 Carnap’s immediate task was to create a canonical language for the formal mode of speech. Taking his cue from Hilbert’s metamathematics, he began by stripping this language down to bare bones, eliminating all problematic assumptions. It would consist simply of strings of dots on a page, and the basic laws of arithmetic would arise unambiguously in the metalanguage from the immediately evident patterns of dots (e.g., the commutative law from the perceptibly equivalent number of dots counted from the left and from the right). Carnap soon found he could not express certain essential concepts in this limited language, and turned instead to a more usual axiomatized arithmetic. This also had the advantage that, by using Gödel’s new trick of arithmetizing syntax, Carnap could now more easily express the syntax of the language (i.e., its logic) in the language itself. So the syntactic metalanguage collapses into the object language, and there is, as before, only a single language. The canonical language for the formal mode of speech seemed within his grasp.