On Definitions I

"Rules for Demonstrations. I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it. II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated. III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions." (Blaise Pascal, "Pensées", 1670)

"Rules necessary for definitions. Not to leave any terms at all obscure or ambiguous without definition; Not to employ in definitions any but terms perfectly known or already explained. […] A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading." (Blaise Pascal, "Pensées", 1670)

"The science [mathematics], once fairly established on the foundation of a few axioms and definitions, as upon a rock, has grown from age to age, so as to become the most solid fabric that human reason can boast." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"Mathematics is an experimental science, and definitions do not come first but later on." (Oliver Heaviside, "On Operators in Physical Mathematics", Proceedings of the Royal Society of London, Series A Vol. 54, 1854)

"Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts." (Georg Cantor," Grundlagen einer allgemeinen Manigfaltigkeitslehre", 1883) 

"The whole history of the development of mathematics has been a history of the destruction of old definitions […] old hobbies, old idols." (David E Smith, American Mathematical Monthly Vol. 1 (1), 1894)

"If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. [...] Hence the question of whether axioms are a priori becomes pointless since they are arbitrary." (Hans Reichenbach, "The Philosophy of Space and Time", 1928) 

"The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings." (Willard van Orman Quine, "From a Logical Point of View", 1953)

"In order that a mathematical science of any importance may be founded upon conventional definitions, the entities created by them must have properties which bear some affinity to the properties of existing things."(John H C Whitehead, A Treatise on Universal Algebra, with Applications, 1960)

"The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity." (Richard Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)