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Home , Modal realism

Aporia vol. 25 no. 1 — 2015

The Tangled Beard of Modal

Kelvin Jensen

avid Lewis is well known for his theory of modal realism. According to this theory, our world — us, the universe we inhabit, Dand anything that has ever existed therein — is just one among many. In fact, modal realism holds that there are countless worlds more or less similar to our own. There is a world, for instance, identical to ours saving one difference: in lieu of wearing a polo shirt today, I wore a button - down shirt. Other worlds are not so similar; one world, for example, consists of planets populated by unicorns. Another is governed by physical laws that permit humans to walk on water. Indeed, for any logically possible state of affairs, there is a world embodying that state of affairs. Since there are infinite possible states of affairs, there are infinite worlds. To be sure, these worlds are spatio - temporally inaccessible and causally isolated from our world, but they exist as fully as our world does. Why would Lewis preach such a bizarre metaphysical doctrine? One sole reason: usefulness (Plurality 3). Lewis believes that his theory resolves important problems in , specifically in , , and . Of particular renown is the solution to a perennial issue in modality, an issue that can be summarized by the following question: what makes modal properties possible? What, for instance, grounds the property I have of possibly wearing a button - down shirt? Modal realism has a ready answer: I possess the property of possibly wearing a button - down shirt because there is a world like ours in every

Kelvin Jensen is a senior majoring in philosophy at Brigham Young University. His primary interests include , , and . After graduating next April, Kelvin plans on attending law school. This essay tied for third place in the 2015 David H. Yarn Philosophcal Essay Contest. 46 Kelvin Jensen respect except that my counterpart is wearing a button - down shirt. That is, modal properties are grounded in their non - modal realization on Lewisian possible worlds. Whether Lewis’s theory can truly explain modal properties — and provide the other benefits that Lewis touts — has been disputed. However, I shall not argue with Lewis here; for the purposes of this paper, I grant the benefits, all of the benefits, that he ascribes to his theory. I do, however, want to explore an objection that he treats. In his book Counterfactuals, Lewis considers several complaints about modal realism. One qualm relates to Ockham’s Razor and can be explained thus: modal realism flies in the face of ontological parsimony, which demands — at the very least — that one not recklessly postulate the of new entities. This prescription is two - pronged: according to quantitative ontological parsimony, one ought not to frivolously postulate additional individual entities; according to qualitative ontological parsimony, one ought not to frivolously postulate additional kinds of entities. Modal realism is thought to run afoul of both senses of parsimony — it not only postulates multiple worlds similar to ours, but also postulates multiple worlds different in kind than ours. Inasmuch as ontological parsimony is an important theoretical virtue, modal realism falls short. Lewis’s response to this objection is threefold: first, he admits that modal realism disrespects quantitative ontological parsimony but claims that this concession is innocuous (87). Quantitative parsimony is irrelevant to a theory’s truth; qualitative parsimony is what matters. Lewis doesn’t argue for this position — he simply takes it for granted. Second, he insists that modal realism in no way violates qualitative parsimony; after all, possible worlds are not different in kind than the actual world. As Lewis observes, “You believe in our actual world already. I ask you to believe in more things of that kind, not in things of some new kind” (87). And finally, he presumes that no Ockham’s Razor objection can be decisive (87). What he means is that violations of ontological parsimony — no matter how flagrant — do not, by themselves, warrant rejecting modal realism. I take issue with Lewis’s response. Quantitative parsimony is a theoretical virtue, and modal realism does disregard qualitative parsimony. That is, Lewis’s theory disrespects both quantitative and qualitative parsimony, both of which are important theoretical considerations. Perhaps a violation of ontological parsimony cannot be decisive, but the violation here is so egregious, even frightful, that we ought to turn our attention to rival theories and remold them to provide the theoretical benefits of modal realism, without the ontological costs. Let’s examine the support for my claims. Lewis is not unique in dismissing quantitative parsimony without a hearing. Many philosophers have presumed that quantitative parsimony The Tangled Beard of Modal Realism 47 is simply irrelevant to the truth of a theory. Why is this assumption so prevalent? According to Alan Baker, many reject quantitative parsimony because it doesn’t appear to connect to “independently recognizable theoretical virtues” (248). For instance, qualitative parsimony can be justified by appeals to epistemic , which holds, at its core, that we ought not to believe in something unless we have good reason to believe in it (248). Syntactical elegance — the other strand of Ockham’s Razor, a strand which demands simplicity in a theory’s basic principles or axioms — can be justified on pragmatic grounds. A theory that is syntactically elegant is easier to use or manipulate, and is generally more comprehensible (248). From which theoretical virtue can quantitative parsimony be derived? It can’t be derived from epistemic conservatism, for quantitative parsimony doesn’t have to do with the postulation of new kinds of entities or mechanisms. Rather, it postulates additional entities of the kinds in which we already believe. Nor does it seem likely that quantitative parsimony can be derived from pragmatic concerns. Thus, inasmuch as quantitative parsimony can’t be tied to any obvious theoretical virtue, Lewis is right — quantitative parsimony ought to be jettisoned. It may be true that quantitative parsimony isn’t justified by appeals to some recognizable theoretical virtue. But I think it can be justified by appeals to the workings of nature. Nature generally uses the simplest means to achieve her ends, and this fact justifies the prescription to keep down the number of individual entities, even if these entities are not different in kind from those in which we believe. If nature uses the simplest means to accomplish her purposes, quantitatively parsimonious theories are more likely to be true ceteris paribus. An example may prove illustrative: in the early twentieth century, physicists observed a puzzling aspect of beta decay, a type of radioactive decay in which an electron is emitted from a nucleus. Upon emission of the electron, the energy of the nucleus decreased by more energy than could be ascribed to the emitted electron. This result bemused scientists, who had anticipated that the diminution of energy in the nucleus would be equivalent to the energy of the emitted electron. Wolfgang Pauli attempted to resolve the discrepancy by conjecturing the existence of a neutrally charged particle — a “neutrino” — emitted concomi- tantly with the electron. This neutrino, Pauli reasoned, would possess an energy mass equal to the difference between the energy loss of the nucleus and the energy of the emitted electron. Pauli’s theory was accepted, and the existence of his neutrino was empirically confirmed many years later. Two features of this example stand out: the quantity of neutrinos actually emitted from the atom, and the quantity of neutrinos Pauli postulated. Only one neutrino was emitted from the anomalous atom. Had the atom emitted two neutrinos, each possessing half of the energy of the original, 48 Kelvin Jensen nature could have achieved the same results (Nolan 333). Indeed, nature could have achieved the same results with three neutrinos, each possessing a third of the energy of the original; or four; or four hundred. But nature didn’t employ four hundred neutrinos, each with one four - hundredth of the necessary charge; she selected one neutrino. In this instance, at least, nature really did use the simplest means to accomplish her ends. Interestingly, Pauli decided to postulate only one neutrino. He could have postulated two neutrinos, each possessing half of the energy needed to account for the discrepancy. This postulation would have yielded the same explanatory power as his first theory (Nolan 333). Or he could have postulated three neutrinos, each possessing a third of the energy needed; or four; or four hundred. Yet Pauli proposed just one neutrino. Pauli was apparently guided by considerations of quantitative parsimony, and even if he wasn’t, adherence to quantitative parsimony would have encouraged him to postulate merely one neutrino had he considered the postulation of additional neutrinos. Therefore, it appears that a commitment to quantitative parsimony helps us to select theories more likely to reflect the workings of nature. At this juncture I anticipate two objections: first, although quan- titative parsimony got it right in this scenario, it may not always pick out the correct theory. There may be some instances in which nature doesn’t use the simplest means to achieve her ends. Moreover, even if there are no such instances, it’s not clear that nature will always continue to employ the simplest means. This is a fair objection, and I fear that my response may be somewhat weak. I’m not sure that the workings of nature vindicate the utility of quantitative parsimony in every instance, and I certainly don’t know whether nature will continue to use the simplest instruments to achieve her ends. However, it does seem true that nature usually employs the simplest means. And the story of Pauli’s neutrino is not unique: choosing the lowest quantity possible of individual entities, ceteris paribus, has helped scientists other than Pauli arrive at the truth (Nolan 342). If we are realists about scientific theories, quantitative parsimony is valuable. Second, although I may have shown that quantitative parsimony is an important principle for scientific theories, I may not have shown that quantitate parsimony is an important principle for philosophical theories. Philosophers may not care very much about proposing theories that map to the world; for instance, moral theories describe how the world should be, not how the world is. If quantitative parsimony is valuable because it takes into account the fact that nature generally uses the simplest means, then quantitative parsimony may not be a valuable or even relevant standard for evaluating some philosophical theories. The Tangled Beard of Modal Realism 49

This objection may have merit. The principle of quantitative parsimony may be irrelevant when considering some philosophical theories, but this is not the case when considering theories that seek to inform us about how things are. And modal realism is a theory that purportedly describes how things are; therefore, quantitative parsimony is important to assessments of modal realism. Hence, Lewis is wrong: to concede that modal realism is quantitatively unparsimonious is not innocuous. Rather, the concession indicates a cost of his theory. Let’s turn to my second claim, which states that modal realism is qualitatively unparsimonious. As mentioned, Lewis believes that possible worlds are not different in kind than the actual world, so he concludes that modal realism is not qualitatively extravagant. But his premise is patently untrue; many of Lewis’s worlds are very different from ours. A plethora of Lewisian worlds are populated by ghosts, witches, unicorns, tooth fairies, talking vacuums, Greek gods and goddesses, and a whole host of creatures whose existence we have rejected. And then there are the worlds themselves. Some of Lewis’s worlds have no past or future, others are bereft of regularity, in others there is reverse causation, and in others still there is no causation. Therefore, to believe in modal realism is to believe in copious entities and mechanisms of a very different kind than those in which we now believe. A more glaring violation of qualitative parsimony we would be hard pressed to find. Not so, responds John Divers on Lewis’s behalf. In Possible Worlds, Divers admits that belief in modal realism does entail belief in fairy tale - like creatures and obscure mechanisms, but he insists that these things are not of a different kind than the things in our world. For purposes of qualitative parsimony, “kind” refers to broad ontological categories, like substances or properties (155). And modal realism advocates only two ontological categories: sets and individuals (155). But we already believe in sets and individuals; thus, modal realism doesn’t postulate further ontological categories, which signifies that it doesn’t posit any new kind of thing. Therefore, concludes Divers, modal realism respects qualitative parsimony. Is Divers’ response plausible? Not very. First, it’s highly unlikely that qualitative parsimony relates merely to Divers’ broad ontological categories; and second, even if it does, modal realism commits us to the existence of every ontological category, rendering it unparsimonious on Divers’ own account. Let’s consider these assertions. Qualitative parsimony is not treated as if it refers only to Divers’ general ontological divisions. For example, Cartesian dualism is thought to be less qualitatively parsimonious than material , for it posits two substances: mind and body. Mind is thought to be fundamentally different from body, so inasmuch as dualism has no more explanatory 50 Kelvin Jensen power than does material monism, dualism is charged with a qualitative parsimony violation, a charge that seems appropriate. But Divers’ inter- pretation of qualitative parsimony would not allow this charge. After all, mind is a substance, just as body is. Therefore, dualism does not postulate further ontological categories, according to Divers. Monists go awry in accusing dualism of being qualitatively unparsimonious. But Divers is clearly wrong: monists don’t go awry at all in their accusation; qualitative extravagance seems to be a very appropriate criticism of dualism. Indeed, if qualitative parsimony is used only when dealing with theories that postulate what Divers considers to be a further ontological category, it wouldn’t be used very much at all. Even if Divers’ interpretation of qualitative parsimony is correct, Lewis’s theory is still qualitatively unparsimonious. For modal realism holds that if it’s logically possible for something to exist — and this something surely includes ontological categories — then it exists. For example, there is nothing logically impossible about the existence of universals, so universals must exist. Indeed, any ontological category whose existence doesn’t entail a contradiction is, according to modal realism, an ontological category that exists on some . Therefore, even on Divers’ interpretation of qualitative parsimony, modal realism is unparsimonious. In fact, it’s as unparsimonious as any theory can possibly be. I have shown that quantitative parsimony is an important theoretical consideration, and that modal realism is qualitatively unparsimonious. But Lewis, as mentioned, doesn’t believe that ontological parsimony objections are decisive, so perhaps I have spilt much ink for naught. Why would Lewis believe that ontological parsimony violations don’t, by themselves, disprove a theory? One might think that an ontological parsimony objection is decisive to a theory only if there exists a rival theory possessing equal explanatory power. If we didn’t insert this condition, a parsimony objection could preclude the acceptance of correct theories. For instance, Ancient Greek chemistry is more parsimonious than is modern chemistry — Empedocles hypothesizes merely four elements (earth, water, air, and fire), but modern chemists hypothesize 110 elements, as shown in the periodic table. Yet no one would accept Ancient Greek chemistry in lieu of modern chemistry; why? Explanatory power; modern chemistry, although more promiscuous, explains a lot more than does Ancient Greek chemistry. Indeed, due to greater explanatory power, we have committed ourselves to many theories that are less ontologically parsimonious than are their predecessors. What this suggests, then, is that the sword of ontological parsimony can’t be wielded unless there are competing theories of equal explanatory capability and of greater parsimony. But we don’t have The Tangled Beard of Modal Realism 51 such a condition with respect to modal realism: Lewis’s theory explains more than does any other rival theory. Hence, an ontological parsimony objection can’t be decisive here. I have a qualm with the foregoing argument: to me, it’s not clear that ontological parsimony is decisive only when dealing with theories of equal explanatory power. Our adjudications among rival theories indicate that ontological parsimony can be applied to a theory even when its explanatory power is unmatched. Consider the debate about string theory, for example. String theory is an attempt to unify quantum physics with Newtonian physics, which together can explain the motion of any particle. While Newtonian mechanics can explain the motion of macroscopic particles, quantum mechanics is able to account for the motion of microscopic particles. Why do we desire a single, unified theory? Simply put, the axioms of Newtonian and quantum physics contradict each other. So we seek a new theory, one with a consistent axiom system and the explanatory power of both Newtonian and quantum mechanics. Several such theories have been proposed, and we group these all under the category of “string theory.” Some scientists don’t think that any version of string theory resolves the contradictions in Newtonian and quantum mechanics, but some do. But of those who do, few are eager advocates of string theory. What holds them back? Some are held by back by concerns about ontological parsimony (Grandy). The least onto- logically promiscuous versions of string theory postulate the existence of seven dimensions; the most promiscuous, twenty six, and existence of twenty six or even seven dimensions is thought to constitute significant ontological baggage. String theory has no peer in terms of explanatory power, but we are hesitant to support such a profligate theory. In other words, we act like ontological parsimony can be decisive, even for a theory that explains more than do its rivals. Thus, if scientific methodology can be used as a guide, we are warranted, on grounds of parsimony, in rejecting a theory of superior explanatory power. In what circumstances is an ontological parsimony objection decisive? Inasmuch as string theory produces discomfort, it does so for two reasons: first, the entities that string theory requires us to believe in are very different from those in which we currently believe; and second, there seems to be a dearth of good reasons to believe them. The first reason strikes me as obvious: we naturally resist a theory which challenges our basic beliefs or assumptions about the world. The second requires some explanation. String theorists don’t postulate seven or twenty six dimensions because they actually have any evidence to support the existence of so many dimensions; rather, they postulate a plethora of dimensions because it makes the math of their theory work (Kuhlmann sec. 3). But 52 Kelvin Jensen this seems to offend epistemic conservatism, which states that we ought not to believe in something without possessing good reasons. Believing in an entity solely because it provides theoretical benefits does not constitute a very good reason. What all this suggests, then, is that an ontological parsimony objection can be decisive against a theory if the theory possesses a profligate and little evidence to warrant the ontology. I think that modal realism meets these criteria: the ontology is profligate, and the only reason Lewis adduces to believe in possibilia is because they are “serviceable” (Plurality 3). Thus, it seems that the ontological parsimony objection waged against modal realism is decisive. Where would the rejection of modal realism leave us? It depends. If we think that the benefits of modal realism are must - haves, then we ought to consider rival modal theories (like Plantinga’s or Rosen’s) and attempt to remold them to provide the benefits that Lewis’s does. Indeed, with the plausibility of modal realism shaved off by the blade of Ockham’s Razor, this appears to be the only viable option. Works Cited

Baker, Alan. “Quantitative Parsimony and Explanatory Power.” The British Journal for the Philosophy of Science 54.2 (2003): 245–59. Divers, John. Possible Worlds. New York: Routledge, 2002. Grandy, David. Personal Interview. 22 Jan. 2015. Kuhlmann, Meinard. “Quantum Field Theory.” The Stanford Encyclopedia of Philosophy. Ed. Edward N. Zalta, Spring 2014. Lewis, David. Counterfactuals. Cambridge: Harvard UP, 1973. ———. On the Plurality of Worlds. New York: Blackwell Publishing, 1986. Nolan, Daniel. “Quantitative Parsimony.” The British Journal for the Philosophy of Science 48.3 (1997): 329–43.