As discussed in Chapter 8, Birnbaum introduces E v (E, y), the evidential meaning of obtaining data y as an instance of experiment E. Following Birnbaum, various authors have wrestled with the problem of developing a single set of postulates under which statistical inference can be made coherent. But as we claim in Section 8.3, E v(E, y)does not exist. Evidence is grounds for belief—an imprecise concept. There must be many valid reasons for believing and hence many ways of making the evidence concept precise. Most of our beliefs are held because mother—or someone else we trust—told us so. The law trusts sworn testimony. Scientific and statistical evidence are other different grounds for belief—supposedly particularly reliable kinds. Instead of E v (E, y) we are concerned with E v(E, T, y), the evidential meaning of observing v as an instance of E, in the context of theory T.