 It should be clear that this notion of style, just like Granger’s, attributes a very important role to style as grounding the objectivity of an entire area of scientific activity but that, unlike Granger’s, it is committed ontologically to a rejection of realism. Styles are essential in the constitution of mathematical objects and the latter do not have a form of existence independent of them. Hacking has not extensively discussed case studies from the history of mathematics although one of his papers (Hacking 1995) deals with four constructionalist images of mathematics (the word “constructionalism” is borrowed from Nelson Goodman) and shows how well they fit with his picture of ‘styles of thinking’. By implication, it is also clear that more robustly committed realistic positions will not fit well with Hacking’s account of reasoning styles.