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Modality and possible worlds 'The Nature of Possibility' - D.M. Armstrong in Metaphysics (eds. Kim
& Sosa). Blackwell (1999) 1 Introductory "I want to defend a combinatorial theory of possibility. Such a view traces the very idea of possibility to the idea of the combinations - all the combinations which respect a certain simple form - of given, actual, elements." 184 2 Ontological Sketch "The world that I begin with contains a number of simple individuals, a, b, c, ... The number is not specified. It might be finite, or be one of the infinite cardinals. It is an a posteriori, scientific question how many individuals the world contains." "These individuals have indefinitely many properties, and stand in indefinitely many relations to other individuals." "Their simplicity is constituted by the fact that they have no proper parts, where parts of individuals are individuals. Candidates for such individuals would be properties point-instants." "The world also contains, in finite or infinite number, simple properties, F, G, H, ...and simple relations, R, S, T, ...(Their simplicity is constituted by the fact that they have no properties or relations as proper parts)." These are universals. There is no universal Not being U1. Just U1. This will be important for his combinatorialism. 185
? "U1 and not-U1 is an impossible combination."
? "Conjunctions of universals, however, seem to be acceptable (complex) universals." "I hold that these 'elements' are essentially aspects of, abstractions from what Wittgenstein and Skyrms call facts and what I shall call states of affairs". "If it is simples that we are dealing with the whole time then we can speak of these as atomic states of affairs." "[W]e may think of an individual, such as a, as no more than an abstraction from all those states of affairs in which a figures, F an abstraction from all those states of affairs in which F figures, and similarly for relation R." "By 'abstraction' is not meant that a, F and R are in any way otherworldly, still less 'mental' or unreal." "A possible property or relation, even if it is empirically possible, is not ipso facto a property or relation." 3 The Wittgenstein Worlds The notion of a molecular state of affairs: these are confined to conjunctive states of affairs (i.e. not disjunctive or negative ones), but the conjunctions can be infinite.
- "The world is a certain conjunction of states of affairs, perhaps an infinite one."
The notion of an atomic statement: suppose that a is F, but is not G. Both 'a is F' and 'a is G' are atomic statements (they don't have to correspond to the actual state of affairs, just have to respect the atomic 'form'.) "A merely possible state of affairs [such as the one expressed in 'a is G'] does not exist, subsist, or have any sort of being. It is no addition to our ontology. But we can refer to it, or, better, make ostensible reference to it." 186 "The simple individuals, properties and relations may be combined in all ways to yield possible atomic states of affairs, provided only that the form of atomic facts is respected. That is the combinatorial idea." "Such possible atomic states of affairs may then be combined in all ways to yield possible molecular states of affairs. If such a possible molecular state of affairs is thought of as the totality of being, then it is a possible world." Wittgenstein world: one that contains each simple individual, property and relation and no others. 4 Haecceities and Quiddities "[I]s it not possible that there should be individuals which are neither identical with actual individuals, nor composed of actual individuals." Call them alien individuals. "[I]s it not possible that there should be universals which are neither identical with actual, that is, instantiated, universals, nor composed of actual universals?" Call them alien universals. These two things seem to be ruled out by our original premises. But Armstrong says that this doesn't work, and in particular accepting the existence of such things will involve deserting naturalism. "Each alien property must have its own nature. But these natures, these quiddities, are not to be found in the space-time world. Lewis can instantiate them in other possible worlds." 187 But for a naturalist, this 'way of analogy' (as it is called) fails to work. "I believe that a naturalist-combinatorialist should deny the possibility of genuinely alien universals."
- "For a combinatorialist, the possible is determined by the actual."
- "So the actual universals set a limit, a limit given by the totality of their recombinations, to the possible universals." "It seems very hard to deny that it is possible that the world should contain more individuals than it actually contains." Armstrong thinks that in this case we can accept them. But that involves denying the doctrine of haecceitism. Example to explain this: Take a contracted world, as a substitute for our actual world, which contains nothing but the simple individuals a and b, along with the
properties, also simple, F and G. The world is exhausted by the states of affairs: I Fa & Gb The combinatorialist will then say that the possible worlds are: II Ga & Fb III Fa & Ga & Fa IV Fa & Fb & Gb V Fa & Ga & Gb VI Ga & Fb & Gb VII Fa & Ga & Fb & Gb A haecceitist would say that the members of the pairs I & II, III & IV, and V & VI differ from each other, but the anti-haecceitist denies this. 188
? A combinatorialist anti-haecceitist therefore allows fewer possible worlds than the haecceitist does. "The haecceitist holds that, apart from repeatable properties (F and G), a and b each have a unique inner essence, a metaphysical signature tune as it were, which distinguishes a and b. Even abstracted from their repeatable properties, a and b differ in nature." "A strong anti-haecceitism denies that individuals are anything more than the 'bundles' of their properties." Armonstrong instead accepts weak haecceitism. "Haecceitism for individuals is parallel to quidditism for universals." Haecceitism "united with a naturalist-combinatorialism appears to make alien individuals impossible, just as quidditism makes alien universals impossible."
- "For the alien individual must be supposed to have some definite haecceity, different from, and not obtainable from, actual haecceities." "If weak anti-haecceitism is true, then individuals, qua individuals, are merely, barely, numerically different from each other. They are simply other." "They are then available to form worlds additional to the Wittgenstein worlds." 5 Contracted Worlds "So the Wittgenstein worlds require to be supplemented by worlds which contain further individuals, but not by worlds which contain further simple universals." "If there is no contraction, then every actual individual, and every simple universal, will appear in every possible world." But that would make both the individuals and the universals necessary beings, which seems odd. "The obvious solution is to allow contraction in the forming of possible worlds." But Armstrong says this raises problems for universals, and this is why:
- Possible worlds are all accessible to each other, i.e. each of them is a possible world relative to all the others.
This means they form an equivalence class (the relation is reflexive, transitive and symmetrical). 189
- Given an anti-haecceitist account of individuals, the situation does not change if worlds are added which add and/or subtract individuals.
- Now consider a contracted world Wc, contracted by the absence of the simple property F, relative to a Wittgenstein world Ww, which contains Fs. Wc is accessible from Ww, but not the other way around. So symmetry of accessibility fails.
- (Are we only saying that it doesn't fail for individuals because of our intuition that there can be no alien individual (since they are contingent)?) "What we must, but I think can, accept about the simple property F is this. F might not have existed, so it is a contingent being."
? "But from the standpoint of a 'world' where F does not exist, it is impossible that it should exist."
? "When we go down to the F-less world, Wc, then we are pretending that that world is the actual world." "On the view being put forward, the possible is determined by the actual. Suppose the actual reduced. Then the sphere of the possible is also reduced." But that doesn't work because, for any given possible world, we can't just go around supposing that it is the actual world all the time. What if we want to consider several at once?
BUT, a combinatorial theory cannot accept the empty world, because it is not a construction from given elements. It is necessary that there be something. Now that seems implausible too. 6 What If There Are No Atoms?
"May it not be that some, or all, individuals have proper parts which in turn have proper parts, ad infinitum. And may it not be that this process fails to reach simple individuals even at infinity?" And similarly for properties & relations. "Or, again, it may be that the property F dissolves into a structure
[of properties]." "[T]hat a certain universal is or is not simple now seems to me to be a necessary truth." But he's not sure about individuals. Suppose that it were contingent whether property F is simple or not.
- There will then be a possible world where F exists and is simple.
- There will be another possible world where F is identical with the conjunction G & H.
- But then this is absurd because what identity across possible worlds exists here? Simple F is identical with G & H: why not so with any other universal, simple, conjunctive, or structural?
o But wouldn't this just be a contingent matter too?
- "They may be said to be identical for practical purposes. But I do not see how a philosopher, at least, can say that they are really identical. At best, they are counterparts of each other." 190
o Why not? Why not just accept that F and G & H are different names referring to the same thing?
- "I conclude that we do have a necessity here, even if one which has to be established a posteriori."
- "The structure, or make-up, of a universal cannot change from one possible world to another." "Nevertheless, it remains doxastically open, a matter to be decided by natural science if to be decided at all, whether or not the world reduces to genuinely atomic states of affairs." Theory needs to be equipped to deal with this possibility. If the atoms are not genuinely atomic, then this set of worlds formed by them is a mere subset of the total number of possible worlds (possibly infinite). These original relative atoms must not merely be distinct from each other, they must be wholly distinct. "Instead of distinct/wholly distinct, we could speak of partial and complete non-identity." "When we come in practice to assert that P is a possible state of affairs, we may assume that the requirement of wholly distinct relative atoms is satisfied when in fact it is not." We must not assume that all 'qualified' types of possibility involve cutting down the number of possible worlds. E.g. doxastically possible, nomically possible. 191 7 A Major Difficulty In reality it seems that it is not in fact possible to have any combination of universals. They tend to come in 'ranges'. "An individual can, at one time, instantiate only one member of a given range." E.g. colour. 192 Wants to solve it by saying that such properties are structural and are made up of other properties. It is the higher level and lower level properties here (as it were) that are not compossible. He thinks colour comes under this explanation. "There are phenomenological objections to even an a posteriori identification of colours (seen colour) with physical bases of the colours." But he thinks such objections are "overrated". 193 'Counterparts or Double Lives?' - Lewis
? Rejects the idea of overlapping possible worlds.
? Argues that individuals (and objects) have 'counterparts' in different possible worlds in order to account for what is possibly true about those individuals.
? On the counterpart relation: o Imagine an individual Humphrey: "Humphrey may be represented in absentia at other worlds, just as he may be in museums in this world." o "By having such a part, a world represents de re, concerning Humphrey - that is, the Humphrey of our
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