 What Stebbing means by a constructed system here is a system that is postulated as a replacement for a conceptual system used in our everyday life—in the way that set theory might be seen as postulating a replacement for our ordinary system of arithmetic. On this view, our everyday concepts and propositions are vague and need to be replaced—or “explicated”, to use Carnap’s later term—by precisely defined concepts, clearly stated axioms and logically derived propositions. Stebbing’s fundamental objection to this conception of postulational or explicatory analysis is that it misunderstands the role of analysis, which is “to understand something more clearly” (1933a: 81). Simply replacing our ordinary vague concepts by precise ones does not genuinely show what it was we understood. Consider, for example, the “replacement” of our ordinary concepts of colour by concepts scientifically defined in terms of the wavelengths of light, etc. Arguably, this can never do justice to what it is we experience when we see colours and describe them in the ordinary ways we do: it does not capture the phenomenology of our experience. In the same way, we might question whether defining numbers as sets genuinely shows what we “really mean” by number terms.