I'm currently preparing the final version of my book manuscipt and being puzzled anew by some passages in Stewart Shapiro's book Philosophy of Mathematics: Structure and Ontology. In particular, I've never seen - and still am not seeing - how to reconcile these claims:
(1) [A] structure is ... determined ... by the relations among the places. ... [T]he correct use of the language determines what the relations are. (p. 137, emphases in the original)
(2) Through successful language use, we structure the objective subject matter. (p. 137)
(3) [T]he way the universe is divided into structures and objects - of all kinds - depends on our linguistic resources. (p. 161)
with this one:
(4) The natural-number structure has objective existence and facts about it are not of our making. (p. 137)
If anyone knows of a charitable interpretation, I would be very interested to hear it.