For a general article on the "Plurality of Worlds" concept, see Cosmic pluralism

Cosmic pluralism

Cosmic pluralism, the plurality of worlds, or simply pluralism, describes the belief in numerous other worlds which harbour extraterrestrial life. The debate over pluralism began as early as the time of Thales Cosmic pluralism, the plurality of worlds, or simply pluralism, describes the belief in...

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On the Plurality of Worlds (1986) is a book by the philosopher David Lewis that defends the thesis of modal realism

Modal realism

Modal realism is the view, notably propounded by David Kellogg Lewis, that all possible worlds are as real as the actual world. It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the...

, "The thesis states that the world we are part of is but one of a plurality of worlds," as he writes in the Preface, "and that we who inhabit this world are only a few out of all the inhabitants of all the worlds." It is not to be confused with the work of Bernard le Bovier de Fontenelle

Bernard le Bovier de Fontenelle

Bernard Le Bovier de Fontenelle , also called Bernard Le Bouyer de Fontenelle, was a French author.Fontenelle was born in Rouen, France and died in Paris just one month before his 100th birthday. His mother was the sister of great French dramatists Pierre and Thomas Corneille...

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The book is divided into four chapters.

Chapter 1 - A Philosopher's Paradise

Chapter 1 begins with an exposition of modal realism

Modal realism

Modal realism is the view, notably propounded by David Kellogg Lewis, that all possible worlds are as real as the actual world. It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the...

. Lewis proposes that possible worlds

Possible Worlds

Possible Worlds may refer to:* Possible worlds, a concept in philosophy* Possible Worlds , by John Mighton** Possible Worlds , by Robert Lepage, based on the Mighton play* Possible Worlds , by Peter Porter...

, including ours, are real concrete things that are isolated from each other. "There are no spatiotemporal relations at all between things that belong to different worlds," and adds, "Nor does anything that happens at one world cause anything to happen at another." He recommends a plural

Plural

In linguistics, plurality or [a] plural is a concept of quantity representing a value of more-than-one. Typically applied to nouns, a plural word or marker is used to distinguish a value other than the default quantity of a noun, which is typically one...

ity of worlds because hypothesizing it is "serviceable," the familiar analysis of necessity as truth at all possible worlds being "only the beginning." Lewis shows that modal realism can be used to give coherent accounts of, among other things, modal logic

Modal logic

Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...

 and counterfactual conditional

Counterfactual conditional

A counterfactual conditional, subjunctive conditional, or remote conditional, abbreviated , is a conditional statement indicating what would be the case if its antecedent were true...

s. Modality turns into quantification

Quantification

Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...

 ("Possibly there are blue swans if and only if

If and only if

In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....

, for some world W, at W there are blue swans"), and counterfactual conditionals

Conditional sentence

In grammar, conditional sentences are sentences discussing factual implications or hypothetical situations and their consequences. Languages use a variety of conditional constructions and verb forms to form such sentences....

 turn into statements of fact about possible worlds ('If it were that A, then it would be that C' is true if and only if C is true at the selected A-world.) He argues that the theoretical utility of modal realism provides a reason to accept it as true, drawing a parallel to the fruitfulness of set theory

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

 in mathematics. Of both the plurality of sets and the plurality of worlds, Lewis holds that "[t]he price is right; the benefits in theoretical unity and economy are well worth the entities." Among the further benefits:

• If possible worlds help with counterfactuals, they will help with causation.
• Closeness of worlds can help spell out what it means for a false theory of nature to be close to the truth.
• Idealizations such as the ideally rational belief system are "among the theoretical benefits to be found in the paradise of possibilia."
• The content of knowledge and belief are given by epistemically and doxastically accessible worlds, respectively—that is, worlds that, for all you know/believe, are the world you live in.
• A property is the set of all its instances in all worlds where the property obtains, and similarly for relations.
• Propositions are properties instantiated only by entire possible worlds, so a proposition is a set of possible worlds, the worlds at which it holds or is true.
• Modal realism is favored over traditional systems of modality because it does not involve primitivity or brute modal facts. Modality can be reduced in the Lewisian account, but in traditional systems modal quantifiers, such as "possibly", are defined in terms of other modal quanitfiers or notions. It has been argued however, that Lewis treats the existence of worlds as primitive or brute and explains modality in terms of that analysis.

Lewis begins his attack on "ersatzism" in this chapter, rejecting Quine's suggestion that a possible world might be taken as a mathematical representation giving the coordinates of the spacetime points that are occupied by matter. No possible world is identical with any Quinean ersatz world, but for every such ersatz world there is a genuine possible world.

Chapter 2 - Paradox in Paradise?

Chapter two contains Lewis's response to several arguments, many set theoretic

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

 in nature, that attempt to show that modal realism flounders because of the quantity of worlds that must be postulated.

Chapter 3 - Paradise on the Cheap?

In chapter three, Lewis considers various views that he calls "ersatz modal realism." These views are attempts to develop a theory that provides the explanatory power Lewis notes in chapter one without modal realism's ontological

Ontology

Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...

 commitment to an infinitude of concrete possible worlds. Lewis argues that all of these attempts fail but that each fails for different reasons.

Chapter 4 - Counterparts or Double Lives?

Finally, chapter 4 contains Lewis's development of counterpart theory

Counterpart theory

In philosophy, specifically in the area of modal metaphysics, counterpart theory is an alternative to standard possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view...

. According to Lewis's theory, each actual object exists only in the actual world and not in any non-actual world. However, each actual object has counterparts in infinitely many possible worlds that are not identical to the actual object, but that "resemble [it] in important respects."