High-fidelity Metaphysics: Ideological Parsimony in Theory Choice

High-fidelity Metaphysics: Ideological Parsimony in Theory Choice Peter Finocchiaro April 10, 2017 Abstract Many metaphysicians consider their field to be one where we develop competing theories of reality and argue which is most worthy of endorsement. One aspect of this approach to metaphysics what I will call the virtue-driven methodology states that one theory is more worthy of endorsement than another insofar as it is more virtuous, where its overall virtue is measured as a function of its more specific theoretical virtues. In this paper, I suggest how such metaphysicians should employ the virtue-driven methodology. I argue that a theory s ideology its undefined terminology should contribute to its theoretical virtue. To make this point, I distinguish between epistemic virtues and virtues of fidelity. Using this distinction, I identify eight principles concerning parsimony in theory choice. I then argue against an increasingly popular position in metaphysics regarding these principles. I assess three arguments in support of this position and show that they all fail. Keywords: Metametaphysics, Methodology, Theory Choice, Theoretical Virtue, Ontology, Ideology, Parsimony, Simplicity Introduction Define a theory s ideology as the stock of undefined terminology employed in stating the theory. Ideology is important in metaphysics in large part because of its relationship with ontology. To illustrate: someone who wants to avoid an ontological commitment to composite objects can paraphrase 1

claims about composites into claims involving plural and perplural quantification over simples. She can meet her ontological goals with some ideological creativity. Yet many are now of the opinion that ideology has realist implications independently of its connection to ontology. Some metaphysicians (like Lewis (1983)) think that we ought to prefer theories whose primitive predicates express natural properties. Others (like Sider (2011)) think that we ought to prefer theories whose entire ideology including allegedly syncategormatic terms like quantifiers and logical operators reflects the metaphysical structure of the world. These metaphysicians endorse a view I call ideological externalism. According to ideological externalism, the ideology of a theory is evaluated by the extent to which it corresponds to features of the world, whatever they may be. 1 I will simply assume ideological externalism in this paper and instead focus on the accompanying methodology. I do this in part because I endorse ideological externalism. But I also think the case for externalism depends on the viability of its methodology. Those who are skeptical of ideological externalism therefore should read my conclusions as conditional on its truth and should feel free to tollens where I ponens. I begin by establishing some background assumptions in section 1. Then, in section 2, I outline some conceptual territory concerning theory choice as a way to situate my paper within the broader literature. First, I present the standard distinction between pragmatic and epistemic virtues. I then argue for the importance of a third approach to theoretical virtue. Some virtues, what I call the fidelic virtues, indicate that a theory s ideology likely matches the objective features of the world. Fidelic virtues, like epistemic virtues, should be held in high esteem by the ideological externalist. Finally, I identify eight principles regarding parsimony that differ along three axes: ontology/ideology, quantitative/qualitative, and truth/fidelity. A metaphysician s choice from among these eight principles will influence how she evaluates competing theories and therefore shape her choice of theory. In section 3, I discuss three arguments that attempt to motivate the metaphysician to endorse an epistemic principle of ideological parsimony: the general simplicity argument, the argument from expressive paucity, and the interaction argument. While these arguments already exist in the metaphysical methodology literature, I pro- 1 Contrast ideological externalism with ideological internalism, where the ideology of a theory is judged by the extent to which it satisfies certain conditions internal to the theoretical process e.g. by being intelligible to the theorizer or employing terminology that has a history of successful projection. 2

vide them some much-needed precision. Then, I argue that they fail. At best, these arguments support the weaker claim that we ought to endorse some principle of ideological parsimony. 1 Background Assumptions In order to better facilitate my discussion of theoretical virtue, I begin with some background assumptions of this paper. I do not think all that much rests on them. I might, however, be wrong about the supposed neutrality of these assumptions. So, in the spirit of openness and honesty, here is how I will frame the issue. First, I assume that a theory is a sort of linguistic entity. Following Quine, Lewis, Sider, and others, I define a theory as a set of sentences more specifically, as a set of sentences each member of which asserts something of the world. Much of what we do as philosophers fails to make it into a theory understood in this way. Arguments against the existence of composite objects, for example, are not part of the theory of mereological nihilism. Rather, arguments and other tools of philosophy occur outside the theory as devices to convince us to endorse the theory itself. David Lewis once talked about total theory and declared that to be the concern of metaphysicians. I ll follow his lead. A total theory is a complete theory, one that is intended to provide a comprehensive picture of the world. A more specific theory is an abstraction from total theories. For example, the theory of mereological nihilism is defined as the disjunction of all total theories that do not employ mereological ideology. I understand that the set-theoretic definition of a theory is unfashionable in some circles. More popular now is a conception on which a theory is a semantic model. I adopt the set-theoretic definition primarily because it seems to be the definition most often used by those who discuss theory choice in metaphysics. Since I am not presently interested in challenging this assumption, I will follow their lead. Along similar lines, I stipulate that a theory s ideology is the stock of undefined terminology employed in stating the theory. Others identify ideology differently. In contrast with my linguistic approach to ideology, others seem to adopt a semantic approach. 2 For them, the ideology of a theory is a collection of intentional entities associated with the theory the concepts employed in 2 Examples of the semantic approach: Cameron (2012); Cowling (2013); Schaffer (2014). 3

stating the theory, for example. Above, I identified mereological nihilism with the disjunction of total theories that do not employ mereological ideology. On my linguistic approach to ideology, mereological nihiism is the disjunction of total theories that never use expressions like proper part and overlap. On the rival semantic approach to ideology, mereological nihilism is the disjunction of total theories that never employ concepts like proper parthood and overlap. Alternatively, if it sounds strange to talk of a theory employing a concept, mereological nihilism is the disjunction of total theories that are such that those who endorse the theory thereby avoid employing mereological concepts. I don t think too much in this paper or otherwise rests on which approach is adopted. Ideology is a term of art we inherited from Quine and we can use it to mean whatever we want it to mean. I do, however, think my linguistic approach is better. I think it is better because it is a more neutral framework without any deficiencies in application. Some metaphysicians would rather not commit themselves to the existence of concepts. The semantic approach would needlessly antagonize such metaphysicians. The semantic approach also introduces difficult issues concerning the nature and individuation of concepts. These issues are best avoided if possible. Finally, my linguistic approach is capable of anything the semantic approach is. At worst, my linguistic approach can be interpreted as an approach regarding the concepts expressible by the primitive terms of the theory. In this sense, the linguistic approach subsumes the semantic approach. One final, stylistic note. For ease of exposition, I will sometimes talk about the ideology used, employed, or required by a theory. By this I mean nothing more than the ideology for which the theory does not provide a definition. For example, some mereological systems take part as primitive and define proper part as: x is a proper part of y = df x is a part of y and x y. In some sense, these systems use the notion of proper part when they say, e.g., The wheel is a proper part of the wagon. But in another, more substantive sense, they do not. The appearance of defined ideology is an illusion. The wheel is a proper part of the wagon, is just shorthand for The wheel is a part of the wagon and the wheel the wagon. A theory that does not define proper part means something different by The wheel is a proper part of the wagon. So, two theories can appear to use, employ, or require the same ideology when in fact they do not. 4

2 Virtue-driven Metaphysics Many metaphysicians, myself included, favor a theory-crafting methodology. 3 We develop competing theories that describe how the world is and then evaluate their relative merits. Our commitments (ontological, ideological, or otherwise) fall out of our choice of theory. Those of us who adopt this methodology owe an account of how the merits of theories are evaluated. Most commonly, theories are evaluated on the extent to which they exhibit theoretical virtues. In this section, I contrast the standard account of theoretical virtues with a more nuanced account that better accommodates ideological externalism. I identify eight distinct principles of parsimony. Which principle someone follows will influence which theory she will ultimately endorse. 2.1 Three Kinds of Theoretical Virtues Most theory-crafting metaphysicians endorse what I will call the virtue methodology. 4 According to the virtue methodology, one theory is more worthy of endorsement than another insofar as it is more virtuous. A theory s overall virtue is measured as a function from its more specific virtues. The interplay between the virtues is complicated and few endorse strict means for weighing them against each other. 5 But, in practice, a metaphysician who adopts the virtue methodology tries to compare metaphysical theories on a particular virtue. These comparisons are admittedly incomplete but nonetheless effective in generating reasons to favor one theory over another. Broadly speaking, the virtue-driven metaphysician recognizes two distinct reasons to care about some feature of a theory. First, that feature might indicate a theory s usefulness. Such a feature is typically called a pragmatic virtue. Someone might think that parsimony is a pragmatic virtue because a simpler theory, when compared to a more complex theory, is more likely to be easy to understand. A pragmatic virtue so understood has to do with the relationship between theory and theorizer. Alternatively, some feature of a theory might indicate its truth. Such a feature is typically called an epistemic virtue. Someone might think that parsimony is an epistemic virtue because a simpler theory, when compared to a more complex theory, is more likely to be true. These associations are conceptually distinct. A theoretical feature that is considered a pragmatic 3 See Lewis (1986); Paul (2012); Sider (2011) for the theory-crafting methodology in action. And see Nolan (2016) for interesting commentary. 4 See Quine (1948); Lewis (1986); Paul (2012); Sider (2013); Schaffer (2014); Nolan (2015). 5 See Paul (2012): Section 2.4. Kuhn (1977) offers a worryingly subjective take on this point. 5

virtue need not be considered an epistemic virtue, and vice versa. Typically, the virtue-driven metaphysician privileges epistemic virtues over pragmatic virtues. She might judge a pragmatically virtuous theory as better than pragmatically vicious but otherwise equal theory. Yet she always prefers an epistemically virtuous and pragmatically vicious theory to an epistemically vicious and pragmatically virtuous theory. Truth is queen. The virtue-driven metaphysician who is also an ideological externalist should acknowledge another reason to care about parsimony and similar theoretical features. This reason builds off a notion that I call fidelity. Fidelity is a way to get things right that is distinct from truth. A theory with a high degree of fidelity a fidelic theory has an ideology that accurately matches the objective features of the world. To use the popular metaphor, a theory with a high degree of fidelity carves nature at its joints. The class of fidelic theories cuts across the class of true theories. Assume that the world has a property greenness which the predicate green accurately matches. Define grue as: x is grue = df x is observed before 3000AD and is green, or x is not observed before 3000AD and is blue A theory that employs the predicate green can be fidelic because it uses the correct ideology but nonetheless false because it misdescribes the world e.g. by describing Taylor Swift s lipstick as green. Likewise, a theory that employs the predicate grue might be true but nonetheless lack fidelity because it has a gerrymandered ideology. Two competing theories might both be true but differ in their level of fidelity. To illustrate, take a theory that truly describes all the green objects in the world as green. We can generate a grue-ified counterpart of that theory by matching each sentence of the first theory with a true sentence that uses grue. The grue-ified theory truly describes all the green objects observed before 3000AD as grue and all the green objects not observed before 3000AD as not grue. Both theories are true but the first theory has a higher degree of fidelity than its grue-ified counterpart. 6 6 Someone might reject the grue-ified theory because it lacks specificity a non-grue object might be green and not observed before 3000AD or it might be purple, etc. But the theory can be made sufficiently specific by complicating the grue-ification procedure. Consider, instead, a theory that employs an exhaustive set of high-fidelity color predicates C 1 C n. The grue-ified counterpart defines grue-like predicates C 1 C n by cycling through disjunctive definitions of high-fidelity predicates as follows: a is C x a is C x and observed before 3000AD, or a is C x+1 and not observed before 3000AD. If C x = C n, then a is C x a is C x and observed before 3000AD, or a is C 1 and not observed before 3000AD. 6

Just as a feature might indicate a theory s truth, so too might a feature indicate a theory s fidelity. I will call such a theoretical feature a fidelic virtue. Fidelic virtue and epistemic virtue are conceptually distinct in the same way that pragmatic virtue and epistemic virtue are. It s an open question how the three kinds of virtue overlap, if at all. Generally speaking, the ideological externalist wants a high-fidelity theory. As Sider puts it: [I]magine a universe that is entirely full of fluid. A plane divides the universe into two halves, one in which the fluid is uniformly red, the other in which the fluid is uniformly blue... Now imagine a group of people who encounter this universe, but accord no special status to the dividing blue-red plane. Instead of thinking of the universe as divided into the red and blue halves, they think of it as being divided in half by a different plane... And they do not use predicates for red and blue. Instead, they have a pair of predicates that they apply uniformly within the two regions separated by their dividing plane. These predicates... cut across the predicates red and blue. The regions to the left of the [dividing] line they call bred ; the regions to the right they call rue. It is almost irresistible to describe these people as making a mistake. But they re not making a mistake about where the red and blue regions are, since they make no claims about red or blue. And they make no mistakes when they apply their own concepts. The regions that they call bred are indeed bred, and the regions they call rue are indeed rue. The problem is that they ve got the wrong concepts. They re carving the world up incorrectly. By failing to think in terms of the red/blue dividing plane, they are missing something. Although their beliefs are true, those beliefs do not match the world s structure (Sider (2011): 2 3). The bred / rue theory is deficient not because it is false but because it lacks fidelity. Its ideology fails to accurately match the objective features of the world. Ideological externalists have given many reasons to justify their commitment to fidelity. I ll briefly sketch three such reasons below. To group these reasons under a slogan: Truth is not enough! First, truth seems too easy to acquire in the absence of further theoretical constraints. Many metaphysician s cite Putnam s model-theoretic argument in support of this claim. 7 According to Putnam, under relatively plausible conditions any theory can come out true, no matter what the world is like. The technical details of the argument go roughly like this. Any theory, in order to be appropriately judged true or false, needs to be interpreted. For our purposes, an interpretation amounts to a function that assigns extensions to all the non-logical expressions of the language i.e. predicates and names. Now consider a theory that posits an infinite amount of objects. It 7 While there are many ways to interpret the argument, I focus on the version found in Lewis (1984). For the original presentation, see Putnam (1977). 7

is plausible to think that the world contains infinitely many objects. No matter what relational constraints are placed on the theory, there will be an abundance of functions assigning extensions to predicates and names that ensure all sentences of the theory are true. Many ideological externalists respond to the model-theoretic argument by imposing some additional constraint on interpretations. David Lewis, for example, restricts the range of interpretations to those that pick out the elite minority of things and classes. Since most of the interpretations generated by Putnam s argument refer to classes that are miscellaneous, gerrymandered, [and] ill-demarcated, in most cases there is no problem identifying the correct interpretation (Lewis (1984): 227). More generally, all else being equal a theory ought to be interpreted as having a high degree of fidelity. Second, fidelity is a necessary precondition of induction. Consider Nelson Goodman (1955) s riddle of induction. We observe a green emerald, and another, and another. Eventually, we decide to project our observations onto the whole class of emeralds and by induction conclude that all emeralds are green. This projection extends both spatially and temporally. That is, we conclude that all emeralds now, wherever they are in the world, are green and we conclude that all the emeralds we see in the future will be green. Recall that the predicate grue is defined as: x is grue = df x is observed before 3000AD and is green, or x is not observed before 3000AD and is blue Every emerald we have so far observed is grue as well as green. Following the intuitively plausible Nicod s principle, observations of Fs that are Gs provide evidence that all Fs are Gs. So it seems we are equally justified in generalizing for grue. But this cannot be the case. Our observations of emeralds are not enough to justify the general claim about grueness. In other words, generalizations involving green seem more legitimate or lawlike than generalizations involving grue. Some ideological externalists explain this difference in legitimacy by appealing to fidelity. They restrict Nicod s principle to high-fidelity terminology. On the plausible assumption that green is relatively high fidelity and grue is a low-fidelity gerrymander, the ideological externalist s commitment to fidelity explains why we legitimately project green but not grue. Finally, a true theory without fidelity often fails to be explanatory. Suppose God told us there was a book, somewhere, in which was written the final theory of the world. Now suppose I introduce 8

a predicate F that applies to an object just in case what is said in God s book is true. The resulting theory (based on the single axiom xfx ) is no less true than what is written in God s book. But it fails to be explanatory. Similarly, I could cook up a mathematical function that successfully matches the past motions of the planets to the past fluctuations of the Dow Jones industrial average. But clearly this function is explanatorily worthless; the value of Mercury Systems Inc. isn t explained by the astronomical characteristics of the planet Mercury. 8 The fact that a theory is high fidelity suggests that it offers genuine explanations. Sometimes, metaphysicians say that joint-carving theories provide distinctively metaphysical explanations, where a metaphysical explanation is an objective, informative explanation of how the world operates. But metaphysicians aren t the only people who think genuine explanations are jointcarving. Scientists and philosophers of science often implicitly hold that natural science theories ought to be stated in high-fidelity terminology. 9. Similarly, Lange (2015) has argued that genuinely explanatory mathematical proofs incorporate natural mathematical properties. Clearly much more can be said about these three reasons to care about a theory s fidelity. My goal here is not to settle the matter once and for all. My goal is to simply motivate the externalist s position. For her, truth alone is unable to differentiate between all the realist implications of competing theories. Fidelity is indispensable for this task. Carrying this point over to the virtue-driven methodology, the ideological externalist should care about fidelic virtues. Whereas she always privilege epistemic virtues over pragmatic virtues when evaluating rival theories, she should not always privilege epistemic virtues over fidelic virtues. More carefully, she should sometimes prefer a fidelically virtuous theory with lower epistemic virtue to an epistemically virtuous theory with lower fidelic virtue. Anyone who has such a preference takes fidelity seriously. Someone who takes fidelity seriously need not weigh fidelic virtue and epistemic virtue equally. She might prefer the relatively high-fidelity theory only when the gap in epistemic virtue is small. She might even weigh fidelic virtue more than epistemic virtue. At the most extreme, she might be willing to endorse a theory she knows to be false when she knows whatever modification needed 8 Compare to Lewis (1983): 367, Sider (2011): 27 28 9 Of course no one is stating the point quite like I am. The general point is that there is a close connection between explanation and naturalness, objective similarity, etc. See, e.g., the species debate in philosophy of biology (Devitt (2011)). 9

to make it true would produce a horrifically gerrymandered ideology. Thus far, I have argued for two claims. First, epistemic virtue and fidelic virtue come apart an epistemically virtuous theory can be fidelically vicious and vice versa. Second, an ideological externalist ought to take fidelity seriously. I suspect many metaphysicians implicitly endorse these two claims. Yet, surprisingly, no one has clearly articulated the methodology as I have here. Sider doesn t distinguish between epistemic virtues and fidelic virtues. In Sider (2011) he says very little about theoretical virtues. In Sider (2013), he appeals to ideological simplicity because ideologically simpler theories are more likely to be true, (239). Nowhere does he explicitly state that a virtue might be indicative of truth but not fidelity, and vice versa. Sam Cowling, like Sider, says that parsimony is an epistemic virtue. His gloss on epistemic virtue is admittedly not as explicitly truth-oriented than mine. He says an epistemic virtue is a feature that makes belief in a theory better justified than belief in otherwise equally good rivals, (Cowling (2013): 3890). Yet justification is usually linked to truth, and Cowling later quotes the above passage from Sider without critique. So it seems that Cowling also doesn t clearly distinguish between epistemic virtue and fidelic virtue. Finally, although David Lewis does distinguish between a theory s truth and its fidelity, he does not seem to distinguish between the corresponding virtues. The closest he gets to making that distinction comes in a passage where he compares the benefits of set theory with those of his theory of modal realism, he says each is a paradise, and by believing in them we can improve the unity and economy of the theory that is our professional concern total theory, the whole of what we take to be true. Lewis understands these as genuine theoretical benefits. But he gives them an epistemic gloss: Why believe in a plurality of worlds? Because the hypothesis is serviceable, and that is a reason to think that it is true, (Lewis (1986): 3 4, emphasis mine). I have motivated the claim that truth comes apart from fidelity. Many virtue-driven metaphysicians agree with me. But no one has yet explicitly acknowledged the impact of this claim on the methodology of theory choice. The virtue-driven metaphysician should acknowledge that there is a class of features that are truth-conducive, a class of features that are fidelity-conducive, and that these classes may or may not overlap. Finally, I want to make explicit the difference between a theory having a theoretical feature and a theory having that which the feature indicates. Theoretical virtue merely increases the likelihood 10

of getting what we want, it does not guarantee it. An epistemically virtuous theory might turn out to be false. Similarly, a fidelically virtuous theory might turn out to not have an ideology that accurately match the structure of the world. Because I am presently concerns with the virtuedriven methodology, I am focused on the virtues themselves and the extent to which they raise the probability of truth or fidelity. I grant that all of this is consistent with the theories failing to be true or failing to have fidelity. 2.2 The Eightfold Path of Parsimony Many virtue-driven metaphysicians compare theories on the basis of the theoretical virtue of parsimony. Such comparisons of parsimony have been used to develop arguments for mereological nihilism, bundle theory, materialism, and nominalism. 10 Frankly, comparisons of relative parsimony are commonplace and seem to have a lot of clout. It is for this reason especially important to consider why and to what extent arguments that appeal to parsimony do (or do not) work. Parsimony is said in many ways. Here, I will identify eight specific principles of parsimony. As I will show, which principle a metaphysician adopts will influence her choice of theory. Furthermore, the motivations for adopting one principle do not carry over to the other. Virtue-driven metaphysicians by and large endorse the Ockham s Razor understanding of parsimony: do not multiply entities beyond necessity. Yet that slogan is itself up for interpretation. Some (like Nolan (1997) think that a theory s parsimony is best measured by a literal counting of the entities posited by the theory. They endorse a principle of quantitative ontological parsimony. Others (like Lewis (1973)) care very little about the size of the domain. What matters to them is the number of kinds of things in the domain. They endorse a principle of qualitative ontological parsimony. The virtue-driven metaphysician s choice from these two principles impacts how she evaluates competing theories. To illustrate this impact, consider how the two principles measure two competing theories of modality: a Lewisian theory of modal realism and a Plantinga-style theory of actualism. On the Lewisian theory, the world we inhabit is just one among many concrete possible worlds. When we talk about what actually exists, we in effect restrict our statements to the inhabi- 10 Nihilism: Horgan and Potr c (2008). Bundle theory: Paul (2017). Materialism: Churchland (1984). Nominalism: Melia (2008). 11

tants of our world. For instance, when I say No state has a professional clown as a governor, I say something true. But according to modal realism there are many more clowns than those located in the actual world. There is a world wherein some state has a clown as governor. (In fact, there is a world wherein all states have clowns as governors.) Likewise, for any possible way an entity might be, there is an entity that is that way. On the face of it, Lewisian modal realism seems to have a massively bloated ontology. But there is a plausible sense in which its ontology is no more bloated than that of its rival. According to the Lewisian theory, a possible clown is just like an actual clown; a possible clown is just as concrete, just as capable of inspiring mirth or fear in the children of their world. That is to say, possible clowns and actual clowns are of the same ontological kind. Similarly, on the Lewisian theory, possible worlds are just like the concrete world we inhabit. So far as the principle of qualitative ontological parsimony is concerned, a theory that posits the existence of such possible worlds and possible clowns is no less virtuous than a theory that only posits the existence of the actual world with actual clowns. In contrast, Plantinga-style actualism denies the existence of merely possible clowns. Plausibly, then, the actualist theory is more quantitatively parsimonious theory than the Lewisian theory. Yet Plantinga-style actualism still posit the existence of possible worlds. These possible worlds are not of the same kind as the concrete world we inhabit. They are (something like) abstract maximal states of affairs. As a consequence, Plantinga-style actualism seems committed to more ontological kinds than Lewisian modal realism. So the actualist theory is less qualitatively parsimonious than the Lewisian theory. Each of the theories is more parsimonious than the other, but in different senses. Of course the relative simplicity of Lewisian modal realism and Plantinga-style actualism is a fraught matter. Nevertheless, what I ve sketched is illustrative of how a metaphysical dispute can be shaped by different principles of parsimony. If someone privileges qualitative parsimony over quantitative parsimony, then if she is truly committed to her methodology she will be disposed to endorse modal realism. But someone else who privileges quantitative parsimony over qualitative parsimony will be disposed to endorse actualism. Consequently, a metaphysical dispute can sometimes be traced back to a prior disagreement about how to measure a theory s parsimony. Though metaphysicians usually understand parsimony in connection to a theory s ontology, 12

some extended it to cover a theory s ideology. Lewis is one of the first and most prominent metaphysicians to endorse a controversial theory on the basis of its ideological parsimony. Independent of modal realism s ontological parsimony, Lewis acknowledges its ability to reduce the diversity of notions we must accept as primitive as [improving] the unity and economy of the theory that is our professional concern total theory, the whole of what we take to be true, (Lewis (1986): 4). Recently, Sider has embraced ideological parsimony as a virtue. To take just one example, Sider endorses a species of modal reductionism. He says, quite straightforwardly, The good reason for opposing modal primitivism is simply: ideological economy, (Sider (2011), 317). Others who have at least tentatively endorsed ideological parsimony as a virtue include: Cowling (2013); Schaffer (2014); Turner (2015); Brenner (2016). Just as with ontology, parsimony can be connected to ideology in two different ways. 11 Someone might think that a theory s parsimony is best measured by the number of undefined terms contained in its ideology. She endorses a principle of quantitative ideological parsimony. Someone might instead think that a theory s parsimony is best measured by the number of ideological kinds and care very little about how well-populated those kinds are. Such a person endorses a principle of qualitative ideological parsimony. It s not obvious what an ideological kind is. Intuitively, though, we can individuate ideological kinds by topic. For instance, there is an ideological kind corresponding to color. All color predicates like green, chartreuse, and Pantone 448C are of this kind, as are relational predicates like is more saturated than. Similarly, there is an ideological kind corresponding to modality. Primitive modal operators, predicates like possibly true and consistency, as well as primitive dispositional predicates like fragile are of this kind. 12 There are, then, at least four different senses in which a theory can be said to be parsimonious. There are also two distinct reasons to care about parsimony: either it helps us determine when a theory is more likely to be true, or it helps us determine when a theory is more likely to have a high degree of fidelity. Thus, there are in total eight different approaches to parsimony: Epistemic Quantitative Ontological Parsimony: A theory that posits fewer entities is more likely to be true. 11 Much of what I say agrees with Cowling (2013). Cameron (2012) also makes this distinction. 12 Some demarcate ideological kinds based on interdefinability. For reasons that are beyond the scope of this paper, I think the interdefinability approach is a nonstarter. 13

Epistemic Qualitative Ontological Parsimony: A theory that posits fewer kinds of entities is more likely to be true. Fidelic Quantitative Ontological Parsimony: A theory that posits fewer entities is more likely to have fidelity. Fidelic Qualitative Ontological Parsimony: A theory that posits fewer kinds of entities is more likely to have fidelity. Epistemic Quantitative Ideological Parsimony: A theory that employs fewer ideological bits is more likely to be true. Epistemic Qualitative Ideological Parsimony: A theory that employs fewer ideological kinds is more likely to be true. Fidelic Quantitative Ideological Parsimony: A theory that employs fewer ideological bits is more likely to have fidelity. Fidelic Qualitative Ideological Parsimony: A theory that employs fewer ideological kinds is more likely to have fidelity. For the virtue-driven metaphysician, it s an open question which of these eight paths should be taken and which should not. 3 Ideological Parsimony is not an Epistemic Virtue I ll skip over arguments for and against adopting principles of ontological parsimony because I don t have much to add to what has already been said. But which principle of ideological parsimony should be adopted, if any? In this section I will discuss three arguments for epistemic ideological parsimony. I call these arguments: the general simplicity argument, the argument from expressive paucity, and the interaction argument. While none of them are novel to me, I substantially improve their strength and precision. I ll note, for instance, where these arguments differentiate between quantitative and qualitative ideological parsimony. Ultimately, I do not think that any of these three arguments succeed as intended. At best, these arguments support the weaker claim that we ought to endorse some principle of ideological parsimony. 14

My verdict might provoke the following worry: ought we to expect a compelling argument for adopting some feature as a theoretical virtue? Is it even possible to provide a neutral argument in defense of such-and-such principle? If not, it would be altogether unsurprising if the three arguments fail. Thankfully, none of what I say presupposes the possibility of such an argument. I claim that the arguments fail even from the assumption-heavy framework of high-fidelity externalism. Plausibly, many of those who reject this framework will also find the arguments unconvincing. But fully addressing the broader methodological issue regarding the independent justification for the virtuedriven methodology is well beyond what I can accomplish in this paper. 3.1 Against the General Simplicity Argument Here is one straightforward argument for the claim that ideological parsimony is an epistemic virtue. We already believe that the relative simplicity of a theory increases the likelihood that the theory is true. Ideological parsimony is a species of simplicity. Insofar as ideological parsimony contributes to overall simplicity, then, ideological parsimony also increases the likelihood that the theory is true. Call this the general simplicity argument. 13 As stated, the general simplicity argument is a non-starter. It cannot be completely general. There are some forms of simplicity that fail to supply even a prima facie reason to believe that the theory is more likely to be true. First, consider two languages, English and English-et. English and English-et are semantically indistinguishable languages. They have identical rules of composition and for any arbitrary expression of one language there is an equivalent expression of the other. The only difference between the languages is that English-et s expressions are longer by one syllable. For any English word the equivalent English-et word has an et attached e.g. bird / birdet ; flying / flying-et ; quickly / quickly-et. It s simpler to utter English sentences than to utter English-et sentences. So in some sense a theory cast in English is more simple than a theory cast in English-et. But there is no reason whatsoever to think that the English theory is more likely to be true than the English-et theory. Someone might plausibly say that the relevant sense of simplicity is not quite as wide-ranging as I implied above. Rather, the general simplicity argument is concerned with objective simplicity, 13 A version of this argument can be found in Sider (2013): 239 243. 15

where objective simplicity means something like simplicity with regards to the picture of the world provided by the theory. A theory cast in English paints a picture of the world no more simple than that painted by an equivalent theory cast in English-et. Furthermore, objective simplicity includes ideology. Recall that the ideological externalist thinks that a commitment to a bit of ideology comes with a corresponding commitment to some feature of reality. So, ideological simplicity is a species of objective simplicity. Yet there are also cases of objective simplicity that fail to supply even a prima facie reason to believe that the theory is more likely to be true. Consider two equivalent theories (both in English this time). The only difference between these two theories is that the first is closed under deduction and the second is almost closed under deduction. By almost closed I mean that it is closed under deduction but for the following exception: when the derived sentence is (i) 10 1010 words long, and (ii) derived via adjunction (i.e. ϕ,ψ ϕ ψ ). The first theory is more simple than the second because it has simpler logical properties closure under deduction as opposed to closure under almost-deduction. The second theory is more simple because it makes fewer claims about the world. Yet neither form of simplicity gives even a prima facie reason to believe the theory is more likely to be true than its rival. Someone might again say that my example involves the wrong sort of simplicity. She might vehemently reject Bertrand Russell s claim, that... logic is concerned with the real world just as truly as zoology, though with its more abstract and general features, (Russell (1919): 169). Thus, the relative simplicity of closure under deduction over closure under almost-deduction is irrelevant when evaluating the objective simplicity of the two theories. She might also deny that the almostclosed theory makes fewer claims about the world. While the theory contains fewer sentences, it expresses just as many propositions as the more expansive theory. Thus, the two theories paint pictures of the world that are equally objectively simple. At this point, I would start to worry that the goalposts would continue to move until I lose. More fairly, I think that someone sympathetic toward the general simplicity argument owes an account of simplicity that avoids the above counterexamples but still includes ideological simplicity. The underspecified notion of objective simplicity is not enough, for what does and does not constitute objective simplicity is very much an open question. So the notion of simplicity must be such that there is some reason to believe that ideological parsimony is positively correlated with the truth 16

of the theory. That is, the argument works only if we assume that ideological parsimony is an epistemic virtue. The general simplicity argument is question-begging. Perhaps the argument can avoid the question-begging charge. Often, the claim that ontological parsimony is a truth-conducive species of simplicity is justified by intuition. It just seems like an ontologically simpler theory is more likely to be true! Analogously, maybe the claim that ideological parsimony is a truth-conducive species of simplicity is also justified by intuition. I don t think this approach will work. First, there are powerful intuitions against the claim that ideological parsimony is a truth-conducive species of simplicity. Second, the interaction between ontology and ideology shows that the intuition in favor of ontologically simpler theories is in tension with the intuition in favor of ideologically simpler theories. There are contexts where many fail to have the intuition that the ideologically simpler theory is more likely to be true. For example, take two sets of propositional logic operators: (i) {,,, }, and (ii) {, } These two sets of operators are expressively equivalent. Sentences in a theory that takes all the elements of the first set as primitive can be matched one-to-one with expressively equivalent sentences of another theory that takes only elements of the second set as primitive. The two-operator theory is ideologically simpler. Yet I suspect most have the intuition that the elimination of the extra logical operators makes no difference as to the truth of the theory. Even I, an unapologetic ideological externalist, have that intuition. Now, some of the variation in intuition can be explained by distinguishing between quantitative ideological parsimony and qualitative ideological parsimony. A theory that takes every member of {,,, } as primitive is committed to fewer bits of ideology than a theory that takes only the members of {, } as primitive. But both theories are committed to the same number of ideological kinds. I suspect that many have the intuition that quantitative ideological parsimony makes no epistemic difference. But, so someone might say, that doesn t impugn the original intuition in favor of ideological parsimony. That intuition is best understood as supporting Epistemic Qualitative Ideological Parsimony. Unfortunately, there are also intuitions that speak directly against Epistemic Qualitative Ideological Parsimony. Suppose I introduce a new theory of fundamental forces. This theory posits three distinct forces: gravitational, electromagnetic, and medium nuclear. Every mention of the weak nuclear force and the strong nuclear force in the standard theory is replaced by a single 17

mention of the medium nuclear force. My new theory has greater qualitative ideological parsimony than the standard theory. Yet it does not have much else going for it. Even though my theory is committed to fewer ideological kinds, I do not have the intuition that it is more likely to be true. Set aside the battle of intuitions. An improvement in ideological parsimony is often paid for with an offsetting increase in complexity elsewhere in the theory. The paradigm example of this tradeoff is the interaction between ideology and ontology. In Lewis and Lewis (1970), Argle and Bargle dispute the existence of holes. Argle offers a theory that avoids commitment to holes by the use of a potentially infinite series of shape predicates. In contrast, Bargle offers a theory that does without those complicated predicates but posits the existence of holes. Argle s theory is more ontologically parsimonious but less ideologically parsimonious; Bargle s theory is more ideologically parsimonious but less ontologically parsimonious. Parsimony in one domain negatively impacts parsimony in the other. There is no theory of holes that is simpler tout court. To be sure, not all improvements in ideological parsimony follow this trade-off pattern. 14 But the point is that, in general, we should not expect the more ideologically parsimonious theory to be overall more simple than a less ideologically parsimonious rival. The general simplicity argument is too crude of a reason to endorse either principle of Epistemic Ideological Parsimony. 3.2 Against the Argument from Expressive Paucity We ought to endorse an epistemic principle of ideological parsimony only if there is a good, independent, non-ad hoc reason to value ideological simplicity. Here s one potential reason: a theory should avoid saying too much about how the world is. More specifically, it should avoid making false claims. The larger a theory s ideology, the more opportunities it has to say something false. To illustrate, assume that mereological nihilism is true. The sentence The wheel is a proper part of the wagon, is therefore false. A theory that doesn t include proper part in its ideology won t even be able to state this claim. It is therefore less liable to falsehood when compared to a theory that does include proper part. More generally, a theory that lacks expressive power is less likely to be false. Since a theory with a smaller ideology has relatively less expressive power, it is less likely to be false. Thus, ideological parsimony is an epistemic virtue. Call this the argument from 14 For instance, Sider (2013) offers a theory of mereological nihilism that in a sense merely deletes mereological ideology and related statements. 18

expressive paucity. Uriah Kriegel discusses a different version of this argument as it applies to ontological parsimony. He asks us to consider a metaphysically vacuum-wrapped micro-sculpture crafted from five particles (Kriegel (2013): 20). According to the ontologically parsimonious theory of mereological nihilism, there are five entities within the wrap. According to the relatively less parsimonious theory of mereological universalism, there are thirty-one entities. Because nihilism makes fewer existence claims, it seems like it is less exposed to error than universalism. So, according to the argument, ontological parsimony is truth-conducive. Kriegel objects to this argument because he denies that nihilism makes fewer existence claims. He does think that it makes fewer positive existence claims. But for every positive existence claim universalism makes nihilism makes the corresponding negative existence claim. For example, when universalism says, There is a composite object that has five proper parts, nihilism says, There is not a composite object that has five proper parts. So the two theories make the same number of existence claims. Nihilism, the ontologically parsimonious contender, is therefore not less prone to error. The argument from expressive paucity fails to justify a principle of epistemic ontological parsimony. Interestingly, the ideological version of the argument avoids Kriegel s objection. A theory that lacks mereological ideology cannot directly say anything, positive or negative, about parthood. Such a theory does not explicitly state that there is an object composed from the metaphysically vacuum-wrapped particles. But it also does not explicitly state that there is not such an object. In a way it remains silent. As a consequence, an ideologically parsimonious theory is genuinely less capable of directly stating falsehoods than its less parsimonious rival. Perhaps, then, ideological parsimony is truth-conducive. The extent to which an ideologically impoverished theory can avoid falsehood depends on background assumptions about when and in what respects a theory says something false. Suppose that the extent to which a theory says something false is measured by the number of false propositions it asserts. On some accounts, the proposition expressed by The wheel is a proper part of the wagon, is distinct from the proposition expressed by The wheel is a part of the wagon and the wheel the wagon. If that s right, then an ideology containing parthood, =, and proper parthood will enable a theory to say more false things than an ideology containing just proper parthood. Con- 19

sequently, the argument from expressive paucity would support Epistemic Quantitative Ideological Parsimony. On a more coarse-grained account of propositions, though, the two sentences express the same thing. If so, the argument does not obviously support quantitative ideological parsimony. The argument would, however, support Epistemic Qualitative Ideological Parsimony. One objection to the argument from expressive paucity is as follows. A theory lacking mereological ideology cannot directly say anything about parthood. But it might nonetheless indirectly say something about parthood. For example, a theory might give a complete description of the world s simples and then say That s all there is. In a sense, that theory entails that proper parthood doesn t occur. If proper parthood does occur, then, the nihilist theory indirectly says something false. What matters is not which propositions the theory expresses but which propositions the theory entails. So long as the theory includes a That s all there is, clause, the argument from expressive paucity fails to justify an epistemic principle of ideological parsimony. Another objection to the argument turns on the notion of an epistemic goal. The classic statement of this notion comes from William James: There are two ways of looking at our duty in the matter of opinion ways entirely different, and yet ways about whose difference the theory of knowledge seems hitherto to have shown very little concern. We must know the truth; and we must avoid error these are our first and great commandments as would-be knowers; but they are not two ways of stating an identical commandment, they are two separable laws... [H]e who says, Better go without belief forever than believe a lie! merely shows his own preponderant private horror of becoming a dupe (James (1969): 203 204). Following James, it would be misleading to suggest that the only thing that matters is avoiding falsehood. We also want to acquire true beliefs. The point plausibly carries over to theory choice. We want more than just a theory that fails to be false. If that were the only goal then we should refuse to endorse any theory whatsoever. What we want is a theory that fails to be false and is interestingly true. Unfortunately, these two epistemic goals often pull in opposite directions and there is no obvious way to weigh them relative to each other. Few would be inclined to totally disregard either goal. That is in large part why the theory that states nothing and the theory that states everything are rightly dismissed. But how many new truths is a falsehood worth? Wayne Riggs distinguishes between two different strategies for answering the weighing question, 20