puzzling. There are two main technical ways to solve this. One is to reduce such relations to properties of tuples, where tuples are special abstract objects formed from concrete objects. The other is Josh Rasmussen’s introduction of structured mereological wholes. Both are clever, but they do complicate the ontology.

But unary partial functions—i.e., unary attributes—are all we need to reduce both properties and relations of arbitrary finate arity. And unary attributes like mass and velocity make perfect intuitive sense.

First, properties can simply be reduced to partial functions to some set with only one object (say, the number “1” or the truth-value “true” or the empty partial function): the property is had by an object provided that the object is in the domain of the partial function.

Second, n-ary relations can be reduced to n-ary partial functions in exactly the same way: x₁, ..., x_n stand in the relation if and only if the n-tuple (x₁, ..., x_n) lies in the domain of the partial function.

Third, n-ary partial functions for finite n > 1 can be reduced to unary partial functions by currying. For instance, a binary partial function f can be modeled as a unary function g that assigns to each object x (or, better, each object x such that f(x, y) is defined for some y) a unary function g(x) such that (g(x))(y)=f(x, y) precisely whenever the latter is defined. Generalizing this lets one reduce n-ary partial functions to (n − 1)-ary ones, and so on down to unary ones.

There is, however, an important possible hitch. It could turn out that a property/relation ontology is more easily amenable to nominalist reduction than a function ontology. If so, then for those of us like me who are suspicious of Platonism, this could be a decisive consideration in favor of the more traditional approach.

Moreover, some people might be suspicious of the idea that purely mathematical objects, like numbers, are so intimately involved in the real world. After all, such involvement does bring up the Benacerraf problem. But maybe we should say: It solves it! What are the genuine real numbers? It's the values that charge and mass can take. And the genuine natural numbers are then the naturals amongst the genuine reals.

God, probabilities and causal propensities

Suppose a poor and good person is forced to flip a fair and indeterministic coin in circumstances where heads means utter ruin and tails means financial redemption. If either Molinism or Thomism is true, we would expect that, even without taking into account miracles:

1. P(H)<P(T).

After all, God is good, and so he is more likely to try to get the good outcome for the person. (Of course, there are other considerations involved, so the boost in probability in favor of tails may be small.)

The Molinist can give this story. God knows how the coin would come out in various circumstances. He is more likely to ensure the occurrence of circumstances in which the subjunctive conditionals say that tails would comes up. The Thomist, on the other hand, will say that God’s primary causation determines what effect the secondary creaturely causation has, while at the same time ensuring that the secondary causation is genuinely doing its causal job.

But given (1), how can we say that the coin is fair? Here is a possibility. The probabilities in (1) take God’s dispositions into account. But we can also look simply at the causal propensities of the coin. The causal propensities of the coin are equibalanced between heads and tails. In addition to the probabilities in (1), which take everything including God into account, we can talk of coin-grounded causal chances, which are basically determined by the ratios of strength in the causal propensities. And the coin-grounded causal chances are 1/2 for heads and 1/2 for tails. But given Molinism or Thomism, these chances are not wholly determinative of the probabilities and the frequencies in repeat experiments, since the latter need to take into account the skewing due to God’s preference for the good.

So we get two sets of probabilities: The all-things-considered probabilities P that take God into account and that yield (1) and the creatures-only-considered probabilities P_c on which:

2. P_c(H)=P_c(T)=1/2.

Here, however, is something that I think is a little troubling about both the Molinist and Thomist lines. The creatures-only-considered probabilities are obviously close to the observed frequencies. Why? I think the Molinist and Thomist have to say this: They are close because God chooses to act in such ways that the actual frequencies are approximately proportional to the strengths of causal propensities that P_c is based on. But then the frequencies of coin toss outcomes are not directly due to the causal propensities of the coin, but only because God chooses to make the frequencies match. This doesn’t seem right and is a reason why I want to adopt neither Molinism nor Thomism but a version of mere foreknowledge.

Can our cells be substances?

A standard Aristotelian principle says:

1. No substance is a part of another substance.

I was just struck by how (1) says less than it seems to. One interesting philosophy of biology question is whether our symbiont bacteria are part of us. But:

2. All bacteria are substances.

3. We are substances.

4. We are not bacteria.

5. So no bacteria are parts of us. (By 1-5)

This argument is fine as far as it goes. But there is a metaphysical possibility that its conclusion leaves open which it is easy to forget.

Let’s grant that our symbiont bacteria are not a part of us. But perhaps their matter is a part of us. In other words, maybe the bacteria are matter-form composites just as we are, but their matter is a part of our matter, whereas their form is not a part of us at all, and hence they as wholes are not parts of us. They merely overlap us in matter.

And the point can be generalized. Before I noticed this point today, I used to think that the Aristotelian commitment to (1) requires us to deny that our cells are substances. But (1) leaves open the possibility that our cells are substances whose matter is a part of us, while the cells as wholes are not parts of us.

I don’t really want to say this. I would like to supplement (1) with this principle which has generally been a large part of my reason for affirming (1):

6. The matter of one substance is never a part of another substance.

My reason for accepting (6) has been that the identify of the matter is grounded in its substance, and if the matter had its identity doubly grounded, it wouldn’t be one thing, but two, and so it wouldn’t be the same matter in each substance.

In fact, (6) is a special case of a stronger claim:

7. No two substances have any matter in common.

Here is an argument that establishes (7) directly. Start with this plausible thesis:

8. No two material substances have all of their matter in common.

But now if (7) is false, then it should be possible to have two plants that have some matter in common. We could further imagine that the non-common matter perishes, but both plants survive. If so, then we would have a violation of (8). So, it’s plausible that if (7) is false, so is (8).

Here is a different line of thought in favor of (7):

9. Matter is grounded in the accidents of a substance.

10. Two substances cannot have any accident in common.

11. If x is entity grounded in a and y is an entity grounded in b and a ≠ b, then x ≠ y.

12. So, two substances cannot have any matter in common.

So, all in all, while (1) leaves open the possibility of our cells and bacteria being substances and yet having their matter be a part of us, we have good reason to deny this possibility on other grounds.

It would be very neat if one could derive (1) from (7). From (7) we do directly get:

13. No substance with matter is a part of another substance.

But it would take more argument to drop the “with matter” qualifier.

Can free will be grounded in quantum mechanics?

Robert Kane famously physicalistically grounds free will in quantum events in the brain. Free choice, on Kane’s view, is constituted by rational deliberation involving conflicting motivational structures with a resolution by an indeterministic causal process—a causal process that Kane thinks is in fact physical.

Here is a problem. Suppose Kane’s view is true. But now imagine a possible world with a physics that is like our quantum physics, but where panpsychism is true. The particles are conscious, and some of them engage in libertarian free choices, with chances of choices exactly matching up with what quantum mechanics predicts. The world still has people with brains, in addition to particle-sized people. The people with brains have particles that are persons in their brains. Moreover, it turns out that those indeterministic causal processes in the brains that constitute free choice are in fact the free actions of the particle-sized people in the breains.

All of Kane’s conditions for freedom will be satisfied by the people with brains. For the only relevant difference is that the quantum-style causal processes are choice processes (of the particle people). But these processes are just as indeterministic as in our world, and it’s the indeterminism that matters.

But the actions of the brain possessors in that world wouldn’t be free, because they would be under the control of the particle people in the brains. We could even suppose, if we like, that the particle people know about brains and want to direct the big people in some particular direction.

One could add to Kane’s account the further condition that the indeterministic causal processes in the brain are not constituted by the free choices of another person. But this seems ad hoc, and it is not clear why this one particular way for the indeterministic causal processes to be constituted is forbidden while any other way for them to be constituted is acceptable. The details of how quantum indeterministic processes work, as long as they are truly indeterministic and follow the quantum statistics, should not matter for free will.

This problem applies to any physicalist account on which free choices are grounded in quantum processes.

There is a way out of the problem. One could accept a pair of Aristotelian dicta:

1. All persons are substances.

2. No substance is a part of another substance.

But it is not clear whether the acceptance of these dicta is plausible apart from the fuller Aristotelian metaphysics which holds that all substances are partially made of non-physical forms. In other words, it is not clear that acceptance of (1) and (2) can be well motivated within a physicalist metaphysics.

Partial fulfillment of promises

A classic joke: You arrive in the Soviet Union. At the airport you see two people working. One is digging holes in the ground. The other is filling them in. You ask them what they are doing. They say: “The guy who was supposed to be planting trees didn’t show up.”

So, suppose I promise to dig a hole in your yard and plant a tree there. But I couldn’t obtain the tree. Obviously, I shouldn’t dig the hole. Thus, sometimes, partial fulfillment of a promise is no use at all, or worse.

But it seems that sometimes partial fulfillment is my duty. If I promise to give you two T-shirts and but I only manage to obtain one, it seems I owe you that one. But even that depends on the context. Suppose the two T-shirts were to be for a party where a parent and their child were to wear matching clothes. Then one T-shirt might be useless.

Perhaps the story is this. When I can’t fulfill a promise, I need to make it up to you as best as possible. Partial fulfillment is a way of making it up, and it is a default component of making up. But sometimes it’s worthless, in which case I should ask you if there is some other way you’d like me to make up for it.

Justification and units of assertion

It’s clear to me that each of two assertions could individually meet the evidential bar for assertibility, but that their conjunction, being typically less probable than either conjucnt, might not. But then there is something very strange about the idea that one could justifiably assert “S₁. S₂.” but not “S₁ and S₂.” After all, is there really a difference in what one is saying when one inserts a period and when one inserts an “and”?

Perhaps the thing to say is that the units of assertion are in practice not single sentences, but larger units. How large? Well, not whole books. Plainly, as the preface paradox notes, one can be justified in producing a book while thinking there is an error somewhere in it (as long as one does not know where the error lies). I think not whole articles, either. Again, we expect to be mistaken somewhere in a complex article. Perhaps the unit of assertion is something more of the order of a paragraph or less, but more than a sentence.

If so, then in typical cases “S₁. S₂.” will be a single unit of assertion, and to be justified in asserting the unit, one needs to be justified in the conjunction. This gives us a pretty precise definition of a unit of assertion: a unit of assertion is an assertoric locution that is lengthwise maximal with respect to needing to be justified.

What in practice determines the unit of assertion is probably determined by a mix of content, context, intonation, length of pauses, etc. For instance, a topic switch is apt to end a unit of assertion, and it may sometimes make a difference how long the pause between the sentences in “S₁. S₂.” with respect to whether the sentences form a single unit of assertion.

Surely people have written on this.

Lying to prevent great evils

Consider this argument:

1. It is permissible to lie to prevent great evils.

2. Not believing in God is a great evil.

3. So, it is permissible to lie to get people to believe in God (e.g., by offering false testimony to miracles).

But the conclusion is absurd. So we need to reject (1) or (2). I think (2) is secure. Thus we should reject (1).

I suppose one could try to calibrate some great level E of evil such that it is permissible to lie (a) to prevent evils at levels greater than E but (b) not to prevent evils lesser than E. I am sceptical that one can do this in a plausible way, given that not believing in God is indeed a great evil, since it makes it very difficult to achieve the primary goal of human life.

Perhaps a more promising way out of the argument is to formulate some subject-specific principle, such as that it is wrong to lie in religious matters or for religious ends. But it is hard to do this plausibly.

It seems better to me to just deny (1), and be an absolutist about lying: lying is always wrong.

Nonsummativism about group belief

Here is a quick argument that a group can believe something no individual does. You hire a team of three consultants to tell you whether a potential employee, Alice, is smart and honest. The team takes on the task. The team leader first leads a discussion as to which of the other two team members is best qualified to investigate which attribute, and unanimous agreement is reached on that question. Both of these then investigate and come to a decision. The team leader writes “Alice is” on a piece of paper, and then passes the piece of paper around to the second team member, who writes down the attribute she investigated or its negation, depending on what she found, followed by “and”. The leader then passes the piece of paper to the third team member, who writes down the attribute they investigated or its negation, followed by a period, without reading (and hence being biased by) what was written already. Job done, the leader without reading folds the paper in half and hands it to you, saying: “Here’s what we think.”

You open the paper and read the verdict of the consulting team: “Alice is smart and not honest.” The team agrees unanimously that the division of labor was the right way to produce an epistemically responsible group verdict, but nobody on the consulting team believes or even knows the verdict. The team leader has no opinions on Alice: she delegated the opinions to the intelligence and integrity experts. The intelligence expert has no view on Alice’s integrity and vice versa.

One could say that the team doesn’t believe its verdict. But to issue a verdict that one does not believe is to fail in sincerity. But there need be no failure in the above procedures.

(My own view is that when we say the team “believes” something, we are using “believes” in an analogical sense. But the points stand.)

Molinism and behavioral dispositions

There is some sort of a link between counterfactuals and dispositions, though there are lots of counterexamples to direct links. Here is a very weak principle affirming such a link:

1. Suppose that x is in state S at time t and that x’s being in S at t grounds x’s being disposed to behavior A after t. Then there is some maximally determinate categorical proposition p describing the world up to time t and logically compatible with x’s being in S at t such that it is false that were p true and x in state S, x would fail to engage in behavior A after t.

To put it very roughly, this messy principle says that if a disposition to a behavior is grounded in a state, then it’s not the case that no matter what one adds to the state, the behavior would not occur. Suppose that (1) is a necessary truth.

Add this:

2. It is possible for a human being to have an unactualized indeterministic disposition with respect to non-derivatively free behavior.

For instance, there is presumably a shade R of red that Jean Vanier has never met someone wearing, and yet he is disposed to behave non-derivatively freely kindly to persons wearing R.

What I have said so far does not, however, cohere with Molinism. For on Molinism, the conditionals of free will logically float free from the indeterministic dispositions of things. There is, for instance, a possible world where Jean Vanier still has the same kindly dispositions that he does in the actual world, but where the Molinist conditionals say that in the case of any of the appropriate maximally deterministic categorical strengthenings of the claim that he meets a person wearing R, if that strengthening were actual, he would behave unkindly to that person. This would violate (1).

[Note added later: This was, of course, written before the revelations about Jean Vanier's abusiveness. I would certainly have chosen a different example if I were writing this post now.]

Hiddenness and Molinism

Schellenberg claims that God cannot coexist with a non-resistant non-believer, since God being love would ensure that everyone who is non-resistant would be given the conditions necessary for a personal relationship with God.

It seems to me that a Molinist has a nice answer to this. A loving God would not want to compel people to have a particular kind of relationship with him, and would hence leave them free. But now imagine a particular non-resistant non-believer, Alice. God could know of Alice that if she believed in God and were free with respect to a relationship with God, she would freely choose a bad relationship with God. Then here are God’s main options with respect to Alice:

1. Not create Alice

2. Ensure Alice believes in God but make it impossible for her to have a bad relationship with God

3. Ensure Alice does not believe in God

4. Ensure Alice believes in God and allow her to have a bad relationship with God.

For Schellenberg’s case to work, (3) has to be an unacceptable option for a loving God. But (3) seems better than (1) and (4), and (2) seems contrary to the way that love requires respect for the freedom of the beloved. So while (3) is not ideal, it seems better than the alternatives.

And it could be—this is parallel to Trans-World Depravity—that in every feasible world there is someone like Alice.

I think the main response would be that a person who would have a bad relationship with God counts as resistant—i.e., a disposition to a bad relationship with God counts as resistance. However, this misses the Molinist point. Molinist conditionals of free will are not grounded in present character. One can be such that one would have a bad relationship with God if one believed in God, without having a disposition to such a relationship. One’s present character might, for instance, be neutral or even favoring of a good relationship with God, but given Molinism, it could be that were one to come to the decision point, one would decide against the relationship.

One could redefine non-resistance as being such that were one to believe, one would be in a good relationship with God. But because Molinist conditionals are ungrounded, we wouldn’t know whether a particular non-believer is resistant or not.

It's a pity that Molinism is false.

Individual and group discrimination

An interesting question is whether a prohibition on discrimination with respect to a determinable P by itself prohibits discrimination against groups with respect to patterns or distributions of P in groups.

If so, then it would be the case that:

• a prohibition of racial discrimination by itself prohibits discrimination against multi-racial groups

• a prohibition of gender discrimination by itself prohibits discrimination against same-gender couples.

But here would be a more surprising up-shot:

• a prohibition of P-based discrimination by itself prohibits discrimination against groups lacking P-diversity.

After all, lack of P-diversity is just a pattern of P-distribution (akin to same-gender couple, except that same-gender couples are by definition pairs while groups lacking P-diversity will often have more than two members). But that prohibiting P-based discrimination prohibits discrimination against groups lacking P-diversity seems implausible. After all, criticism is one of the forms of adverse treatment that when based on a protected characteristic will constitute discrimination. But it seems absurd to suppose that a prohibition on discrimination with respect to P also prohibits criticism of groups for lacking P-diversity.

If this is right, then a prohibition on discrimination against groups exhibiting particular patterns or distributions of the protected characteristic does not follow from a prohibition on discrimination on the basis of that characteristic, but requires a separate step. Sometimes, of course, that separate step is a no-brainer, as in the case of moving from prohibiting discrimination on the basis of race to prohibiting discrimination against multi-racial groups (including couples).

Let me add that I am neither a social nor a legal philosopher, so it may be that this has already been well-established or thoroughly refuted in the literature.

Haecceity and esse

I wonder if the haecceity of a thing isn't identical with its esse.

A Thomistic argument for essentiality of origins

Here is a suggestive Thomistic line of thought in favor of the essentiality of origins—i.e., the principle that the causes of things are essential to them.

Consider two possible cases where a seed is produced in the same apple tree T:

1. A seed is produced at t because of the tree’s exercise of seed-producing powers together with God’s cooperative exercise of primary causation.

2. A seed is created directly at t by God and not by the exercise of the tree’s powers.

And suppose that the seeds in the two cases are exactly alike, occur in the same place on the tree, etc.

I will argue that the Thomist should say that these will be numerically different seeds, and the best explanation of their difference is given by essentiality of origins.

For the Thomist is committed to there being a genuine difference between the two cases. Cooperative divine-creaturely causality is metaphysically different from divine primary causality. But where does the difference lie? Well, in (1) the tree’s causal powers are activated, while in (2) they are not. But it is a standard scholastic maxim that the effect is the actuality of the cause qua cause. Thus it seems that the difference between cases (1) and (2) should be found in the effect, namely the seed.

Furthermore, suppose that the difference between the cases is solely located in the cause, namely that in case (1) the tree’s causal powers are activated but not in (2), and that this activation is an accident A of the tree. The difference between cases (1) and (2) then is that in case (1), A occurs in the tree and in case (2) it does not. But for any accident of the tree, God could miraculously suppress any effects of that accident. Thus, there will be a case where A occurs in the tree and no seed results. And we could, further, imagine that:

3. Not only does God suppress the effects of A but he additionally directly miraculously produces an effect exactly like the one that A would have produced.

The difference between (3) and (1) can’t be in the activation of the tree’s causal power, since that is still there in (3). So we really should suppose a difference in the effects between (3) and (1). But a similar difference should exist between (2) and (1).

Note that the Thomist cannot say that there is a difference on the side of the causes lies in God, namely that in case (1), God’s causal power is unactivated but it is activated in (2) and (3). For an intrinsic difference in God between possible worlds would violate divine simplicity.

Thus, it is the effects, namely the seeds, that are numerically different, and they are different precisely because their causes are different. But the seeds are exactly alike. So the difference must be a metaphysical difference between the seeds. And this strongly suggests essentiality of origins. Indeed, it suggests that entities have encoded within them the identity of their cause.

Objection: The argument at most suggests that there has to be a numerical difference when something is produced by a finite cause (with God cooperating) and when something is produced directly by God. But why think there is also a difference when the effect is produced by one finite cause rather than another?

Response: The simplest metaphysical explanation of why it makes a difference whether God produces the effect or it is produced by finite causes is that the effect has metaphysically encoded in it what its cause was. In fact, my own view is that this may be found in the effect’s esse: perhaps an effect’s esse is to be caused by this-and-that.

Moreover, suppose that there need be no numerical difference between effects of different finite causes, but there is a numerical difference between direct effects of divine causation and the effects of finite causes. Then in principle scientists could have directly made the numerically same seed that the tree made in (1), but God couldn’t have directly made the numerically same seed. That seems unacceptable. (Of course, one might rejoin that essentiality of origins is unacceptable as it implies that God couldn’t directly make the numerically same seed that the tree could make. But when, as I suppose, an effect of necessity encodes in itself what its cause is, the impossibility of something’s being made by a different cause does not seem to be a limitation on that cause.)