• In §6, Giere addresses the issue that separated many of the views outlined in §3. Those, like Popper, who take the derivation of new predictions from hypotheses to be central to science are opposed by those who see support by any evidence (new or old) to be of equal value. Giere tries give an account of why, from his perspective, some successful predictions provide greater support than would comparable old evidence.

• Section 7 fills out the account of testing in §4 in a more formal and explicit way. In case the notation used for “decision rules” on p. 288 is not clear, each rule is specified by noting the actions to be taken when a prediction proves to be correct or incorrect (true or false). A rule is thus labeled by the pair (action when prediction true, action when prediction false) where the possible actions are accepting the hypothesis (A) or rejecting it (R). The “expected values” in the second matrix are calculated by adding multiplying the value of each action by the probability of taking it (on the given rule). The table of probabilities and values in Fig. 1 apply to the action (A, R), so the calculation for its value when the hypothesis is true would be:

If you want to think through the calculations behind the rest of the second table, it may help to think of separate tables of probabilities and values because these match up differently for different rules.

• The brief §8 provides the basis for a comparison with Popper. Notice that, while degrees of support of a hypothesis by evidence do not flow readily from Giere’s account, he does not reject them entirely.

• Giere’s discussion of approximation is probably the most valuable part of §9, but his discussion of van Fraassen’s views presents a side of the latter’s position complementary to the one we have discussed.

• The key thing to think about in §10 is Giere’s comment that “whether a proposed test of a theoretical hypothesis is a satisfactory test is itself an empirical question” (p. 296). It points to the view that the choice of a methodology for science is not fundamentally different from science itself.