Inter-level metaphysics

The quest for fundamental categories

Now, consider a world with not three, but only a pair of prima facie distinct sets of objects \(\mathbf{A}\) and \(\mathbf{B}\). We can broadly outline five relations:

• \(\mathbf{A}\) and \(\mathbf{B}\) form two fundamental categories of being: \(\{\mathbf{A}\mathbf{\parallel}\mathbf{B}\}\).

• \(\mathbf{A}\) is derived from \(\mathbf{B}\): \(\{\mathbf{A}\mathbf{\prec}\mathbf{B}\}\).

• \(\mathbf{B}\) is derived from \(\mathbf{A}\): \(\{\mathbf{A}\mathbf{\succ}\mathbf{B}\}\).

• Only \(\mathbf{A}\) exists: \(\{\mathbf{A}\}\).

• Only \(\mathbf{B}\) exists: \(\{\mathbf{B}\}\).

As much as we’d like to go from this general framework to more concrete matters, there’s still an elephant in the room to deal with. What in the world is "\(\prec\)"? We’d like this to denote a sense in which a class of objects is ontologically subsumed into another, which is then by definition more fundamental.

For instance, all laypersons and even most ontologists would agree that clouds exist. Yet presumably no one would argue that clouds constitute a fundamental category of being. Indeed, we all know that if air and water are present, clouds will form under certain conditions. This is due to a physical phenomenon, but bringing this back to ontology, it is reasonable to say that clouds are derived from air and water, or conversely that air and water are both more fundamental than clouds. In a more picturesque manner: once God had created air and water, He could rest easy: clouds would not require an additional act of creation.

Every cosmogony, every philosophical system, need to give an account, not only of what is in the world, but of what is fundamental. Empedocles doesn’t have much to say about the mental or the abstract, but he very cleanly outlines a four-category ontology: every bit of matter derives from air, water, fire or earth, and there’s no indication in his philosophy of a lower ground where those fundamental elements could merge. To take another example, the book of Genesis tells us that having animals roam the planet took an extra act of creation after the sun, the earth, the sea (and presumably all chemical elements therein) had been created. If God couldn’t just leave all the carbon, oxygen and hydrogen alone, waiting for animals to eventually develop, it thus means that something over and above was needed — some would call it a "vital force". To believe in that book’s teaching then seems to entail some form of vitalism.

Today of course, a majority of people, and most of the scientific and philosophical communities, would disagree with both Empedocles and the Bible. It is widely accepted that the biological derives from the chemical, which derives from the physical. In turn, "the physical" (that is, every thing or fact in the physical realm) is thought to derive from a single, yet unknown, theory describing both the physical universe and its elementary content in a unified way. No other physical object or kind can be deemed fundamental.

But let’s not get bogged down in these specific examples: they are familiar, but may mislead, as they correspond to a specific case called reduction (more on that later). I’d like to take a step back. To define the derivation relation \(\prec\) that will serve our purposes, I will rely on a much more general concept: that of metaphysical grounding. Instead of saying that "\(\mathbf{A}\) derives from \(\mathbf{B}\)", we will say that "\(\mathbf{B}\) grounds \(\mathbf{A}\)". The ultimate aim of the neo-Aristotelian approach would then be, following Schaffer, to answer the question: "what grounds what?".

An astute reader would not be unreasonable to ask: "so what?". Seemingly, I’ve done little more than taking the concepts of fundamentality and derivation, not very well defined but still quite comprehensible, and sticking the "ground" terminology onto them. And yet that choice is not entirely neutral: there really is something to this. The idea that some things are more fundamental than others has been boilerplate in metaphysics for millenia (hence the label "neo-Aristotelian"), but since then more rigorous formulations have been devised, especially by analytic philosophers in the past few decades. Those formulations are not equivalent, and picking out the grounding one as a reference for our discussions has import.

I will start by describing what metaphysical grounding is, as best I can, then I will compare and contrast it with other accounts of fundamentality. This hopefully should demonstrate in what way it differs and is more suited to my purposes. It’s important to bear in mind that debates about these various notions are on-going, and any form of consensus, even on definitions, is far on the horizon. I’ll try to give a fair account of prevalent views at the time of writing, but keep in mind, this is one of the more volatile areas of enquiries I’m writing about here.

Grounding

Grounding, a metaphysical primitive, is a many-to-one relation between facts that is a metaphysical form of non-causal explanation. It is irreflexive, asymmetrical, transitive, non-monotonic, intensional and factive.

Roughly speaking, one fact f is said to ground another g if g exists because f exists, or in virtue of f existing. In some sense, that f exists makes g exist. This is consistent with its explanatory nature, although of course this could lead to confusion with other forms of explanation, if the stage isn’t correctly set first.

Clearly, we still have some unpacking to do... But before going through these concepts one by one, let’s go straight to a few examples

• Parthood: This is steel because this contains iron.

• Set-membership: The set \(\{1\}\) exists because \(1\) exists.

• Quantification: The fact that someone is wise is grounded in the fact that Socrates is wise

• Determination: The fact that the dress is blue is grounded in the fact that the dress is indigo.

• Modality: Socrates is necessarily human in virtue of Socrates being essentially human.

• Disposition: Diamond is near-unbreakable in virtue of its crystalline structure.

• Aesthetics: The Fighting Temeraire is a beautiful painting in virtue of its physical characteristics.

• Ethics: Violence is wrong because it causes harm.

• Reduction: The soup’s temperature is \(T\) because its mean molecular kinetic energy is \(<k>\).

• Constitution: A statue existing is grounded in the shape of the clay it is made of.

This probably seems very generic. Someone who’s just discovering what grounding is may well wonder what does not qualify... Let’s start by unpacking our long definition: grounding is...

• A metaphysical primitive: by that I simply mean that grounding cannot be further analyzed or decomposed. It cannot be expressed in terms of propositions, properties, or other prior concepts. This shouldn’t, however suggest that idea is confused or unjustified — after all there must always be primitive concepts in any system.

• A relation between facts: this may seem like a hurdle. Didn’t we start out trying to define a relation between "realms" (sets or classes of objects)? This can be side-stepped by expanding the applicability of grounding to objects (which also avoids making an ontological commitment to facts) or just by re-phrasing our desiderata. We’ll come back to this important point after our unpacking exercise.

• Many-to-one: it seems uncontroversial to assume several things can ground another. Analyzing a simple disjunction can give an idea of why: "this marble is a blue sphere because it is blue and it is a sphere". Most facts are grounded in a multitude of more fundamental facts. If a fact has more than one ground, then each indivual one can be called a partial ground.

• Explanatory: we are used to view explanation through the prism of scientific causality, which links an effect (the apple falls) back to a cause (the Earth’s gravitational field) via a law (the law of gravitation). This has been expanded to build a general epistemic concept of explanation that relies on the same type of tripartite structure between result, source and link. In addition, there is an idea that explanation should make the existence of facts intelligible, which certainly has a taste of "you know it when you see it". This sharply distinguishes explanatory relations from merely modal or logical ones. One could say that for Caesar to have been assassinated, it was necessary for Caesar to exist. But this does not explain much. However saying that the assassination happened because Caesar’s power had grown too much, too fast, is an explanation. It is equally true that if Caesar was assassinated, then necessarily \(1+1=2\), but that explains nothing at all.

  We also need to introduce here the concepts of full ground and partial ground. A full ground has the capacity to fully explain a fact — this in itself, like explanation, is a brute concept, which we cannot analyze. Consider the idea that I have a weight in virtue of having a mass. That is only a partial ground. If the Earth wasn’t massive, then my having mass wouldn’t entail my having weight, so my mass alone is "not enough" to fully ground my weight. However, that soup has a certain temperature because of its mean molecular kinetic energy is a full ground.

  Since a ground has to be either full or partial, then a full ground is maximal, in the sense that it cannot be conjoined with another fact to form a ground. It is also key to note that a full ground is not unique. The fact there are wise people is grounded by Socrates being wise. But it is also grounded by Buddha being wise. Both are full grounds, since each one is a full explanation.

  In what follows, whilst using the notation \(f\succ g\), we will be referring to full grounding.

• Non-causal: as we’ve just said, causal explanation is the historical archetype of explanation as a topic of philosophical enquiry, but it’s not the only one. Some logical inferences can be considered as logical explanations (and are non-causal because mathematical objects are typically assumed to be causally inert): \(6\) is not a prime number because it is the product of two primes. Semantic relations are also non-causal: Martin is a sibling because he has a brother, but there is no cause nor effect here. In the case of grounding, we’ve further qualified it by calling it a metaphysical form of explanation. This can only be as precise as any definition of metaphysics can be, which is very little... This is also not exclusive of other kinds: grounding can also be causal, or logical. The aim is just to ensure that we keep the initial objective in our crosshairs: to give an account of what is fundamental, which is a metaphysically involving goal.

• Irreflexive: nothing can ground itself. Indeed, nothing explains itself; explanation needs to make a fact more intelligible, but it’s hard to see how the fact itself could. Pretty consensual on the surface, but important consequences can ensue, which is why the consistency of one’s definition of grounding with prior principles needs to be carefully considered. For instance, if you admit that a statue is grounded in its clay, you cannot at the same time posit — as some do — that the statue is identical to the clay.

• Asymmetric: grounding is directional. If f grounds g, then g cannot ground f. This is also what we’d come to expect form an explanatory relation, and is consistent with the idea that "f is (strictly) more fundamental than g", since all relations of this kind would be asymmetric.

• Transitive: it’s not nearly as intuitive that grounding should be transitive. Most notions of explanation involve some concept of proximity. Going through a backwards sequence of causes, I could find that my eating eggs for breakfast today was caused by the Big Bang. Yet that seems to be a poor case of explaining something. On the other hand, imposing a vague notion of proximity seems impractical and could make discussions of grounding much less nimble. Of particular interest, the combination of irreflexivity, asymmetry and transitivity would entail that grounding generates a strict partial order (SPO), a useful conceptual tool.

  In order to preserve grounding’s explanatory nature (without which, there’s not much to that relation at all), I’ll posit it’s not transitive (which of course doesn’t mean it’s never transitive). However I’ll also define a transitive extension of grounding which I’ll call sequential grounding: \[f\stackrel{\textrm{seq}}{\succ}g \hat{\iff} \exists (f_n) _{n \in \mathbb{N}}, f \succ f_0 \succ f_1 \succ \dots \succ f_k \succ g\] Obviously, sequential grounding is not explanatory, but it does generate an SPO.

• Non-monotonic: this property means that: \[f \succ g \not\Rightarrow (f \land f') \succ g\] For instance, that the ball is red grounds the fact that it is colored. But the fact that the ball is red and on the table doesn’t. This is consistent with the nature of explanation: adding an arbitrary fact that is non-explanatory makes the conjunction non-explanatory.

• Intensional: this is inherited from explanation and its asymmetrical nature. Let’s hark back to the canonical example. Facts about Venus and about Hesperus are co-extensional: the corresponding propositions have matching truth-values in every possible world. And yet, it is clear that Hesperus exists in virtue of Venus existing. Since Venus’s existence could not ground itself, this demonstrates that grounding provides an intensional context.

• Factive: saying that grounding is factive means that if f grounds g, then f and g exist. Pulling the thread further, this implies that the corresponding state of affairs obtain, and that every object thereby involved also exists. So somebody claiming that facts about brains ground facts about mental states could not be an eliminativist, denying that mental states exist. Factive grounding is, again, consistent with explanation. The state of affair "John Lennon living to be 80 year-old" does not obtain. The resulting fact doesn’t exist, so it’s hard to see what could "explain" it.

Let’s now take a step back and show, as promised, how the grounding concept could apply to whole classes of objects. The convention I’ll adopt is as follows: by stating that "the chemical is grounded in the physical", I really mean that "chemical facts are grounded in physical facts" and in turn, that "every individual chemical fact is fully grounded in physical facts".

Let’s call \(\mathbf{\varphi}\) the set of physical facts and \(\mathbf{\chi}\) the set of chemical facts, and assume that \(\varphi\) is closed under conjunction, i.e.: \[\forall (f_n) \in \varphi^{\mathbb{N}}, \bigwedge_n f_n \in \varphi\] Then more formally: \[\varphi \succ \chi \hat{\iff} \forall x \in \chi, [(\exists f\in \varphi, f \succ x) \land (\forall g, g\succ x \implies g \in \varphi)]\] (\(\varphi\)’s closure ensures that when we posit the existence of at least one full physical ground, it could well be a conjunction of physical facts, which can then be interpreted as a chemical fact having multiple partial physical grounds).

Circling back towards the notion of full and partial grounding, I need to highlight again how careful we need to be in using those. These are brute concepts, which outside of an "ideal" setting should be handled with the utmost care. Take a concept like "France". It seems easy to pick out partial grounds, such as "the territory of France", or "The French Republic"; but anyone would agree that a full ground is wholly un-expressable. Conversely, partial grounds are also hard to delineate. We can accept that something containing iron is a partial ground for being steel. We probably also could accept "being a metal" as a partial ground. But "being made of atoms" would surely be rejected as lacking any explanatory power. Despite the mathematical notation that we use as a formal tool here, grounding is not reducible to objective, demonstrable rules.

Other relations

I’m confident that the above examples of grounding and the discussion of its features have made matters a tad clearer already. Yet, the choice to use grounding specifically might still seem less than momentous. To remedy that, I propose to list a few other relations that are important in inter-level metaphysics, and to contrast them with grounding, with the hope that it will make its advantages more salient.

Entailment

is the simplest modal relation: necessarily if a dress is indigo, then it is blue. It is generally accepted that modal entailment is necessary for grounding: \[f \succ g \rightarrow \square (f \rightarrow g)\] However, it is clearly not sufficient for grounding. If a dress is indigo, then necessarily, a dress is an item of clothing. If a dress is indigo, then necessarily \(2+4=6\). But those inferences are in no way explanatory.

Supervenience

is a different type of modal relation that’s had its heyday in inter-level metaphysics. It is generally applied to properties rather than facts. The core idea is captured by the slogan "there cannot be an A-difference without a B-difference"; in that case we can say that A-properties supervene on B-properties. For instance, the thermodynamic properties of a system supervene on its physical properties: if all atoms in a gas are in the exact same state, the gas’s temperature, pressure, energy, entropy...will be the same. But the same thermodynamic state could be generated by distinct physical states. Supervenience is also a modal notion but it differs quite sharply from entailment. For instance, "being a brother" entails "being a sibling", but the latter doesn’t supervene on the former: if Alice is a sister and Bob an only child, none of them are brothers but they differ in sibling-ness.

Supervenience has been found lacking as the foundation of theses like physicalism. Mental properties’ supervenience over the physical is by most accounts necessary for physicalism, but its sufficiency is hard to establish. Malebranche’s psychophysical parallelism posits the existence of a soul that’s perfectly coordinated with the body (by God), without any causal efficiency of its own. This is compatible with supervenience, but could hardly be considered a form of physicalism.

With the benefit of our newfound knowledge of grounding, we can easily pinpoint the cause of such misgivings: as a modal notion, supervenience doesn’t evidence much more than the covariance of certain properties. It lacks the metaphysical and explanatory nature of grounding, as well as its directionality. What we gain in verifiability (unlike grounding, supervenience is not a brute fact), we may pay in the form of coarse-grainedness. In particular, supervenience is reflexive, and it is non-symmetric: for instance the properties that \(a\) exists and that \(\{a\}\) exists supervene on each other. There is no logical or modal reason to argue that the former grounds the latter, but that directionality is key to any metaphysical notion of fundamentality.

Ontological dependence

covers a family of relations between entities. The core idea is that something’s existence depends on something else existing, or exhibiting certain properties. The most common form is called existential dependence, and comes in rigid and generic flavours. The existence of a tennis match between Federer and Nadal depends on the existence of Federer and Nadal, and that relation is rigid (i.e. it involves specific particulars). Put another way, there cannot be a world where a match takes places with Federer as one of the players, and where Federer doesn’t exist. The existence of electricity depends on the existence of electrons, but that is not a rigid dependence; instead it is generic (it involves a class or a kind, the existence of one specific electron is irrelevant). Existential dependence appears to just be an ontological subset of modal entailment: it simply states the necessity of some entity’s existence for another to exist. In its most general form, it suffers from the same ills as other modal relations: Federer existentially depends on the number \(2\), because \(2\) is a necessary entity in the first place; Federer and \(\{\)Federer\(\}\) existentially depend on each other. Once again the lack of irreflexiveness and asymmetry are an impediment to the explanatory power we’re seeking.

That realization led, from the same non-modalist urge that brought about the revival of grounding, to forms of essential dependence being proposed, whereby the existence of an object does not merely necessitate that of another, it does so because of its essential nature. Essence is a whole topic in itself, but in short, essential properties are those without which an object couldn’t possibly be itself (unlike accidental properties). Rin Tin Tin is essentially a dog (there can be worlds in which a sheep or tortoise actor is named Rin Tin Tin, but there is little sense in which they could be deemed "the same animal"). So Rin Tin Tin essentially depends on the kind "dog". However, Rin Tin Tin only existentially depends on the set \(\{\)Rin Tin Tin\(\}\). Other canonical examples include holes and boundaries. Cheese holes essentially depend on the existence of cheese. The boundaries of France essentially depend on France.

Reduction

is generally invoked as an epistemic thesis. Roughly speaking, a theory is said to be reducible if its conceptual resources (laws, kinds, types, properties...) can be derived from those of another, more fundamental theory. Nagel, who formalized this concept, started from the well-known fact that, in the history of science, more inclusive theories tend to replace antecedent, less inclusive ones by absorbing their laws and covering the same observational phenomena. A so-called primary science (the reducing theory or base theory) then reduces to a relatively autonomous secondary science (the reduced theory, or target theory). For instance, thermodynamics reduces to statistical mechanics, optics reduces to electromagnetism, and Mendelian genetics (the study of genes and alleles) reduces to molecular genetics (the study of DNA genetic code). Following a series of successful reductions, reductionism has become an intentional research program in many a field. However, it’s important to bring some nuance. First, I’ll highlight that reduction comes in many flavours, with two overarching categories:

• Bridge reduction, as I would call it, purports to match basic concepts directly. Light (from Augustin Fresnel’s physical optics) is an electromagnetic radiation (from J.C. Maxwell’s model). This would be called a bridge principle (or coordinating definition) in the context of Nagelian views. Such bridge laws, which can be borne out of arbitrary postulates or of empirical fact, are meant to permit a full derivation of the reduced theory (direct reduction) — or an approximation thereof (indirect reduction) — by sheer logical deduction. Indeed, descriptive terms specific to the reduced theory can be paired with those from the reducing theory in such a way that the resulting descriptions co-refer.

• Functional reduction instead purports to replace the bridge-law concept with "functionalization". First, one would define concepts from the reduced theory in terms of the role they play, which is generally a causal role, but could also be relational, or teleological. For instance, the type "gene" cannot be defined as a token-sequence of nucleotides (that would be a token-gene), nor as a generic sequence of nucleotides (which is way too general — a random sequence is extremely unlikely to match a gene). Instead it is usually defined in terms of its function: that of encoding the synthesis of a certain RNA molecule or protein. The second step is to identify the realizers of the functionally defined concepts — in this example, DNA molecules. Lastly, the reducing theory needs to explain how the realizers can indeed fulfill that function.

Whether such distinctions even make sense is a matter of debate: there is a good case to be made that the line between bridge and functional reduction is much finer indeed than how I’ve made it appear. I’ll leave that question to rest and shift the focus from the epistemic nature of theory reduction back to the metaphysical approach. Grounding is about facts. Reduction is ostensibly about theories, which are sets of facts of a specific nature (that topic alone is the subject of a whole literature; for now, suffice it to say, following Nagel, that theories are "formalized" sets of facts). Theories are definitely a narrower lens to consider reality with, but it seems reasonable to at least assume that reducing a theory to another does entail metaphysical grounding between certain facts. For instance, from the reduction of thermodynamics to statistical mechanics, we can conclude that "the water in this pot becomes warmer" is grounded in "the mean kinetic energy of the water molecules increases".

Is "reduction grounding" full or partial? It’s tempting to stipulate that a "good" reduction process should entail full grounding. But that may be setting a high bar. Nagel’s bridge-law model and Kim’s functional reduction both seek to impose rigid principles... in the abstract. The more detailed study of actual cases in the decades that followed have led to more skepticism that such spotless reductions were demonstrably prevalent. In some cases, we are indeed close to that ideal. Both Kepler’s laws of planetary motion and Galileo’s law of free fall seem to "neatly" reduce to Newton’s classical mechanics, or more precisely to its restriction to a non-universal scope (respectively, astral bodies orbiting in a vacuum around a much heavier Sun, and objects at a low altitude above a planet’s surface — relatively to that planet’s radius). Both derivations are straightforward, and staples of undergraduate physics courses, but are still indirect reductions since the reduced theories’ results can only approximate Newtonian physics. Kepler’s first law stated that a planet’s orbit was necessarily elliptic. Newton understood that this was true only of two-body systems with a large mass disparity. Thus even in that quasi-ideal case the grounding is only partial. The orbits from all planets in the Solar System are near-elliptic, in virtue of Newton’s theory, but also of the fact that planets are always fairly distant from one another and of the Sun’s very large mass compared to each planet.

Are all reductions approximate and imperfect? Direct reductions can easily be found, but there is often a fine line between those and simple reformulations. Classical electrostatics reduces to Maxwell’s electromagnetism, but Maxwell’s first law is literally identical to Gauss’s law for the electric field, which itself is a mathematical translation (from the point-charge picture to the field picture) of Coulomb’s law.

On the other hand, many inter-theoretic relations that are commonly seen as "good" reductions are decidedly less than. Thermodynamics to statistical mechanics is often bandied about as the archetype of reduction, including by Nagel himself. The ideal gas law, and more, can be readily derived. But the second law cannot, nor bodies’ behavior under phase transitions. To take another case, it is an oft-repeated tenet that classical physics reduces to quantum mechanics by way of the "semi-classical limit". A closer examination shows how hand-wavy that is. One procedure involves varying the constant \(\hbar\), the other describes a classical point-particle as a dense wave packet with relatively well-defined position and momentum. Both are subtle comparisons between theories, by way of mathematical analogies, rather than explanations of classical behavior in a realistic context.

Does that mean we could make a serious case that phase transitions or Newton’s laws of motion are fundamental laws of our universe? Not either, definitely. But it highlights that the type of reduction that may underpin full grounding is nary a common occurence. As such, some form of reduction relation between theories may be a guiding light, but little more. The idea that chemistry can reduce to quantum mechanics is certainly common, but also has also come under heavy challenges. You would be hard-pressed finding anyone to argue the point that a complete reduction can be achieved given the current shape of the two theories. And yet, given the undisputed fact that all chemical objects are mereologically composed of quantum-mechanical objects, it seems reasonable to posit some form of metaphysical reduction, which contains the potentiality of a future epistemic reduction, and directly entails full metaphysical grounding.

Now there is still one point I’ve somewhat sidestepped. Grounding, at least, following my own exposition, is factive; for reduction to entail grounding, the reduced theory’s whole conceptual apparatus needs to exist. Naturally, the question only makes sense in a metaphysical context. The continued use of objects and properties from the epistemically reduced theory is strictly motivated by pragmatic judgment: phlogiston and aether were discarded, while Newton’s gravitational force is still put to much more use than its successor. The ontological question is bound to arise when a relation of metaphysical reduction is assumed, and is likely orthogonal to the realization of that reduction. Two directions of travel appear:

• Eliminative reduction is true to its word: it reduces the overall number of theories or entities by dispensing with the target theory altogether. Naturally, this position can be entirely predicated by broader attitudes: a mereological nihilist would of course not accept that molecules may have a place in our world’s ontology.

• Retentive reduction, on the other hand, tends to conserve the entities and properties to be purportedly reduced.

As a closing point: the interaction between theory reduction and metaphysical grounding is far from straightforward, though it should be clear by now that reduction, when it exists, is stronger in general than grounding, and should certainly entail "some" form of grounding (and not the other way around: grounding is nimble enough to accomodate all sorts of non-reductive approaches).

Emergence

is a broad umbrella of a term, that has been common currency in philosophy of science since J.S. Mill and C.D. Broad developed their "emergentist" theses. Nowadays, this frequently encompasses weak emergence, which merely affirms the reality of emergent phenomena and properties. This is usually accompanied with a support for some special science as the only accessible level of enquiry to explain the emergent entities. Therefore, weak emergence is entirely compatible with retentive reduction from a metaphysical perspective: at no point does it deny that the "emergent theory" could possibly be reduced to some base theory. The nuance resides in the suggestion that this reduction is not provable now — epistemic reduction may not be achieved, but metaphysical reduction can be accepted all the same.

Strong emergence is much closer to what the original Emergentists had in mind. It maintains that the emergent properties of complex objects or phenomena are not determined by the intrinsic or relational properties of their components, but that conversely, emergent properties can affect the behavior of those components. The latter phenomenon, called downward causation or macro-determinacy, implies that the "higher level" can be causally efficacious towards the "lower level". This sets up strong emergence to be a firmly anti-reductionist, anti-functionalist thesis. On the opposite side, emergentism is often assumed to be a monist position: it still posits that one substance is fundamental — even though the emergent properties are largely autonomous, they are not taken to delineate a separate domain of being.

This means that emergence entails supervenience; indeed, the absence of a supervenience relation is often conventionally taken to imply dualism. However, strong emergence cannot entail full grounding, since the emergent properties cannot be fully explained by more fundamental ones..

28 solutions

This voyage through inter-level metaphysics should, or so I hope, showcases the diversity of notions that are often conflated. At the same time, it highlights the lack of consensual definitions; and because those definitions often differ in the objects they involve or the methods they adopt (modality, sui generis characterization,...), direct comparisons are difficult. The objective of the present work is not to develop a rigorous treatment of such questions, so we need to accept this imprecision. This was not all for naught though, as I feel able to draw the following conclusions:

• Reduction (eliminative, bridge, functional) is a stronger thesis than metaphysical grounding.

• Essential dependence is a metaphysical thesis whose relative strength versus grounding is indeterminate (in the present work).

• Modal relations (existential dependence, supervenience, entailment) are weaker theses than metaphysical grounding.

• Emergence, weak and strong, is a mediating notion conjoining reduction and dualism that ranges over this whole spectrum.

As alluded to at the outset to justify the focus on grounding, that relation will be taken as a litmus test and a characterization of fundamentality in what follows. Thus, "\(\mathbf{A}\) is derived from \(\mathbf{B}\)", or \(\{\mathbf{A}\mathbf{\prec}\mathbf{B}\}\), will be conventionally equivalent to "\(\mathbf{B}\) grounds \(\mathbf{A}\)".

Furthermore, supervenience will be considered to be the outer reach of monism: any situation where \(\mathbf{A}\) does not supervene on \(\mathbf{B}\) (i.e. \(\mathbf{A}\)-changes are observed without any \(\mathbf{B}\)-change) must imply some form of ontological distinctness of \(\mathbf{A}\). No supervenience then implies clear dualism \(\{\mathbf{A}\mathbf{\parallel}\mathbf{B}\}\), while grounding and a fortiori stronger relations like reduction imply that monism is true \(\{\mathbf{A}\mathbf{\prec}\mathbf{B}\}\). Relations weaker than grounding but stronger or equal to supervenience are then in an intermediary state of ontological indeterminacy, and can be compatible with both monist or dualist outlooks (epiphenomenal dualism about the soul being a prime example).

At last we can circle back to our 3 realms: physical objects (realm \(\mathbf{1}\)), mental states (realm \(\mathbf{2}\)) and abstract entities (realm \(\mathbf{3}\)).

There are twenty-eight ways to represent how they relate to each other under this framework:

Rather than consider the twenty-eight one by one, I will analyze the issue into its two components:

1. The mind-body problem: What is the relation between \(\mathbf{1}\) and \(\mathbf{2}\)?

2. The problem of universals: What is the relation between \(\mathbf{3}\) and the \(\mathbf{1}\)-\(\mathbf{2}\) dyad?