#
Is geometry purely mathematical or does it rely on spatiality which is beyond mathematics?

I take your question to be whether geometry can be axiomatized into a deductive system based on certain definitions, as some philosophers believe mathematics can be, or whether, because geometry is in some way related to space--unlike mathematics--it cannot so be axiomatized. I begin by noting that there is disagreement among philosophers of mathematics whether mathematics can indeed be axiomatized in this way. Charles Parsons, for example, following Kant, believes that mathematics requires intuition. Since I don't know the details of Parsons's account, presented in his book Mathematical Thought and Its Objects , I draw instead on Kant's view, which inspired Parsons (who is also a great Kant scholar): consideration of Kant's view of mathematics will also lead us back to geometry. According to Kant, both mathematics and geometry yield a body of necessary truths, truths which are, in Kant's terminology, ' a priori '; moreover, according to Kant, the truths of both mathematics and geometry...

- Log in to post comments