In seeking general accounts of evidence, confirmation, or inference, philosophers have looked to logical relationships between evidence and hypotheses. Such logics of evidential relationship, whether hypothetico-deductive, Bayesian, or instantiationist fail to capture or be relevant to scientific practice. They require information that scientists do not generally have (e.g., an exhaustive set of hypotheses), while lacking slots within which to include considerations to which scientists regularly appeal (e.g., error probabilities). Building on my co-symposiasts contributions, I suggest some directions in which a (...) new and more adequate philosophy of evidence can move. (shrink)

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of p-values rather than as formal procedures for ‘acceptance‘ and ‘rejection‘. A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of p- values in the specific circumstances of each application, as contrasted with a long-run interpretation. A number of more complicated situ- ations are discussed (...) in which modification of the simple p-value may be essential. (shrink)