Phi 272 F06, reading guide

Each of these chapters touches on several topics. I’ll mention each of them and note the ones that I suggest we discuss.

Ch. 10 is an extension of Carnap’s account of measurement (after several chapters in which he has addressed specific issues concerning the measurement of space and time). I can discern four topics:

• Derived magnitudes (pp. 96-98). Not all magnitudes need be given rules of measurement directly since some are defined from others. The most significant issue here is the physical meaningfulness of the idea of continuity (see p. 98), but Carnap really doesn’t say enough here to introduce the issue in a way that would allow us to discuss it profitably.

• Interdependence of measurements (pp. 98-99). What is the problem Carnap poses concerning temperature and length and is his solution satisfactory? (The idea of a correction for thermal expansion is probably clear enough without turning to his earlier discussion; but, if you want to see that, it is on pp. 94-95.)

• Can everything be measured? (pp. 99-100). Think how you would answer this, then look at Carnap’s answer (recalling the variety of kinds of measurement distinguished by him and Stevens).

• Operational definitions (pp. 101-104). This is probably the most important of the topics in this chapter. The idea of operational definitions, due to P.W. Bridgman (1882-1961), derives from an American philosophical movement known as “Pragmatism,” but its motivation is close enough to the spririt of European positivism that it would be natural for Carnap to be sympathetic. He is, but with significant qualifications. You should watch for these qualifications and his reasons for him. Who do you think has the stronger position, Carnap or Bridgman? (You will find some quotations from Bridgman at the end of this guide.)

Ch. 11 will serve us as the conclusion of Carnap’s discussion of measurement. The point of measurement is to assign numbers to physical quantities; and, in this chapter, Carnap asks what is gained and what is lost by doing that.

• What is gained (pp. 105-109). Before reading this, try to guess what Carnap will say. Then see if you were right and see if you agree with him.

• What is lost (pp. 109-114). Carnap introduces this issue and focuses much of his discussion on the account of color offered in opposition to Newton by the poet Goethe. Carnap’s presentation of his own views (pp. 112-114) uses a distinction that is of interest in its own right. Think about it and ask yourself whether it is a satisfactory response to concerns to which Carnap addresses it.

Selections from: P. W. Bridgman, The Logic of Modern Physics (New York: Macmillan, 1927).

…What do we mean by the length of an object? We evidently know what we mean by length if we can tell what the length of any and every object is, and for the physicist nothing more is required. To find the length of an object, we have to perform certain physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined. In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations.…

… In principle the operations by which length is measured should be uniquely specified. If we have more than one set of operations, we have more than one concept, and strictly there should be a separate name to correspond to each different set of operations.

P. 16 (in reference to measurement of distances on the earth’s surface by triangulation where points are marked by lights)

We thus see that the concept of length has undergone a very essential change of character even within the range of terrestrial measurements, in that we have substituted for what I may call the tactual concept an optical concept, complicated by an assumption about the nature of our geometry. From a very direct concept we have come to a very indirect concept with a most complicated set of operations. Strictly speaking, length when measured in this way by light beams should be called by another name, since the operations are different. The practical justification for retaining the same name is that within our present experimental limits a numerical difference between the results of the two sorts of operations has not been detected.

We thus see that in the extension from terrestrial to great stellar distances the concept of length has changed completely in character. To say that a certain star is 10⁵ light years’ distant is actually and conceptually an entire different kind of thing from saying that a certain goal post is 100 meters distant.…

This somewhat detailed analysis of the concept of length brings out features common to all our concepts. If we deal with phenomena outside the domain in which we originally defined our concepts, we may find physical hindrances to performing the operations of the original definition, so that the original operations have to be replaced by others. These new operations are, of course, to be so chosen that they give, within experimental error, the same numerical results in the domain in which the two sets of operations may be both applied; but we must recognize in principle that in changing the operations we have really changed the concept, and that to use the same name for these different concepts over the entire range is dictated only by considerations of convenience, which may sometimes prove to have been purchased at too high a price in terms of unambiguity. We must always be prepared some day to find that Ian increase in experimental accuracy may show that the two different sets of operations which give the same results in the more ordinary part of the domain of experience, lead to measurably different results in the more unfamiliar parts of the domain. We must remain aware of these joints in our conceptual structure.…