The Atlas of Reality
Page 9
3. Catching “cheaters” Yes Arguably by supervenience Arguably, by supervenience Arguably, by supervenience
4. Simple Combinatorial Theory of Possibility Yes Yes Yes No
5. Causal relata Yes Only for positive causation No No
6. Identifying fundamental truths No Yes Yes No
We have postponed a discussion of some issues directly relevant to various truthmaker theories until later portions of the book (e.g., the nature of the causal relation, the issue of so-called ‘natural’ properties and relations, the question of just what facts might be). And issues about truthmaking will continue to crop up throughout later chapters. In particular, Part II takes up one area where truthmaking looms large: conditional statements, powers, and laws.
In the next chapter (Chapter 3), we will look at a way of extending the idea of fundamentality beyond the relation between propositions into the world itself, through the idea of metaphysical grounding or explanation.
Notes
1. Philosophers distinguish between types and tokens. Standardly, tokens are time- and place-specific instances of some type of thing. For example, in the following list, there are two tokens of a single word type: BEN, BEN. An individual cat is a token of the type, CAT. And so on.
2. Some philosophers would question whether a single group of things, the propositions, really does play these two roles. David Lewis (1986a) famously did so, arguing that the roles were at cross-purposes.
3. It is important to note that Aristotle's use of ‘cause’ here is not limited to so-called ‘efficient’ causation, that type of causation involved when a baseball causes a window to break or when one billiard ball causes another to move.
4. We'll consider an alternative to the Correspondence Theory—the deflationary theory of truth—in Section 2.3 below. While there are alternatives to both the Correspondence and deflationary theories, notably the ‘coherence’ and ‘pragmatic’ theories, we believe the two we consider are the only theories with much hope for success at the end of the day. Thus we ignore their alternatives.
5. This argument assumes that if something is a truthmaker for a proposition, then it is essentially so. In other words, it assumes that if something x makes it true that grass is green in the actual world, then x makes it true that grass is green whenever x exists. As we shall see below, this is exactly the step that will be challenged by defenders of Spectral Truthmaker Theory.
6. See Section 9.3.1.1 for a further discussion of intrinsicality.
7. There is a possible intermediate position, in which there is no one property of truth, but rather a finite number of distinct kinds of truth (such as, perhaps, physical truth and historical truth). We will count such a position as a version of anti-deflationism. Thus, we will assume that the deflationist denies that there is either a single property of truth or a finite number of such properties. We'll simply ignore the view according to which there are an infinite number of fundamental properties of truth, since such a theory would involve an egregious violation of Ockham's Razor.
8. In fact, we might even consider the possibility that some universals do have more than one associated totality fact, resulting in a kind of ontological indeterminacy or even inconsistency, that could be useful as a model of vagueness (see Chapter 12.2.2). Perhaps the universals that are of most interest and use to us (especially in science) are the ones that tolerate no more than one totality fact.
9. A first-order universal is a universal instantiated by ordinary objects; higher-order universals are instantiated by other universals.
10. Why can we limit ourselves to first-order universals? What can we do about uninstantiated higher-order universals. It is plausible that there are no such uninstantiated higher-order universals to worry about. All universals have their properties essentially, and it is plausible to suppose that they all exist necessarily. If so, all higher-order universals will have their non-empty classes of instances essentially.
11. Why weakly supervenes? Philosophers have defined a family of supervenience relations. Jaegwon Kim (1993) was responsible for classifying them into weak and strong versions.
12. This assumption was not entirely unwarranted, since it is plausible to think that truthmakers will have a metaphysical structure that mirrors the syntactic structure of the truth it makes true.
3
Grounding, Ontological Dependence, and Fundamentality
Metaphysicians seek to understand the world, and a large part of that project is building an ontology: a theory of what exists, and of what those existing things are like. However, metaphysicians have traditionally sought more than this. They have also sought to uncover the fundamental structure of reality. This includes understanding what depends upon what, and how.
In addition, metaphysicians want to know, not just what exists, but what exists most fundamentally and really. These last two tasks may be closely related. It may be that what most fundamentally or really exists are those things that exist independently, and upon which all other things depend. At the very least, it seems clear that what exists fundamentally cannot depend for its existence on things that do not exist fundamentally. So, a theory of metaphysical dependence would greatly constrain our theory of what is fundamental.
Finally, as we have seen, an appeal to ontological parsimony or economy (PMeth 1) plays an important, perhaps indispensable, role in evaluating metaphysical theories. However, we want to minimize our ontological commitments to fundamental entities, not to derived ones. At the very least, economy with respect to fundamental entities seems to be of much greater importance than economy with respect to less fundamental ones:
PMeth 1.0 The Zeroth Corollary of Ockham's Razor. Other things being equal, prefer the theory that posits the smallest number of fundamental entities.
In recent years, many metaphysicians, following the lead of Kit Fine, have used the term ‘grounding’ to represent a relation of metaphysical dependency: if x is grounded in y, then x (in a certain sense) depends upon y, for its existence, or truth, or nature. We could identify fundamental entities or truths with those that are not grounded in other entities or truths, either by being absolutely ungrounded or by being in some special way grounded without being grounded in or by anything.
Some new terminology will aid the present discussion. If x grounds y, call x the ‘fundans’ (plural: ‘fundantia’) and y the ‘fundatum’ (plural: ‘fundata’), from the Latin verb ‘fundare’, to found or ground.
There are a number of different theories about what the relation of grounding is like. They are not all pair-wise incompatible. Some of these theories may be combined, others cannot. We can identify at least three conceptions of grounding:
(1) Grounding is a kind of explanation: the metaphysical explanation of some facts or truths in terms of others.
(2) Grounding is a relation of dependency between entities that is generated by the essences or real natures of those entities: x depends on y just in case y occurs as a constituent within the definition of x's essence or real definition. We will call this relation ‘ontological dependence’.
(3) Grounding is a relation of constitution or construction between entities: x depends on y just in case x is constructed from y, or y is an essential element in the constitution of x.
In this chapter, we focus primarily on the first conception of grounding, grounding as metaphysical explanation. We also discuss briefly (in Section 3.4) the relation of ontological dependency and its connections with grounding as explanation. We set aside the third conception, primarily because it presupposes an answer to a question that we examine critically in future chapters, namely, do wholes always depend on their parts, or are there cases where a part can depend upon some whole to which it belongs?
If grounding is a kind of explanation, what kind of explanation is it? Jon Litland (2013) suggests that it is a matter of explaining how something is the case. When p grounds q, that p is the case is a way for q to be the case. As we shall see, this talk of ‘what is the case’ can be understood
in either of two ways: (i) in a conceptual or logical way, explaining the truth of one proposition in terms of the truth of other propositions, by reference to the essences of the conceptual components of the propositions involved, or (ii) in a purely ontological way, explaining the existence of one fact or the actuality of some state of affairs in terms of other facts or arrangements of things in the world. We investigate both conceptual and ontological grounding in Section 3.5.
We also explore (in Section 3.2) the relationship between grounding and truthmaking. Can one be defined in terms of the other? Do they form a kind of inter-definable circle? Is there any reason to prefer one over the other? We also consider various alternatives or competitors to grounding theory in Section 3.3.
Sections 3.6 through 3.8 take up several important questions about grounding:
Can facts about grounding themselves be grounded? (3.6)
Do grounds entail what they ground? (3.7)
How is grounding different from causal explanation? (3.8)
We conclude in Section 3.9 by examining the connection between grounding, fundamentality, and Ockham's Razor (PMeth 1). We also point to some recent literature on the formal properties of grounding (transitivity, asymmetry, and well-foundedness).
3.1 Is Grounding Real?
In this section, we consider whether there is any reason to think that there is such a thing as grounding or metaphysical explanation.
3.1T Real Grounding. There is a relation of metaphysical grounding.
There are several reasons for thinking so, which we take up presently.
3.1.1 Connections with natural language
The notion that some facts are grounded in others is a matter of common sense, well marked in the conventional features of natural language. In English, we express a relation of grounding by means of expressions like ‘by virtue of’, ‘in virtue of’, ‘thereby’, and ‘makes’ (in a certain sense).
(1) Four is an even number by virtue of its divisibility by two.
(2) The word ‘wounded’ is in the past tense in virtue of its ‘-ed’ ending.
(3) Mary crossed the finish line first and thereby won the race.
(4) Jamie's valid election to the office makes her the president of this club.
Latin actually has a separate case, the ablative case, to capture just this sort of meaning. It is important to note that none of these cases seems to involve a cause-and-effect relationship between two events or conditions. Being divisible by two doesn't cause four to be even. Two's evenness just consists in it being divisible by two. Similarly, it would be odd to say that Mary's crossing the finish line caused her to win the race. The causes of her winning must be separate, typically earlier events and conditions, like her rigorous training regimen or her well-regulated diet. To cross the finish line (in the right circumstances) just is to win the race.
3.1.2 Plausible examples of grounding
There are many actual cases that seem to be cases of grounding between facts or between other kinds of entities. Jonathan Schaffer (2009) gives some examples:
A singleton set, like {2}, the set containing just the number 2, is grounded in the existence of its member. The set exists, at least in part, because its member exists, but the member does not seem to exist because the set exists.
The shape or topological form of a piece of Swiss cheese is the ground for the existence, the number, and the arrangement of its holes. There is an obvious asymmetry here. Bits of Swiss cheese can exist and have a definite shape without any Swiss-cheese holes, but Swiss-cheese holes cannot exist in the absence of Swiss cheese. However, even if we consider holey Swiss cheese (which by definition cannot exist without holes), it still seems clear that the holes depend on the location of the bits of cheese and not vice versa.1
The existence and shape of a heap of sand depends on the existence and the location of each of the grains of sand that make it up. Even though it may be true that the location of some grains of sand can be causally explained by the locations of other grains, it would be very odd to think that the location of all the individual grains consists in or depends on the overall shape of the heap, instead of the other way around.
Consider the property of being made of wood or aluminum. The existence of this complex property presupposes (in some sense) the prior existence of the properties of being made of wood and of being made of aluminum. In addition, to have or instantiate the complex property just is to have one or the other of the simpler ones. All of the facts involving the instantiation of the complex properties can be derived from facts about the instantiation of the two simpler components.
We argued, in Chapter 2, that in some cases the truth of a proposition is grounded in the existence of a truthmaker. The truth of the proposition that atoms exist is explained by the existence of atoms, not vice versa.
Jaegwon Kim (1994) noted other cases involving determination without causal determination. Given the right social context and conventions, one's signing a check is a way of paying a debt that one owes another. One's signing the check does not cause the debt to be discharged, though in some sense, it is the discharging of the debt. And yet, there seem to be two facts here. First, there is the fact that one signed the check, and second, there is the fact that one paid the debt. One could have paid the debt in many other ways, but as things actually turned out, one paid the debt by signing the check. One's signing the check was the way in which one paid the debt. The relation between these two facts seems to be one of metaphysical grounding: the paying of the debt is grounded in the signing of the check.
3.1.3 Philosophical debates that turn on grounding claims
Debates about grounding are a recurring theme in the history of Western philosophy. This has been especially true in the field of moral philosophy or ethics. To take a famous example, let's consider Plato's dialogue, the Euthyphro (Plato 1997: 1–17). In this dialogue, Socrates and Euthyphro are seeking the definition or essence of piety. They agree that every holy (pious) act is loved by the gods, and that everything that is loved by the gods is holy. However, Socrates is not satisfied with this extensional coincidence: the fact that the same acts that can be called ‘holy’ are loved by the gods is not enough to make being loved by the gods the definition of holiness. He wouldn't be satisfied even if it turned out that the two properties are necessarily coincident (which logicians call intensionally equivalent). Instead, Socrates wants to know if an act is holy because it is loved by the gods, or if the gods love an act because it is holy. Plato seems to be investigating a question of grounding: is the holiness of an act grounded in the gods' love of it, or is the gods' love of it grounded in its holiness?
Much of Aristotle's metaphysical method also presupposes the existence of a grounding relation. He assumes in the Metaphysics (Aristotle 1984: 1552–1728) that when we have discovered the definition of a species in terms of a genus and a differentia, then the fact that something belongs to that species is grounded in its belonging to the genus and its having the differentiating feature. This is true even when the membership in the species coincides exactly and necessarily with the class of things possessing the differentia. For example, if the correct definition of the class of mammals is hairy animal, then a dog's being a mammal is grounded in its being an animal and in its being hairy, even if being hairy and being a mammal coincide in extension. It would still be the case that being mammal is partly grounded in being hairy, and not vice versa.
The concept of grounding is also needed to make sense of debates in more contemporary philosophy. For example, moral philosophers ask whether the right is grounded in the good. Are reasons grounded in other normative truths, or vice versa? Are legal facts partly grounded in moral truths? Questions of grounding arise in epistemology as well. Is the fact that a belief is justified always partly grounded in other beliefs that one has, or can it be wholly grounded in one's experience, or can it be totally ungrounded?
3.1.4 Fruitfulness of grounding
As Schaffer (2009) points out, the no
tion of grounding can be very useful for defining other metaphysical notions. For example:
x is fundamental = x is not grounded by anything
x is derivative = x is grounded by something
x is an integrated whole = x wholly grounds each of x's proper parts
x is a mere heap = x is wholly grounded by its proper parts
We could also define fundamental truths or facts as those that are ungrounded, or perhaps either ungrounded or “zero-grounded,” as Kit Fine (2012a: 47–48) says, meaning grounded by the null or empty set of facts).
If we take the relation of grounding between facts or truths as fundamental, we could perhaps define a relation of grounding between other entities in something like the following way:
Def D3.1 Entitive Grounding. Entity x (entitively) grounds y if and only if y's existence and all of the facts intrinsic to y are wholly grounded in the fact of x's existence and all of the facts intrinsic to x.
We can also use grounding (as an explanatory relation between facts) to define which properties or facts are intrinsic to an entity, as we did in Chapter 2:
Def D2.3 Intrinsicality. x is intrinsically F if and only if nothing that is not x or a part of x is part of the ground of x's being F.
Grounding as a relation between facts is normally taken to be factive: that is, if the fact that p grounds the fact that q, then both p and q are true. On this conception, if the shape S of the Swiss cheese grounds its having seven holes, then the cheese really does have shape S and seven holes. We could also introduce a non-factive grounding relation between propositions or possible facts. Proposition p non-factively grounds proposition q if and only if it is possible that p (factively) grounds q. (Or, perhaps, it is necessarily true that if p and q are both true, then p factively grounds q. The two definitions are probably equivalent. See Section 3.7.) If we instead take non-factive grounding as primitive, we could define the factive grounding of p by q in this way: p and q (are both true), and q non-factively grounds q.