  In addition to Benacerraf’s, a variety of metaphysical objections to mathematical platonism have been developed. One of the more famous examples is an argument of Nelson Goodman’s against set theory. Goodman (1956) defends the Principle of Nominalism, which states that whenever two entities have the same basic constituents, they are identical. This principle can be regarded as a strengthening of the familiar set theoretic axiom of extensionality. The axiom of extensionality states that if two sets x and y have the same elements—that is, if ∀u(u ∈ x ↔ u ∈ y)—then they are identical. The Principle of Nominalism is obtained by replacing the membership relation with its transitive  closure.[14]  The principle thus states that if x and y are borne ∈* by the same individuals—that is, if ∀u(u ∈* x ↔ u ∈* y)—then x and y are identical. By endorsing this principle, Goodman disallows the formation of sets and classes, allowing only the formation of mereological sums and the application to the standard mereological operations (as described by his “calculus of individuals”).