All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers.

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On what became knows as the Peano axioms, in "I fondamenti dell’aritmetica nel Formulario del 1898", in Opere Scelte Vol. III (1959), edited by Ugo Cassina, as quoted in "The Mathematical Philosophy of Giuseppe Peano" by Hubert C. Kennedy, in Philosophy of Science Vol. 30, No. 3 (July 1963)

More quotes by Giuseppe Peano

Any property belonging to 0 and to the immediate successor of any number that also has that property belongs to all numbers.

As expressed in Galileo's Finger: The Ten Great Ideas of Science (2003)

0 is not the immediate successor of any number.

As expressed in Galileo's Finger: The Ten Great Ideas of Science (2003)

Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses.

Sui fondamenti della geometria (1894)

Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.

Geometric Calculus (1895)

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.

All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers.

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