Compossibility is a philosophical concept from Leibniz. According to Leibniz a complete individual thing (for example a person) is characterized by all its properties, and these determine its relations with other individuals. The existence of one individual may contradict the existence of another. A possible world is made up of individuals that are compossible — that is, individuals that can exist together. Possible worlds exist as possibilities in the mind of God. One world among them is realized as the actual world, and this is the most perfect one.

According to the Stanford Encyclopedia of Philosophy article on Leibniz's Modal Metaphysics by Brandon C. Look, views on "compossibility" and the closely related best of all possible worlds

Best of all possible worlds

The phrase "the best of all possible worlds" was coined by the German polymath Gottfried Leibniz in his 1710 work Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal...

 argument are to be found in On the Ultimate Origination of Things, The Discourse in Metaphysics, On Freedom, and throughout his works. The term itself is found in Die philosophischen Schriften III when Leibniz writes to Louis Bourguet

Louis Bourguet

Louis Bourguet was a polymath and correspondent of Leibniz who wrote on archaeology, geology, philosophy, Biblical scholarship and mathematics....

.

Alain Badiou

Alain Badiou

Alain Badiou is a French philosopher, professor at European Graduate School, formerly chair of Philosophy at the École Normale Supérieure . Along with Giorgio Agamben and Slavoj Žižek, Badiou is a prominent figure in an anti-postmodern strand of continental philosophy...

 borrows this concept in defining philosophy as the creation of a "space of compossibility" for heterogeneous truth

Truth

Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...

s.

Gilles Deleuze

Gilles Deleuze

Gilles Deleuze , was a French philosopher who, from the early 1960s until his death, wrote influentially on philosophy, literature, film, and fine art. His most popular works were the two volumes of Capitalism and Schizophrenia: Anti-Oedipus and A Thousand Plateaus , both co-written with Félix...

 uses it in Cinema II taking support from Leibniz's explanation of the problem of future contingents. He then creates the notion of in-compossible, and drawing on Jorge Luis Borges

Jorge Luis Borges

Jorge Francisco Isidoro Luis Borges Acevedo , known as Jorge Luis Borges , was an Argentine writer, essayist, poet and translator born in Buenos Aires. In 1914 his family moved to Switzerland where he attended school, receiving his baccalauréat from the Collège de Genève in 1918. The family...

 explains that several mutually contradictory worlds do in fact exist.

The word itself, if not the concept, won some notoriety for being marked for elimination from the Collins dictionary.

See also

• David Kellogg Lewis
  David Kellogg Lewis
  David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...
  
  's On the Plurality of Worlds
  On the Plurality of Worlds
  On the Plurality of Worlds is a book by the philosopher David Lewis that defends the thesis of modal realism, "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...
  
  (1986)
• Many-worlds interpretation
  Many-worlds interpretation
  The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
  
   of quantum mechanics
  Interpretation of quantum mechanics
  An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...