„Mathematics is that form of intelligence in which we bring the objects of the phenomenal world under the control of the conception of quantity. [Provisional definition. ]“

"The Departments of Mathematics, and their Mutual Relations," Journal of Speculative Philosophy, Vol. 5, p. 164. Reported in Moritz (1914)
Journals

Última atualização 22 de Maio de 2020. História
George Holmes Howison photo
George Holmes Howison135
American philosopher 1834 - 1916

Citações relacionadas

James Joseph Sylvester photo
James Martin (author) photo

„From a very early age, we form concepts. Each concept is a particular idea or understanding we have about our world. These concepts allow us to make sense of and reason about the things in our world. These things to which our concepts apply are called objects.“

—  James Martin (author) British information technology consultant and writer 1933 - 2013

James Martin (1993, p. 17) as cited in: " CIS330 Object Oriented Approach Ch2 http://webcadnet.blogspot.nl/2011/04/cis330-object-oriented-approach-text_3598.html" webcadnet.blogspot.nl. 2011/04/16

Leonhard Euler photo
Werner Heisenberg photo
Benjamin Peirce photo

„Mathematics, under this definition, belongs to every enquiry, moral as well as physical.“

—  Benjamin Peirce, Linear Associative Algebra

§ 1.
Linear Associative Algebra (1882)
Contexto: The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law.
Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by, observation.

Isaac Asimov photo

„If, as I maintain and firmly believe, there is no objective definition of intelligence, and what we call intelligence is only a creation of cultural fashion and subjective prejudice, what the devil is it we test when we make use of an intelligence test?“

—  Isaac Asimov American writer and professor of biochemistry at Boston University, known for his works of science fiction and popular … 1920 - 1992

"Thinking About Thinking" in Magazine of Fantasy and Science Fiction, January 1975
General sources

Hans Reichenbach photo
Johannes Kepler photo
George Holmes Howison photo
Varadaraja V. Raman photo
George Boole photo

„It is not of the essence of mathematics to be conversant with the ideas of number and quantity.“

—  George Boole English mathematician, philosopher and logician 1815 - 1864

Fonte: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: Alexander Bain (1870) Logic, p. 191

John R. Commons photo
Umberto Boccioni photo

„.. if the objects will be mathematical values, the ambient in which they live will be a particular rhythm in the emotion which surrounds them. The graphic translation of this rhythm will be a state of form, a state of color, each of which will give back to the spectator the 'state of mind' which produced it..“

—  Umberto Boccioni Italian painter and sculptor 1882 - 1916

in a letter of 12 Feb. 1912 from Paris, to his friend Nino Barbantini (director of the Ca' Pesaro in Venice); as cited in: Shannon N. Pritchard, Gino Severini and the symbolist aesthetics of his futurist dance imagery, 1910-1915 https://getd.libs.uga.edu/pdfs/pritchard_shannon_n_200305_ma.pdf Diss. uga, 2003, p. 67
1912

Walter A. Shewhart photo
James Jeans photo
Georg Cantor photo

„Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established.“

—  Georg Cantor mathematician, inventor of set theory 1845 - 1918

From Kant to Hilbert (1996)
Contexto: Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.

William Stanley Jevons photo

„All acts of mathematical reasoning may… be considered but as applications of a corresponding axiom of quantity“

—  William Stanley Jevons English economist and logician 1835 - 1882

The Substitution of Similars, The True Principles of Reasoning (1869)
Contexto: Aristotle's dictim... may then be formulated somewhat as follows:—Whatever is known of a term may be stated of its equal or equivalent. Or, in other words, Whatever is true of a thing is true of its like.... the value of the formula must be judged by its results;... it not only brings into harmony all the branches of logical doctrine, but... unites them in close analogy to the corresponding parts of mathematical method. All acts of mathematical reasoning may... be considered but as applications of a corresponding axiom of quantity...

Eduard Jan Dijksterhuis photo

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“