“This compositional variety is mediated by a highly redundant set structure, a second-order all-combinatorial set; each set form is hexachordally equivalent to or totally disjunct from fifteen other set forms, so that one-third of all the available set forms belong to a collection of sets which are hexachordally aggregate forming, that is, hexachordally identical.”

—  Milton Babbitt

On Igor Stravinsky's Movements. Perspectives of new music, Spring-Summer 1964

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "This compositional variety is mediated by a highly redundant set structure, a second-order all-combinatorial set; each …" by Milton Babbitt?
Milton Babbitt photo
Milton Babbitt6
American composer 1916–2011

Related quotes

“When the Löwenheim-Skolem theorem is applied to particular formal systems, we obtain as special cases: Every group, field, ordered field, etc., has a countable subsystem of the same type. A more spectacular result follows from applying the theorem to set theory (a system which we shall later formalize): There is a countable collection of sets, such that if restrict the membership relation to these sets alone, they form a model for set theory (more precisely all the true statements of set theory are true in this model). In particular, within this model which we may denote by M, there must be an uncountable set. This paradox, that a countable model can contain an uncountable set, is explained by noting that to say a set is uncountable merely asserts the nonexistence of a one-one mapping of the set with the set of integers. The "uncountable" set in M set actually has only countably many members in M, but there is no one-one correspondence \underline {within} M of this set with the set of integers.”

Paul Cohen (1934–2007) American mathematician

Set theory and the continuum hypothesis, pp. 19–20 https://books.google.com/books?id=Z4NCAwAAQBAJ&amp;pg=PA19 <br class="br">Set Theory and the Continuum Hypothesis (1966)

“What nevertheless subsists is the desire of an absolute ideal form, a form which can adapt itself to any setting and to any scale.”

Fritz Wotruba (1907–1975) Austrian sculptor (23 April 1907, Vienna – 28 August 1975, Vienna)

Source: The Human Form: Sculpture, Prints, and Drawings, 1977, p. 7.

Bruce Lee photo

“Don't get set into one form, adapt it and build your own, and let it grow, be like water.”

Bruce Lee (1940–1973) Hong Kong-American actor, martial artist, philosopher and filmmaker

Bruce Lee: A Warrior's Journey (2000); here, Lee was reciting lines he wrote for his short lived role on the TV series Longstreet.
Context: Don't get set into one form, adapt it and build your own, and let it grow, be like water. Empty your mind, be formless, shapeless — like water. Now you put water in a cup, it becomes the cup; You put water into a bottle it becomes the bottle; You put it in a teapot it becomes the teapot. Now water can flow or it can crash. Be water, my friend.

Bernard Mandeville photo

“The economic doctrine of Adam Smith is the doctrine of Mandeville set out in a form which is no longer paradoxical and literary, but rational and scientific.”

Bernard Mandeville (1670–1733) Anglo-Dutch writer and physician

La doctrine économique d'Adam Smith, c'est la doctrine de Mandeville, exposée sous une forme non plus paradoxale et littéraire, mais rationnelle et scientifique.
Élie Halévy La formation du radicalisme philosophique (Paris: F. Alcan, 1901-4) vol. 1, p. 162; Mary Morris (trans.) The Growth of Philosophic Radicalism (Clifton, N.J.: A. M. Kelley, 1972) p. 90.
Criticism

“Thus finally we must abandon even the title. It is not the proletariat that is being formed into a class: it is a variety of persons some of whom are separated from the system of production. Processes of forming workers into a class do not take place in a vacuum; rather, they are inextricably tied to the totality of processes through which collectivities appear in struggle at particular moments of history. And the outcomes of these processes, while not arbitrary, are not determined uniquely by the structure of social relations. More than one outcome lies within the limits set by those relations.”

Adam Przeworski (1940) Polish-American academic

"Proletariat into a Class: The Process of Class Formation from Karl Kautsky’s The Class Struggle to Recent Controversies", Politics & Society (1977)

Karl Marx photo

“The philosopher, who is himself an abstract form of alienated man, sets himself up as the measure of the alienated world.”

Karl Marx book Economic and Philosophic Manuscripts of 1844

Der Philosoph legt sich – also selbst eine abstrakte Gestalt des entfremdeten Menschen – als den Maßstab der entfremdeten Welt an.
Paris Manuscripts (1844)

Hilary Putnam photo

“The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets.'”

Hilary Putnam (1926–2016) American philosopher

"Mathematics without foundations"
Source: Philosophical Papers Volume 1: Mathematics, Matter, and Method (1975, 1979)
Context: (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory.

Eric R. Kandel photo

“What is learning but a set of sensory signals from the environment, with different forms of learning resulting from different types or patterns of sensory signals?”

Eric R. Kandel (1929) American neuropsychiatrist

In Search of Memory (2006)

Peter L. Berger photo

“The second level of legitimation contains theoretical propositions in a rudimentary form. Here may be found various explanatory schemes relating sets of objective meanings. These schemes are highly pragmatic, directly related to concrete actions. Proverbs, moral maxims and wise sayings are common on this level. Here, too, belong legends and folk tales, frequently transmitted in poetic forms.”

Peter L. Berger book The Social Construction of Reality

1991; 112
The Social Construction of Reality, 1966

L. P. Jacks photo

“The human mind loves the bondage of words and is apt, when freed from one form of their tyranny, to set up another more oppressive than the last.”

L. P. Jacks (1860–1955) British educator, philosopher, and Unitarian minister

The Usurpation Of Language (1910)
Context: The human mind loves the bondage of words and is apt, when freed from one form of their tyranny, to set up another more oppressive than the last.
The highest function of philosophy is to enforce the attitude of meditation and therewithal restrain the excessive volubility of the tongue. To us it seems that the reflective thinker wins his greatest victories when by what he says he compels us to recognise the relative insignificance of anything he can say. His task is not to capture Reality, but to free it from captivity.

Related topics