Humeanism and knowledge of fundamental laws

On a "Humean" Best System Account (BSA) of laws of nature, the fundamental laws are the axioms of the system of laws that best combines brevity and informativeness.

An interesting consequence of this is that, very likely, no amount of advances in physics will
suffice to tell us what the fundamental laws are: significant advances in mathematics will also be needed. For suppose that after a lot of extra physics, propositions formulated in sentences p₁, ..., p_n are the physicist’s best proposal for the fundamental laws. They are simple, informative and fit the empirical data really well.

But we would still need some very serious mathematics. For we would need to know there isn’t a simpler collection of sentences {q₁, ..., q_m} that is logically equivalent to {p₁, ..., p_n} but simpler. To do that would require us to have a method for solving the following type of mathematical problem:

1. Given a sentence s in some formal language, find a simplest sentence s′ that is logically equivalent to s,

in the case of significantly non-trivial sentences s.

We might be able to solve (1) for some very simple sentences. Maybe there is no simpler way of saying that there is only one thing in existence than ∃x∀y(x=y). But it is very plausible that any serious proposal for the laws of physics will be much more complicated than that.

Here is one reason to think that any credible proposal for fundamental laws is going to be pretty complicated. Past experience gives us good reason to think the proposal will involve arithmetical operations on real numbers. Thus, a full statement of the laws will require including a definition of the arithmetical operations as well as of the real numbers. To give a simplest formulation of such laws will, thus, require us to solve the problem of finding a simplest axiomatization of the portions of arithmetic and real analysis that are needed for the laws. While we have multiple axiomatizations, I doubt we are at all close to solving the problem of finding an optimal such axiomatization.

Perhaps the Humean could more modestly hope that we will at least know a part of the fundamental laws—namely the part that doesn’t include the mathematical axiomatization. But I suspect that even this is going to be very difficult, because different arithmetical formulations are apt to need different portions of arithmetic and real analysis.

The fundamentality of souls

Some dualists say that the soul is a fundamental entity.

I think we’re not in a position to think that. Compare this. We have no reason to think electrons are not elementary particles. They certainly aren’t made of any of the other particles we know of, so they are, we might say, “relatively elementary” with respect to the particles we know. But we would not be very surprised if electrons turned out to be made of other particles.

Similarly, we have good reason to think the soul is not grounded in any of the other things we know of (matter, accidents, etc.) But we should not be really surprised if a finer-grained analysis would reveal the soul to have a grounding structure beyond our current knowledge. We should be cautious and say the soul is “relatively fundamental” with respect to the entities we know.

Against Monism

According to Monism:

• (M) Necessarily if there are any concrete physical objects, then there is a concrete physical fundamental object (“a cosmos”) that has all concrete physical objects as metaphysically dependent parts.

Here an object is fundamental just in case it is not metaphysically dependent. But Monism is difficult to reconcile with the Intrinsicness of Fundamentality:

• (IF) Necessarily, if x is a fundamental object, then any exact duplicate of x is fundamental.

For simplicity, let’s call concrete physical objects just “objects”, and let’s only talk of the concrete physical aspects of worlds, ignoring any spiritual or abstract aspects.

Now consider a world w₁ that consists of a single simple object (say, a particle) α. Let w₂ be a world consisting of an exact duplicate α′ of α as well as of one or more other simple objects. Then by (M), α′ is not fundamental in w₂, since it is dependent on w₂’s cosmos (which is not just α′, since w₂ has some other simple objects). But α is the cosmos of w₁, and hence is fundamental, and thus by (IF), α′ is a duplicate of a fundamental object, and hence fundamental.

I can think of one way out of this argument for the defender of (M), and this is to deny the weak supplementation axiom of mereology and say that in w₁, there are two objects: α and a cosmos c₁ which has exactly one proper part, namely α. This allows the monist to deny that α is fundamental in w₁. Many people will find the idea that you could have an object with exactly one proper part absurd. I am not one of them in general, but even I find it problematic when the object and the proper part are both purely physical objects.

Still, let’s consider this view. We still have a problem. For in w₁, there is an object, namely c₁, that has α as its only proper part. Now, suppose a world w₃ that contains a duplicate c₁′ of c₁, and hence a duplicate α′ of α that is a part of c₁′, as well as one or more additional simples. Then c₁′ has only one simple as a proper part, and hence is not the cosmos of w₃, and thus is not fundamental by (M), which contradicts (IF).

So, we cannot have a world w₃ as described. Why not? I think the best story is that a cosmos is a unique kind of organic whole that encompasses all of reality, and that exists in every world which has a (concrete physical) object, and nothing but the cosmos can be a duplicate of the cosmos.

But this story violates the following plausible Distinctness of Very Differents principle:

• (DVD) If x and y are organic wholes made of radically different kinds of particles and have radically different shape and causal structure, then x ≠ y.

But now consider a world consisting of a cloud of photon-like particles arranged in a two-dimensional sheet, and a world consisting of a cloud of electron-like particles arranged in a seven-dimensional torus. The cosmoses of the two worlds are made of radically different kinds of particles and have radically different shape and causal structure, so they are not identical.

Fundamentality and anthropocentrism

Say an object is grue if it is observed before the year 2100 and green, or it is blue but not observed before 2100. Then it is reasonable to do induction with “green” but not with “grue”: our observations of emerald color fit equally well with the hypotheses that emeralds are green and that they are grue, but it is the green hypothesis that is reasonable.

A plausible story about the relevant difference between “green” and “grue” is that “green” is significantly closer to being a “perfectly natural” or “fundamental” property than “grue” is. If we try to define “green” and “grue” in fundamental scientific vocabulary, the definition of “grue” will be about twice as long. Thus, “green” is projectible but “grue” is not, to use Goodman’s term.

But this story has an interesting problem. Say that an object is pogatively charged if it is observed before Planck time 2ⁿ and positively charged or it negatively charged but not observed before Planck time 2ⁿ. By the “Planck time”, I mean the proper time from the beginning of the universe measured in Planck times, and I stipulate that n is the smallest integer such that 2ⁿ is in our future. Now, while “pogatively charged” is further from the fundamental than “positively charged”, nonetheless “pogatively charged” seems much more fundamental than “green”. Just think how hard it is to define “green” in fundamental terms: objects are green provided that their emissive/refractive/reflective spectral profile peaks in a particular way in a particular part of the visible spectrum. Defining the “particular way” and “particular part” will be complex—it will make make reference to details tied to our visual sensitivities—and defining “emissive/refractive/reflective”, and handling the complex interplay of these, is tough.

One move would be to draw a strong anti-reductionist conclusion from this: “green” is not to be defined in terms of spectral profiles, but is about as close to fundamentality as “positively charged”.

Another move would be to say that projectibility is not about distance to fundamentality, but is legitimately anthropocentric. I think kind of anthropocentrism is only plausible on the hypothesis that the world is made for us humans.

Against anti-interactionist intuitions

1. Fundamental and non-fundamental things are at least as deeply metaphysically different from each other as physical and non-physical things.

2. Fundamental things can cause non-fundamental things and non-fundamental things can cause fundamental things. (E.g., particles can cause a heap, and lab equipment can cause a particle emission.)

3. Therefore, being at least as deeply metaphysically different as physical and non-physical things are cannot be sufficient for making causal relationships impossible.

Inclusive vs. proper parthood

Contemporary analytic philosophers seem to treat the “inclusive” concept of parthood, on which each object counts as an improper part of itself, as if it were more fundamental than the concept of proper parthood.

It seems to me that we should minimize the number of fundamental relations that all objects have to stand in. We are stuck with identity: every object is identical with itself. But anything beyond that we should avoid as much as we can.

Now, it is plausible that whatever parthood relation—inclusive parthood or proper parthood—is the more fundamental of the two is in fact a fundamental relation simpliciter. For it is unlikely that parthood can be defined in terms of something else. But if we should minimize the number of fundamental relations that all objects must stand in, then it is better to hold that proper parthood rather than inclusive parthood is a fundamental relation. For every object has to stand in inclusive parthood to itself. But it is quite possible to have objects that are not proper parts of anything else.

On this view, proper parthood will be a fundamental relation, and improper parthood is just the disjunction of proper parthood with identity.

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.

Red cars and playdough

A red chunk of playdough needs to be red through and through. A red car need only be red on the outside. Peanut butter to be smooth must be smooth all the way through. But a mattress needs to only be smooth on the upper side to be smooth.

In other words, predicates like “is smooth” and “is red” apply to objects in different ways. A seemingly arbitrary decision needs to be made to how to apply them to a particular kind of object.

But perhaps this is only the case because chunks of playdough, cars, blobs of peanut butter and mattresses are not substances. Perhaps we can hope that for substances such decisions do not need to be made? But that hope is quickly dashed when we realize that a decision has to be made whether to call an electron a wave or a particle or both or neither, and that a decision has to be made which of a horse’s muscles are relevant to saying that the horse is strong (does it need to have strong eyelid muscles? tail muscles?).

Maybe when we descend to the level of applying fundamental predicates to substances, then the problem disappears. But that’s not clear. Position predicates seem to be fundamental but there is arbitrariness in deciding how to apply them to quantum objects when they are not in an eigenstate of position.

Perhaps where the arbitrariness disappears is when we consider cases where a fundamental predicate fundamentally applies to a substance. A fundamental predicate might non-fundamentally apply to a substance: thus, a dog might be negatively charged, and “is negatively charged” might be fundmental, but the dog is not fundamentally negatively charged—rather it is charged in virtue of mathematical facts about the overall distribution of fundamental charge properties throughout its body.

Qualia are not all fundamental entities if theism is true

This argument is sound. I am not sure if premise (2) is true, though.

1. If God exists, then all fundamental entities are intrinsically good.
2. Pain qualia are not intrinsically good.
3. So, pain qualia are not fundamental entities.

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.

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.

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.

Realism and anti-reductionism

The ordinary sentence "There are four chairs in my office" is true (in its ordinary context). Furthermore, its being true tells us very little about fundamental ontology. Fundamental physical reality could be made out of a single field, a handful of fields, particles in three-dimensional space, particles in ten-dimensional space, a single vector in a Hilbert space, etc., and yet the sentence could be true.

An interesting consequence: Even if in fact physical reality is made out of particles in three-dimensional space, we should not analyze the sentence to mean that there are four disjoint pluralities of particles each arranged chairwise in my office. For if that were what the sentence meant, it would tell us about which of the fundamental physical ontologies is correct. Rather, the sentence is true because of a certain arrangement of particles (or fields or whatever).

If there is such a broad range of fundamental ontologies that "There are four chairs in my office" is compatible with, it seems that the sentence should also be compatible with various sceptical scenarios, such as that I am a brain in a vat being fed data from a computer simulation. In that case, the chair sentence would be true due to facts about the computer simulation, in much the way that "There are four chairs in this Minecraft house" is true. It would be very difficult to be open to a wide variety of fundamental physics stories about the chair sentence without being open to the sentence being true in virtue of facts about a computer simulation.

But now suppose that the same kind of thing is true for other sentences about physical things like tables, dogs, trees, human bodies, etc.: each of these sentences can be made true by a wide array of physical ontologies. Then it seems that nothing we say about physical things rules out sceptical scenarios: yes, I know I have two hands, but my having two hands could be grounded by facts about a computer simulation. At this point the meaningfulness of the sceptical question whether I know I am not a brain in a vat is breaking down. And with it, realism is breaking down.

In order for the sceptical question to make sense, we need the possibility of saying things that cannot simply be made true by a very wide variety of physical theories, since such things will also be made true by computer simulations. This gives us an interesting anti-reductionist argument. If the statement "I have two hands" is to be understood reductively (and I include non-Aristotelian functionalist views as reductive), then it could still be literally true in the brain-in-a-vat scenario. But if anti-reductionism about hands is true, then the statement wouldn't be true in the brain-in-a-vat scenario. And so I can deny that I am in that scenario simply by saying "I have two hands."

But maybe I am moving too fast here. Maybe "I have two hands" could be literally true in a brain-in-a-vat scenario. Suppose that the anti-reductionism consists of there being Aristotelian forms of hands (presumably accidental forms). But if, for all we know, the form of a hand can inform a bunch of particles, a fact about a vector or the region of a field, then the form of a hand can also inform an aspect of a computer simulation. And so, for all we know, I can literally and non-reductively have hands even if I am a brain in a vat. I am not sure, however, that I need to worry about this. What is important is form, not the precise material substrate. If physical reality is the memory of a giant computer but it isn't a mere simulation but is in fact informed by a multiplicity of substantial and accidental forms corresponding to people, trees, hands, hearts, etc., and these forms are real entities, then the scenario does not seem to me to be a sceptical scenario.

Ineffability

Consider this argument against divine ineffability: Let p be the conjunction of all fundamental truths intrinsically about God (I'm thinking here of something like the Jon Jacobs account of ineffability, but the point should work on other similar accounts). Stipulate that the sentence "It divines" (a feature-placing sentence or zero-place predicate, like in "It rains") expresses p. It divines. It seems I have just said the conjunction of all fundamental truths intrinsically about God. Hence God is not ineffable.

But this argument cannot be sound, since God is in fact ineffable--divine ineffability is, for instance, part of the creed of the Fourth Lateran Council. So what goes wrong with the argument?

First, one might have technical worries about infinite conjunctions or arbitrary linguistic stipulations. I'll put those to one side, though they are worth thinking about.

More deeply, one might worry whether there are any fundamental truths intrinsically about God. Truths are true propositions. Perhaps the fundamental reality of God not only cannot be expressed in language, but cannot even be given propositional form. I am not sure about this, though it is a promising response to the argument. But, plausibly, propositions are divine thoughts. And God surely does express his fundamental reality in his thought (indeed, this is central to Augustine's Trinitarianism).

I want to try out a different response to the argument: question the last step in the argument, the inference "Hence God is not ineffable." This response allows that we can stipulate and assert a sentence that means the conjunction of all fundamental truths intrinsically about God, but denies that this is a problem for ineffability. Ineffability isn't a denial of the possibility of asserting a sentence whose semantic content is such-and-such truths about the divine nature. Rather, it is the denial of the possibility of linguistically communicating these truths. For me to linguistically communicate a truth to you it is required that my sentence give rise to your thinking that truth. But the truth expressed by "It divines" isn't a truth you can think. On this understanding, divine ineffability is an immediate consequence of divine incomprehensibility, and rather than being a doctrine about semantics, it's a doctrine about communication.

If this is right, then stipulation allows the semantics of our language to outrun communication and thought. You can think some deep philosophical truth that I don't know, and I can stipulate that "It xyzzes" means that truth, and I can sincerely assert "It xyzzes." But I don't thereby think that truth. I can, of course, think the second order thought that "It xyzzes" is true, but to do that is not the same as to think that it xyzzes. Similarly, I can think that "It divines" is true, but that's a thought about a piece of stipulated language rather than a thought about God. Indeed, it divines, but I don't understand the sentence "It divines" as I can't grasp the proposition it expresses.

Sometimes people are accused of a certain kind of insincerity like this: "You're just saying the words but don't really understand." This is a different kind of insincerity than when people are lying. A person who is "just saying the words" may believe that the sentence composed of the words is really true, and if so, then she isn't lying. (Corollary: One can say something one doesn't believe and yet not be a liar, as long as one believes that what one is saying is true.) The reason that there may be insincerity in "just saying the words" is that normally one implicates that one believes (and hence has a minimal understanding of) the content of what one says. But that's an implicature that can be canceled to avoid even this kind of insincerity: "I don't exactly know what 'God loves you' means, but I believe that it is true. God loves you." And when people are talking of a topic neither is close to being an expert on, the implicature of understanding one's words may be contextually canceled.

Minimizing the number of fundamental relations between concreta

An interesting metaphysics project that could use more work is to minimize the number of fundamental non-intentional relations between substances. How few can we do with? I think it would be really great if one could reduce the number of such relations to a handful of relations, or at least determinable families of relations. There is only one candidate really clear to me: causation. I think it would be an interesting research project to adopt the working hypothesis that causation is the one and only such relation and see how things go.

A lot of people will want to add parthood to this list, but I don't think a substance can be a part of another substance. (Parts are grounded in wholes, and substances are not grounded in other things.) Spatial relations like being seven meters apart (on relationalism about locations) and being located at (on substantivalism about locations) are a family of plausible candidates.

Do theists have to believe the privation theory of evil?

St. Augustine argued somewhat like thus:

1. Everything that exists is sustained by God.
2. God sustains only good.
3. Thus everything that exists is good insofar as it exists.
4. Thus evil is only a privation of good.

I've found the argument compelling for most of my life. I continue to be confident of (3). But I am now not sure about the inference from (3) to (4). Here's why. Essential to Augustine's account is an ontology sufficiently sparse not to include lacks. After all, if holes, lacks and privations exist then Augustine's account is in trouble. But if the true ontology is sparse enough not to include lacks, then there will likely be other "things" that don't exist. And these other "things" will escape Augustine's argument.

For instance, why couldn't some evils instead of being privations be mismatches? The mismatch between Jones' belief that Americans never landed on the moon and the fact of the moon landing could be an evil. An ontology could, for instance, include both Jones' belief and the moon landing, but not include as a further item the mismatch between the two. One might try to argue that a mismatch is a privation of a due match. But the correct ontology might not include matches either. Or consider the example, discussed in the secondary literature, of the man with two noses. It's an evil to have two noses, but at least prima facie (sorry!) the extra nose isn't a privation. But if we do not suppose that evil has to be a privation, then we can say that the problem is the mismatch between the face and the human form.

This approach would allow one to retain the central anti-Manichean insight that Augustine has, namely (3), while at the same time escaping some counterexamples. I am not sure it escapes the biggest counterexample, namely pain. Though if we take Mark Murphy's theory that what is bad is not pain itself, but the disharmony between reality and desire that tends to correlate with pain, then the above approach helps, since a disharmony is a kind of mismatch.

I am not claiming every mismatch is an evil. The argument doesn't establish that every "thing" that doesn't exist is an evil (remember the remark that matches might not be in the correct ontology).

Final note: An alternative to the above would be to weaken (1) to the claim that everything that fundamentally exists is sustained by God, and hence everything that fundamentally exists is good insofar as it does so.

Big or small?

Isn't it interesting that we are currently don't know whether the fundamental physical entities are the tiniest of things—particles—or the largest of things—fields—or both?

The essential properties of our spacetime

Suppose that spacetime really exists. Name our world's spacetime "Spacey". Now, we have some very interesting question of which properties of Spacey are essential to it. Consider a possible but non-actual world whose spacetime is curved differently, say because some star (or just some cat) is in a different place. If that world were actual instead of ours, would Spacey still exist, but just be curved differently, or would a numerically different spacetime, say Smiley, exist in Spacey's place?

There are three different views one could have about some kind K of potential properties of a spacetime:

1. All the properties in K that Spacey has are essential to Spacey.
2. None of the properties in K are essential to Spacey.
3. Some but not all the properties in K that Spacey has are essential to Spacey.

Suppose K is the geometric properties. It's plausible that at least the dimensionality is essential to Spacey: if Spacey is four-dimensional, it is essentially four-dimensional. Any world with a different number of dimensions doesn't have our friend Spacey as its spacetime. If so, we need only to decide between (1) and (3).

Here is an argument for (3). Spacey's properties can be divided into earlier and later ones, since one of the four (or more) dimensions of Spacey is time. Further, according to General Relativity, some of Spacey's later geometric properties are causally explained at least in part by Spacey's own earlier causal influences. But if (1) were true, then Spacey would not have existed had the later geometric properties been different from how they are, and a part of the explanation of why it is Spacey that exists lies in the exercise of Spacey's own causal influences. But nothing can even partly causally explain its own existence. (Interesting consequence: If Newtonian physics were right, we might think that view (1) was true with respect to geometric properties. But this is implausible given General Relativity.)

Similar arguments go for the wavefunction of the universe, if it's a fundamental entity.

Essential properties and self-dependence

My being seated now is causally explained by my having sat down. Suppose that my being seated now is an essential property of me. Then, had I not sat down, I wouldn't have existed. So my very existence would have counterfactually depended on my own causal activity. But that would absurdly make me be something too much like a causa sui.

This seems to generalize into an argument for a general principle:

1. No property that counterfactually depends on an entity's own non-essential causal activity can be essential to that entity.

I needed to specify that the relevant causal activity is non-essential, because there is nothing deeply absurd about an entity that has some essential properties follow from causal activity that's essential to the entity.

But the form of argument that I used to get to (1) gives other results. For instance, a leading theory of personal identity holds that in cases where symmetric fission occurs—apparently, a person splitting into two—there were already two co-located people there before the fission. But why are there two people there? Presumably precisely because fissioning occurred—otherwise, there would have been only one.[note 1] Thus the existence of the two people is explained by the fission. But surely if fission is possible, it's possible that it be triggered by the non-essential action of the fissioning individual or individuals. In that case, then, the existence of the two people is explained in part by their very own activity. So this account of fission leads to something like self-dependence and should be rejected.

There may, however, be an objection to the argument. Suppose that the causal self-dependence is not fundamental. Instead, more fundamentally, we have a case where the whole depends on the contingent causal activity of a part. For instance, we may think that the length of an event is an essential property of an event. But the length of an event frequently depends on the contingent causal activity of a part of the event. (Thus, the length of World War II depends on the effects of D-Day, even though D-Day is a part of World War II.) In some such cases we might say that the whole depends on its own causal activity, since the causal activity of the part can sometimes be attributed to the whole.

I am not convinced. I think that in cases like this, it is incorrect to say that the whole depends on the whole's causal activity, but that it depends on the part's causal activity, and in this case the part's causal activity is not in fact correctly attributed to the whole.

In any case, the part-based objection will only apply in cases where the whole's causal activity is derivative from the part's causal activity. I think free choices are not derivative from the causal activity of anything other than the person as a whole, so in the fission case it's still impossible that whether there are two persons should depend on their choices. But this is rather controversial.

If there are cases where the whole depends on its own causal activity because its causal activity is derivative from a part's causal activity, then (1) needs to be qualified to apply to fundamental entities.

Four arguments that there must be concrete entities

An entity is concrete provided that it possibly causes something. I claim that it is necessary that there is at least one concrete entity.

Argument A:

1. The causal theory of possibility is true.
2. So, necessarily there is at least one concrete entity.

Argument B:

3. Necessarily, if there is time (respectively: space, spacetime, laws), there are concreta.
4. Necessarily, there is time (respectively: space, spacetime, laws).
5. So, etc.

Argument C:

6. Every possible fundamental fact can be reasonably believed (respectively: known).
7. Nobody can reasonably believe (respectively: know) there are no concreta.
8. Necessarily, if there are no concreta, then that there are no concreta is a fundamental fact.
9. So, etc.

Argument D:

10. Necessarily, if there is nothing concrete, the only fundamental contingent fact is that there is nothing concrete.
11. Necessarily, some fundamental contingent fact has a potential explanation.
12. Necessarily, that there is nothing concrete has no potential explanation.
13. So, etc.

And since, plausibly (though controversially),

14. If it necessary that there is a concrete entity, there is a necessary concrete being,

it follows that there is a necessary concrete being. And this some call God. :-)