It is possible to identify three traditional topics in the philosophy of science in these two chapters: reduction and the unity of science, the demarcation of science and non-science, and instrumentalist vs. realist interpretations of scientific theories. In each case, I’ll note ways the topic appears in Carnap’s discussion as well as ways of looking beyond what he says.

Reduction and the unity of science. Carnap begins ch. 25 with a discussion of the derivation of laws from theories. Here he elaborates the idea mentioned in ch. 23 that theories serve to explain and predict empirical laws much as empirical laws serve to explain and predict facts. It’s worth thinking through the illustrations of this idea that he gives here.

Also in ch. 23, he noted a disanalogy between the relation of theories to empirical laws and empirical laws to facts: while empirical laws generalize facts, theories do no simply generalize empirical laws but instead begin speaking of nonobservables. This allows them to achieve a generality that transcends particular realms of experience. Because they must be explicitly connected to observable, they may be connected to a far greater variety of empirical laws than could any principle stated solely by reference to observable.

Carnap notes one consequence of this in ch. 25: it is possible for one branch of a science to be derived from another that began as the study of entirely different phenomena. He gives the examples of acoustics and optics (p. 243). When this happens the branch whose laws have been explained is sometimes said to be reduced to the branch that explains these laws. As Carnap notes in passing on pp. 243f, this sort of reduction can draw together branches of science. It not only links a reduced branch of science to the branch it is reduced to but also links the various branches that can be reduced to a given more fundamental branch.

This sort of unification was seen as an important goal of science by the logical positivists. Indeed, one of their chief publications, one that Carnap has cited several times, was the International Encyclopedia of Unified Science. (In a way, you will read part of this work since it is one of central ironies of the philosophy of science in the 20^th century that the work that did the most to move the philosophy of science away from logical positivism—Kuhn’s The Structure of Scientific Revolutions—was first published as a component of the Encyclopedia of Unified Science.)

Carnap has relatively little to say of reduction as such in his book. I’m not entirely sure of the reasons for this; but this form of unification came to seem less important to people by the time he was writing, and it later came to be actively rejected. Few would be interested in disputing a reduction of acoustics or optics to other branches of physics, but it was also part of the program of unification that sciences like biology would eventually be reduced to others, like physics, and this idea was always more controversial.

Since the argument about the eventual reduction of biology to physics is not about the significance of derivations of laws that have been carried out but instead about what is in principle possible and desirable, it may be hard to evaluate; but one motivation for rejecting reduction is easily accessible: people find it hard to believe that one science could absorb another whose methodology and subject matter is apparently quite different. To put the point in a slightly different way, people find it hard to believe that biologists will ever practice science in the way physicists do; and they argue that, if these differences remain, there is little reason to say that biology and physics have become part of a single science.

The demarcation problem. Although one motivation for the derivation of laws from theories can be the unification of science, a more direct one is usually that theories provide a deeper understanding of the phenomena explained. However, as Carnap notes, this motive has often been regarded as questionable because it has often been used to justify links between science and metaphysical speculation. And philosophers, like the logical positivists, who both valued empiricism and thought that explanation was tantamount to unification must be especially concerned that empirical science not be absorbed into metaphysics.

The task of distinguishing science from other intellectual activities is often described as the project of demarcating the boundaries of science. This interest is not limited to the logical positivists; indeed, Popper was probably the philosopher most concerned with this issue, and the term demarcation was his. For Popper, the distinguishing feature of science is falsifiability, the possibility that a theory will be rejected because its predictions have failed. How would Carnap draw the line between science and non-science? How would you draw that line? Along the way in his discussion, Carnap makes a point that was also emphasized by Popper: even if metaphysical speculation is not science, it can play an important role in the development of science. Would you agree? If so, what do you think its role is?

Realism vs. Instrumentalism. The beginning of ch. 26 is devoted to an explanation of a particular way of reformulating scientific theories due to Frank Ramsey (1903-1930), who also played an important role in the early development of the idea of subjective probability. This reformulation is somewhat technical, so much of the chapter is devoted to describing it. But the upshot is an important question. Ramsey’s reformulation removes the theoretical terms that Carnap had taken as the hallmark of theories as opposed to empirical laws. That raises the question whether theories have any special value after all. If you think they do, you should ask whether this value is preserved when they are reformulated in the way that Ramsey suggests.

At the end of ch. 26 (pp. 255-256), Carnap links Ramsey’s idea to a view of scientific theories known as instrumentalism. Carnap presents realist arguments against instrumentalism more fully than instrumentalist arguments (though he characteristically refuses to choose sides), but you can take the paragraph before the introduces the distinction to suggest the motivations for instrumentalism.