The structuralist vigorously rejects any sort of ontological independence among the natural numbers. The essence of a natural number is its relations to other natural numbers. The subject-matter of arithmetic is a single abstract structure, the pattern common to any infinite collection of objects that has a successor relation, a unique initial object, and satisfies the induction principle. The number 2 is no more and no less than the second position in the natural number structure; and 6 is the sixth position. Neither of them has any independence from the structure in which they are positions, and as positions in this structure, neither number is independent of the other. Shapiro, Thinking About Mathematics, p.258, quoted by Seldin in Handbook of the History of Logic, Vol. 5, p.855