Wrinch and Jeffreys on Russell’s Epistemology of Science

In the following paragraphs, Wrinch and Jeffreys describe a tension between philosophers and scientists who write on the epistemology of science. The fundamental problem is that existing theories of epistemology make it extremely difficult, or even impossible, for us to have scientific knowledge. Philosophers generally have regarded inductive generalization as formally fallacious, and this casts doubt on the possibility of scientific knowledge. Scientists, on the other hand, start with the belief that their methods work (the results speak for themselves!), and most of them would condemn philosophy before admitting any epistemic shortcomings. Wrinch and Jeffreys then mention more recent writers who have tried to resolve this problem by showing that scientific knowledge is possible without the use of inductive generalization, by the addition of certain fundamental postulates. Unfortunately, they say, these attempts are unsatisfactory because there is no reason to think that such postulates are true.

Here, Wrinch and Jeffreys explicitly name Bertrand Russell and A. N. Whitehead as such writers, and they say that their objection to them is fundamentally the same—that these epistemological views require an uncritical use of postulates that involve infinite classes of entities. Here, I will focus on their rejection of Russell’s theory, for which they cite the essay “The Relation of Sense-Data to Physics”, published in Mysticism and Logic (Russell 1917). Here is what Russell has to say about the epistemology of physics:

In physics as commonly set forth, sense-data appear as functions of physical objects: when such-and-such waves impinge upon the eye, we see such-and-such colors, and so on. But the waves are in fact inferred from the colors, not vice-versa. Physics cannot be regarded as validly based upon empirical data until the waves have been expressed as functions of the colors and other sense data.

Thus if physics is to be verifiable we are faced with the following problem: Physics exhibits sense-data as functions of physical objects, but verification is only possible if physical objects can be exhibited as functions of sense-data. We have therefore to solve the equations giving sense-data in terms of physical objects, so as to make them instead give physical objects in terms of sense-data. (Russell 1917, pp. 146-147)

This is a statement of the epistemology of physics as involving a kind of inverse problem. That is, Russell is saying that you can think of physics as providing a function that maps physical objects onto sense-data—given some particular layout of physical objects and a human, physics provides a way of calculating, in principle, what sense-data that human would experience. But the epistemology of physics is the opposite of this. You start with sense-data, and you are supposed to arrive at physical objects. Russell states this process as taking the functions from physical objects to sense-data, and inverting them.

It’s worth pointing out here the parallel between the problem stated by Russell, and a problem that Harold Jeffreys was really interested in. Think of the problem of determining the properties of the deep interior of the earth based on observations of seismic waves at its surface. Given the density and the values of the elastic constants at each point in the earth’s interior, you can uniquely determine what observations you ought to have at the earth’s surface, such as the travel times of seismic waves. Physics provides us with a function that maps the properties of the earth’s interior to seismic wave observations. But the problem that Jeffreys was interested in is the inverse of this problem—given the data we record at the surface, what are the density and values of the elastic constants at each point in the earth’s interior? This is, in fact, exactly the problem that Jeffreys attempts to solve later in the 1930s and 1940s—the determination of detailed models of the earth’s interior based on travel times of seismic waves. The problem, as Jeffreys realized very well, is that the inverse problem is massively underdetermined—in fact, radically different earth models could be compatible with observations at the earth’s surface. And this is still, I think, the central problem in the epistemology of seismology.

But let’s get back to Russell. How does Russell propose to solve this inverse problem? Here is Russell’s solution:

The supreme maxim in scientific philosophizing is this: Wherever possible, logical constructions are to be substituted for inferred entities. [...] This method, so fruitful in the philosophy of mathematics, will be found equally applicable in the philosophy of physics, where I do not doubt it would have been applied long ago but for the fact that all who have studied this subject hitherto have been completely ignorant of mathematical logic. (Russell 1917, pp. 155-157, emphasis in the original)

An example that Russell gives is irrational numbers. Instead of inferring the existence of irrational numbers, you define irrational numbers in terms of a cut between two sets of rational numbers. This gets rid of the problematic inference to mysterious entities that cannot be accessed directly, namely irrational numbers. The proposal is to construct all of physics out of sense-data in a similar manner, getting rid of problematic inferences to inaccessible entities. And this is supposed to solve the problem of inversion that Russell states.

Now, whatever the merits of this solution in mathematics, Wrinch and Jeffreys believe that it will not work for physics. The approach that Russell takes towards solving the inverse problem takes the existence of physical objects to be epistemologically problematic, and he suggests the construction strategy to avoid this existence problem. But the problem in which Wrinch and Jeffreys are interested, while having a similar structure, is entirely different. This becomes clear when you think about trying to apply this procedure to an actual science. Suppose you want to determine the properties of the deep interior of the earth, based on observations at its surface, as indeed Wrinch and Jeffreys wanted. The existence of things in the earth’s deep interior is not at all in question. What they want to determine are the properties of these things—for example, what is the value of the density 1000 km from the earth’s center?

Now, suppose you tried to define values for the properties of the physical objects as constructions out of sense-data. A feature of Russell’s picture is that he proposes to define physical objects not just as constructions out of sense-data, but constructions out of sensibilia—things that are like sense-data, but which are not actually experienced by anyone. On this picture, physical objects are then infinite classes of sensibilia. But in order to define specific values for the properties of the physical objects, you would have to guarantee that these infinite classes would converge on certain limits. Wrinch and Jeffreys point out that there is no such guarantee. Now, you could try to choose values for the unobserved sensibilia in such a way that the infinite classes would converge. But this then would be arbitrary—many different sets of values for the properties of the sensibilia could be compatible with any given set of values for the sense-data. The sense-data would underdetermine the properties of the physical objects.

Wrinch and Jeffreys do not state this explicitly, but as I just mentioned, the real problem with the inversion procedure, is not existence, but nonuniqueness (or underdetermination). And this is clear if we go back to the case of determining properties of the earth’s interior based on observations at its surface. Given any set of observations at the Earth’s surface, more than one distribution of properties in the Earth’s interior could be compatible with those observations, and some of them may be radically different from each other.