The urn model is to be the expression of three postulates: (1) the constancy of a probability distribution, ensured by the solidity of the vessel, (2) the randomcharacter of the choice, ensured by the narrowness of the mouth, which is to prevent visibility of the contents and any consciously selective choice, (3) the independence of successive choices, whenever the drawn balls are put back into the urn. Of course in abstract probability and statistics the word " choice " can be avoided and all can be done without any reference to such a model. But as soon as the abstract theory is to be applied, random choice plays an essential role.

p. 80; Cited in: Lev D. Beklemishev (2000) Provability, Computability and Reflection. p. 9 - The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961)