ABSTRACT
This chapter compares two kinds of analysis of the basic concepts of theories, first that due to Frege and second that due to Hilbert. These approaches are only two among many, but it is useful to examine them, since they present a stark difference between a compositional approach starting from individually meaningful primitives and the axiomatic approach where whatever meaning the basic concepts acquire is given through the axioms governing the system of which they are the basic concepts. The difference is important, because it highlights two very different views of the foundations of mathematics, the view, which was at the root of logicism, that one must seek ultimate primitives of a special kind and the view that there are no ultimate primitives and that further analysis is always possible.
