Strawson's Constructed Concepts

I'm reading Strawson's, Analysis, Science, and Metaphysics, and am pondering over his description of system building, by what he seemingly calls philosophical clarification.

Yet, I have a question about constructed concepts and system building. Namely, is the system building to be performed on idealized languages or ordinary common sensicle languages? I ask this because one cannot attempt to design a conceptual construct outside of what I would call, decidable or truth apt propositions.

Thoughts? @Banno?