In Part 1, we learned that the philosophy of mathematics is the branch of philosophy that relates to the foundation of mathematics. In Part 2, we learned that the philosophy of mathematics is also the branch of philosophy that deals with the nature of mathematics. Now in Part 3, we ponder whether mathematics is discovered or invented. The book Mathematics Through the Eyes of Faith by James Bradley and Russell Howell helps us ponder The Question: Is mathematics discovered or invented?
Before responding to The Question, remember Platonism holds that numbers have a real existence independent of human thought. Aristotelianism holds that numbers are a human modeling of patterns they find in the world around them. The phrase “out there” describes Platonism. The phrase “in here” describes Aristotelianism.
In their chapter on ontology, Bradley and Howell respond to The Question by focusing on a Christian philosophical perspective. They state, “The answers provided by Christian formulations that stem from the Platonist and Aristotelian traditions differ.” Bradley and Howell also respond that while both Plato and Aristotle answer mathematics is discovered, an Aristotelian answer also includes features of invention.
Bradley and Howell further respond, “The two positions we have primarily focused upon in this chapter agree that mathematics is ‘out there,’ but in different ways. The Platonist places the location in the divine mind; the Christian mathematical empiricist view places it in the creation. The latter position also adds an ‘in here’ dimension by stating that, although God created the patterns of creation, humans identify and conceptualize those patterns.”
~ Boethius ~