An improvement for LISPs

So I'm starting to learn LISPs quite a lot lately, and I'm fascinated by how everything is a list! It's brilliant! Absolutely brilliant. But I had second thoughts when I found out that LISP has _primitives like integers and strings. This disturbed me greatly, so I was forced to come up with a superior LISP model that only uses lists:

1. An integer i is a list li of empty lists such that (length li) == i.
2. A character is an integer i such that i < 256.
3. A string is a list of characters.
4. A float is a list of integers of length two.

What do you guys think of my idea?

(apply '((x) (+ x 1)) '(2))