Compos Mentis

Numbers

It's interesting to me that wherever I go, I manage to find people to have philosophical discussions with. Last night I was up past midnight talking with a girl about people and how they think (or don't think), then today I got into an argument with my Philosophy teacher on the Ontological argument of Anselm before coming back and talking with an agnostic on matters of faith and how it works in all sorts of people. I love talking with people because they show me what I don't know, what I've overlooked, and what I've reasoned falsely. But one thing I notice is that whatever I talk about, I remember something very similar has already been written or discovered. This is one of those instances. I had this conversation with an old friend of mine, then a week later read a book by the philosopher Gottlieb Frege coming up with the exact same conclusion from a different angle.
We were looking at people eating lunch at tables in a cafeteria, and it started to become clear to us that people have odd notions about tables: namely that they are all the same. They can count groups at a table as a group because they have a common property with the other groups: they are sitting at tables. The groups are not the same, but because they have similar properties that are group together in the mind, they that are similar are also same, just in lesser degree. But this is the best we can get: in a physical world, you can't get two things that share the exact same properties: There would not be room for them as they tried to fill the same space. However, there is a place that perfect sameness exists.
In mathematics, the most basic property is that a=a, or that 1+1+1=1+1+1. Here = really means completely equal, the same, sharing all properties. But using numbers in the real world forces us to call equal what is only similar or approximate, like the people at the tables. One book and another book become two books because they share the properties of "bookness" we hold in our minds, but they still have different words on their pages. If we look at the pages something else comes out. Say a book has 300 pages. Try to think where the number 300 comes from, or what it is associated with. The number 300 is neither part of the book or of any of the pages. Each page does not hold within itself the idea of 300, and neither does the book. It is something outside both the book and its pages, something within our minds in order to organize the group or set. The 300 is a concept of the multitude of pages that are in the set of the book, but is still neither a property of the book or of the pages. Think of a pair of men standing together. The number two is not identical with these men. The number two is instead something that all pairs have in common, and is a way for us to organize groups in our minds, namely all groups with a pair hold the number two.
But this idea has already been taken. So I'll keep thinking, and try to come up with something no one has come up with in quite the same way. Maybe.

posted by Emmett @ 16:25