In a similar vein, I'm currently halfway through 'Thinking About Mathematics' by Stewart Shapiro. It's a great introduction to the various philosophies of mathe

In a similar vein, I'm currently halfway through 'Thinking About Mathematics' by Stewart Shapiro. It's a great introduction to the various philosophies of mathematics: logicism, formalism, intuitionism, structuralism, basically all of the different sorts of philosophical positions prominent people have taken on the nature of mathematics, going back to Plato and Aristotle. It's wonderfully approachable as well, I highly recommend it.