In the present chapter we discuss some of the major responses to Benacerraf's dilemma. In particular, we will discuss some of those that in § 3.3 have been classified, following Hale and Wright (2000), as non-conservative. We will consider four of these: Field's nominalism; fic-tionalism, both in Field's and in Yablo's version; Hellman's eliminative modal structuralism; and the version of platonism advanced by Maddy on cognitive grounds.