“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

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)

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 "It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at al…" by Hermann Weyl?

Hermann Weyl28

German mathematician 1885–1955

Related quotes

“[The environment of a system is] a set of elements and their relevant properties, which elements are not part of the system, but a change in any of which can cause or produce a change in the state of the system.”

Russell L. Ackoff (1919–2009) Scientist

1970s, Towards a System of Systems Concepts, 1971

“A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Source: 1960s, Fuzzy sets (1965), p. 338

“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 (1795–1881) Scottish philosopher, satirical writer, essayist, historian and teacher

1840s, Past and Present (1843)

“The truth is that the mathematical sciences are growing in complete security and harmony. The ideas of Dedekind, Poincare, and Hilbert have been systematically developed with great success, without any conflict in the results. It is only from the philosophical point of view that objections have been raised. They bear on certain ways of reasoning peculiar to analysis and set theory. These modes of reasoning were first systematically applied in giving a rigorous form to the methods of the calculus. [According to them, ] the objects of a theory are viewed as elements of a totality such that one can reason as follows: For each property expressible using the notions of the theory, it is [an] objectively determinate [fact] whether there is or there is not an element of the totality which possesses this property. Similarly, it follows from this point of view that either all the elements of a set possess a given property, or there is at least one element which does not possess it”

Paul Bernays (1888–1977) Swiss mathematician

Paul Bernays, Platonism in mathematics http://sites.google.com/site/ancientaroma2/book_platonism.pdf (1935)

“In the most general mathematical sense, a space is a set of elements which conform to certain postulates.”

James Grier Miller (1916–2002) biologist

Source: Living Systems: Basic Concepts (1969), p. 51

“A system is a set of two or more elements that satisfies the following three conditions. (1) The behavior of each element has an effect on the behavior of the whole. (2) The behavior of the elements and their effects on the whole are interdependent. the way each element behaves and the way it affects the whole depends on how at least one other element behaves. (3) However subgroups of the elements are formed, each has an effect on the behavior of the whole and none has an independent effect on it.”

Russell L. Ackoff (1919–2009) Scientist

Source: 1980s, Creating the Corporate Future, 1981, p. 15-16.

“A system may actually exist as a natural aggregation of component parts found in Nature, or it may be a man-contrived aggregation – a way of looking at a problem which results from a deliberate decision to assume that a set of elements are related and constitute such a thing called ‘a system.”

C. West Churchman (1913–2004) American philosopher and systems scientist

C. West Churchman, , I. Auerbach, and Simcha Sadam (1975) Thinking for Decisions Deduction Quantitative Methods. Science Research Associates. cited in: John P. van Gigch (1978) Applied General Systems Theory. Harper & Row Publishers
1960s - 1970s

“Once the first principles are disposed of, the body of doctrine contained in the recent textbooks of elementary geometry does not, and from the nature of the case cannot, show any substantial differences from that set forth in the Elements.”

Thomas Little Heath (1861–1940) British civil servant and academic

Introduction, p. v
The Thirteen Books of Euclid's Elements (1908)

“Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.”

Joseph Fourier book The Analytical Theory of Heat

Source: The Analytical Theory of Heat (1878), Ch. 1, p. 1

“It is very possible that a proper understanding of string theory will make the space-time continuum melt away…. String theory is a miracle through and through.”

Edward Witten (1951) American theoretical physicist

as quoted by K.C. Cole, "A Theory of Everything" New York Times Magazine (1987) Oct.18

Help us to complete the source, original and additional information

Hermann Weyl28

Related quotes

Related topics