“All is number” – Pythagorean School
In Part 1 I attempted to present some of the philosophical reasons why we may think infinity is a pretty dodgy concept. I now want to address the second and third questions I posed
What do we mean when we say mathematics exists?
What do we mean when we say the universe exists?
Much has been said about reality and existence, probably way too much. I’m not trying to introduce new ground here, just present a view that I think goes nicely with the idea that everything is finite. That view is known as the Mathematical Universe Hypothesis (MUH) an idea originated by Max Tegmark. It states that our universe is nothing more nor less than a mathematical structure. It implies that any mathematical structure exists in the same sense that our universe exists. I won’t elaborate on this in great detail (I hope to in a later post) but I’d like to give some brief motivation to this idea. Continue reading