 Thus, in Granger’s theory mathematical styles are modes of presentation, or modes of grasping the mathematical structures. At least in some cases these effects of style leave the mathematical objects or structures unaffected although they will affect the cognitive mode in which they are apprehended, therefore affecting how they might be subjected to extension, applied in various areas etc. Even though Granger might have sympathized with a Kantianism without a transcendental subject, and thus think of style as constitutive, it seems that his position is at least compatible with a form of realism about mathematical entities. This does not seem to be the case for the third and final epistemological position to be discussed, which is due to Ian Hacking.