Thread: Mathematical Numbers are Theoretical; Not Proven

Originally Posted by Xei

The problem is that the absolutes are completely arbitrary, so mathematics isn't an entity at all.

I could say that 3 * 4 = 2, and 2 * 9 = 8, and 6 * 6 = 6, and so on (and then 1 * 10 = 0). It wouldn't be wrong, in fact it would form a completely coherent system. The thing is that whether it has any relevance to what I'm doing depends solely on what I'm trying to do.

Maths generalises reality, that's all.

Originally Posted by Xei

You can change the symbols to mean anything you want, and the rules of manipulating the symbols. Each time you would get a new, different system, only true in itself. You say one system of maths is real; then what about other, contradictory systems?

I think you are misunderstanding the difference between the language of mathematics and the world of mathematics. It is similar to the observable universe and human language. There is (so far) only one observable universe. It exists without language. As humans, we create language to describe it. So far, we have created hundreds of coherent sets of languages (english, japanese, hungarian, etc...) that all make sense describing the world around us. Even though they use completely different sets of rules and sometimes symbols, they all describe one unchanging world. Calling a dog different words doesn't change the fact that its a dog.

The world of math is exactly the same. There is only one world of mathematics, and it exists without language. You can use different languages to describe it (decimal, hex, binary, etc...) but they only make sense if they are coherent throughout the whole world of mathematics. You say you can throw random symbols together and they would make a coherent system...it doesn't work like that. I can say "asjdh jkahsldkah jvhkjlhl" and tell you it makes sense in another language, but it doesn't mean it does. Just like you can spout gibberish in language, you can spout gibberish in math. Just like a dog is a dog no matter what the name, adding the idea of one to the idea of one will create the idea of two. Changing the symbols used to represent that just changes how it looks on paper.

Originally Posted by Inside This Fantasy

I can say "asjdh jkahsldkah jvhkjlhl" and tell you it makes sense in another language, but it doesn't mean it does. Just like you can spout gibberish in language, you can spout gibberish in math. Just like a dog is a dog no matter what the name, adding the idea of one to the idea of one will create the idea of two. Changing the symbols used to represent that just changes how it looks on paper.

He's actually saying that he can construct a language such that "asjdh jkahsldkah jvhkjlhl" has a meaning. That doesn't mean just substituting symbols so they represent different letters/sounds , but creating an entire system (grammar, syntax, etc)

Originally Posted by Inside This Fantasy

Changing the symbols used to represent that just changes how it looks on paper.

That's the point, you don't just change the symbols, you can also change the relationships between them. You can do that and still get a consistent system.

Originally Posted by SnakeCharmer

He's actually saying that he can construct a language such that "asjdh jkahsldkah jvhkjlhl" has a meaning. That doesn't mean just substituting symbols so they represent different letters/sounds , but creating an entire system (grammar, syntax, etc)


That's the point, you don't just change the symbols, you can also change the relationships between them. You can do that and still get a consistent system.

If he does create an entire system from those words, then he has succesfully made a new language to describe the world of math. He hasn't changed the world of math. You can change the symbols and the relations to get a consistent system, but it just makes a new language to describe the same world. I was just trying to say you don't change the world itself when you use a different set of symbols to describe it.