An Inquiry on Modal Metaphysical Puzzling Possible Worlds

The concept of possible worlds is useful because it defines the four modalities - possibility, necessity, contingency, and impossibility - but a challenge lies in defining it. David Lewis' polemical hypothesis ("genuine modal realism" as it is called) succeeds in it. Lewis' modal realism stirred controversy because he maintains that a plurality of worlds exists. Some philosophers suggest that the Lewisian view is a violation to the law of parsimony, also known as Ockham's Razor, i.e. not multiply entities beyond necessity. While avoiding a circular definition, Lewis constructs an inflated ontology. Is it worth it, and if we do not want to assume too many Lewisian worlds, what alternatives remain? Actualist modal realism and modal antirealism are the most relevant alternatives because modal abstentionism simply will not progress in this direction. This study evaluates the theories of possible worlds.

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Chapter 3.2.2 Combinatorialism:
Quine suggests that a possible world is a mathematical representation. We represent spacetime points occupied by matter, but ontology requires only matter and the structure of classes of individuals (cf. Quine 1968, p. 12). Quine was first one to sketch combinatorialism: "A possible world, finally can be explained in somewhat the same way but with four dimensions, representing space-time. A possible world becomes, roughly, any class whose members are all the classes that are geometrically similar to some one class of number quadruples" (Ibid., p. 14). Lewis does not identify world with any mathematical representation (cf. Lewis 1986, pp. 86-92). Cresswell first held a combinatorialist account, a recombination of certain metaphysical simples. Combinatorialists take possible worlds to be recombinations of elements. Circularity is avoided by giving a combinatorial definition of a possible world. Cresswell (as Quine does) takes possible worlds to be sets of spacetime points, and each set represents possibilities. All spacetime points are occupied with abstract matter, and the combinatorial nature of set theory gives rise to possible worlds. This type of actualist modal realism has a reduction that is clearly non-modal. We have these coordinates with which any pattern is possible. If we identify worlds with sets of spacetime points, modality is eliminated. Combinatorialism is based on the Leibnizian conception. A proposition is possible if and only if it is true in some possible world. A counterargument is that modality reappears in the definition of "true in". Note that combinatorialism cannot dispose of possibility and necessity. The problem lies in circularity when accepting that modality reappears when saying "true in". Based on Ludwig Wittgenstein's Tractatus Logico-philosophicus, Brian Skyrms proposes:
Possible worlds are collections of compossible facts. We think about possible facts and possible worlds in two quite different ways. For possible worlds whose objects and relations are subsets of this world our possibilities are essentially combinatorial. We rearrange some or all of our relationships between some or all of the objects to get our possibilities (Skyrms 1981, p. 201).
Inspired by Skyrms, Armstrong offers the most developed theory of combinatorialism, in which possible worlds are sets (i.e., conjunctions) of fundamental states-of-affairs. States-of-affairs involve particulars and universals. He has a preference for a fictionalist form of combinatorialism (cf. Armstrong 1989, p. 49). The world Armstrong begins with contains simple individuals (i.e., particulars), simple because they do not have individuals as proper parts. The world also contains simple properties (i.e., universals), simple because they lack proper constituents (cf. ibid., p. 38). Particulars and universals are constituents of the states-of-affairs. We have various elements, all those we have in our actual world such as headphones, music, and dancing, so a possible world is a recombination of existing elements and relations. We rearrange a world containing headphones and dancing, but not music. This would be a possibility without music (where life would be a mistake). Such a combination does not exist, and life cannot be a mistake in a possible world without music because we are talking only about logical possibilities.
3.2.3 Nature Modal Realism:
The problem in this type of actualist modal realism is underdeveloped. We know only that world-natures are a special structural property because they are complete properties of maximal individuals. So, a possible world is a possible way things could have been for the entire cosmos. A third type of ersatzism is nature modal realism, advocated by Robert Stalnaker. Nature modal realism sees possible worlds as world-natures, world-properties, or ways our world might have been. The actualised world is the only worldnature that is instantiated. A nature realist