I love wittgensteins take on the reality of math. He thought that there were true statements, false statements, nonsense, and tautologies. True and false are e

I love wittgensteins take on the reality of math. He thought that there were true statements, false statements, nonsense, and tautologies. True and false are easy enough. “The cat is on the mat” is true or false depending on where the cat is in the room. It’s verifiable. Nonsense is what he would call any value statement, such as “the flowers are beautiful”. By using the word nonsense he doesn’t disparage, it just isn’t a verifiable statement. Tautologies are where math comes in. He thought that constructions of language were like symbolic pictures that had relation to states of the real world. Math however is statements about statements themselves. So “1+1=2” isn’t “true” in the same way that “the cat is on the mat” is true. But it is a tautology; a declaration that when you have two cats you can say there are “2” cats or you can say there are “1+1” cats. It’s the same thing. He likened our knowledge of math to our knowledge of chess. Just like we humans invented the game of chess to pas time, we invented the game of math to better understand what statements make sense.