„When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.“

As quoted in John von Neumann, 1903-1957 (1958) by John C. Oxtoby and B. J. Pettis, p. 128

Última atualização 22 de Maio de 2020. História
John von Neumann photo
John von Neumann
1903 - 1957
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Fonte: The Character of Physical Law (1965), chapter 2, “The Relation of Mathematics to Physics”
Contexto: Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.

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Contexto: There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

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„Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

Fonte: 1910s, Mysticism and Logic and Other Essays http://archive.org/stream/mysticism00russuoft/mysticism00russuoft_djvu.txt (1918), Ch. 5: Mathematics and the Metaphysicians

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„Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.“

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Original: (la) Quaestiones, quae ad mathematicae fundamenta pertinent, etsi hisce temporibus a multis tractatae, satisfacienti solutione et adhuc carent. Hic difficultas maxime en sermonis ambiguitate oritur. Quare summi interest verba ipsa, quibus utimur attente perpendere.

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