 The term \(\psi\) in the lower bound of this probability depends on a measure of the empirical distinctness of the two hypotheses \(h_j\) and \(h_i\) for the proposed sequence of experiments and observations \(c^n\). To specify this measure we need to contemplate the collection of possible outcomes of each experiment or observation. So, consider some sequence of experimental or observational conditions described by sentences \(c_1,c_2 ,\ldots ,c_n\). Corresponding to each condition \(c_k\) there will be some range of possible alternative outcomes. Let \(O_{k} = \{o_{k1},o_{k2},\ldots ,o_{kw}\}\) be a set of statements describing the alternative possible outcomes for condition \(c_k\). (The number of alternative outcomes will usually differ for distinct experiments among those in the sequence \(c_1 ,\ldots ,c_n\); so, the value of w may depend on \(c_k\).) For each hypothesis \(h_j\), the alternative outcomes of \(c_k\) in \(O_k\) are mutually exclusive and exhaustive, so we have: