# „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.“

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

Última atualização 22 de Maio de 2020. História
1916 - 2011

### „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 American mathematician 1934 - 2007

Set theory and the continuum hypothesis, pp. 19–20 https://books.google.com/books?id=Z4NCAwAAQBAJ&pg=PA19
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 Austrian sculptor (23 April 1907, Vienna – 28 August 1975, Vienna) 1907 - 1975

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

### „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 Anglo-Dutch writer and physician 1670 - 1733

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

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

—  Bruce Lee Hong Kong-American actor, martial artist, philosopher and filmmaker 1940 - 1973

Bruce Lee: A Warrior's Journey (2000); here, Lee was reciting lines he wrote for his short lived role on the TV series Longstreet.
Contexto: 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.

### „Mathematics… is the set of all possible self-consistent structures“

—  Michio Kaku, livro Hyperspace

Fonte: Hyperspace (1995), Ch.15 Conclusion<!--p.328-->
Contexto: Mathematics... is the set of all possible self-consistent structures, and there are vastly more logical structures than physical principles.

### „And while the ice was melting to form a flood in which I threatened to drown I awoke one afternoon to find that my first northern winter had set.“

—  Ralph Ellison, livro Invisible Man

Fonte: Invisible Man (1952), Chapter 12.

### „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 British educator, philosopher, and Unitarian minister 1860 - 1955

The Usurpation Of Language (1910)
Contexto: 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.

### „When free discussion is denied, hardening of the arteries of democracy has set in, free institutions are but a lifeless form, and the death of the republic is at hand.“

—  William Randolph Hearst American newspaper publisher 1863 - 1951

"In the News" (June 13, 1941)

### „The spiral is a spiritualized circle. In the spiral form, the circle, uncoiled, has ceased to be vicious; it has been set free.“

—  Vladimir Nabokov, livro Speak, Memory

Fonte: Speak, Memory

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

—  Karl Marx, livro 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)

### „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.“

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

### „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 American neuropsychiatrist 1929

In Search of Memory (2006)

### „men's hearts ought not to be set against one another; but set with one another, and all against the Evil Thing only.“

—  Thomas Carlyle Scottish philosopher, satirical writer, essayist, historian and teacher 1795 - 1881

1840s, Past and Present (1843)

### „Perhaps the least inadequate description of the general scope of modern Pure Mathematics—I will not call it a definition—would be to say that it deals with form, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.“

—  E. W. Hobson British mathematician 1856 - 1933

Fonte: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 287; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/4/mode/2up, (1914), p. 5: Definitions and objects of mathematics.

### „The government, which was designed for the people, has got into the hands of the bosses and their employers, the special interests. An invisible empire has been set up above the forms of democracy.“

—  Woodrow Wilson American politician, 28th president of the United States (in office from 1913 to 1921) 1856 - 1924

Section II: “What is Progress?”, p. 35 http://books.google.com/books?id=MW8SAAAAIAAJ&pg=PA35&dq=%22The+government,+which+was+designed%22
1910s, The New Freedom (1913)

### „Persons are set on fire by someone who is already aflame. It is a trumpet call to high adventure that starts the forward movements away from old forms.“

—  Rufus M. Jones American writer 1863 - 1948

What Will Get Us Ready (1944)
Contexto: Most persons are awakened and set on their new track of life through the quickening and kindling power of some person who becomes for them the instrument of inspiration and of the creation of faith and the vision of a nobler way of life. Persons are set on fire by someone who is already aflame. It is a trumpet call to high adventure that starts the forward movements away from old forms.
That is one of the greatest stories in the long history of religion. It was through a long and wonderful circuit of souls, in a succession of forerunners, that the kindling idea of “Something of God in the soul of man” came to George Fox.

### „The error arises from the learned jurists deceiving themselves and others, by asserting that government is not what it really is, one set of men banded together to oppress another set of men, but, as shown by science, is the representation of the citizens in their collective capacity.“

—  Leo Tolstoy Russian writer 1828 - 1910

The Kingdom of God is Within You (1894)
Variante: Government is an association of men who do violence to the rest of us.

### „It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum.“

—  Hermann Weyl German mathematician 1885 - 1955

Riemanns geometrische Ideen, ihre Auswirkungen und ihre Verknüpfung mit der Gruppentheorie (1925), as quoted/translated by Erhard Scholz, "Philosophy as a Cultural Resource and Medium of Reflection for Hermann Weyl" (2004)

### „Knowledge can in part be set aside, and one can then go further in order to collect new; the natural scientist can set aside insects and flowers and then go further, but if the existing person sets aside the decision in existence, it is eo ipso lost, and he is changed.“

—  Sören Kierkegaard Danish philosopher and theologian, founder of Existentialism 1813 - 1855

Papers VI B 66, 1845
1840s

### „Set all at sixe and seven.“

—  John Heywood English writer known for plays, poems and a collection of proverbs 1497 - 1580

Part I, chapter 11.
Proverbs (1546), Bartlett's Familiar Quotations, 10th ed. (1919)