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I recently asked if we can know whether other possible worlds exist. However, I should have asked first what the definition of a possible world is, for only then can we know whether other possible worlds exist. What is the standard definition of a possible world in the philosophical literature?

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  • There isn't a settled definition, but a good thematic range is: a world is a really "big" conjunction, like, "At time 0, everything is condensed in one point AND at time 1, everything starts expanding and set of particles X occupies half the expanse, set Y occupies the other half AND ... AND you are, at time 10,000,000,000,000,000(...) reading this very comment, AND..." So possible worlds are alternative maximally consistent conjunctions of that sort (actualism), or they are objectively alternative conjunctions (possibilism), or actuality/possibility are indexical (Lewis). Jun 20, 2023 at 22:47
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    That is such a good question. It seems the device of possible worlds is abused left and right to push various opinions. Maybe we can restrict possible worlds to those that are logically compatible with some set of axioms of interest. But even then, one could presumably introduce new axioms as required to remove "possible worlds" they wouldn't like.
    – Frank
    Jun 20, 2023 at 22:55
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    There is no "standard" definition, one's definition depends on one's preferred way of handling them. The most common variants are modal realism (causally disconnected universes), erzatzism of various stripes (various linguistic/symbolic constructs or abstracta), and fictionalism (fictional stories with rules). See IEP for details.
    – Conifold
    Jun 20, 2023 at 23:27

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§§3/3.1 of "The Possibilism-Actualism Debate" reads (in part):

Possibilism would almost surely not be taken as seriously as it is were it not for the dramatic development of possible world semantics for modal logic in the second half of the twentieth century. For it not only enables the possibilist to formulate truth modal conditions with particular clarity and cogency, it yields a natural and elegant quantified modal logic, known as SQML, in which possibilism’s fundamental metaphysical principles fall out as logical truths. In order to appreciate the cogency of possibilism, therefore, it is important to understand basic possible world semantics.

... Intuitively, a Tarskian interpretation of an applied non-modal language represents a possible world, a way in which the properties and relations expressed by the predicates of the language might be exemplified by the things in the universe of the interpretation. The idea underlying possible world semantics is simply to interpret a modal language ℒ by bringing a collection of Tarskian interpretations together to represent a modal space of many possible worlds in a single interpretation of ℒ.

The possibilist is styled as denying the direct truth of, "If it is possible that an x exists such that x is F, then there already exists an x such that it is possible that x is F." For such a possibilist, a possible world is a not-quite-existent "place" besides our actual world. So by contrast, the actualist (or, more strictly, the combinatorialist) thinks:

The idea of possibility being rooted in arbitrary recombinations of the actual world, rearrangements of its objects and universals, is intuitively appealing. Clearly, however, not just any such recombination can count as a possible world. ... Worlds, in particular, can be defined as special cases of [specified] recombinations, together with appropriate totality facts. To state this, we need a condition that ensures the existence of a unique actual world[.]

A corollary option for actualism-minded folks is to postulate haecceities:

One of the best known responses to the possibilist challenge was developed by Alvin Plantinga (1974, 1976). ... A critical, and distinctive, element of Plantinga’s account is that there are many unexemplified essences, i.e., essences that are not, in fact, the essences of anything, specifically, those he dubs haecceities. Haecceities are “purely nonqualitative” properties like being Plantinga, or perhaps, being identical with Plantinga, that do no more than characterize an object a as that very thing.

A rough (preliminary) haecceitist version of a merely possible world, then, is a recombinant world (over the facts whose possibility is encoded into the lone actual world, there) featuring only unexemplified haecceities. But that is a sort of minimum (or maximum) modulo a special parameter, so there are mixed-possibility worlds (worlds that have some merely possible, others actualized-possibility, objects) yet recombined over the singular given world.

Arguably "halfway between" the two kinds of options described above is David Lewis' modal realism. According to Lewis, the word "actual" is itself an indexical. There are no merely possible worlds in the normal sense; the closest counterpart concept is, "X is not actual in our world, but it is actual in some other world." And other worlds are self-actual, too. Lewis' view strains the intuitions of Occamist devotion, but does find purchase in the apparent equivalence of, "X is actually possible," and, "X is possibly actual," and their iterations ("X is actually possibly actual, actually possibly actually possible, possibly actually possibly actually possible, ...").

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