The Way of Actuality* Sam Cowling In this paper, I defend an indexical analysis of the abstract--‐‐concrete distinction within the framework of modal realism. This analysis holds the abstract--‐‐concrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstract--‐‐concrete distinction. This indexical analysis also provides a solution to a skeptical problem regarding our concreteness, which parallels the skeptical problem that motivates indexicalism about actuality. §1. Introduction This paper defends a view about the distinction between abstract and concrete entities. This view holds the abstract--‐‐concrete distinction to be conceptually inseparable from the distinction between actual and merely possible entities. Given their inseparability, the resulting view draws conceptual ties between two familiar ontological debates. Specifically, it connects the debate between realists and anti--‐‐realists, who disagree over the existence of abstract entities (e.g., sets, properties, and propositions), with a parallel debate between actualists and possibilists, who disagree over the existence of merely possible entities (e.g., flying pigs and the Sino--‐‐Canadian suspension bridge). And, while it is controversial, a familiar version of possibilism is assumed in what follows. This form of possibilism, Lewisian modal realism, holds that there are merely possible worlds of the same ontological kind as our actual world.1 Within the framework of Lewisian modal realism, I will argue that the abstract--‐‐ concrete distinction is indexical in nature. Roughly, the status of an entity as abstract or concrete is not metaphysically fundamental, but is instead a relative matter, depending upon the relations between entities. 2 This indexical view of the abstract--‐‐concrete distinction, which we can call the Way of Actuality, therefore parallels Lewisian modal realism's actuality--‐‐indexicalism, according to which you and I are actual relative to each other but merely possible relative to entities in other worlds. Actuality--‐‐indexicalism can be motivated in several ways. Most notably, it provides modal realists with a solution to a skeptical problem: if there are many possible worlds, how can we know that this is the actual world? As Lewis [1986] argues, once actuality is held to be indexical, this skeptical problem dissolves and an epistemological objection to modal realism can be set aside. Indexicalism about the abstract--‐‐concrete distinction can also be motivated in several ways. Not only does it provide a reductive analysis of a thorny metaphysical concept, it directly contributes to the case for modal realism since this analysis is yet * This is a preprint of an article whose final and definitive form will be published in the Australasian Journal of Philosophy [2013/2014]; the Australasian Journal of Philosophy is available online at: http://www.tandf.co.uk/journals/. 1 Lewis [1986] is the canonical presentation of Lewisian modal realism. 2 On indexical expressions, see Kaplan [1989]. Little here will turn on the precise semantics for indexicals. 2 another demonstration of modal realism's credentials as a powerful and fertile metaphysical theory. The Way of Actuality also resolves a skeptical worry regarding abstract entities that parallels Lewis' own skeptical worries about mere possibilia. Specifically, indexicalism about the abstract--‐‐concrete distinction dissolves the following skeptical problem: if there are abstract entities, how can we know that we are concrete? The Way of Actuality also represents a novel extension of an indexicalist methodological program in metaphysics. This program offers indexical analyses of metaphysical concepts instead of positing fundamental ontological distinctions. By way of example, consider standard four--‐‐dimensionalism, which uses indexical means to account for temporal passage, and 'moving spotlight' eternalism, which posits a fundamental metaphysical distinction between the present and the non--‐‐present. 3 According to the indexicalist, moving spotlight views traffic in obscure and poorly supported metaphysics. Better, says the indexicalist, to reduce putatively fundamental distinctions through indexical means and avoid theoretically costly metaphysical distinctions. A general motivation for the Way of Actuality is, then, to analyze the abstract--‐‐concrete distinction without commitment to primitive or fundamental distinctions and in keeping with the preferred resources of four--‐‐dimensionalism and Lewis' actuality--‐‐indexicalism. Recently, some have expressed doubt about the significance of the abstract--‐‐ concrete distinction.4 Here, it is assumed that we cannot reasonably do without it. Methodologically, this distinction earns its keep in formulating metaphysical claims. For example, theses like physicalism, dualism, and monism are typically formulated as restricted claims, concerning only concrete entities.5 Additionally, the evaluation of theories often turns on their relation to abstract or concrete entities. For example, unlike set theory, mereology is often touted as an especially attractive theory of collections precisely because it avoids commitment to abstracta.6 More controversially, the abstract--‐‐ concrete distinction plays a substantive role in ontology. For some of us, the distinction isolates those entities for which a certain pattern of ontological argument reasonably licenses ontological commitment. Specifically, it is the apparent abstractness of entities like properties, propositions, and possibilities, coupled with their covert implication in the truth--‐‐conditions of ordinary claims (e.g., through biconditionals like F is possible if and only if there are F--‐‐worlds), that provides a prima facie case for their existence. Naturally, this view of the role of the abstract--‐‐concrete distinction is controversial, but such a view, like many others, assigns the distinction a significant status in ontology. And, for those who reject this particular role, there remains ample methodological 3 Sider [2001] rejects the moving spotlight view as 'simply unmotivated.'' Bricker [2006] defends the modal analogue of the moving spotlight. 4 See Sider [2013] on eliminativism about the abstract--‐‐concrete distinction. 5 Stoljar [2009] restricts physicalism to concrete entities. Schaffer [2010] restricts monism to the domain of concrete entities. On the concreteness of Cartesian souls, see Burgess and Rosen [1997]. On mereology and its relation to nominalism, see Simons [1987]. 6 In contrast, ontological commitment to concrete entities is not supportable by this kind of covert implication. See Yablo [2000] for discussion. 3 reason for retaining the distinction in our metaphysical practice. The significance of the abstract--‐‐concrete distinction is therefore assumed in what follows. My case for the Way of Actuality will proceed as follows. Section Two examines extant views of the abstract--‐‐concrete distinction. Section Three clarifies and defends the Way of Actuality. Section Four considers a skeptical problem concerning abstract entities and argues that the Way of Actuality provides us with an attractive resolution. Section Four also defends a novel view of the significance of skeptical problems in metaphysical theory choice. Section Five addresses several objections to the Way of Actuality prior to concluding in Section Six. §2. The Abstract and the Concrete Views about the abstract--‐‐concrete distinction divide into three general kinds. According to primitivism, the distinction is theoretically significant, but resists reductive analysis and must be taken as conceptually primitive.7 Like any form of primitivism, this commitment to an indefinable primitive represents a costly addition to a theoretical economy. An alternative view, eliminativism, avoids this cost by denying the significance of the abstract--‐‐concrete distinction. For the eliminativist, no account of the distinction is required, since the theoretical work associated with it can be accomplished by more familiar distinctions (e.g., the distinction between spatiotemporal and non--‐‐ spatiotemporal entities). The remaining option is reductionism, according to which the abstract--‐‐concrete distinction has a substantive theoretical role but admits of analysis in a non--‐‐circular fashion. More carefully, reductionism holds that the distinction admits of an analysis that is (i) extensionally adequate, counting intuitively abstract entities as abstract, (ii) finitely stateable (e.g., something other than an infinitely long list of abstract entities), and (iii) informative, providing non--‐‐circular necessary and sufficient conditions for being abstract.8 My case for the Way of Actuality begins by surveying a range of reductionist proposals. Doing so raises a methodological challenge: how do we determine the extensional adequacy of a proposed analysis given the controversial status of certain abstract entities? Here, my strategy is to weigh the verdicts of various analyses in proportion to whether the entities in question are more or less paradigmatic cases of abstractness or concreteness. It is therefore of greater importance to ensure the abstractness of paradigm cases like sets and universals rather than more contentiously abstract entities like novels and governments. This strategy leaves open some difficult questions, but usefully allows us to set aside concerns that an exhaustive catalogue of potential abstract entities has not been offered. Perhaps most notably, we can postpone concerns raised by more contentious entities like fictional characters and musical works.9 7 On theoretical ideology, see Sider [2013]. Here, we can set aside complications about whether abstractness or concreteness is the target of analysis, and speak loosely about analyzing the distinction. 8 On this conception of metaphysical analysis, see Markosian [1998]. 9 There are principled grounds for this omission. The case for abstract entities is strongest when it issues from broadly naturalistic premises and, since musical works and similar entities are neither part of our best scientific theories, the case for such entities is considerably weaker. 4 Granted this methodology, another question remains: why should those who reject the existence of, say, in re universals or sets find fault with reductionist proposals apparently undermined by such entities? This problem naturally arises from a tension between the project of giving a metaphysical analysis wedded to one's committed theory and an analysis that is neutral between competing philosophical theories. Reconciling these projects is no simple matter, but, since my present aim is to defend a novel analysis of the abstract--‐‐concrete distinction, the most conservative strategy is the most neutral one. In evaluating competing analysis, it will therefore be useful to aim at neutrality about which kinds of putatively abstract entities exist. For those already firmly in the grip of their preferred theory, this should ensure that the Way of Actuality is extensionally adequate even while antecedent commitments leave some without reason to endorse it. With these methodological questions in view, the following survey of reductionist proposals considered in Lewis [1986] (or suggested elsewhere) serves one of two dialectical purposes. On the more ambitious line of argument, the problems with these proposals are decisive, but, given the ideological cost of primitivism, the Way of Actuality emerges as the best available option. On the less ambitious line of argument, the evaluation of these proposals delivers a modest result: none of these views are superior to the Way of Actuality, but, since the Way of Actuality enjoys additional virtues, we have reason to prefer it to its competitors. Whether taken together or separately, I believe these lines of argument provide a strong case for the Way of Actuality.10 2.1. The Way of Example: According to the Way of Example, an entity is abstract if and only if it is sufficiently similar to paradigm abstract entities like sets and universals. For Lewis and others, the Way of Example is useful as a heuristic for grasping the abstract--‐‐ concrete distinction but is not put forward as a genuinely reductive analysis. The Way of Example is therefore properly set aside as neither genuinely reductionist nor a viable alternative to primitivism. In setting aside the Way of Example, we can also set aside a nearby proposal, which proceeds by offering a disjunctive list that enumerates various kinds of abstract entities (i.e., an entity is abstract if and only if it is a set or a proposition or a property, and so on). This is motivated by methodological considerations. Specifically, merely disjunctive proposals are likely to forego the explanatory virtues of non--‐‐disjunctive analyses--‐‐--‐‐namely, explaining what unifies certain entities as abstract entities, and addressing open questions about the abstractness of non--‐‐paradigm cases. This disjunctive view also faces a second hurdle, since it is unclear how it can be formulated without settling controversial questions about which kinds of entities exist.11 And, while a disjunctive analysis may be an option of last resort, we are better served by pursuing a non--‐‐enumerative analysis and the theoretical benefits that come with it. 10 My thanks to an anonymous referee for their suggestions throughout this section. 11 This disjunctive view will also prove inadequate if there are infinitely many kinds of set--‐‐like entities satisfying different axioms. 5 2.2. The Way of Conflation: According to the Way of Conflation, 'the distinction between concrete and abstract entities is just the distinction between individuals and sets, or between particulars and universals, or perhaps between particular individuals and everything else.'12 So understood, the Way of Conflation is something like an analysis schema: provided a background ontology, it holds that there is some ontological category--‐‐--‐‐e.g., individual or particular--‐‐--‐‐that properly distinguishes the abstract from the concrete. The Way of Conflation faces problems similar to those faced by the Way of Example. Most notably, if a verdict on the abstractness of, say, propositions and other less familiar entities is needed, a background ontology must be accepted and a desirable neutrality must be foregone. If, however, no background ontology is assumed, abstractness depends upon an additional distinction to be drawn within a range of different ontologies. A neutral analysis of the abstract--‐‐concrete distinction would therefore require an analysis of this additional ontology--‐‐relative distinction. But, since no such analysis has been provided, the Way of Conflation is no less costly than primitivism about the abstract--‐‐concrete distinction. 2.3. The Way of Abstraction: According to a historically informed conception of abstraction, abstract entities 'result from somehow subtracting specificity, so that an incomplete description of the original concrete entity would be a complete description of the abstraction.'13 The Way of Abstraction therefore proceeds by taking abstract entities to correspond to or, in a more idealistic vein, be created by a cognitive process of 'subtracting specificity.' Regardless of which approach one prefers, the resulting analysis is too vague to provide a suitably informative analysis and requires either an implausible view of abstract entities as wholly mind--‐‐dependent or a supernatural constraint on our cognition of abstract entities (i.e., our cognitive systems can 'abstract' only pre--‐‐existing abstract entities). 2.4. The Way of Indiscernibility: According to the Way of Indiscernibility, an entity is abstract if and only if there is no distinct entity qualitatively indiscernible from it. While this proposal is reductive and requires no controversial metaphysical resources, Lewis [1986] provides two reasons to reject this account. First, if there are qualitatively indiscernible sets (e.g., sets with qualitatively indiscernible members), this analysis is extensionally inadequate. Second, if there are no qualitatively indiscernible possible worlds, then all possible worlds are abstract. Since it is controversial whether there are qualitatively indiscernible worlds, the Way of Indiscernibility threatens to count all possible worlds, including our own, as abstract. Moreover, if the Identity of Indiscernibles holds for both worlds and objects within them, absolutely all things are abstract. These results strongly suggest that this proposal simply employs the wrong resources for analyzing the abstract--‐‐concrete distinction. 12 Lewis [1986: 84]. 13 Lewis [1986: 84]. 6 2.5. The Way of Existence: For Quineans, existence is a univocal notion.14 For others, there are distinct yet equally natural interpretations of 'exists' and cognate idioms of quantification. Granted these equally natural meanings, anti--‐‐Quineans hold that there is an intelligible and substantive sense in which entities can be said to 'exist in different ways.' If this locution can withstand metaphysical scrutiny, it seems well suited for marking metaphysically significant distinctions like the one between abstract and concrete entities. According to the Way of Existence, an entity is abstract if and only if it exists in the way of existing, A, and does not exist in the way of existing, C. Here, the different ways of existing are different domains with, say, numbers and universals falling only within A and, say, cats and kayaks falling only within C. And, while this talk of 'ways of existing' may be metaphysically above board, the Way of Existence does not further our reductive ambitions. Although it tells us abstract and concrete entities exist in different ways, unless the distinction between these specific ways of existing is understood independently of and expressible without invoking the abstract--‐‐concrete distinction, the resulting view is not genuinely reductive. And, since the view in question invokes these specific ways of existing solely to make sense of the abstract--‐‐ concrete distinction, it is a view of the metaphysical nature of the abstract--‐‐concrete distinction rather than a reductive analysis of the distinction. 2.6. The Way of Priority: The Way of Priority analyzes the abstract--‐‐concrete distinction by appeal to a primitive relation of ontological priority between, say, properties and the objects on which they metaphysically depend, or between singletons and the individuals that ground them.15 If we take individuals as paradigm concrete entities, we have the makings of an analysis: an entity is abstract if and only if it exists in virtue of some individual. But, for the Way of Priority to be a suitable analysis, controversial views about the structure of ontological priority are required. Most notably, this proposal requires that no concrete entities are prior to other concrete entities, no abstract entities are prior to other abstract entities, and all abstract entities are posterior to some concrete entities. But, since pure sets are presumably grounded in the null set, the Way of Priority admits of counter--‐‐example. Similarly, if concrete mereological sums exist in virtue of their concrete parts (or vice versa), the Way of Priority faces another counter--‐‐example. It seems, then, that the Way of Priority provides no reductive analysis of the abstract--‐‐ concrete distinction unless defenders of ontological priority are willing to drastically tailor their metaphysical views to accommodate an analysis of the abstract--‐‐concrete distinction. This is evidence enough that the Way of Priority fails as a reductive proposal. 2.7. The Way of Location: According to the Way of Location, an entity is abstract if and only if it lacks spatiotemporal location. As Lewis notes, however, this analysis is extensionally inadequate given that in re universals are paradigm abstract entities but are wholly located wherever instantiated. Similarly, although more controversially, 14 See Quine [1953]. On ontological pluralism, see Turner [2010]. 15 On ontological priority and its direction, see Schaffer [2010]. 7 Lewis [1986] suggests that sets might share their locations with their members and therefore present a second counter--‐‐example to the Way of Location. Crucially, Lewis offers no argument for the locatedness of sets, merely taking issue with those who uncritically assume that sets are not located. Pace Lewis, there are two reasons to believe that sets are not located. The first reason owes to the impossibility of extended simples, and the requirement that objects occupy regions only by having parts at regions. If singletons are both located where their members are and lack parts, then a singleton with a spatially extended member violates this thesis qua extended simple object. The second reason owes to what Forrest [2001] calls Hume's Razor: the injunction to avoid positing undue necessary connections between entities. To hold that sets are located where their members are located is to require both the well--‐‐motivated necessary connection of membership between singletons and their members and the under--‐‐ motivated necessary connection between singletons and the regions occupied by their members. Since this latter necessary connection delivers no theoretical advantages, there is no reason to flout parsimony by positing it. Now, although both considerations offered against the locatedness of sets are controversial, they are sufficient break the evidential deadlock concerning whether sets are located. Even so, the concern regarding in re universals remains: some putative abstracta are located, so the Way of Location is inadequate. 2.8. The Way of Causation: The Way of Causation aims to analyze the abstract--‐‐concrete distinction by holding that abstracta, unlike concreta, are causally inert.16 The primary challenge for such a view is to make explicit the sense in which abstract entities are 'causally inert' without contravening our intuitive judgments about the distinction. For example, if events are causal relata and properly identified with sets of spacetime points or ordered n--‐‐tuples, then, in a fairly robust sense, sets do enter into causal relations. Similarly, if individuals have causal powers in virtue of instantiating universals, it is unclear in what sense universals, viewed as constituents of individuals, fail to stand in causal relations. And, while it is unclear how to formulate a plausible version of the Way of Causation, any version would seem to violate a plausible thesis about the plenitude of possibilities: that there could be epiphenomenal concrete entities. Following Forrest [1983], consider the possibility of epiphenomenalons, particles 'that than which no more useless can be conceived.' There is ample reason to believe such entities are possible, but the Way of Causation will incorrectly classify them as abstract. §3. The Way of Actuality Having undermined various proposals for reducing the abstract--‐‐concrete distinction, we can turn to a novel alternative: the Way of Actuality. A common presupposition of the preceding views is that the abstract--‐‐concrete distinction is absolute--‐‐--‐‐i.e., that entities bear absolute, non--‐‐relational properties of being abstract and being concrete. The Way of 16 On the causal efficacy of abstract entities, see Cheyne and Pidgen [1996]. 8 Actuality rejects this presupposition.17 According to the Way of Actuality, an object x is abstract relative to an object y if and only if x is not a worldmate of y. Conversely, an object x is concrete relative to an object y if and only if x is a worldmate of y. Granted this analysis, there are no facts about whether entities are abstract or concrete simpliciter. 18 Rather, the truth--‐‐value of claims about the abstractness and concreteness of entities varies with the context of utterance, depending on the world of the speaker and the speaker's relation to entities ascribed abstractness or concreteness.19 Since the Way of Actuality invokes the worldmate relation in analyzing abstractness, an analysis of the worldmate relation is required. Following the preliminary account in Lewis [1986], let us say that two objects, x and y, are worldmates if and only if every part of x is spatiotemporally related to every part of y. Accordingly, you are worldmates with any entities spatiotemporally related to you in this way, while anything that has parts at another world fails to qualify as your worldmate. This preliminary account of the worldmate relation raises a general concern: by analyzing worldmatehood in spatial and temporal terms, we rule out the possibility of worlds unified by exotic, non--‐‐spatiotemporal relations. Suppose, for example, that spacetime is essentially continuous. It seems possible, however, that a world be spacetime--‐‐like yet discrete in nature. Following Lewis, we can therefore generalize our account of the worldmate relation to include analogically spatiotemporal relations as well. Alternatively, we can follow Bricker [1996] in generalizing the worldmate relation even further, taking any external relations to suffice for worldmatehood. Having noted these complications regarding the worldmate relation, it will be useful to speak simply of 'the worldmate relation' in what follows, leaving open which generalization of the preliminary account we ought to prefer.20 The Way of Actuality parallels Lewis's analysis of actuality. According to Lewis' actuality--‐‐indexicalism, an object x is actual relative to an object y if and only if x and y are worldmates. The conjunction of actuality--‐‐indexicalism and the Way of Actuality therefore holds concreteness and actuality to be coextensive: any object that is actual relative to an object is concrete relative to that same object. Additionally, any object that is merely possible relative to an object is abstract relative to that same object.21 Having presented the Way of Actuality, we can now examine its implications for paradigmatic abstracta like mathematical entities, universals, and possible worlds. Mathematicalia: If sui generis numbers exist, it is unlikely that they are located in space or time, and, as argued earlier, sets are properly held to lack spatial or temporal 17 Parsons [Unpublished ms] considers a view that admits a plurality of equally fundamental actuality properties. 18 The Way of Actuality does not entail that we are contingently concrete. While our counterparts are abstract relative to actuality, each world represents itself as actual and concrete. So, just as your counterparts represent possibilities according to which you are actual, your counterparts represent possibilities according to which you are concrete. 19 See Lewis [1986: 94] on the semantics for 'actual'. 20 The Way of Actuality can naturally allow the disjunction of spatial, temporal, or spatiotemporal relations to unify worldmates and thereby accommodate the concreteness of non--‐‐spatial objects like Cartesian minds. 21 Not every abstract entity is a merely possible entity, since transworld fusions are abstract yet impossible. 9 locations. As such, mathematical entities are never worldmates of anything, given that they stand in no spatiotemporal relations. Mathematical entities are therefore abstract relative to the actual world and any given possible world. Since mathematical entities and other non--‐‐spatiotemporal entities are abstract relative to each and every possible world, we can use the resources of the Way of Actuality to distinguish between what we can call platonic and non--‐‐platonic abstract entities, where platonic entities are those entities that are abstract relative to every possible world. It is worth noting, then, that the Way of Actuality naturally distinguishes platonic entities as a special subspecies of abstracta, differing notably from possible worlds and their inhabitants, which are concrete relative to their own worlds. Universals: The Way of Actuality provides a straightforward account of the abstractness of universals. If universals are transcendent entities, existing outside of space and time, they are abstract by virtue of having no worldmates. If, however, universals are in re entities, our analysis of the worldmate relation must ensure that they nevertheless qualify as abstract entities. Notably, on any plausible conception of plenitude, a sparse universal like redness is instantiated at various worlds and is therefore a worldmate of entities at various worlds.22 To prevent this result and ensure the abstractness in re universals, we can handily amend our analysis of the worldmate relation as follows: two entities, x and y, are worldmates if and only if every part of x is spatiotemporally (or analogically spatiotemporally) related to every part of y and, for all z such that x is related in this way to z, y is also related in this way to z. This modification guarantees that universals are not worldmates of anything, even granting that they are wholly located at distinct worlds.23 Possible Worlds: Modal realism is often characterized as the thesis that there are concrete yet merely possible worlds. According to the Way of Actuality, this is a mistake. Since no two possible worlds are worldmates, other worlds are abstract relative to our world. While this standard characterization of modal realism must therefore be rejected, the result is beneficial for the modal realist, since the proper characterization of modal realism squares with the intuition that, if merely possible worlds exist, they are most naturally held to be abstract entities. This consequence of the Way of Actuality also comports with a core intuition that guides our judgments about nominalism and realism: that the pernicious character of abstract entities owes to their failure to bear causal or spatiotemporal relations to us. For example, Burgess and Rosen [1997: 124] suggest that this indexical intuition plays a significant and under--‐‐recognized role in our grasp of the abstract--‐‐concrete distinction: Now one can quibble over whether or not the unactualized possible inhabitants of an unactualized possible world should be called 'abstract', since they may be causally active in the sense that they causally interact 22 On the bilocation of universals, see Lewis [1986: 2]. 23 Perhaps some universals exist in only a single world and are therefore concrete relative to exactly one world; however, since such a view would violate plausible and relatively weak assumptions about plenitude, I assume that each in re universal is instantiated in a plurality of worlds. 10 with each other; but since they are causally isolated in the sense that none of them causally interact with us, such exotica as unactualized possibilia are quite as repugnant to nominalists as are numbers or sets. The Way of Actuality takes seriously the intuition that abstractness is a relative matter. As a consequence, it counts merely possible worlds, universals, and mathematical entities as abstract. Since these are the paradigm cases of abstractness, the Way of Actuality satisfies our initial desiderata: it is extensionally adequate, finitely stateable, and informative. And, while it categorizes the modal realist's possible worlds as abstract, it does so on principled grounds and without foregoing the enormous analytic utility that comes with them.24 §4. Concreteness Skepticism We can now examine an additional motivation for the Way of Actuality that runs parallel to Lewis' motivation for actuality--‐‐indexicalism: overcoming skepticism about our concreteness. While skeptical problems involving dreams and illusions can be presented with relative ease, some 'metaphysical' skeptical problems require considerable stage setting and appeal to distinctively metaphysical notions.25 Among these metaphysical skeptical problems is Actuality Skepticism, which denies that we are justified in believing that we are actual rather than merely possible. After all, what evidence would guarantee our actuality and not also be available to some merely possible individuals? Lewis [1986] defends actuality--‐‐indexicalism as means to address the problem of Actuality Skepticism. Since any individual is actual relative to their own world, knowledge that one is actual is cheap and easy to come by. Actuality--‐‐indexicalism therefore allows modal realists a swift resolution to this particular kind of 'metaphysical' skepticism.26 But, following Lewis, Bricker [2006: 56] presents the parallel problem of Concreteness Skepticism, according to which we lack knowledge of our concreteness: Now, I suspect that most realists about sets would accuse anyone who raises the question – how do I know I am not a set? – of being (intentionally) obtuse. Surely, they will say, there are numerous properties that I know I have and that I know no set has. It then follows, by an application of Leibniz's Law, that I know I am not a set. But it is no simple matter to come up with the required discerning properties. I will not challenge our claim to know, for many ordinary properties, whether 24 The primary difference between ersatz possible worlds and the worlds of modal realism now concerns their respective ontological categories rather than their abstractness or concreteness. For ersatzists, possible worlds are typically properties, propositions, or sets, while the modal realist identifies worlds with individuals. 25 Williams [1962] raises a metaphysical skeptical problem regarding our own existence. 26 I offer no defense of actuality--‐‐indexicalism here, but follow Lewis in denying the possibility of island universes. 11 we have the property. The problem, rather, is with our claim to know that sets do not have the property. The threat of Concreteness Skepticism arises, by Bricker's lights, because we do not know that sets or universals lack the properties that we take to be distinctive of concrete entities. Bricker points out that, if sets and universals are mereologically complex or conscious, we would be unable to discern whether we are abstract rather than concrete entities on the basis of the features we typically ascribe ourselves (e.g., consciousness, mereological complexity, etc.). Additionally, some have defended metaphysical views that identify persons with abstract rather than concrete entities. For example, Sider [2013] argues that macrophysical objects--‐‐--‐‐persons included--‐‐--‐‐are sets of mereological simples rather than concrete individuals. For the Concreteness Skeptic, the epistemic possibility of these kinds of views, coupled with the fact that we do not know that sets or universals lack consciousness or mereological complexity, ensures that we cannot rule out our own abstractness. As a consequence, the Concreteness Skeptic concludes that we cannot lay claim to knowledge of our own concreteness.27 Since realism about abstract entities is far more commonplace than possibilism, Concreteness Skepticism is properly viewed as a more widespread concern than Actuality Skepticism. It is notable, then, that, just as actuality--‐‐indexicalism provides a swift solution to Actuality Skepticism, the Way of Actuality and actuality--‐‐indexicalism provides a swift solution to Concreteness Skepticism: we know that we are actual, given actuality--‐‐indexicalism, and, by virtue of knowing ourselves to be actual, we know that we are concrete. A notable virtue of the Way of Actuality, aside from its economy, extensional adequacy, and consilience with indexicalist methodology, therefore lies in its ability to deliver a response Concreteness Skepticism.28 Perhaps unsurprisingly, resolving Concreteness Skepticism isn't quite so simple. Consider the following objection: the preceding defense of the Way of Actuality touts it as a solution to Concreteness Skepticism, but skeptical problems regarding our own actuality and concreteness still remain. Suppose, for example, that one of your molecules resides at another possible world. You are therefore a transworld fusion, an impossible object stranded between worlds. Since things would seem the same to you regardless of whether you were a transworld fusion or lacked the erstwhile molecule, you are 27 An alternative line of response: since we know we are persons and that persons are concrete, we therefore know we are concrete. As noted above, Bricker considers the skeptical possibility that persons are set--‐‐ theoretic complexes. So, unless we illicitly assume that we know that we are not sets or that we are special concrete sets, the present response will not meet the threat of Concreteness Skepticism on its own terms. Additionally, one might worry that the epistemic possibility that we are sets presupposes the epistemic possibility that sets are not concrete. If so, the deeper skeptical problem concerns our non--‐‐sethood rather than abstractness. Here, I follow Bricker in assuming knowledge of the abstractness of sets. Thanks here to anonymous referee. 28 The parallels between Concreteness and Actuality Skepticism suggest that they ought to be addressed in the same way. So, for those untroubled by Concreteness Skepticism or uninterested in the Way of Actuality as a response, there is reason to reconsider the status of Actuality Skepticism and actuality--‐‐indexicalism. See Bricker [2006] for an alternative anti--‐‐skeptical response. 12 ignorant of whether you are an actual and therefore concrete entity or an impossible and therefore abstract entity.29 Since nothing in the Way of Actuality precludes this state of affairs, it fails to resolve Concreteness Skepticism. Notice that this challenge threatens both the Way of Actuality and Lewis' response to Actuality Skepticism. Properly evaluating this objection therefore requires us to clarify the role of skeptical arguments within metaphysical inquiry. This leads towards deep waters, but there is a natural view on which the Way of Actuality still emerges as virtuous even if the relevant skeptical challenges are not conclusively resolved. There are three general stances toward the proper role of skeptical arguments within metaphysics. According to what we can call dismissivism, skeptical arguments have no purchase in metaphysical disputes, since skeptical arguments are cheap, insurmountable, and can always be pushed further. Furthermore, skeptical arguments drive us towards bad metaphysics. Worried about knowledge of other minds? Accept behaviorism and reduce knowledge of minds to knowledge of bodies. But, then again, how can we know that there are other bodies out there? For the dismissivist, there is simply no value in a solution to Concreteness or Actuality Skepticism since there is no genuine vice generated by skeptical problems of the kind in question. According to anti--‐‐dismissivism, skeptical arguments are of paramount importance, so, if a metaphysical view generates a skeptical problem, this is a significant and perhaps fatal vice. For the anti--‐‐dismissivist, the Way of Actuality is therefore a noble but ultimately futile effort, since the only satisfactory response to Concreteness Skepticism is something like nominalism. As one might expect, anti--‐‐dismissivism is not comfortably avowed by anyone who hopes to maintain justified beliefs on controversial metaphysical matters. Skeptical arguments are cheap, after all. Anti--‐‐dismissivism therefore threatens to wash out our justification for metaphysical beliefs, given the remarkably slims margins of argument in metaphysics. And, since we cannot pick and choose which skeptical arguments to address, anti--‐‐dismissivism undermines an enormous range of metaphysical theories. Dismissivism and anti--‐‐dimissivism are both theoretically unsatisfying. The possibility of justified metaphysical beliefs seems genuine, but anti--‐‐dismissivism seriously threatens the prospects for any such beliefs. At the same time, dismissivism is poorly positioned to explain the methodological significance of skeptical concerns in metaphysical debate. It is, for example, unclear how a dismissivist can account for the apparent virtue of Lewis' actuality--‐‐indexicalism as a resolution of Actuality Skepticism. In order to sustain a middle ground between these views, we are therefore best served to assess the value of 'metaphysical' skeptical arguments in terms of theoretical virtues like fertility and conservativeness.30 29 Notably, this skeptical problem does not require any relevant metaphysical possibility but, rather, a metaphysical impossibility. Examples of this sort cast further doubt on anti--‐‐skeptical strategies that delimit metaphysical possibilities to foreclose epistemic possibilities. See Schaffer [2005: 19] for discussion. 30 On fertility, see Nolan [1999]. On conservativeness, Lewis [1986: 235]. 13 For illustration, we can associate the value of skeptical arguments with the virtue of conservativeness and the vice of anti--‐‐fertility. (There are other virtues and vices one might draw upon, but these diachronic theoretical features suffice for present purposes.) Let us say that a theory suffers from anti--‐‐fertility if it does not suggest novel theoretical applications, but, rather, becomes bogged down by unprofitable concerns, stifling its analytic ambitions. Let us also say that a theory enjoys conservativeness when its current iteration is stable with respect to the commitments of previous iterations unless properly motivated. Conservativeness is therefore flouted when the present theory opts for gratuitous alternatives in its formulation or commitments. Within metaphysical debates, conservativeness and anti--‐‐fertility provide a natural way to understand the role of skeptical problems: if the commitments of a metaphysical theory generate novel skeptical problems, this is a vice, since new skeptical problems are a break from the aims of previous iterations, stifling a theories' analytic ambitions by forcing it to deal with skeptical problems rather develop novel applications. So, while it is not a decisive strike against a theory, it is undesirable if a theory draws our knowledge of a subject matter into question when that knowledge was not previously hostage to the skeptic. Fortunately, this cost can be offset by supplying a 'solution' to these novel skeptical worries, where the requisite solution explains how the knowledge in question is either insubstantial or had on the cheap, and is not a proper object of theoretical scrutiny. Drawing on our present case: modal realism raises the problem of Actuality Skepticism, which was of no previous concern to actualists. Modal realism thereby incurs a cost; it flouts the virtue of conservativeness and suffers the vice of anti--‐‐fertility by generating a novel skeptical worry. The value of Lewis' actuality--‐‐indexicalism therefore lies in its capacity to offset this cost by transforming knowledge of our actuality into cheaply acquired, insubstantial knowledge. By minimizing the significance of the relevant skeptical concern and denying the fundamentality of the actual--‐‐merely possible distinction, actuality--‐‐indexicalism undercuts any theoretical motive for pursuing a resolution to further sharpenings of Actuality Skepticism; efforts can instead be directed towards novel applications of the theory. Anti--‐‐fertility is thereby avoided. Along the same lines, the Way of Actuality delivers a valuable response to Concreteness Skepticism, which emerges as a threat for realists about abstract entities. The Way of Actuality disarms this threat by showing knowledge of our concreteness to be cheap, insubstantial and no deterrent to theoretical progress: we know ourselves to be concrete by knowing that we are actual. The Way of Actuality therefore provides a response to Concreteness Skepticism that parallels Lewis' grounds for actuality--‐‐ indexicalism and a notable reason to endorse the Way of Actuality. §5. Against the Way of Actuality Having defended the Way of Actuality, we can now consider objections to the view. Objection One: The Way of Actuality delivers a revisionary indexicalism about the abstract--‐‐concrete distinction. Why should we prefer this view to analyses that employ 14 similar resources and preserve the absoluteness of the distinction? For example, what reason to do we have to prefer the Way of Actuality to, say, the Way of Counterparts, according to which something is concrete if and only if it is a counterpart of something? Response: The indexical element of the Way of Actuality plays three roles. First, it ensures a methodological consilience with theories that use indexicality to explicate metaphysical distinctions between ontological categories. It therefore unifies the metaphysics of the abstract--‐‐concrete distinction with similarly indexical distinctions between the actual and merely possible and the present and non--‐‐present. Second, this indexical element underwrites our response to Concreteness Skepticism that explains easy knowledge of our concreteness. Third, for those of us who take properties, possible worlds, and propositions to form a unified kind, the Way of Counterparts and other absolutist proposals lacks a notable virtue of the Way of Actuality: ensuring that Lewisian possible worlds are just as abstract as properties and propositions. This verdict respects the common systematic role of possible worlds, properties, and propositions in the truth--‐‐conditions of modal, semantic, and property--‐‐theoretic claims. Taken together, these features of the Way of Actuality provide reason to accept indexicalism despite its somewhat revisionary character. In contrast, the Way of Counterparts provides no comparable response to Concreteness Skepticism, since counterpart relations are non--‐‐ indexical relations determined by spatiotemporal or external relatedness.31 Objection Two: For some, the absoluteness of the abstract--‐‐concrete distinction will seem non--‐‐negotiable. As a consequence, the Way of Actuality serves as a reductio of reductionism, forcing a commitment to either primitivism or eliminativism. What reasons can be offered for maintaining indexicalist reductionism as an alternative to primitivism or eliminativism? Response: The reductionist's response to those who opt for primitivism rather than indexicalism is twofold: primitivism is simply too costly, and intuitions of absoluteness are defeasible in light of considerations of total theory. Notice, for example, that the parallel primitivism about actuality, comes at the excessive cost of a murky fundamental distinction. In characterizing absolute actuality, Bricker [2006: 50] claims that actual entities have a 'special ingredient that distinguishes them, ontologically' and adds that there is little else that can be said about absolute actuality. And, while these remarks are precisely what the primitivist about actuality ought to say, they remain unsatisfying. Although actuality--‐‐indexicalism may prove surprising, absolutist intuitions are of uncertain evidential weight, and actuality--‐‐indexicalism is both parsimonious and theoretically fruitful. Since the Way of Actuality enjoys comparable virtues, it is preferable to primitivism about abstractness. And, while some may find their commitment to absolutism or primitivism unshakeable, the present version of 31 While no linguistic evidence has been offered for indexicalism about the abstract--‐‐concrete distinction, I follow Lewis in taking indexicalism to admit of support on metaphysical and epistemic grounds. 15 reductionism about the abstract--‐‐concrete distinction enjoys a range of features that cannot be easily dismissed. The reductionist's response to the eliminativist takes the form of a challenge. This is because the eliminativist must meet two requirements. First, she must successfully show that the conceptual work done by the abstract--‐‐concrete distinction can be done without deploying our concepts of abstractness or concreteness. Second, she must provide reason to dispense with our familiar appeals to the abstract--‐‐concrete distinction. This second task is crucial. While eliminativism is guaranteed to be more parsimonious than primitivism, reductionism comes with no ideological costs, and, in the present case, the virtue of conservativeness is firmly on the reductionist's side given the methodological and ontological uses of the abstract--‐‐concrete distinction. These considerations provide reason enough to prefer reductionism to eliminativism. Objection Three: According to the Way of Actuality, no actual entities are abstract. But, if our ordinary domain of discourse includes only actual entities, then, in an ordinary context, it is true that there are no abstract entities. But, intuitively, the present view should ensure that it is true, in ordinary contexts, that there are abstract entities. Response: This objection is a serious one, but it is unfair to lay it solely at the door of the defender of the Way of Actuality. Recall that Lewis identifies properties, abundantly conceived, with sets of possible individuals. For example, since there are some non--‐‐ actual humans, humanity is a set that has members drawn from various worlds and is not a worldmate of anything. Lewisian modal realists must therefore deny that properties like humanity actually exist even while they exist, unrestrictedly speaking. The Lewisian modal realist and the defender of the Way of Actuality therefore owe some explanation of why it seems true to say, in ordinary contexts, that numbers and certain other abstract entities exist. For Lewis, a suitable explanation appeals to the various disambiguations of our talk of 'being in a world.'32 Along with more demanding senses of 'being in a world,' Lewis holds that an entity exists 'from the standpoint of a world' if and only if 'it belongs to the least restricted domain that is normally--‐‐--‐‐modal metaphysics being deemed abnormal--‐‐--‐‐appropriate in evaluating the truth at that world of quantifications.' This disambiguation provides Lewis and the defender of the Way of Actuality with a natural explanation of the relevant intuitions about truth--‐‐value: the ordinary domain of discourse is not the most stringent domain, including only mereological parts of the actual world, but, rather, the least restricted domain normally associated with the actual world, which includes abstract entities. The core idea here is that, in ordinary contexts, the weaker relation of 'existing from the standpoint of a world' determines the domain 32 Lewis [1983] distinguishes three senses of 'being in a world'': (i) when an entire individual is a part of a world, (ii) when an individual has only a proper part in a world, and (iii) when an entity-e.g., a set-exists 'from the standpoint of a world.'' 16 of discourse and relevant truth--‐‐values, even while the more stringent worldmate relation determines which entities are genuinely actual.33 §6. Conclusion The Way of Actuality provides a reductive analysis of the abstract--‐‐concrete distinction that further demonstrates the theoretical power and fertility of modal realism. It also provides a solution to Concreteness Skepticism that parallels Lewis' own solution to Actuality Skepticism. And, while diehard actualists may be unimpressed with any view tethered to modal realism, the Way of Actuality warrants close consideration as a viable account of the abstract--‐‐concrete distinction.34 §7. References Bricker, Phillip 1996. Isolation and Unification: The Realist Analysis of Possible Worlds, Philosophical Studies 84/2:225--‐‐238. Bricker, Phillip 2006. Absolute Actuality and the Plurality of Worlds, Philosophical Perspectives 20:41--‐‐76. Burgess, John, and Rosen, Gideon 1997. A Subject With No Object, Oxford: Oxford University Press. Cheyne, Colin, and Charles Pidgen 1996. Pythagorean Powers or a Challenge to Platonism, Australasian Journal of Philosophy 74/4:639--‐‐645. Cowling, Sam 2011. The Limits of Modality, Philosophical Quarterly 61/244: 473--‐‐495. Divers, John 1999. A Genuine Realist Theory of Advanced Modalizing, Mind 108/430:217--‐‐39. Forrest, Peter 1983. Occam's Razor and Possible Worlds, The Monist 65/4:456--‐‐464. Forrest, Peter 2001. 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