Henri Poincaré - Objects Quotes

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Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.

Henri Poincaré
Now what is science?... it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations.... it is in relations alone that objectivity must be sought.... it is relations alone which can be regarded as objective.
External objects... are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation.

Henri Poincaré
There is no science apart from the general. It may even be said that the very object of the exact sciences is to spare us these direct verifications.

Henri Poincaré
Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have proved that it involves no contradiction either in its terms or with the truths previously admitted.

Henri Poincaré
What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

Henri Poincaré
Zero is the number of objects that satisfy a condition that is never satisfied. But as never means no case, I do not see that any progress has been made.

Henri Poincaré