Reality and Virtual Reality in Mathematics

This article introduces three of the twentieth century's main philosophies of mathematics and argues that of those three, one describes mathematical reality, the \reality" of the other two being merely virtual. What are mathematical objects, really? What, for example, is that thing that we call \the number one", or \the set of all positive whole numbers", or \the shortest path between two points on the surface of a sphere"? Most mathematicians (let alone most people) would

• Type: Journal
• Year: 2002
• Where: EATCS
• Authors: Douglas S. Bridges
• Keywords: EATCS 2002, Mathematical, Mathematical Objects, Perfect Form