„We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking.“


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Géza Révész photo

„Ebbinghaus: Language is a system of conventional signs that can be voluntarily produced at any time.
Croce: Language is articulated, limited sound organized for the purpose of expression.
Dittrich: Language is the totality of expressive abilities of individual human beings and animals capable of being understood by at least one other individual.
Eisler: Language is any expression of experiences by a creature with a soul.
B. Erdmann: Language is not a kind of communication of ideas but a kind of thinking: stated or formulated thinking. Language is a tool, and in fact a tool or organ of thinking that is unique to us as human beings.
Forbes: Language is an ordered sequence of words by which a speaker expresses his thoughts with the intention of making them known to a hearer.
J. Harris : Words are the symbols of ideas both general and particular: of the general, primarily, essentially and immediately; of the particular, only secondarily, accidentally and mediately.
Hegel: Language is the act of theoretical intelligence in its true sense, for it is its outward expression.
Jespersen: Language is human activity which has the aim of communicating ideas and emotions.
Jodl: Verbal language is the ability of man to fashion, by means of combined tones and sounds based on a limited numbers of elements, the total stock of his perceptions and conceptions in this natural tone material in such a way that this psychological process is clear and comprehensible to others to its least detail.
Kainz : Language is a structure of signs, with the help of which the representation of ideas and facts may be effected, so that things that are not present, even things that are completely imperceptible to the senses, may be represented.
De Laguna: Speech is the great medium through which human co-operation is brought about.
Marty: Language is any intentional utterance of sounds as a sign of a psychic state.
Pillsbury-Meader: Language is a means or instrument for the communication of thought, including ideas and emotions.
De Saussure: Language is a system of signs expressive of ideas.
Schuchardt. The essence of language lies in communication.
Sapir: Language is a purely human and non-instinctive method of communicating ideas, emotions and desires by means of a system of voluntarily produced symbols.“

—  Géza Révész Hungarian psychologist and musicologist 1878 - 1955
Footnote at pp. 126-127; As cited in: Adam Schaff (1962). Introduction to semantics, p. 313-314

Willem de Sitter photo
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Hermann Weyl photo
Bertrand Russell photo

„The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970
Context: The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself. Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 5

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Franz Marc photo
Zayn Malik photo
Maurice Allais photo

„Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits“

—  Maurice Allais French economist; 1988 winner of the Nobel Memorial Prize in Economics 1911 - 2010
Context: Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means. in La formation scientifique, Une communication du Prix Nobel d’économie, Maurice Allais http://www.canalacademie.com/Maurice-Allais-la-formation.html, address to the Académie des Sciences Morales et Politiques (1997).

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Leonard Nimoy photo

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