 A third version of the third strategy has been developed by Resnik (1997) and Shapiro (1997). Both of these philosophers endorse (platonistic) structuralism, a view that holds that our mathematical theories provide true descriptions of mathematical structures, which, according to this view, are abstract. Moreover, Resnik and Shapiro both claim that human beings can acquire knowledge of mathematical structures (without coming into any sort of information-transferring contact with such things) by simply constructing mathematical axiom systems; for, they argue, axiom systems provide implicit definitions of structures. One problem with this view, however, is that it does not explain how we could know which of the various axiom systems that we might formulate actually pick out structures that exist in the mathematical realm.