In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that canno… - Giuseppe Peano

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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.

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About Giuseppe Peano

Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician, logician, and one of the founders of modern mathematical logic and set theory. His work, summarized in Formulario mathematico (1895) was highly influential and the standard Peano axioms of the natural numbers are named in his honor.

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Additional quotes by Giuseppe Peano

Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses. But in order that this work merit the name of Geometry, it is necessary that these hypotheses or postulates express the result of the more simple and elementary observations of physical figures.

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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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