Property inheritance

There seems to be such a thing as property inheritance, where x inherits a property F from y which has F in a non-derivative way. Here are some examples of this phenomenon on various theories:

1. I inherit mass from my molecules.

2. A person inherits some of their thoughts from the animal that constitutes the person.

3. A four-dimensional whole inherits its temporary properties from its temporal parts.

These are all cases of upward inheritance: a thing inheriting a property from parts or constituent. There can, however, be downward inheritance.

4. When a whole has the property of belonging to you, so do its parts, and often the parts inherit the property of being owned from the whole, though not always (you can buy a famous chess set piece by piece).

There may also be cases of sideways inheritance.

5. A layperson possesses the concept of a quark by inheritance from an expert to whom they defer with respect to the concept.

There seems to be some kind of a logical connection between property inheritance and property grounding, but the two concepts are not the same, since x’s possession of a property can be grounded in y’s possession of a different property—say, a president’s being elected is grounded in voters’ electing—while inheritance is always of the same property.

It is tempting to say:

6. An object x inherits a property F from an object y if and only if x’s having F is grounded in y’s having the same property F.

That’s not quite right. For if p grounds q, then p entails q. But this bundle of molecules’ having mass may not not entail my having mass, since it might be a contingent feature of the bundle that they are my molecules, so there is a possible world where the bundle exists and has mass, but I don’t (if only because I don’t exist). It seems that what we need in (6) is something weaker than grounding. But partial grounding seems too weak to plug into an account of property inheritance. Consider my property of knowing something. One of my pieces of knowledge is that you know something. So my knowing something is partially grounded in your knowing something, but I do not think that this counts as property inheritance. (Suppose one bites the bullet and says that my knowing something is inherited from you. Then, oddly, I have the property of knowing something both by inheritance and not by inheritance—inherited and non-inherited property possession are now compatible. I don’t know if that’s right, but at least it’s odd.)

I think we can at least say:

7. An object x inherits a property F from an object y only if x’s having F is grounded in y’s having the same property F.

But I don’t know how to turn this into a necessary and sufficient condition.

An act with a normative end

Here’s an interesting set of cases that I haven’t seen a philosophical discussion of. To get some item B, you need to affirm that you did A (e.g., took some precautions, read some text, etc.) But to permissibly affirm that you did A, you need to do A. Let us suppose that you know that your affirmation will not be subject to independent verification, and you in fact do A.

Is A a means to B in this case?

Interestingly, I think the answer is: Depends.

Let’s suppose for simplicity that the case is such that it would be wrong to lie about doing A in order to get B. (I think lying is always wrong, but won’t assume this here.)

If you have such an integrity of character that you wouldn’t affirm that you did A without having done A, then indeed doing A is a means to affirming that you did A, which is a means to B, and in this case transitivity appears ot hold: doing A is a means to B.

But we can imagine you have less integrity of character, and if the only way to get B would be to falsely affirm that you did A, you would dishonestly so affirm. However, you have enough integrity of character that you prefer honesty when the cost is not too high, and the cost of doing A is not too high. In such a case, you do A as a means to permissibly affirming that you did A. But it is affirming that you did A that is a means to getting B: permissibly affirming is not necessary. Thus, your doing A is not a means to getting B, but it is a means to the additional bonus that you get B without being dishonest.

In both specifications of character, your doing A is a means to its being permissible for you to affirm you did A. We see, thus, that we have a not uncommon set of cases where an ordinary action has a normative end, namely the permissibility of another action. (These are far from the only such cases. Requesting someone’s permission is another example of an action whose end is the permissibility of some other action.)

The cases also have another interesting feature: your action is a non-causal means to an end. For your doing A is a means to permissibility of affirming you did A, but does not cause that permissibility. The relationship is a grounding one.

Tables and organisms

A common-sense response to Eddington’s two table problem is that a table just is composed of molecules. This leads to difficult questions of exactly which molecules it is composed of. I assume that at table boundaries, molecules fly off all the time (that’s why one can smell a wooden table!).

But I think we could have an ontology of tables where we deny that tables are composed of molecules. Instead, we simply say that tables are grounded in the global wavefunction of the universe. We then deny precise localization for tables, recognizing that nothing is localized in our quantum universe. There is some approximate shape of the table, but this shape should not be understood as precise—there is no such thing as “the set of spacetime points occupied by the table”, unless perhaps we mean something truly vast (since the tails of wavefunctions spread out very far very fast).

That said, I don’t believe in tables, so I don’t have skin in the game.

But I do believe in organisms. Similar issues come up for organisms as for tables, except that organisms (I think) also have forms or souls. So I wouldn’t want to even initially say that organisms are composed of molecules, but that organisms are partly composed of molecules (and partly of form). That still generates the same problem of which exact molecules they are composed of. And in a quantum universe where there are no sharp facts about particle number, there probably is no hope for a good answer to that question.

So maybe it would be better to say that organisms are not even partly composed of molecules, but are instead partly grounded in the global wavefunction of the universe, and partly in the form. The form delineates which aspects of the global wavefunction are relevant to the organism in question.

Two priority monisms

According to priority monism, the cosmos is fundamental, and everything is a metaphysically dependent part. Priority monism is distinguished from existence monism according to which there exists only one thing (say, the cosmos).

Interestingly, one can split priority monism into a weaker and stronger version, where I restrict quantification over objects and facts to concrete objects and facts:

1. Weak priority monism: The existence and intrinsic features of the cosmos fully ground the existence of everything else.

2. Strong priority monism: The existence and intrinsic features of the cosmos fully ground all other facts.

Strong priority monism implies weak priority monism. As far as I can tell from Jonathan Schaffer’s discussion of heterogeneity, he subscribes to strong priority monism. But I think it is worth thinking about merely weak priority monism, because it avoids a certain problem that its strong cousin has.

On strong priority monism, given the asymmetry of grounding, no intrinsic feature of the cosmos can be even partly grounded in facts about an entity other than the cosmos. But suppose that Alice and Bob are fundamental particles located at the same position x, but with Bob having more mass than Alice. Then on strong priority monism, Alice’s and Bob’s masses are fully grounded in (the existence and intrinsic features of) the cosmos. But it is difficult to see how the cosmos can ground the facts that Alice is the one with less mass and Bob is the one with more mass without some kind of dependence on Alice and Bob. If Alice and Bob were at different locations, we could ground the difference in the fact that the cosmos is more massive in one location and less massive in the other. (But then we would have another problem: What grounds the fact that Alice is at the one location and Bob at the other, rather than vice versa?)

On merely weak priority monism, however, we can say that Alice and Bob’s existence is fully grounded in the cosmos, but facts about the mass distribution of the cosmos are grounded in the masses of the secondary beings like Alice and Bob. In other words, we have a two-way dependence in different respects. What makes the cosmos green here is that there is grass here, and the grass is green. What makes the grass exist is facts about the cosmos.

Identity and quantification

One way of posing the question of diachronic identity is to ask for an explanation of facts like

1. The xs compose the very same object at t₁ as the ys compose at t₂

where we do not use sameness or identity or similar concepts in the explanation.

This task turns out to be quite easy. The following is logically equivalent to (1) and does not use sameness or identity:

2. There is an object z such that the xs compose z at t₁ and the ys compose z at t₂.

This is a variant of the point made here.

Plural and singular grounding

Here’s a tempting principle:

1. If x and y ground z, then the fusion of x and y grounds z.

In other words, we don’t need proper pluralities for grounding—their fusions do the job just as well.

But the principle is false. For the principle is only plausible if any two things have a fusion. But if x and y do not overlap, then x and y ground their fusion. And then (1) would say that the fusion grounds itself, which is absurd.

This makes it very plausible to think that plural objectual grounding does not reduce to singular objectual grounding.

Aristotelian metaphysics and global physics

Too much of the contemporary ontological imagination is guided by the idea that the fundamental physical stuff in the world is discrete particles. Yet this is clearly dubious, since quantum mechanics (on non-Bohmian interpretations) suggests that the world is full of superpositions of states with different numbers of particles, while if discrete particles really exist, there had better be a well-defined number of them. Quantum mechanics instead suggests an ontology of the physical world where there is exactly one entity, “the Global Wavefunction”, whose physical state can be aptly represented as a vector in an infinite-dimensional vector space. And even if we didn’t have quantum mechanics’ vector-based approach on the table, we still wouldn’t be in an epistemic position to know that the right physics is based on particles rather than fields.

An ontology of material objects that composes these objects out of particles is held hostage to a particle-based physics that may well not be true. It would be best if one could work on the ontology of material objects without presupposing an answer to the question whether fundamental physical reality is field-like, vector-like or particle-like. I do not know if this is tenable. If it’s not, then the ontology of material objects needs to be done conditionally: If fundamental physical reality is of this sort, then material objects are like this.

Interestingly, some metaphysical problems may become easier given a non-particulate physical substratum. For instance, one of the hardest problems for a contemporary Aristotelian metaphysics has been the problem of what happens to particles that get incorporated into a substance, in light of the axiom that a substance cannot be composed of substances. But if we do not see fundamental physical reality as made of apparently substantial particles, the problem dissolves.

Today I want to sketch two Aristotelian approaches that take globalized vector- and field-approaches seriously. On the vector- and field-approaches, fundamental physical reality consists of a mere handful of entities: a single vector-like entity or several (hopefully no more than a dozen, and ideally only one) field-like entities. But being Aristotelian, we will think there are at least billions of substances: every organism is a substance. If these substances are to be related to fundamental physical entities, billions of them will have to be related to the same fundamental physical entities.

The ordinary substances on my stories will be organisms. There are billions of them. In addition to the ordinary substances, there are extraordinary substances: one for each of the handful of fundamental physical entities (fields or a vector).

My stories now diverge. On the first story, the billions of ordinary substances each encode and ground local features of the global fundamental physical entities. On a field version of the story, you encode and ground the features that the global fields have where you are located and your dog encodes and grounds the features that the global fields have where your dog is located (I am less clear on how to describe the vector version). This is not enough. For there aren’t enough organisms in the universe to ground all of the richness of the global fundamental physical entities: too much of the universe is lifeless. Thus, I propose that there are additional substances located where the organisms are not, and the features of these substances ground the rest of the features of the global fundamental physical entities. One way to run this story is to say that there is one of these additional substances per global fundamental physical entity, and each grounds the features of its corresponding global fundamental phsyical entity away from organisms. These additional substances are like swiss cheese, with the holes being filled with organisms like people and dogs.

On this version of the Aristotelian story—which can be varied in a number of ways—the global fundamental physical entities are not metaphysically fundamental. They are grounded in the many substances of the world.

On the second story, the global fundamental physical entities are substances. They are global substances. These global substances interact with the ordinary substances (there are many ways to spell out this interaction). We can now identify the matter of an ordinary substance x either with x’s powers and liabilities for interaction with the global substances or with the plurality of these global substances qua interacting with x.

There are many options here. Much detail to be worked out. Some options may be inferior to others, but I doubt in the end we will come to a single clearly best option.

The present doesn't ground the past

I will run an argument against the thesis that facts about the past are grounded in the present on the basis of the intuition that that would be a problematically backwards explanation.

Suppose for a reductio:

1. Necessarily, facts about the past are fully grounded in facts about the present.

Add the plausible premises:

2. Necessarily, if fact C is fully grounded in some facts, the Bs, and the Bs are fully causally explained by fact A, then fact A causally explains fact C.

As an illustration, suppose that the full causal explanation of why the Nobel committee gave the Nobel prize to Bob is that Alice persuaded them to. Bob’s being a Nobel prize winner is fully grounded in his being awarded the Nobel prize by the Nobel committee. So, Alice’s persuasion fully causally explains why Bob is the Nobel prize winner.

3. It is possible to have a Newtonian world such that:

   1. All the facts about the world at any one time are fully causally explained by the complete state of the universe at any earlier time.

   2. There are no temporally backwards causal explanations.

   3. There are at least three times.

Now, consider such a Newtonian world, and let t₁ < t₂ < t₃ be three times (by (3c)).

Suppose that t₃ is now present. Let U_i be the fact that the complete state of the universe at time t_i is (or will be or was) as it is (or will be or was). Then:

4. Fact U₁ is fully grounded in some facts about the present. (By (1))

Call these facts the Bs.

5. The Bs are fully causally explained by U₂. (As (3a) holds in our assumed world)

Therefore:

6. Fact U₁ is fully causally explained by U₂. (By (1))

7. So, there is backwards causal explanation. (By (6))

8. Contradiction! (By (7) and as (3b) holds in our assumed world)

I think we should reject (1), and either opt for eternalism or for Merricks’ version of presentism on which facts about the past are ungrounded.

"On the same grounds"

Each of Alice and Seabiscuit is a human or a horse. But Alice is a human or a horse “on other grounds” than Seabiscuit is a human or a horse. In Alice’s case, it’s because she is a human and in Seabiscuit’s it’s because he’s a horse.

The concept of satisfying a predicate “on other grounds” is a difficult one to make precise, but I think it is potentially a useful one. For instance, one way to formulate a doctrine of analogical predication is to say that whenever the same positive predicate applies to God and a creature, the predicate applies on other grounds in the two cases.

The “on other/same grounds” operator can be used in two different ways. To see the difference, consider:

1. Alice is Alice or a human.

2. Bob is Alice or a human.

In one sense, these hold on the same grounds: (1) is grounded in Alice being human and (2) is grounded in Bob being human. In another sense, they hold on different grounds: for the grounds of (1) also include Alice’s being Alice while the grounds of (2) do not include Bob’s being Alice (or even Bob’s being Bob).

Stipulatively, I’ll go for the weaker sense of “on the same grounds” and the stronger sense of “on different grounds”: as long as there is at least one way of grounding “in the same way”, I will count two claims as grounded the same way. This lets me say that Christ knows that 2 + 2 = 4 on the same grounds as the Father does, namely by the divine nature, even though there is another way in which Christ knows it, which the Father does not share, namely by humanity.

Even with this clarification, it is still kind of difficult to come up with a precise account of “on other/same grounds”. For it’s not the case that the grounds are literally the same. We want to say that the claims that Bob is human and that Carl is human hold on the same grounds. But the grounding is literally different. The grounds of the former is Bob’s possession of a human nature while the grounds of the latter is Carl’s possession of a human nature. Moreover, if trope theory is correct, then the two human natures are numerically different. What we want to say is something like this: the grounds are qualitatively the same. But how exactly to account for the “qualitatively sameness” is something I don’t know.

There is a lot of room for interesting research here.

Fundamental mereology

It is plausible that genuine relations have to bottom out in fundamental relations. E.g., being a blood relative bottoms out in immediate blood relations, which are parenthood and childhood. It would be very odd indeed to say that a is b’s relative because a is c’s relative and c is b’s relative, and then a is c’s relative because a is d’s relative and d is c’s relative, and so on ad infinitum. Similarly, as I argued in my infinity book, following Rob Koons, causation has to bottom out in immediate causation.

If this is right, then proper parthood has to bottom out in what one might call immediate parthood. And this leads to an interesting question that has, to my knowledge, not been explored much: What is the immediate parthood structure of objects?

For instance, plausibly, the big toe is a part of the body because the big toe is a part of the foot which, in turn, is a part of the body. And the foot is a part of the body because the foot is a part of the leg which, in turn, is a part of the body. But where does it stop? What are the immediate parts of the body? The head, torso and the four limbs? Or perhaps the immediate parts are the skeletal system, the muscular system, the nervous system, the lymphatic system, and so on. If we take the body as a complex whole ontologically seriously, and we think that proper parthood bottoms out in immediate parthood, then there have to be answers to such questions. And similarly, there will then be the question of what the immediate parts of the head or the nervous system are.

There is another, more reductionistic, way of thinking about parthood. The above came from the thought that parthood is generated transitively out of immediate parthood. But maybe there is a more complex grounding structure. Maybe particles are immediately parts of the body and immediately parts of the big toe. And then, say, a big toe is a part of the body not because it is a part of a bigger whole which is more immediately a part of the body, but rather a big toe is a part of the body because its immediate parts are all particles that are immediately parts of the body.

Prescinding from the view that relations need to bottom out somewhere, we should distinguish between fundamental parts and fundamental instances of parthood. One might have one without the other. Thus, one could have a story on which we are composed of immediate parts, which are composed of immediate parts, and so on ad infinitum. Then there would be fundamental instances of the parthoood relation—they obtain between a thing and its immediate parts—but no fundamental parts. Or one could have a view with fundamental parts while denying that there are any fundamental instances of parthood.

In any case, there is clearly a lot of room for research in fundamental mereology here.

Aristotelians shouldn't be presentists

A foundational commitment of Aristotelian philosophy is that all facts are grounded in what substances and features intrinsic to substances, namely forms and accidents, exist. But it is possible for the past to have been different without there being any difference in what substances and features intrinsic to substances presently exist. Therefore, the Aristotelian cannot equate present existence with existence.

In other words, Aristotelians cannot escape the standard grounding arguments against presentism.

Objection 1: A theistic Aristotelian can ground facts about the past in features of God (say, God’s memories).

Response: Only if God is mutable. And there are good reasons to believe that if God exists, he is immutable.

Objection 2: Past events affect present substances in various ways.

Response: There is a possible world with laws of nature similar to ours that starts at time 0 with nothing but two material causally isolated substances A and B (and God, if theism is true) that wiggle around in indeterministic ways. A month later, substance A ceases to exist (maybe God stops sustaining its existence), and no new substances come into existence. Now, in month 2, there is only one substance B. Since the two substances were causally isolated, substance B is not affected in its intrinsic features by anything that substance A did. Thus, the facts about how substance A used to wiggle about are not grounded in the intrinsic features of material substances in month 2. (If one says that we regain grounding when we take God’s intrinsic features into account, that will take us back to Objection 1.)

One might respond that complete causal isolation is impossible. But that’s not right. For imagine that, like in our world, causal influences cannot propagate faster than at the speed of light, and A and B start off one light-year apart, and while A perishes after a month, B perishes after six months. Then B is not going to be affected by A’s wiggles.

Objection 3: But maybe there has to be some kind of a metaphysical influence whereby all present substances are affected by all past substances.

Response: This is not plausible in light of the response to Objection 2. But let’s grant it. Then I transpose my argument to the future. Obviously, future contingent events don’t normally (apart from supernatural cases, like prophecy) affect how substances presently are. Hence even if we grant the mysterious metaphysical influence of past substances on present ones, we still have a problem about the future. That problem could be solved if we embraced an open future, as Aristotle did, but we shouldn’t follow Aristotle in that.

Explanation, grounding and divine simplicity

Here is a plausible principle:

1. If p is partly grounded in q, then p does not explain q.

But the best account of divine simplicity commits one to:

2. That God willed horses to exist is partly grounded in there existing horses.

(For, that God willed horses is a contingent fact. By divine simplicity any contingent fact about God must be partly grounded in realities outside of God. And the only plausible candidate for the reality outside of God here is the fact that there exist horses.)

Therefore:

3. That God willed horses to exist does not explain why there are horses.

This seems very counterintuitive, sufficiently counterintuitive to provide an argument against divine simplicity, or against (1).

But I think one should just accept (3). For even apart from considerations of divine simplicity, it is plausible that God’s will is so strongly efficacious that his willing something just is his making it be so:

4. God’s willing horses to exist just is God’s causing horses to exist.

But in general, even apart from the divine case, x causing y is partly grounded in both x and y, and hence is partly grounded in y. Thus:

5. God’s causing horses to exist is partly grounded in horses existing.

It seems to follow (there are tough issues involving the hyperintensionality of grounding) that:

6. God’s willing horses to exist is partly grounded in horses existing.

In fact, once we understand that God’s (consequently) willing and God’s causing are the same thing, then the paradox in (3) is just very much like:

7. My causing a boomerang to exist does not explain why the boomerang exists.

But we have good reason to accept (7). For when I made a boomerang some years back, that I caused a boomerang to exist was partly grounding in a boomerang existing. (A boomerang might not have eventuated from what I was doing. Instead, I might have been left with a broken piece of wood.) But then by (1), I have to accept (7).

What is unfortunate for me is that for a long time, in print and in speech, I’ve been happy to accept claims like:

8. My causing a boomerang to exist explains why the boomerang exists.

9. God’s willing horses to exist explains why horses exist.

I still find it difficult to deny (8) and (9).

Maybe I should deny (1) instead. But I don’t want to. I am strongly committed to there not being any circles of explanation, even ones involving different kinds of explanation (say, causal and grounding).

Maybe I can save the intuitions behind (8) by saying:

10. My actuating my causal power of boomerang production explains why the boomerang exists.

(Note that my actuating that causal power does not entail a boomerang exists. A causal power can be actuated unsuccessfully.)

And maybe I can save the intuitions behind (9) with:

11. God’s desiring that horses exist explains why horses exist.

(God’s desiring something doesn’t entail that thing’s existing, since God desires every good, and some goods are incompatible with one another.)

More on grounding of universals

The standard First Order Logic translation of “All As are Bs” is:

1. ∀x(A(x)→B(x)).

Suppose we accept this translation and we further accept the principle:

2. Universal facts are always partially grounded in their instances.

Then we have the oddity that the fact that all ravens are black seems to be partially grounded in my garbage can being black. Let R(x) and B(x) say that x is a raven and black, respectively, and let g be my garbage can. Then an instance of ∀x(R(x)→B(x)) is R(g)→B(g), and the latter material conditional is definable as ¬R(g)∨B(g). But a disjunction is grounded in its true disjuncts, and hence this one will be grounded in B(g) (as well as in ¬R(g)).

There are three things to dispute here: the translation (1), the grounding principle (2), and the claim that a material conditional is grounded in its consequent whenever that consequent is true. Of these, I am most suspicious of the translation of the two-place universal quantifier and the grounding principle (2).

Grounding of universals and partial grounding

It is common to claim that:

1. The fact that everything is F is partially grounded in the fact that a₁ is F and in the fact that a₂ is F and so on, for all the objects a_i in the world.

But this can’t be right if partial grounds are parts of full grounds. For suppose you live in a world with only two objects, a and b, which are both sapient. Then everything is sapient, and by (1) it follows that:

2. The fact that everything is sapient is partially grounded in a being sapient and in b being sapient.

But suppose partial grounds are parts of full grounds. The facts that a is sapient and b is sapient are not a full ground of the fact that everything is sapient, because the full grounds of a fact entail that fact, and a being sapient and b being sapient doesn’t entail that everything is sapient (since it’s possible for a to be sapient and b to be sapient and yet for there to exist a c that is not).

So we need to be able to add something to the two particular sapience facts to get full grounds. The most obvious thing to add is:

3. Everything is a or b.

Clearly fact (3) together with the facts that a is sapient and b is sapient will entail that everything is sapient.

But applying (1) to (3), we get:

4. Fact (3) is partially grounded in the facts that a is a or b and that b is a or b.

But, once again, if partial grounds are parts of full grounds, then we need a fact to add to the two facts on the right hand side of the grounding relation in (4) such that together these facts will entail (3). But the obvious candidate to add is:

5. Everything is a or b.

And that yields circularity.

So it seems that either we should reject the particular-grounds-universal principle (1) or we should reject the principle that partial grounds are parts of full grounds.

Here is a reason for the latter move. Maybe we should say that God’s creating me is partially grounded in God. But that’s merely a partial grounding, since God’s existence doesn’t entail that God created me. And it seems that the only good candidate for a further fact to be added to the grounds so as to entail that God created me would be my existence. (One might try to add the fact that God willed that I exist. But by divine simplicity, that fact has to be partly constituted by my existence or the like.) But my existence is grounded in God’s creating me, so that would be viciously circular.

Causal powers, imperfection, free will and divine simplicity

Here is a plausible connection between normativity and causal powers:

1. If x has a power to ϕ in C, and x is in C but does not ϕ, then x qua having that power imperfect.

2. x is imperfect simpliciter if x is imperfect qua having ϕ for some ϕ that x has in virtue of its nature.

(I think one can make biconditionals out of these.)

But here is a problem. By omnipotence, God has the power to make reality be such that there are horses and they are all green, and he has the power to make reality be such that there are horses and they are all red. And he has these powers in the same circumstance C, namely that of creation. He exercises only one of these two powers. So it seems that God is imperfect qua having at least one of these powers. But he has these powers in virtue of his omnipotence and hence in virtue of his nature. Hence it seems that God is imperfect simpliciter.

Here is my best solution. Revise 1 to:

3. If x has a power P such that P is a power to ϕ in C, and x is in C but does not successfully exercise P, then x qua having P is imperfect.

This sounds like it is equivalent to 1. After all, this seems like a necessary truth:

4. If P is a power to ϕ in C and x successfully exercises P in C, then x must ϕ.

But actually 4 need not be true. For the same entity, P, could be both a power to ϕ in C and a power to ψ in C. And if so then when the possessor of P ψs in C, that would be a successful exercise of P.

This fits really well with divine simplicity on which all of God’s causal powers are ontologically the same, and indeed are identical to God. Given that, God’s powers are always fulfilled as long as God exercises one of them. (And perhaps even ensuring that God is alone would count as an exercise of God’s creative power.)

Here is another interesting thought. When I exercise free will, I have the power to ϕ and the power to ψ where ϕing and ψing are incompatible. It seems at first sight that one of these powers is unexercised, and hence thus far I am imperfect by 1. But perhaps sometimes the power to ϕ and the power to ψ are ontologically the same entity, either my nature or a single accident of me, in virtue of which entity I can ϕ and I can ψ. If so, then either ϕing or ψing could suffice for perfection qua having that power.

And now here is a very speculative thought. When we choose between right and wrong on earth, maybe the power to choose the right and the power to choose the wrong are distinct entities. Thus, we are imperfect even if we choose the right, for the power to do the wrong is unexercised. However, this sort of imperfection is not found in heaven, because there we lack the power to choose the wrong, due to the perfection of our character. But the same question will still come up in heaven when we choose between two incompatible goods, say reciting a piece of prose or reciting a piece of verse. However, perhaps, our mind will have such a deep internal unity in heaven that our abilities to choose between the various incompatible goods will be grounded in a single entity, and so no matter what we choose, we will thus far be perfect. (Not that I think it is disastrous to admit certain kinds of imperfections in heaven, so perhaps we don’t need recourse to this.)

From a dualism to a theory of time

This argument is valid:

1. Some human mental events are fundamental.

2. No human mental event happens in an instant.

3. If presentism is true, every fundamental event happens in an instant.

4. So, presentism is not true.

Premise (1) is widely accepted by dualists. Premise (2) is very, very plausible. That leaves (3). Here is the thought. Given presentism, that a non-instantaneous event is happening is a conjunctive fact with one conjunct about what is happening now and another conjunct about what happened or will happen. Conjunctive facts are grounded in their conjuncts and hence not fundamental, and for the same reason the event would not be fundamental.

But lest four-dimensionalist dualists cheer, we can continue adding to the argument:

5. If temporal-parts four-dimensionalism is true, every fundamental event happens in an instant.

6. So, temporal-parts four-dimensionalism is not true.

For on temporal-parts four-dimensionalism, any temporally extended event will be grounded in its proper temporal parts.

The growing block dualist may be feeling pretty smug. But suppose that we currently have a temporally extended event E that started at t₋₂ and ends at the present moment t₀. At an intermediate time t₋₁, only a proper part of E existed. A part is either partly grounded in the whole or the whole in the parts. Since the whole doesn’t exist at t₋₁, the part cannot be grounded in it. So the whole must be partly grounded in the part. But an event that is partly grounded in its part is not fundamental. Hence:

7. If growing block is true, every fundamental event happens in an instant.

8. So, growing block is not true.

There is one theory of time left. It is what one might call Aristotelian four-dimensionalism. Aristotelians think that wholes are prior to their parts. An Aristotelian four-dimensionalist thinks that temporal wholes are prior to their temporal parts, so that there are temporally extended fundamental events. We can then complete the argument:

9. Either presentism, temporal-parts four-dimensionalism, growing block or Aristotelian four-dimensionalism is true.

10. So, Aristotelian four-dimensionalism is true.

Infinite grounding regresses

Suppose, as seems possible, that every day for eternity you will toss a coin and get heads.

Then that you will get heads on every future day seems to be grounded in:

1. You will get heads on day 1, and you will get heads on every day starting with day 2.

And the second conjunct of (1) seems to be grounded in:

2. You will get heads on day 2, and you will get heads on every day starting with day 3.

And the second conjunct of (2) seems to be grounded in:

3. You will get heads on day 3, and you will get heads on every day starting with day 4.

And so on.

So, it seems, infinite propositional grounding regresses are possible.

I suspect that infinite existential grounding regresses are not possible, though.

Against nihilism

Argument A:

1. Necessarily, if there is nothing, it is impossible that anything exists.

2. Something exists.

3. So, by Brouwer Axiom, necessarily possibly something exists.

4. So, the consequent of (1) is impossible.

5. So, it is impossible that there is nothing.

The most controversial premise in this argument is (1). Premise (1) follows from a picture of modality on which possibility is prior to necessity, and the possibility of non-actual things is grounded in possibilifiers. Absent possibilifiers, nothing is possible. But suppose that instead we like a picture of modality as grounded in necessitators. Then instead we have this argument.

Argument B:

6. Necessarily, if there is nothing, no proposition is necessary.

7. It’s necessary that it’s necessary that 2+2=4. (Obvious, or else a consequence of S4 and the fact that it’s necessary that 2+2=4.)

8. So the consequent of (6) is impossible.

9. So, it is impossible that there is nothing.

And finally we have:

Argument C:

10. Necessarily, if there is nothing, either it is impossible that anything exists or no proposition is necessary.

11. Necessarily possibly something exists. (Premise (3))

12. It’s neccessary that it’s necessary that 2+2=4. (Premise (7))

13. So, the consequent of (10) is impossible.

14. So, it is impossible that there is nothing.

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:

2. 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:

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

Ontological grounding nihilism

Some people are attracted to nihilism about proper parthood: no entity has proper parts. I used to be rather attracted to that myself, but I am now finding that a different thesis fits better with my intuitions: no entity is (fully) grounded. Or to put it positively: only fundamental entities exist.

This has some of the same consequences that nihilism about proper parthood would. For instance, on nihilism about proper parthood, there are no artifacts, since if there were any, they'd have proper parts. But on nihilism about ontological grounding, we can also argue that there are no artifacts, since the existence of an artifact would be grounded in social and physical facts. Moreover, nihilism about ontological grounding implies nihilism about mereological sum: for the existence of a mereological sum would be grounded in the existence of its proper parts. However, nihilism about ontological grounding is compatible with some things having parts--but they have to be things that go beyond their parts, things whose existence is not grounded in the existence and relations of their parts.