I'm just starting to learn about the philosophy of mathematics, and was asked to read this paper for a course: Danielle Macbeth, Seeing How it Goes: Paper-and-Pencil Reasoning in Mathematical Practice, which appears in the Philosophia Mathematica. I've posted the paper here in case you can't access it otherwise.
I'm supposed to respond to the following question:
Is Danielle Macbeth's position in the paper in tension with mathematical platonism or, rather, does her position presume it?
I'm curious to hear some thoughts on this question. I'm kind of struggling with this, because in my view the position of Macbeth is that good mathematical notations embody mathematical arguments and reasoning, while the position of a mathematical platonist seems to be that mathematical objects are abstract and independent of human thought. I'm finding it hard to argue convincingly in response to the question above. Thoughts and ideas welcome!