“The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111, 777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library.”

—  Bertrand Russell , Principia Mathematica

Principia Mathematica, written with Alfred North Whitehead, (1910), vol. I, Introduction, ch. II: The Theory of Logical Types. This is a statement of the Berry paradox.
1910s

Adopted from Wikiquote. Last update Sept. 29, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must…" by Bertrand Russell?
Bertrand Russell photo
Bertrand Russell 562
logician, one of the first analytic philosophers and politi… 1872–1970

Related quotes

Richard Dedekind photo

“Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

Leopold Kronecker photo

“God made the integers, all the rest is the work of man.”

Leopold Kronecker (1823–1891) German mathematician who worked on number theory and algebra (1823–1891)

Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
Quoted in "Philosophies of Mathematics" - Page 13 - by Alexander George, Daniel J. Velleman - Philosophy - 2002

“The integers, the rationals, and the irrationals, taken together, make up the continuum of real numbers. It's called a continuum because the numbers are packed together along the real number line with no empty spaces between them.”

Brian Hayes (scientist) (1900) American scientist, columnist and author

Source: Group Theory in the Bedroom (2008), Chapter 11, Identity Crisis, p. 206 (See also: George Cantor)

“But what, after all, are the integers? Everyone thinks that he or she knows, for example, what the number three is — until he or she tries to define or explain it.”

Carl B. Boyer (1906–1976) American mathematician

As quoted in Everything and More: A Compact History of Infinity (2013) by David Foster Wallace, p. 8

Aryabhata photo

“He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes.”

Aryabhata (476–550) Indian mathematician-astronomer

Roger Cooke in: The history of mathematics: a brief course http://books.google.co.in/books?id=z-ruAAAAMAAJ, Wiley, 7 October 1997, p. 207.

Henry Burchard Fine photo

“Judged by the only standards which are admissible in a pure doctrine of numbers i is imaginary in the same sense as the negative, the fraction, and the irrational, but in no other sense; all are alike mere symbols devised for the sake of representing the results of operations even when these results are not numbers (positive integers).”

Henry Burchard Fine (1858–1928) American academic

Source: The Number-System of Algebra, (1890), p. 86; Reported in Moritz (1914, 282)

“It was Mr. Littlewood (I believe) who remarked that "every positive integer was one of his personal friends."”

John Edensor Littlewood (1885–1977) English Mathematician

(about Ramanujan) p. lvii of [Hardy, G. H., G. H. Hardy, Obituary Notices: Srinivasa Ramanujan, Proceedings of the London Mathematical Society, 19, xl-lviii, 1921, http://www.numbertheory.org/obituaries/LMS/ramanujan/index.html, 2008-05-26]

Georg Cantor photo

“That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

Letter to Gustac Enestrom, as quoted in Georg Cantor : His Mathematics and Philosophy of the Infinite (1990) by Joseph Warren Dauben ~ ISBN 0691024472

“Can the ear hear a thirteen-syllable line as consisting of thirteen syllables? I don't think so, but I think that a series of thirteen-syllable lines (supposing that was the length chosen) would, after a while, begin to have a characteristic resemblance. For the most part, though, counting the syllables seems to be something that works, if it works, for the poet. It is a private method of organization.”

James Fenton (1949) poet

Source: An Introduction to English Poetry (2002), Ch. 18: Syllabics (p. 99)

Related topics