Russell on Sense-Data and Physics

The following is a draft of a final paper I had to turn in for my Analytic Philosophy paper. Enjoy. 

Russell’s Structural Collapse

In this paper, I critically examine Bertrand Russell’s theory on the relationship between our sense-data and physics. Russell aims to show that we construct about the world from our sense-data, we do not infer the world from our sense-data. He does this by arguing from analogy. Since we do away with hypothetical entities in math, then we should do it in physics. The relative property between math and physics in Russell’s view is that physics really is just reducible to math. However, I show that there are problems with the mathematical content of the analogy itself and Russell’s understanding between the relationship of math and physics which absurdly tells little to nothing than what we commonly understand physics tells us, thus making his argument by analogy a weak one. 

Russell is out to set out a theory concerning the relationship between sense-data and physics. Physics is based upon observation and experimentation, but we don’t learn anything about objects through observation and experimentation. Russell recognizes this as a gap problem. All we know is our experiences or sense-data, strictly speaking, and so any verification of objects must be done through their relations to our sense-data (Russell, 1914, p. 1-2). What that relation is and how that sets out the boundaries of our knowledge of physics is what Russell labors to show. 

The basic thrust of Russell theory says that the correlation between our sense-data and the objects themselves is a logical construction. One is tempted to think that sense-data is a function of the object itself. For example, we think that the color red which emits from an apple is a function of the apple. For Russell, this is mixed up (Russell, 1914, p. 3). The apple is a function of the redness which is our sense-data. We do not infer that something is red because the apple is omitting red, rather, we construct an apple because our sense-data registers redness. 

This may sound a bit simplistic because obviously not everyone has the same sense-data. If you look at the apple at this angle, and I look at the apple in this other angle, it is probable that we will not register exactly the same sense-data, even if they are similar. So the problem arises, if we construct an apple from the sense-data, but not all sense-data is the same, then we will not be constructing the same apple. If there is no same apple, then how do we know we are verifying the same object token? It seems like we are back at square one. Russell answers this by appealing to Occam’s razor (Russell, 1914, p. 9). Occam’s razor states that we should not multiply entities beyond necessity. For Russell, we can identify the object with the whole class of appearances, not just one subset of them. The temptation of the objection is to then posit an underlying substance which explains all the subsets of sense-data. The force of Russell’s reply is that positing such an entity like a substance is unnecessary when the sense-data by itself will suffice. 

Russell argues that he stands on precedent here. He writes, “In old days, irrationals were inferred as the supposed limits of series of rationals which had no rational limit; but the objection to this procedure was that it left the existence of irrationals merely optative, and for this reason the stricter methods of the present day no longer tolerate such a definition. We now define an irrational number as a certain class of ratios, thus constructing it logically by means of ratios, instead of arriving at it by a doubtful inference from them.” (Russell, 1914, p. 10). The argument is that of analogy. Since in math we do not infer the existence of an irrational number from rational ones, but rather we construct irrational numbers from what we already know about rational ones, we can likewise do away with inferring about objects in the world and merely construct them from what we already do know. 

This seems prima facie false. Ratios are compared values, like ⅔. Rational numbers are numbers that can be expressed as a ratio, or a fraction. If a number has a repeating patterned or terminal decimal, that is said to be rational. So .3 would be rational, .123 would be rational and so would .1212. Irrational numbers are those numbers which cannot be expressed as a ratio or fraction. Pi would be an irrational number since it doesn’t terminate nor does have a repeating pattern of decimals. So by definition, no irrational number can be a member of a class of ratios. This explicitly contradicts Russell when he says as quoted above, “We now define an irrational number as a certain class of ratios.” The strength of an analogy depends on how close the relevant properties are in both cases. Since the methodology is shown to be false in the former cases, it cannot be said to properly apply to the latter case which takes the methodology to be true. Thus the analogy would be weak. Or, if it can be said to apply in the latter case, then we must also say that the latter case is analogously false, thus the argument would still be weak. In either case, the analogy is weak. 

Another problem with this analogy is that it seems to not satisfy Russell’s own criteria. Russell writes, “...we then construct some logical function of less hypothetical entities which has the requisite properties.” (Russell, 1914, p. 10) Emphasis my own. That the function has the requisite properties is necessary since Russell wants to apply Occam’s razor. However, in the example Russell gave, the inference of irrational numbers from rational ones, it doesn’t meet the criteria. Irrational numbers were inferred from a false assumption of the Euclideans that all numbers have to be able, in principle, to be put in a relational fraction. They discovered that their assumptions couldn’t account for their very real discovery of irrational numbers. What that means is that the Euclidean assumptions actually do not have the requisite properties to explain irrational numbers. Similarly, mathematicians could not, using a Cartesian plane, figure out what the square root of -1 was on the numberline or Cartesian plane. So the limits of Cartesian planes gave mathematicians the tools to infer the existence of imaginary numbers, beyond real numbers. But there is no property the real numbers share with the distinctive imaginary numbers, nor could there be in principle, for that is what makes them distinct. We could not say, as Russell would like, that we know rational numbers share the requisite properties of irrational numbers, or real numbers share the requisite properties of imaginary numbers. Those are contradictions in terms. It is precisely because they do not have the requisite properties that we know these numbers exist. So the criteria here that Russell sets up seems to be problematic.

Russell gives a second analogy dealing with cardinal numbers. Similarly to the previous example, Russell says that when given two equally numbered sets, what they have in common is their cardinal number, or common number. If my left hand has five fingers, and my right hand has five fingers, five is the cardinal number. But, Russell says, if we infer the cardinal number from the sets, instead of constructing the cardinal number from the sets, then the existence of the cardinal number remains doubtful (Russell, 1914, p. 10). Unfortunately, Russell doesn’t spell out exactly how we can come to doubt this. In any case, this second argument from analogy is the same kind of argument employed in the first, which is to say that in math, we do not infer the existence of a thing from sense-data, we only construct them. 

The question can be raised then about the appropriateness of the analogies. The analogy is supposed to be something like, “We eliminate inferring entities for making constructions in this case, so we can do the same thing in this other case.” But this can be easily pushed against by asking why think that since it can be done in one case, it can be done in other cases? Russell says that they’re similar, but similar in what respect? What is it about them both that makes it appropriate to apply the same methodology? Because both analogies are math related, it is reasonable to suppose that it is because Russell thinks there’s a strong math connection to physics. This is not an implausible thought. But how strong of a relationship is there between math and physics and is it sufficient to carry the analogy? 

As it turns out, Russell thinks the relationship between physics and math is so strong, that it seems all physics really is, and all we really know about physics, is the mathematical structure of an event, and not anything about the event itself. Russell writes, “Physics started historically...with matters that seem thoroughly concrete. Levers and pulleys, falling bodies...etc., are all familiar in everyday life...But in proportion as physics increases the scope and power of it's methods, in that same proportion it robs it's subject-matter of concreteness.” (Feser, 2019, p. 160). In another work, Russell comments, “It is not always realised how exceedingly abstract is the information that theoretical physics has to give. It lays down certain fundamental equations which enable it to deal with the logical structure of events, while leaving it completely unknown what is the intrinsic character of the events that have the structure. We only know the intrinsic character of events when they happen to us...All that physics gives us is certain equations giving abstract properties of their changes. But as to what it is that changes, and what it changes from and to - as to this, physics is silent.” (Feser, 2019, p. 162). For Russell then, while naive little children may think of physics as being about very real and concrete things like one ball hitting another, the more broad it gets as an explanatory system, the more abstract physics becomes and correspondingly less concrete. 

Take for instance a bowling ball rolling down a bowling alley. Suppose a physicist wants to know at what speed a 12lb bowling ball is going and with what force it will knock down the pins. This seems like a typical question physicists would like to answer. The first piece of information the physicist has is that the ball is 12 lbs. With this information, the bowling ball itself begins to disappear, and only a 12 lb mass remains. The bowling ball is only a pointer to the 12 lb mass. The 12 lbs mass need not refer to any real object, we just need to know what 12 lbs of mass is to figure out the question the physicist sets out to know. Further, suppose the slope of the bowling alley is -1/720. Again, what happens is that the particular bowling alley disappears only to leave the bare particular of the slope. If the slope of -1/720 has the requisite properties to explain why the 12 lbs mass travels the way it does, then we don’t really need to posit the reality of a bowling alley and every metaphysical commitment that entails. Occam’s razor would eliminate that. For Russell, what we can have is not the nature of the things or events themselves, but merely the mathematical structure of them. In this way, physics is really reducible to math, and if that’s the case, then Russell’s analogy about doing away with inferences and setting up constructions and structure in math is justifiable in physics. Hence Russell writes, “When physics is brought to [a high] degree of abstraction it becomes a branch of pure mathematics, which can be pursued without reference to the actual world, and which requires no vocabulary beyond that of pure mathematics.” (Feser, 2019, p. 163). 

One problem with this view, as raised by M. H. A. Newman, is that it tells us too little. Newman argues that to speak of a structure of things without properly defining what the relation between those things are is meaningless (Newman, 1928, p.140). For example, if my left and right hand have this cardinal constraint of “5”, and that’s all we know, then this is trivial. What does this tell us other than that some things, whatever they are since we don’t know them, relate to other things, whatever those are since we don’t know those either, in a “5” way? Nothing. We may know that such relations exist, but not much can be deduced from mere relations existing. For example, how informative would it be if I said, “X is to the left of Y, but I will not tell you what X and Y are.” Not very, I would guess. If we could know more about the nature of those relations, then we know something more than just the structure of the world, contrary to Russell’s initial position that the structure of the world is all we know of the external world. But it seems counter-intuitive to say that physics doesn’t give us more information than this. Russell may try to make a distinction between important relations and non important ones, and this distinction can help him claw out of this problem, as it does in mathematics. Surely, the relation of being greater than or less than is a more important relation and thus more informative. However, argues Newman, the distinction between important and unimportant relations has no clear criteria, and if there were, it would suggest knowledge of the world apart from structures, which Russell’s position denies (Newman, 1928, p.147). 

If Russell’s argument from analogy rests on the premise that physics is mathematical in this way, but this relation between physics and math leads to certain absurdities, then we can safely reject the premise, and thus his argument by analogy does not carry much weight. Is there any way we can salvage Russell’s theory then? One suggestion given by Russell himself is that the structure of reality and our sense-data of reality have an isomorphic relation (Feser, 2019, p. 167). Isomorphisms are those which are related in an accidental way. A toupee may look like real hair, but is not really hair at all. It is related to real hair only in an isomorphic way. In the same way, what Russell is suggesting is that we have knowledge of the world, but only in an accidental way. But this doesn’t justify knowledge at all. If I believed the sky was blue only because the imaginary fairy in my head told me so, I may be accidentally correct, but knowledge would require more than just being accidentally right. 

Another way to possibly salvage Russell’s theory is to say that physics captures more than mere mathematical structure. They can possibly capture natural kinds or we can abstract from them certain modal properties. If this is the case, I think it would remain on safe grounds, however, it would leave behind much of what is distinctive about Russell. If they captured natural kinds, for example, then this can easily be argued for a more Aristotelian metaphysic, a metaphysic which was so repulsive to Russell in the first place. The same can be said about modal properties. What is modally true about a thing seems constrained by their nature, which Russell says we don’t know anything about. So while Russell may leave the door open for things other than structure and constructs, he does seem to close the door on natures themselves. If he would like to keep structuralism, he would have to be a realist about nature and substances, and not a nominalist about nature and substances. 

I have labored to demonstrate that Russell’s argument fails in three crucial ways. First it fails in understanding the history of mathematics necessary to make his analogy work. Second, the criteria of having similar properties to understand new phenomena like irrational numbers is not met. Third, the analogy rests on the premise that physics is sufficiently mathematical, however, Russell’s view of the relation between physics and math is so constrained that it leads to the absurd conclusion that we really know nothing about the world other than relations, which is not to know much, if anything, at all. I have suggested Russell salvage his theory of construction and structure by adding some Aristotelian elements to it instead of denying the knowability of natures or substances. In this way, we can be structural realists and not structural nominalists. In this way, we come closer to truth. 

Works Cited

Feser, Edward. Scholastic Metaphysics: A Contemporary Introduction. Vol. 39, Editiones Scholasticae, 2014. 

Newman, M. H. A. “Mr. Russell's ‘Causal Theory of Perception.’” Mind, vol. 37, no. 146, 1928, pp. 137–148. JSTOR, www.jstor.org/stable/2249202. Accessed 29 Oct. 2020.

Russell, Bertrand. “The Relation of Sense-Data to Physics.” 1914