5 Seeing with the Mind's Eye
The Platonist Alternative
The most vexing question about mathematical knowledge is rather simple: How do we get it? We cannot learn about numbers the way we learn about apples, by looking at them. We cannot see them indirectly either, the way we see electrons by looking at streaks in a cloud chamber. To say it's a mystery would be an understatement. Nevertheless, Platonism has an answer. In fact, it can offer several different types of answer to explain how we acquire mathematical knowledge. I will describe some of the more unusual in this chapter.
In Chapter 2 I briefly sketched some of the main features of Platonism. I will do it again but in more detail this time. That will come later. First, an unusual example ...
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