Paper Review: The Regression of the Unstructural

What is the nature of meaning? This is one of the core questions on which the Vienna Circle, a group of early 20th century philosophers, took a stance. The kind of bumper sticker version of their answer is that a sentence only has meaning if it can be empirically verified (or tested, or confirmed, or something of that sort).

For example, a specific law of physics — something like “the force of gravity between two objects decreases with the inverse of the distance between the objects” — has meaning because we could come up with some kind of way to test whether it is true or false (or at the very least, provide some kind of evidence for it). In contrast, a statement about ethics — something like “it is wrong to steal” — would have no meaning, since it is not empirically verifiable; there is not experiment you could do to test it.

This notion of meaningfulness has been highly influential and highly contested. Indeed, very few today would hold the very strong form of the thesis. However, it certainly has an appeal in that it seems to solve many philosophical puzzles by rendering them meaningless.

I find it interesting to see not just how contemporary philosophers grapple with this notion, but also how earlier thinkers did. This account of meaning is the driving force behind The Regression of the Unstructural by J. Clay, from the same 1937 issue of Erkenntnis as my last post.

***The original paper can be found here.***

I enjoyed doing a careful paragraph by paragraph annotation in the previous post, and this paper is short enough that I think I will do the same. Sometimes the prose is more straightforward than the previous paper, so after some sections I might do less unpacking if the original seems sufficiently clear.

Clay starts

Logical positivism teaches us that a notion is only completely understood when we know its structure and when it is reduced to a complex of elements which are connected with one another is some knows relation. In science we have only structural relations between elements. And only these structural relations, Carnap concludes in his Logische Aufbau der Welt, pp. 15-16, can be transferred into an objective form, and he adds that it is necessary to limit ourselves to these structural statements.

There is also a short German quote at the end I won’t reproduce.

This is related to the idea I mentioned earlier about meaning. If we encounter some kind of notion we are trying to understand, and we want to make it sharp enough to have verification conditions, it helps to understand the structure. Furthermore, by talking only about structure, it avoids a lot of the metaphysical nonsense the Vienna Circle was intent on avoiding. For example, suppose you want to say something about massive bodies, and their effects on other objects. We might wonder what a massive body even is — what is its essence? However, to someone who accepts the Vienna Circle’s account of meaning, this sounds rather metaphysical. Instead, we might describe mathematically how a massive object changes the trajectory of other objects — without going into its essence.

This may possibly be taken as a tautology, by arguing that a scientific statement which is understood by another person cannot eo ipso be anything else but a structural relation. In this conclusion, however important it may be, one thing seems to have been forgotten.

We might see this as a tautology because it simply follows from the Vienna Circle’s definition of scientific knowledge — since scientific sentences, the only sentences with meaning, have to avoid all metaphysics, anything we understand about them must be structural. However, Clay thinks something is missing.

Let us consider geometry where the foregoing idea was first conceived. It was found, when investigating the axioms, that every statement about points is just as meaningful if applied to planes, and conversely. Consequently, the sentence remained meaningful even if the elements were completely changed. Still, it cannot be denied that in practice, in every case when the sentence is used, one will have to know whether one is dealing with points or with planes.

The idea is that in geometry we might have a true statement that talks about relationships between points. However, the statement is true in virtue of the relationship between the points it captures. If we think that instead of points the same statement is talking about planes, then the statement remains true. This is a kind of invariance condition. The true statements of geometry remain true regardless of whether they refer to points or planes. The elements don’t matter; only the relationships between them matter.

However, if we want to actually apply geometry, the objects between which these relations hold will matter. Even if the sentence remains true if the words refer to different things, we have to know what we are talking about.

If we now enter into the domain of physics and biology, we notice that there is a phenomenon, which I should like to call the regressions from the unstructural. And I should like to take this as a warning against the aversion of positivism to the unstructural and unknown.

This is just introducing the name of the phenomena that should make us care a little more about the stuff we are talking about, and not just the relations between them.

A great number of the phaenomena in physics can be explained today with the aid of molecular and crystal structure. The elements of this structure are the atoms, and at the time when these explanations were given first, nothing was known of these elements. Moreover, it seemed impossible to open a way to obtain information.

So in physics we use explanations that rely on relations between atoms, which we originally thought were structureless.

If the supposition was made that all molecules were perfectly elastic spheres (just like manufactured articles, as Maxwell said), it nevertheless remained impossible to give indications as to how this could be tested. At the present time, positivism would say that this statement was senseless. This was the reason, at the beginning of the molecular theory, that men like Kirchhoff, Ostwald, Mach tried to avoid these theories and considered them as dangerous metaphysical hypotheses.

We have a case in which, due to an inability to imagine how a certain hypothesis could be tested, some took this hypothesis to be meaningless. This makes sense in the context of the meaningless criterion I discussed at the beginning of the post. So even though we could propose different hypotheses about the structure of molecules — for example, that they were spherical — these were considered meaningless.

If this had been true, there would have been little chance for physical science to obtain the knowledge about molecular structure which has been obtained today. Therefore, on the contrary, the theories of the period of Ostwald and Mach have proved to be very useful for this achievement.

This is an example of a regression from the unstructural. What earlier physicists and philosophers took to be meaningless metaphysical conjectures actually contained the seeds of massive developments, which could grow once we had developed sophisticated techniques capable of testing these theories.

Similar to the situation in physics has been that in chemistry with respect to the chemical atom, the last unstructural element of chemical theory. Most of the chemists held that atomic weights had a meaning only as binding-relations. And according to positivism a sentence like ‘there exists a chemical atom chloride’ was senseless, as there was no way to test it.

This is pretty clear, but one interesting thing to call attention to is that when something about the atoms seemed meaningful — the atomic weight — this was not attached to the atom, but was instead attached to something called a binding relation — structure. I think this is kind of interesting, where instead of quickly taking on board the idea that atoms had some structure, this structure was instead attributed to relations between atoms instead of the atoms themselves.

The chemical elements were the last of the unstructural elements. Nowadays the situation has changed, and since 1913 we have learned to understand the atoms as structural relations of nucleus and electrons. Then, again, the nucleus was an unknown unstructural element until 1932, when the first traces of structure were revealed here in Cambridge by Rutherford and his collaborators. But not the neutron and the electron are the unknown unstructural elements of today.

We see the general idea. What earlier scientists took to be the primitive, unstructured elements actually ended having a whole lot of structure. From molecular structures, to the structure of a single molecule, to the structure of a single atom, to the structure of a single nucleus, and so on. If we had decided to stop investigating seemingly meaningless statements, we would have missed out on learning all about these previously hidden structures.

The statement that the neutron is an indivisible entity is, according to Carnap, a senseless one today, since we cannot give any indication as to how to test it. But I believe it to be useful to make this statement capable of obtaining a meaning. The same applies to the electron. The electron is a perfectly incomprehensible element. But I am nearly sure that it will not remain so for the following generation, and as science is advancing rapidly today, we shall perhaps witness this transition ourselves. But then the neutron as well as the electron will be a structural relation between unstructural elements to which we have not yet given a name. This is what I would call the regression of the unstructural, and I think that we do not have to limit ourselves to statements of structures.

The idea is that whenever we think we have hit bedrock and found the kind of true, unstructured elements, we in fact find that these elements end up being structures of even smaller elements, and so on — the process repeats itself. We shouldn’t at any stage restrict ourselves to statements of these structure — we should be able to make conjectures about the elements themselves, and endeavor to invent ways to test these hypotheses.

The same phenomenon we meet in biology. After Schwann had found that all living organisms are built up of cells, it was at first help that the cell was the element, until later it was discovered that the cell itself was structural, its essential part being the nucleus. This nucleus in turn was found to be a structure of chromosomes, and today we know that the chromosomes are parcels of genes. It seems, moreover, today that every gene is a complicated molecule. This regression, obtaining alongside with the physical regression, may this be considered to furnish the principal connection between biological and physical entities.

A parallel case runs in biology. Also, however, it is precisely through breaking down the basic unit of biology that we can connect it up to physics. Once biology reached down to the molecular level, we were able to use the knowledge of physics to help understand biology.

But now I think that there is not only a regression to the unknown unstructural smallest elements, but that there is also a progression in the opposite direction to the unknown great complex, this tendency being as natural as the other.

In addition to being able to uncover smaller and smaller structures, Clay thinks we can also go upwards. This seems broadly right even in hindsight, as we investigate clusters of clusters of galaxies. Why does he think this, though?

The reason for this is that there is no natural phenomenon whose structure is completely definable. The evolution of science shows us tat there are structural relations which tend to infinity. The aim of theory for instance, is to define the inertial mass as depending upon the mass of the universe. So we have to realize that we do not know the structure of a thing, as long as we do not know its relations to the exterior world. The earth would be incomprehensible in its motion and behaviour, without the knowledge of the influences of the sun and the solar system. Is our solar system a structural entity completely definable in itself? Surely not, since there are influences which are caused by the fact that our solar system is a part of the galaxy.

The idea is that if by “completely definable” we mean something like exhausts all we could know about the dynamics of the system, then due to how physical forces work, we would have to know everything in order to fully “define” anything. This seems somewhat right to me in a strict way; in order to properly understand the motion of everything within the solar system we would need to know about how the galaxy affects it.

However, it also seems to be maybe a bit too strict. Often I want to investigate some structure in order to further my purposes. For example, I might investigate the structure of DNA in order to develop technology to treat genetic diseases. In Clay’s strict sense, in order to completely define the structure of DNA I would need to know how alpha centauri’s gravitational force affects DNA on earth. However, it seems clear that this effect is so incredibly tiny that I can discount it while trying to cure a disease. It is this sensitivity to out purposes that makes this “completely definable” notion seem somewhat unimportant to me.

When Lorentz discussed the influence of the earth’s motion through the ether, he thought of the velocity through space on account of the orbital motion around the sun, but not of its rotational motion in the galaxy which is perhaps ten times faster. But in how far is our milky system influenced by milliards of star systems surrounding out system?

This is another particular example to illustrate how in order to understanding something you must incorporate information about more than the immediate system. Light is a wave. Now we think that it can travel through empty space — the void. However, for a long time physicists thought that, just like most waves, light my have some medium through which it travels. They called this the ether. When trying to discover things about the ether and the motion of light through it, Lorentz incorporated the spin rotation of the earth into his calculations. Though this theory of the ether was eventually falsified by such experiments, Clay’s point is that just as we had to take into account the rotation of the earth to make the calculations about the ether, we might also have needed to take into account larger and larger rotations.

In any case, there is a constant exchange of photon and corpuscular energy. The mass and the motion of our systems cannot be completely structurally determined without taking the outer parts of the cosmos into consideration. And up till now we have been unable to fix and limit or to test the statements we make in this direction.

Now we see another parallel. Just like we thought certain statements about small things were meaningless because we don’t know how to test them (leading us to neglect them), since we as of now have no way to test certain statements about large structures we neglect them in our science as well.

We find the same situation with respect to organisms. The majority of organisms are complexes of a great number of unities. Still it seems that they have a closed structure. But this is certainly not true, for, obviously, the organisms are divided into different sexes, which are necessary for the preservation of the species.

Clay is again trying to draw this parallel between physics and biology. Here the claim seems to be that in order to understand things about a single organism — for example, a male dog, we need to understand things about the broader ecological system of which it is apart. For example, we can understand certain things about why the male dog behaves in a particular way only if we understand the relation between male and female dogs.

This kind of thing seems plausible to me. It seems to depend on the kind of question we want to ask. As usual, relevant context would seem to help.

The species forms a wider structure that the individual. And there are many phenomena in which the individual cannot be understood without knowledge of the structure of the species. One of the most remarkable phenomena in this connection is the behaviour of the slime-fungus. After the individuals have lived for a certain period as completely separate organisms, they join together and, for a subsequent period, they live as one whole. One could not say that they are different organisms. Similarly we know that there is a dependence of groups of animals and plants upon each other. In many cases we do not know these relations and, moreover, we have no indication as to how to test them.

This elaborates on what I wrote above, with the added particular example of the slime-fungus. It seems like a straightforward yet neat example to me. And we also get the kind of broader ecosystem type context being mentioned.

Clay ends with the following remarks:

But we have to conclude that we cannot limit ourselves to statements of known structure. This limitation may be very useful for knowledge already completed. It may be typical for a logician or a mathematician. But if people had conformed to this rule in their research work, most of what is known today of nature would still be awaiting discovery.

The broad lesson is, then, don’t stifle research directions between we don’t know how to test things yet.

I have to admit, I am a little underwhelmed by this “lesson” — it kind of seems obvious. And yet, that might be because it is now in the water so to speak. Perhaps before Clay and people like him, as the Vienna circle and other philosophers of science like Popper grappled with these problems this kind of exploratory mindset was more fresh and needed. Indeed, Carnap’s claim that the claim “the neutron is an indivisible entity” is meaningless seems very narrow-sighted and kind of ridiculous to modern ears.

So, even if the actual lesson has already been learned, it might be precisely because of arguments like Clay’s that we have learned it.

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