1. Introduction. Against GMR: The Incredulous Stare (Lewis 1986: 133 5).

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1 Lecture 3 Modal Realism II James Openshaw 1. Introduction Against GMR: The Incredulous Stare (Lewis 1986: 133 5). Whatever else is true of them, today s views aim not to provoke the incredulous stare. We ll be looking at a cluster of views usually called actualist or abstractionist. According to these views, there are possible worlds, but they are not concrete individuals. They are abstract, and indeed actual, representations of ways things could have been. There is just one concrete world. The actual world proper is the one abstract entity which accurately and completely represents it. Actualism and Possibilism To understand why actualism has traditionally been seen as a thesis worth defending, consider what its negation amounts to: there are things which do not actually exist. There is a real ontological distinction between existence and being, the former a sub-category of the latter. Many philosophers have wanted to reject the claim that there are merely possible beings. Actualists will agree that there could have been things which don t (actually) exist, but they won t agree that there are, in any sense, things which don t (actually) exist. All existence is actual existence. Instead, possible worlds merely represent such things as existing. NB: GMR is a non-standard kind of possibilism, since it reduces the non-actual to what (concretely) unrestrictedly exists, and denies the actual is ontologically privileged in any sense. It has come to seem that there is something unsatisfying about this debate. (What exactly is the extra thing that beings have to do in order to (actually) exist?) While we ll be exploring views traditionally marketed as actualist, the issue of actualism vs. possibilism won t itself be our focus. 1.2 Actualist Worlds as Representations Although the actualist denies that Aliens exist, she wants to accept the claim that they could have existed. How can she accept worlds without accepting the individuals that exist at them? (P) It is possible that p iff there is a possible world at which p is true. In GMR, what is true at a world, or according to a world, is just what is true of it. But for actualists, truth at a world is a (non-factive) representational notion.

2 The Sherlock Holmes novels don t contain Sherlock Holmes, only paper and ink. But Sherlock Holmes nonetheless exists according to the books. The same goes for actualist worlds. What is true at them may depend on what is true of them, but the two are not the same thing. (1) There could have been talking donkeys. (2) x [Wx & At x ( y (Ty & Dy))] (3) Clinton could have won the election. (4) x [Wx & At x (Vh)] While the actualist s worlds actually exist, only one has the property of being actualised. How do these abstract entities represent? 2. Linguistic Abstractionism The best ersatzism by far is linguistic (Lewis 1986: 165). All abstractionists identify worlds with actually existing objects, or constructions built out of actually existing objects. The hope is that we can do this using resources we already need anyway. LA takes the analogy of worlds as books seriously. Worlds are books, or sets of sentences. Is this really realism about possible worlds? After all, if there weren't any language users there wouldn't be any sentences. As we ll see, we needn t take books to be the ink and paper affairs we re used to. All we need is language in a generalised sense: a system of structures that can be interpreted. The words can be anything that safe and sane ontology has to offer. They can be individuals that are part of the concrete world, set-theoretic constructions out of those, pure sets, or anything else we believe in (Lewis 1986: 144). 2.1 Constraints on a World-Making Language Richness. If the language is expressively impoverished, there won t be enough worlds to underwrite the truth of (P). Precision. The language had better be disambiguated and context-insensitive, else it will be underdetermined what is true at its worlds. Natural languages are unlikely candidates, then. Universality. For every thing a name, for every property a predicate, lest worlds be silent on certain matters. And nothing may have two names, lest a world both affirm and deny that it is F. Option 1. Suppose spacetime is infinite and that once the distribution of matter over the points is specified, all other facts are determined. Given an adequate coordinate system, we can associate

3 each point with a quadruple of real numbers. If there are two ways for a point to be, occupied or vacant, then a world can simply be a set of quadruples, specifying the set of occupied points. Option 2. We can identify worlds with set-theoretic constructions of individuals and properties. In particular, let s use each individual as its own name and each property as its own predicate. Then an ordered pair < a, F > can serve as an atomic sentence according to which a is F. (In general, an atomic sentence is an ordered n-tuple consisting of n-1 names and an n-1 place predicate.) For complex sentences, we can introduce infinitary sentential connectives, generating sentences of infinite length, such as that a is F and b is G and c is H and d is I Call this a Lagadonian language. 2.2 Which sentences are the worlds? Option 1: All of them. Every Lagadonian sentence is a world. A sentence S is true at a world w when w has S as a member. To exist at a world w is to be a name in a sentence which is a member of w. And w is actualized iff only true sentences are members of (or perhaps entailed by members of) w. Can this language underwrite the truth of (P)? Problem 1: There could have been more things than there actually are is false. Problem 2: Consistency. How we can insure against the instantiation of incompatible properties, like being both red (all over) and green (all over)? Problem 3: Maximality. What about negative truths such as that Trump does not exist at w? Option 2: Only the maximal and consistent sentences are worlds. A set of sentences S is maximal iff for every sentence s, either s ϵ S or s ϵ S. A set of sentences S is consistent iff those sentences, as interpreted, could all be true together. Can we define consistency syntactically? A set of sentences S is consistent iff no subset of S is such that the negation of any of its members is a theorem (can be proved given a particular set of inference rules). While this may detect subsets containing Fa & Fa, what is the guarantee that all impossibilities are syntactically manifestable in this way? There is also only so much you can express by recombining individuals and properties. We might want to say that so-and-so is the case according to a world not because it contains a sentence which means that so-and-so, but because there are sentences which together entail so-and-so.

4 Like consistency, entailment is a modal notion So the present version of LA commits itself to primitive modality. (S entails s iff the conjunction of the members of {S} { s} is inconsistent.) On the upside, having entailment means the LA needn t have a predicate for every property: the fundamental properties will do. A fundamental-level description will entail truths about donkeys. For any (non-modal) sentence S, S is true at w iff the sentences which are members of w entail S. For any individual a, a exists at w iff w entails that y (y = a). And w is actualized iff all and only the true sentences are (entailed by) the members of w. 2.3 Problems for Linguistic Abstractionism Problem 1: Aliens? While we re defining worlds on the model of languages, we can introduce pure set-theoretic resources to be variables and logical expressions. Using and =, we can write down a sentence according to which there are non-actual individuals and actually uninstantiated properties: x (x a & x b &... & x z), where a, b,..., z is a (perhaps infinite) list of all the actual individuals. (5) x Ax is true at some world. The semantics of (5) must stop here, for there are ex hypothesi no objects which are witness to its truth; which make it true. Problem 2: Iterated Modalities As above, for names of alien individuals, terms like The F which is G, or open sentences Fx & Gx will have to suffice. But using only descriptive resources to pick out individuals brings problems. (6) Pope Francis could have had a son who was contingently a Liverpool supporter. (6*) x (Sxp & Lx). Note that the second occurrence of the variable x is de re with respect to the second. What (6) means is that there is some world w which entails that there is an x which is a son of Pope Francis and a Liverpool supporter, and there is a world v which entails that x (the very same x) exists and is not a Liverpool supporter. But the only general way we have of representing existence at v of the very same x that exists at w is by having as a member of the domain of v the representation in w, namely: The x which is a son of Pope Francis and a Liverpool supporter. But then the truth-condition cannot be fulfilled

5 3. Plantingan Realism Plantinga s worlds are certain kinds of states of affairs e.g. Socrates being a jazz musician. Which state(s) of affairs are actualized depends on what goes on in concrete reality. So while all states of affairs are actual, most states of affairs e.g. Socrates being a jazz musician are unactualized: they could have been actualized by concrete reality but they are not. Many of these unactualized states of affairs represent the existence of Alien individuals. Therefore, states of affairs are unlikely to be considered structured. They do not have individuals as parts, members, or constituents, else this would entail their (actual) existence. States of affairs, then, are simple, unstructured, abstract objects. Finally, like properties, propositions, and other abstract objects, states of affairs necessarily exist. Which states of affairs are the worlds? Let s say that state of affairs S includes S' iff it is not possible for S to be actualized without S' being actualized. S precludes S' iff it is not possible for S' to be actualized with S. We can now define the following notions: o A state of affairs S is a world iff S is possible and for every state of affairs S', S includes S' or precludes S'. o For any state of affairs S and world w, S is true at w iff w includes S. o An individual x exists at a world w iff w includes the state of affairs of x s existing. (PR1) S is possible iff there is some world w which includes S. (PR2) It is possible that there are talking donkeys is true iff the state of affairs There being talking donkeys is included by some world. PR provides the following truth-condition for our problematic (6) from earlier: (6-PR) At some world w there is an essence E which is co-instantiated at w with the property of being a son of Pope Francis and being a Liverpool supporter, and at some world v, E is not co-instantiated with the property of being a Liverpool supporter. Possible Individuals? If worlds are abstract, unstructured simples, where are the possible talking donkeys?

6 Plantinga interprets quantification over non-actual individuals as quantification over uninstantiated essences. A property F is essential to an individual x iff it is not possible for x to exist and fail to instantiate F. An essential property E of x is an essence of x iff, necessarily, for all individuals y, y instantiates E iff y = x. Like states of affairs, properties are unstructured. If Alien essences were structured, they would (presumably) entail the (actual) existence of the Alien, the essence being instantiated after all. The (actually existing) uninstantiated essences are our surrogates for Alien individuals. And the uninstantiated properties are our Alien properties. One benefit? Essentialist claims can be true once and for all, no matter the context. 3.1 Problems for Plantingan Realism Ideological costs. The advertised ideology of GMR comprised of: individuals, sets, parthood, similarity, and spatiotemporal relatedness. For PR, it is at least: individuals, sets, parthood, properties, instantiation, states of affairs, actualization, and necessity (entailment or inclusion). What are the identity conditions for the (unactualized) states of affairs, the (uninstantiated) properties or essences? For one thing, the property of being Socrates and the state of affairs of Socrates being self-identical could exist even if Socrates did not exist And all Alien essences do (actually) exist. 3.2 Lewis (1986) Master Argument Against PR For GMR, truth at a world is analysed in terms of worlds parts having certain qualitative features. For LA, truth at a world is analysed in terms of set-membership (and perhaps entailment). In each case, what is true at a world depends on what is true of that world. PR does not offer a substantive account of representation. We only have (something like): S is true at w iff, necessarily, if w is actualized then S is actualized. So Lewis asks to hear more about this relation of being actualized by. It should be classifiable into one of two categories. Either it is an internal relation or it is an external relation

7 Internal = Whether a state of affairs is actualized depends (only) on the intrinsic natures of the relata. Actualization is like being similar to or being taller than So the claim is that if part of what goes on in concrete reality is that there is a talking donkey, that will mean that states of affairs with certain intrinsic properties will be actualized and others not. What kind of intrinsic property could suffice for this disposition? (R) R is the property of representing that a talking donkey exists iff, necessarily, if S instantiates R and S is actualized then a talking donkey exists. But this is trivial. we ve gone in a circle. There is an SOA such that, necessarily, it is actualized iff a donkey talks; that SOA has some distinctive intrinsic property; that property is named `representing that a donkey talks'; the property with that name singles out the SOA that, necessarily, is actualized iff a donkey talks. Not a thing has been said about what sort of property that might be It is no use telling me by name what property it is, if it bears that name exactly because it plays that role (Lewis 1986: 178). External = Whether a state of affairs is actualized depends (only) on the intrinsic nature of the composite of the relata taken together. Actualization is like being 5m away from or being on top of But in that case, actualization is not any ordinary external relation, it is a relation which holds of necessity. What makes a relation external, I would have thought, is that it holds independently of the natures of the two relata. We wanted the relation to be independent of the intrinsic nature of the elements, because once we see past the empty words those alleged natures turn out to be an utter mystery. But now we want the relation not to be independent of what goes on within the concrete world. How can we have it both ways? (1986: 180) Imagine two fundamental particles, A and B. The further one from Earth, A, glows iff there ever exist talking donkeys on Earth, the other, B, iff there never exist talking donkeys. Furthermore, which one glows has nothing to do with their intrinsic natures because A and B are perfect duplicates. Which one glows depends only on external relations borne by each to Earth

8 Why, though, could it not possibly have been such that particle B glows iff there ever exist talking donkeys, and particle A glows iff there never exist talking donkeys? [The PR s claim is that] Necessarily, if a donkey talks, then the concrete world actualizes these SOAs; if a cat philosophises, it actualizes those; and so on. I ask: how can these connections be necessary? It seems to be one fact that somewhere within the concrete world, a donkey talks; and an entirely independent fact that the concrete world enters into a certain external relation with this SOA and not with that. What stops it from going the other way? (Lewis 1986: 180). 4. Conclusion GMR advertises: o o o An account of the content of modal talk in which no modal concept is taken as primitive. (Modal reality is reduced to unrestricted existence.) An account of the nature of various entities (properties, propositions, states of affairs ) on which they re understood extensionally, as sets of individuals. The most straightforward interpretation of the claim that we quantify over ways things might have been, and individuals which might have existed. Whether or not GMR fulfils those ambitions is up for some debate. But what exactly are the distinctive benefits of PR? Further reading: J. Melia (2003), Modality (Cambridge: Cambridge University Press), Chs P. van Inwagen (1986), Two Conceptions of Possible Worlds, Midwest Studies in Philosophy 11: D. K. Lewis (1986), On the Plurality of Worlds, (Oxford: Blackwell), Ch. 3. D. K. Lewis (1990), Noneism or Allism?, Mind 99(393): T. Williamson (1998), Bare Possibilia, Erkenntnis 48(2/3):

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