 There is another structuralist position from the 1980s that is quite different and explicitly not realist, namely that introduced by Geoffrey Hellman (cf. Hellman 1989, 1996, and later articles). While for Resnik and Shapiro the inspiration was Benacerraf’s 1965 article, the starting point for Hellman is Putnam’s 1967 article. In fact, Hellman’s “modal structuralism” is meant to be a systematic development of Putnam’s modalized if-then-ism.  The modal aspect is now spelled out in detail and with real ingenuity, including for the case of set theory (building on work by Zermelo etc.). For Hellman, a sentence such as “\(2+3 = 5\)” is analyzed as follows: 