3 + 2 is actually 3.+(2) which is the right thing.There's nothing stopping you from doing
(defmethod add ((x number) (y number)) (+ x y))
(defmethod add ((x string) (y string)) (concatenate 'string x y))
or whatever (multiple dispatch, too), and you could even call it + instead of
ADD if you wanted (but not COMMON-LISP:+, so other code would continue to
work; your packages could import your + instead of the standard one).First, + does dynamic dispatch based on the types of its arguments. It does different things when adding fixnums, vs. integers, vs. rationals, and so on, as well as a default method that signals a type error (in safe code). So it has methods, even if they aren't necessarily implemented as standard methods (but they could be).
Secondly, a user might want to make + work on other, user-defined classes (for example, if he user wanted it to work on a class representing quaterions). To make that work, the user would have to be able to add methods for those classes. One can imagine many CL builtins being implemented as generic functions to which users could add methods. This would be consistent with the standard.
My opinion only, of course.