The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  Quietists (e.g., Chisholm, Plantinga, van Inwagen) believe in properties as abstract objects, but they do not believe that properties ground the character of particular things. Instead, they suppose that a particular instantiates a property like whiteness because it is white. For this reason, we classify Quietists as Ostrich Nominalists. Quietists tend to believe in the objective truth of many subjunctive conditionals, but they typically do not give a reductive account of such truth in terms of possible worlds or causal powers. Plantinga (1974: 45–48), for example, treats the truth of counterfactual conditionals as an undefinable primitive, and uses such conditionals in his explication of notions like ‘true-in-a-world’ or ‘exists-in-a-world’. Thus, we have classified Quietists as Hypotheticalists, but not as Strong Hypotheticalists, since Quietists don't aspire to offer accounts of powers or laws in terms of counterfactual conditionals. Most Quietists, including both Plantinga and van Inwagen, are ardent Actualists, and they favor Magical Abstractionism with Anti-Indexicalism and Transworld Identity as the best account of modality. We have attributed Organicism to the Quietists, treating van Inwagen's Material Beings (1990a) as a paradigm of Quietism. On other issues, we have assigned what we take to be the most common-sensical position, including Tensism, Endurantism, and Body-Space Dualism, but these would seem to be quite optional for the package as a whole.

  In the following two tables we record appeal by each of the first three packages to each of our metaphysical principles (as tabulated in Appendix B). We list which specific theses associated with the package an argument for which included the principle as a premise. In this way, we can see clearly the methodological and foundational differences among the three approaches.

  All four packages rely, to a considerable extent, on Imagination as Guide to Possibility. This is not surprising, given the central role of thought experiments within analytic philosophy generally. Aristotelians also rely very heavily on Patchwork Principles, as an adjunct to imagination in exploring modal space.

  Ludovicians rely on just four sources of information: Ockham's Razor, scientific realism, Imagination as Guide to Possibility, and the principle that Truth Supervenes on Being. Fortibracchians are very similar in methodology to Ludovicains. In practice, Fortibracchians give more weight to a kind of naive realism with respect to scientific theory than do Ludovicians. That is, they tend to take the ontology of science at face value, leading to Classical Endurantism, in contrast to the Ramsey-Lewis-Sider Perdurantism of the Ludovicians.

  Quietists are quite different. They rely almost exclusively on a priori intuitions and common sense.

  Aristotelians represent a hybrid of the two methodologies. They rely strongly on Ockham's Razor and on the correspondence theory of truth, but they also strongly respect common sense and a priori intuition, especially intuition about the essences of material things.

  Which package is most likely to be true? Obviously, our answer to this question will depend in large part in how much weight we give to the various sources of evidence, which is a matter of good judgment, rather than mere logical acumen.

  Of course, the evidence we have surveyed in this book is not the final word. Our ability to ascertain the truth will improve as we understand more fully the implications of the theses in question, and as we gain more insight into the significance of what we already know. We hope that this book will be a stimulant to further metaphysical research. We have attempted to bring the reader as close as possible to the state of the art in metaphysics while presupposing very little prior knowledge of the field.

  Appendix A

  Metaphysical Theses and Antithesis

  In this appendix, we have compiled the theses and anti-theses discussed throughout the book. Though the theses are arranged according to the chapters in which they appear, they are not always listed in the order of their appearance in the book. Rather, they are arranged here to display their relative structure: sub-theses (like 2.1T.1T and 2.1T.1A) are therefore listed immediately following their respective theses (2.1T). Each of the entries in this appendix has a corresponding entry in the index, allowing the reader to identify where in the text these theses are discussed

  2. Truthmakers

  2.1T Classical Truthmaker Theory. There are classical truthmakers for all truths, or for some very large sub-classes of truths. 2.1T.1 Truthmaker Maximalism. Every truth has a strict truthmaker.

  2.1T.3 Totality Fact Maximalism. Every true proposition has a truthmaker, which includes one or more totality facts, possibly together with one or more ordinary existing things. Each universal is associated with at most one totality fact.

  2.1T.4 Atomic Truthmaker Theory. Every atomic (simple, positive) truth has a (classical) truthmaker.

  2.1A No Classical Truthmaker. Few, if any, truths have classical truthmakers. 2.1A.1T Non-Classical Truthmaker Theory. Metaphysical Fundamentalism is true, and propositions are made true by the way things are in the world, but there are no truthmakers. 2.1A.1T.1 Spectral Truthmaker Theory. Every fundamental atomic truth is made true by something's existing and being a certain way intrinsically.

  2.1A.1A No Truthmakers. Truths have no truthmakers, classical or otherwise. 2.1A.1A.1T Truth Supervenes on Being. The property of being true weakly supervenes on the property of being a truth about what things exist (and don't exist) and about exactly which natural properties they have and which natural relations they stand in.

  2.1A.1A.1A Truth does not supervene on being.

  3. Grounding, Ontological Dependence, and Fundamentality

  3.1T Real Grounding. There is a relation of metaphysical grounding. 3.1T.1T Indefinable Grounding. Grounding is a unique and indefinable relation. 3.1T.1T.1 Conceptual Analysis and Indefinable Grounding. Grounding is not definable in terms of conceptual analysis.

  3.1T.1T.2 Theoretical Reduction and Indefinable Grounding. Grounding cannot be defined in terms of theoretical reduction.

  3.1T.1T.3 Ontological Reduction and Indefinable Grounding. Grounding cannot be defined in terms of ontological reduction.

  3.1T.1T.4 Supervenience and Indefinable Grounding. Grounding is not definable in terms of metaphysical supervenience.

  3.1T.1A Definable Grounding. The grounding relation is definable in terms of other relations.

  3.3T Truthmaker to Grounding Link. The fact that p (wholly) grounds the fact that q if and only if: (i) p & q, (ii) the truth of p necessitates the truth of q, and (iii) necessarily, if p & q, then every truthmaker for p is a truthmaker for q. 3.3T.1 Generalized Truthmaker to Grounding Link. The facts corresponding to set Γ of propositions (wholly) grounds the fact that q if and only if (i) q and every member of Γ is true, (ii) the joint truth of the members of Γ metaphysically necessitates the truth of q, and (iii) necessarily, if both q and every member of Γ are true, then, for every p in Γ, every truthmaker for p is contained in (is a part of) a truthmaker for q.

  3.4T O-Fundamentality Entails G-Fundamentality. Necessarily, all O-fundamental entities are also G-fundamental. 3.4T.1 Formality of Grounding. Whenever p grounds q, there exist forms Φ and Ψ such that (i) for some x, p = Φ(x) and q = Ψ(x), and (ii) for all true propositions r and s such that for some y, r is Φ(y) and s is Ψ(y), the fact that r grounds the fact that s.

  3.4T.2 Mediation of Grounding by Essence. Every grounding fact of form (ii) (in Formality) is itself grounded in or derivable from some essential truths about the constituents of forms Φ and Ψ.

  3.5T.1 Grounding-Essence Correspondence. The fact that p grounds the fact that q if and only if (i) p & q, and (ii) some generalization of the form For all x, if p(x), then q(x) follows logically from the essences of p and q, together with the essences of things that the facts p and q contain.

  3.5T.2 Plural Grounding-Essence Correspondence. The facts that p1, that p2,…, and that pn jointly ground the fact that q if and only if (i) p1 & p2 &… & pn & q; (ii) some generalization of the form For all x, if p1(x) & p2(x) &…. & pn(x), then q(x) follows logically from the essences of p1, p2,…, pn, and q, together with th
e essences of things that the facts p and q contain; and (iii) if n = 1, i.e., there is only one grounding fact, then p1 ≠ q.

  3.6T Conceptual-Grounding to Essence Link. The truth of the proposition p grounds the truth of the proposition q only if p and q are both true, and if p, then q follows logically from the essence of the conceptual and logical elements of the propositions p and q.

  3.7T Distinct Fundamental Properties. F-ness and G-ness are distinct fundamental properties if and only if it is necessarily the case that, for any x, a truthmaker for the proposition x is F is distinct from any truthmaker for the proposition x is G.

  3.8T Grounding-Entailment Entailment. Necessarily, if the fact that p grounds the fact that q, then p metaphysically entails q (i.e., necessarily if p is true, then q is true).

  4. Conditionals

  4.1T Hypotheticalism. There are fundamentally conditional or hypothetical truths.

  4.1A Anti-Hypotheticalism. All conditional truths are grounded in non-conditional categorical facts.

  4.2T Nomic Fundamentalism. Some truths about the laws of nature are fundamental.

  4.2A Nomic Reductionism. No truths about the laws of nature are fundamental.

  4.3T Power Fundamentalism. Some truths about the powers of particular things are fundamental.

  4.3A Power Reductionism. No truths about powers are fundamental.

  4.4T Neo-Humeism. None of the truths of counterfactual conditionals and none of the truths about laws of nature or about the powers of particulars are fundamental.

  4.4A Anti-Humeism. Some truths about counterfactual conditionals, laws of nature, or powers of particulars are fundamental. 4.4A.1 Strong Hypotheticalism. Some of the truths of counterfactual conditionals are fundamental, but no truths about particular powers or the laws of nature are fundamental.

  4.4A.2 Strong Nomism. Some of the truths about laws of nature are fundamental, but no truths about particular powers nor any of the truths of counterfactual conditionals are fundamental.

  4.4A.3 Strong Powerism. Some of the truths about the powers of particular things are fundamental, but no truths about the laws of nature nor any of the truths of counterfactual conditionals are fundamental.

  6. Powers

  6.1T Causal Individuation of Properties (Weak Thesis). Some fundamental properties are individuated by the set of powers they confer. 6.1T.1T Strong Causal Individuation of Properties (Strong Thesis). All fundamental properties are individuated by the set of powers they confer.

  6.1A Sicceity Theory. No fundamental properties are individuated by the set of powers they confer.

  6.2T Essentiality of Powers (Weak Thesis). Some fundamental property has its causal profile of necessity. 6.2T.1T Strong Essentiality of Powers. All fundamental properties have all of their causal profile of necessity: that is, each power is either necessarily conferred or necessarily not conferred by each property.

  6.2A Strong Accidentality of Powers. No fundamental property has any of its causal profile of necessity: that is, no property confers or fails to confer any power necessarily.

  7. Universals

  7.1T Realism. Universals exist and ground the character of ordinary objects. 7.1T.1T UP-Realism. There are fundamental universals and fundamental particulars, and the latter instantiate the former.

  7.1A Nominalism. Universals do not ground the character of ordinary objects. 7.1A.1A Ostrich Nominalism. Nominalism is true, and there is no general explanation of the fact that some particulars have properties in common.

  7.1A.1T Reductive Nominalism. Nominalism is true, and there is a general explanation of the fact that some particulars have properties in common. (=8.1T)

  7.2T Universal-Particular Distinction. There is a clear and coherent distinction between universals and particulars. 7.2T.1 Aristotelian UP. Universals can be predicated of other things, while particulars cannot be predicated of anything.

  7.2T.2 Russellian UP. Particulars are necessarily located in only one place at a time, while universals can be wholly present at many places at once.

  7.2T.3 Wise UP. Any particular can coexist with another particular indistinguishable from it, but it is impossible for any universal to be indistinguishable from anything else.

  7.3T Identity of Indiscernibles. If (thing a exemplifies Fness if and only if thing b exemplifies Fness), then a is identical to b. 7.3T.1 Restricted Identity of Indiscernibles. If (thing a exemplifies Fness if and only if thing b exemplifies Fness), where Fness is a natural, monadic property, then a is identical to b.

  8. Nominalism

  8.1T Reductive Nominalism. Nominalism is true, and there is a general explanation of the fact that some particulars have properties in common. (=7.1A.1T) 8.1T.1 Predicate Nominalism. Reductive Nominalism is true, and whenever two particulars have a property in common, this fact is grounded in the fundamental fact that the two fall under some one predicate of some language.

  8.1T.2 Concept Nominalism. Reductive Nominalism is true, and whenever two particulars have a property in common, this fact is grounded in the fundamental fact that the two fall under some one concept.

  8.1T.3 Class Nominalism. Reductive Nominalism is true, and whenever two particulars have a property in common, this fact is grounded in the fundamental fact that the two belong to some one set or class.

  8.1T.4 Resemblance Nominalism. Reductive Nominalism is true, and whenever two particulars have a property in common, this fact is grounded in fundamental facts of resemblance between them. 8.1T.4.1T Extreme Resemblance Nominalism. There are only ordinary particulars, and whenever two ordinary particulars resemble each other, their resemblance is metaphysically fundamental.

  8.1T.4.1A Moderate Resemblance Nominalism (Trope Nominalism). There are only particulars, and whenever two ordinary particulars resemble each other, their resemblance is grounded in the fundamental fact that the two are characterized by tropes whose resemblance is metaphysically fundamental.

  8.2T Trope Theory. Tropes ground the character of ordinary objects. 8.2T.1T Modifier Trope Theory. Trope Theory is true, and tropes are modifying tropes.

  8.2T.1A Modular Trope Theory. Trope Theory is true, and tropes are modular tropes.

  8.2A Anti-Tropism. Tropes do not ground the character of ordinary objects. 8.2A.1 Extreme Nominalism. The character of ordinary objects is grounded neither in universals nor in tropes.

  8.2A.2 Classical UP-Realism. The character of ordinary objects is grounded in universals and not in tropes.

  9. Particulars and the Problem of Individuation

  9.1T Constituent Ontology. When a substance instantiates a property, the instantiation relation between the two consists in the fact that the property is a part of the substance. 9.1T.1T Bundle Theory. The only constituents of each substance are its characterizing properties. 9.1T.1T.1T Trope Bundle Theory. Bundle Theory is true and tropes ground character.

  9.1T.1T.1A Classical Bundle Theory. Bundle Theory is true and universals ground character. 9.1T.1T.1A.1 Constructive Bundle Theory. Substances correspond one-to-one to sets of universals.

  9.1T.1T.1A.2 Simple Bundle Theory. Substances correspond one-to-one to co-instantiated sets of universals; that is, a substance S exists if and only some set of universals U is co-instantiated, and S exemplifies a universal F if and only if F is a member of U.

  9.1T.1T.1A.3 Nuclear Bundle Theory. Substance correspond one-to-one to nuclei of universals. That is, a substance S exists if and only if some set of universals U has the property of being nuclearly co-instantiated, and S exemplifies a universal F if and only if F belongs to some peripherally co-instantiated set (a bundle) that contains U.

  9.1T.1A Substrate Theory. Each substance has a constituent other than its characterizing properties, a substrate. 9.1T.1A.1T Trope Substrate Theory. Substrate Theory is true and tropes ground character.

  9.1T.1A.1A Classical Substrate Theory. Substrate Theory is true and universals ground character.

  9.1T.1A.2T Modular Substance Theory. Substrate Theory is true, and substrates have one property in them
selves.

  9.1T.1A.2A Bare Particular Theory. Substrate Theory is true, and substrates have no properties in themselves.

  9.1A Relational Ontology. Instantiation is a fundamental relation between substances and properties, and instantiation is not a case of the part-whole relation. 9.1A.1T Classical Relational Realism. Relational Ontology and Extreme UP-Realism are both true.

  9.1A.1A Trope Relational Ontology. Relational Ontology and Trope Theory are both true.