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In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that cannot be reduced among them, and that one can define no further. These are the primitive ideas of the science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction.

— Giuseppe Peano Notations de Logique Mathématique (1894)

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Source: Notations de Logique Mathématique (1894), p. 173, as quoted in "The Mathematical Philosophy of Giuseppe Peano" by Hubert C. Kennedy, in Philosophy of Science Vol. 30, No. 3 (July 1963)
Work: Notations de Logique Mathématique, 1894
Source quality: Secondhand citation Quoted from another book or article rather than from the original.

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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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Quote text and notes from Wikiquote: Giuseppe Peano (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.