Review: Robert Kowalski, Logic for Problem Solving

view that mathematics may differ from science only in degree when it comes to revisability in face of experience. Formalism and intuitionism are not mentioned. Lambert and Brittan also treat other topics to a large extent in terms of positivist doctrines and reactions to them. As regards explanation, they treat Hempel's DN and statistical accounts, the symmetry thesis, lawlikeness, counterfactuals, and the attempt to understand lawlikeness in terms of theoretical connectedness. They consider whether statistical explanations are truly explanatory and whether intentional behavior will submit to treatment within the DN account. Confirmation theory is dealt with entirely in terms of qualitative instance confirmation, with no discussion of Carnap or Bayesianism. The authors explain Hempel's and Goodman's paradoxes and survey suggested resolutions. They continue with a look at theoretical connection, fruitfulness of hypotheses, and simplicity (on which they closely follow Hempel's text). I wish they had included a discussion of auxiliary hypotheses and the complications to which they give rise. I must complain here about a mistake (as opposed to a questionable argument reported for the student to pick apart as an exercise). The authors incorrectly claim that if the grue hypothesis is true then such things as emeralds will change color in the year 2000. One of the beauties of Goodman's dramatization of the old curve-fitting problem (a connection which Lambert and Brittan bring out very clearly) is that it does not allow this attractive toe-hold for a solution.