Skip to content

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

— Giuseppe Peano Sui fondamenti della geometria (1894)

Another quote →

Source and credibility

Wikiquote does not flag this quote as disputed or misattributed.

Source: "Sui fondamenti della geometria" (1894), p. 141, as quoted in "The Mathematical Philosophy of Giuseppe Peano" by Hubert C. Kennedy, in Philosophy of Science Vol. 30, No. 3 (July 1963)
Work: Sui fondamenti della geometria, 1894
Source quality: Secondhand citation Quoted from another book or article rather than from the original.

More by Giuseppe Peano

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.

Notations de Logique Mathématique (1894)

All Giuseppe Peano quotes →

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)

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

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.

All Giuseppe Peano quotes →

Attribution

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.