Indeterminism in the context of "Complex systems"

Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. Determinism is often contrasted with free will, although some philosophers argue that the two are compatible. The antonym of determinism is indeterminism, the view that events are not deterministically caused.

Historically, debates about determinism have involved many philosophical positions and given rise to multiple varieties or interpretations of determinism. One topic of debate concerns the scope of determined systems. Some philosophers have maintained that the entire universe is a single determinate system, while others identify more limited determinate systems. Another common debate topic is whether determinism and free will can coexist; compatibilism and incompatibilism represent the opposing sides of this debate.

Jorge Francisco Isidoro Luis Borges (/ˈbɔːrhɛs/ BOR-hess; Spanish: [ˈxoɾxe ˈlwis ˈboɾxes] ; 24 August 1899 – 14 June 1986) was an Argentine short-story writer, essayist, poet and translator regarded as a key figure in Spanish-language and international literature. His best-known works, Ficciones (transl. Fictions) and El Aleph (transl. The Aleph), published in the 1940s, are collections of short stories exploring motifs such as dreams, labyrinths, chance, infinity, archives, mirrors, fictional writers, and mythology. Borges's works have contributed to philosophical literature and the fantasy genre, and have had a major influence on the magical realist movement in 20th century Latin American literature.

Born in Buenos Aires, Borges later moved with his family to Switzerland in 1914, where he studied at the Collège de Genève. The family travelled widely in Europe, including Spain. On his return to Argentina in 1921, Borges began publishing his poems and essays in surrealist literary journals. He also worked as a librarian and public lecturer. In 1955, he was appointed director of the National Public Library and professor of English Literature at the University of Buenos Aires. He became completely blind by the age of 55. Scholars have suggested that his progressive blindness helped him to create innovative literary symbols through imagination. By the 1960s, his work was translated and published widely in the United States and Europe. Borges himself was fluent in several languages.

John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde. Critics have lauded him as one of the most influential composers of the 20th century. He was also instrumental in the development of modern dance, mostly through his association with choreographer Merce Cunningham, who was also Cage's romantic partner for most of their lives.

Cage's teachers included Henry Cowell (1933) and Arnold Schoenberg (1933–35), both known for their radical innovations in music, but Cage's major influences lay in various East and South Asian cultures. Through his studies of Indian philosophy and Zen Buddhism in the late 1940s, Cage came to the idea of aleatoric or chance-controlled music, which he started composing in 1951. The I Ching, an ancient Chinese classic text and decision-making tool, became Cage's standard composition tool for the rest of his life. In a 1957 lecture, "Experimental Music", he described music as "a purposeless play" which is "an affirmation of life – not an attempt to bring order out of chaos nor to suggest improvements in creation, but simply a way of waking up to the very life we're living".

Metaphysical libertarianism is the philosophical view that free will exists, that it is incompatible with determinism, and therefore that determinism is false. In the branch of philosophy known as metaphysics, libertarianism is one of the main positions related to the problems of free will and determinism. In particular, libertarianism is an incompatibilist position which argues that free will is logically incompatible with a deterministic universe. Libertarianism states that since agents have free will, determinism must be false.

One of the first clear formulations of libertarianism is found in John Duns Scotus. In a theological context, metaphysical libertarianism was notably defended by Jesuit authors like Luis de Molina and Francisco Suárez against the rather compatibilist Thomism of Domingo Báñez. Other important metaphysical libertarians in the early modern period were René Descartes, George Berkeley, Immanuel Kant and Thomas Reid.

The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max Born, and others. While "Copenhagen" refers to the city where Bohr and Heisenberg worked, the use as an "interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed in the 1925–1927 period, glossing over his disagreements with Bohr. Consequently, there is no definitive historical statement of what the interpretation entails.

Features common across versions of the Copenhagen interpretation include the idea that quantum mechanics is intrinsically indeterministic, with probabilities calculated using the Born rule, and the principle of complementarity, which states that objects have certain pairs of complementary properties that cannot all be observed or measured simultaneously. Moreover, the act of "observing" or "measuring" an object is irreversible, and no truth can be attributed to an object except according to the results of its measurement (that is, the Copenhagen interpretation rejects counterfactual definiteness). Copenhagen-type interpretations hold that quantum descriptions are objective, in that they are independent of physicists' personal beliefs and other arbitrary mental factors.