How Should the Periodic System be Regarded?
A brief look at some published proposals.

Eric Scerri

Introduction

In recent years the history and especially the philosophy of chemistry have experienced something of a revival. Some of this renewed interest has been directed at the central icon and organizing principle of chemistry, the familiar periodic table of the elements. In this article I consider some of these developments and try to give a chemist’s reaction to the work of the historians and the philosophers, although I too have contributed to this field.¹

It is quite remarkable to find that the periodic table has been characterized as a representation, an ordered domain, a classification (obviously), a system, a model, a law and even as a theory. Historians and philosophers of science cannot seem to reach a unanimous decision on this seemingly uncontroversial question. Before presenting the views of various authors I begin by sketching what I think is a well-accepted hierarchy of scientific concepts which will be listed in order of increasing depth and generality.

At the top of an inverted pyramid (Figure 1) are placed the phenomena, such as the properties of the elements in the case under discussion here. Then comes ‘classification’ which seems to lack explanatory power but is nonetheless capable of making predictions as in the famous cases of Mendeleev’s predictions of the elements gallium, scandium and germanium. This feature has caused many authors concern since they believe that scientific predictions are supposed to only come from laws or theories.

Models are listed next. They too hold some explanatory power but not to the same extent as laws and theories do. One way to regard models is as being special instances of laws or theories in which particular conditions apply or under which a particular approximation might hold. One example from quantum chemistry might be the independent-electron model in which one ignores dynamical correlation among electrons. An even cruder model consists in disregarding repulsions between electrons in a many-electron system, although such a model is quantitatively impotent

Laws are altogether more abstract than models and can be used to deduce explanations for phenomena, although this view has been increasingly debated in the philosophy of science. Nancy Cartwright, in particular, has spawned something of a cottage industry among philosophers of science who uphold that it is models rather than laws and theories that carry the burden of scientific explanations. Cartwrights’s view is summarized in the title of her first book which is “How the Laws of Physics Lie”.² The last word here is intended in the sense of failing to tell the truth rather than in the sense of ‘lying down’

At the most fundamental level of the inverted pyramid, at least in the traditional hierarchy, we have scientific theories such as quantum mechanics, relativity theory, thermodynamics and so on. These are large bodies of well-supported knowledge each encompassing many laws and models and not surprisingly they are regarded as the most cherished of all these scientific concepts, contrary to the layperson’s false notion whereby theories somehow ‘grow-up’ to become laws

Michael Gordin

Now what about the periodic table in all of this? The first author whose views on the periodic table I will consider is the Princeton historian of science, Michael Gordin, who has written an excellent intellectual biography of Mendeleev.³

As a good historian Gordin attempts to stay close to the chronological development. He presents a sequence of events in which Mendeleev first described the periodic table as a classification, then as a ‘system’ and finally regarded it as a scientific law. Gordin claims that is only when Mendeleev started focusing on the periodic table as embodying a law, that he was able to make his many bold predictions, which would eventually seal his scientific reputation. This all sounds very plausible but I am going to suggest that it runs the risk of concentrating too much on the historical account while avoiding the normative issue.

It is not surprising that Mendeleev should want to elevate his discovery to the status of a law rather than that of a classification or system, since this would seem to confer a more fundamental status to the periodic table. But was Mendeleev’s periodic law any more explanatory than the classification or system that he first discovered?

First let us recall how Mendeleev expressed his periodic law, namely that the properties of the elements are periodic functions of their atomic weights. However, this law remains at the level of the phenomena and does not purport to explain why the periodicity occurs. It simply states that chemical periodicity exists. Admittedly this statement draws together many diverse phenomena about all the elements and connects them together, but in terms of providing an explanation it is no better than regarding the periodic table as a classification. Was it essential for Mendeleev to believe that he was operating with a law of nature in order for him to make predictions? Certainly not, since he had begun to make predictions even in his first paper in which he left several gaps and even ventured to guess their atomic weights that they might have.⁴ These predictions were made before Mendeleev had made any mention of there being a periodic law.

In any case it is worth pausing to ask whether what Mendeleev called the periodic law really is law-like. First of all, it is a rather unusual law in that the elements do not recur exactly, and nor is the repeat distance constant. More seriously, as we now know, it is atomic number rather than atomic weight that serves as the ordering criterion. If anything the properties of the elements are a periodic function of their atomic numbers. Nevertheless, Mendeleev succeeded in making many successful predictions even though he was operating with an incorrect law if one insists on calling it a law.

Michael Weisberg

This now brings me to the second author that I want to consider, who is the philosopher of science Michael Weisberg. Weisberg goes further than most authors by even elevating the periodic table to the status of a scientific theory.⁵ Weisberg is impressed by Mendeleev’s predictions because he believes that Mendeleev had no empirical knowledge that there were any empty slots to be filled in the periodic table. He thus concludes that Mendeleev was acting as a theorist. For what it’s worth I believe that Weisberg has it backwards.

It was entirely on empirical grounds that Mendeleev left spaces in his periodic table. If one considers Mendeleev’s tables of 1869 and 1871, (Figure 2), it is clear that a large gap in values of atomic weights occurs between zinc (65) and arsenic (75). The necessity to create one, or maybe two, empty spaces is made clearer if one considers the second dimension of the periodic table, namely chemical similarities as summarized in vertical groups of elements. Mendeleev could not simply have moved arsenic and selenium to the left in order to avoid an empty space in the table. To do so would have resulted in destroying the vertical analogies between arsenic and phosphorus and also between selenium and sulfur among others.

Weisberg also appeals to the trends in the formulas of the highest oxides and the fact that they range from R₂O to R₂O₇, where R is taken to be any element, as one traverses any horizontal row of the periodic table. Weisberg claims that these trends were explained by Mendeleev’s periodic law and that they would have otherwise remained mysterious. Unfortunately this is not the case since formulas or the trends in these formulas were not rendered any less mysterious by being subsumed under the claimed periodic law. There is nothing explanatory in the periodic law as expressed by Mendeleev. It might be more accurate to say that the periodic law is consistent with the pattern of oxide formulas but not that it provides any kind of explanation for that pattern. How then, we must ask Weisberg, is the periodic table supposed to be functioning as an explanatory theory?

Dudley Shapere

A third view among philosophers of science is due to Dudley Shapere who has concluded that the periodic table is an ordered domain. Shapere goes to great lengths to argue that although the periodic table provided many successful predictions at the hands of Mendeleev, it should still not be considered as a theory and not even as a scientific law. First of all he stresses that although Mendeleev was not averse to calling his periodic table a ‘law’, Mendeleev and some contemporaries considered the true expression of this law to be a mathematical one. Shapere argues that Mendeleev’s statement of a periodic law was only vague but nevertheless was clear enough to allow rough results to be achieved. Indeed, after discussing the inadequacies of attempted formulations of this periodic function, Mendeleev found it necessary to conclude that although it had greatly enlarged our vision, the periodic law needed further improvements in order that it might become a “trustworthy instrument in further discoveries”.

As late as 1900 this was still the widely held view as can be seen from a remark by Ramsey the discover of several of the noble gases:

We have not been able to predict accurately any one of the properties of these noble gases from a knowledge of those of the others; an approximate guess is all that can be made.⁶

Shapere believes that although the periodic table was widely referred to as a law, the general opinion of the time was that it could only be called a ‘law’ in a loose sense. By contrast, the true law would have been a precise mathematical expression of the periodic function relating, the atomic wrights and other properties of the elements and their compounds.

Let us now take stock of the three views that have been briefly examined. Who should we believe? Is it Gordin who stresses the importance of the periodic law or Weisberg’s idea that the periodic table is a theory or Shapere’s talk of the periodic table as an ordered domain? If we must choose between these three accounts I suggest that it should be with Shapere’s account since this author correctly recognizes that even though predictions were made using the periodic table, this does not confer upon it the status of either a law or a theory.

A fourth view

Finally, I would like to consider yet a fourth view, but not one which attempts to categorize the periodic table as in the case of the above three authors. This fourth view has been separately proposed by several philosophers, including Rebecca Bryant⁷ and John Dupré.⁸ These authors believe that the elements as specified by their atomic numbers are not ‘natural kinds’. That is to say that these authors deny that elements are objectively existing entities for which there is one correct, or most correct, means of classification as embodied in the modern periodic table. These authors consider classification of all kinds, including the case of the periodic table, to be a contingent matter in which humans influence the way that the elements should be classified because of their particular aims and aspirations.

For example, in commenting specifically on the periodic table Dupré writes that there is

…much potentially wrong with the supposition that there is a right way of classifying things in the world.

Dupré also claims that

the chemists' belief that they have arrived at an ideal classification is an illusion, … because of the specific aims implicit in the history of chemistry.

So what are these specific aims that chemists apparently possess and that have rendered their classification system biased in some way? Dupré considers that it is because chemists aim at the structural analysis of matter and if, as appears to be the case, all matter is composed of a small number of structural elements, a classification based on those elements will be best suited to those purposes.

I think that Dupré is incorrect for two reasons. First of all, the periodic system of classification was arrived at completely independently of any conception of structure, atomic or otherwise. Mendeleev, the chief architect of the periodic system, repeatedly expressed his dislike for atomic theories and never accepted the discovery of the electron that took place in 1897, a full ten years before his death in 1907.

More importantly, Dupré’s claim is somewhat circular. The aim of chemists is not necessarily the structural analysis of matter but rather the analysis of matter period. It so happens that the analysis of matter in general later revealed that a structural approach, in terms of atoms, protons and electrons, was a fruitful path to adopt. Chemists did not impose a structural prejudice upon chemical analysis from the outset. The latter is a feature that arose naturally, presumably because the world itself contains discrete structural components such as atoms and electrons.

Conclusion

The clear conclusion to arise from this brief analysis seems to be the large variety of views by historians and philosophers about how the periodic system should be regarded. Perhaps the positive message to draw from this situation is that the periodic system possesses a rather unique and enigmatic nature that deserves greater attention than it has received up to this point.⁹

References

¹ E.R. Scerri, Collected Papers on the Philosophy of Chemistry (Imperial College Press, London, 2008).

² N. Cartwright, How the Laws of Physics Lie (Oxford University Press, New York, 1983).

³ M. Gordin, A Well-Ordered Thing (Basic Books, Cambridge, MA, 2004).

⁴ W.B. Jensen (ed.), Mendeleev on the Periodic Law: Selected Writings, 1869 – 1905 (Dover Publications, Mineola, NY, 2005).

⁵ M. Weisberg, "Who is a Modeler", British Journal for the Philosophy of Science 58 (2007), 207-233.

⁶ W. Ramsey quoted in I. Freund, The Study of Chemical Composition (Cambridge University Press, Cambridge, 1904).

⁷ R. Bryant, Discovery and Decision: Exploring the Metaphysics and Epistemology of Scientific Classification (Associated University Press, London, 2000).

⁸ J. Dupré, "Scientific Classification", Theory, Culture & Society 23 (2006), 320-32.

⁹ E.R. Scerri, The Periodic Table: Its Story and Its Significance (Oxford University Press, New York and Oxford, 2007); Selected Papers on the Periodic Table (Imperial College Press, London, 2009).

¹⁰ Estestvennaya sistema elementov i primenie ee k ukaza-niyu svoistv neotkrytykh elementov, Zhurnal Russkeo Fiziko-Khimicheskoe Obshchestvo, 3, 25–56, 1871.