3.1. Constant and Multiple Proportions

One of the first and most basic chemical facts that Dalton's atomism was intended to explain was the law of constant proportions—the fact that chemical compounds are made up of constant proportions of elements by weight. Dalton reasoned that there must be ultimate particles of elements whose weights form the basis of these proportions. Needham criticizes this explanation in the following way:

In my view (and presumably Dalton's), taking the ultimate combining units out of sight is precisely the “magic” explanatory ingredient. Fixed proportions of chemically indivisible particles on the invisible level explain homogeneity on the level of our senses. We have no direct evidence that there is homogeneity “all the way down” because we cannot see “all the way down.” Therefore, Dalton did not need to provide an explanation for anything but homogeneity on the sensible level. On the contrary, after the discovery of constant proportions, anyone who rejected atomism and proposed that it is possible to have homogeneity “all the way down” had to provide a reason for chemical combination only occurring in specific proportions. Dalton's explanation answered the question of why elements in chemical combinations always occur in specific weight ratios and not in a continuum of combinatory ratios.

On the basis of chemical atomism, Dalton saw that there was also a straightforward explanation of the law of multiple proportions. Why should the same set of elements combine in not only one set of ratios but sometimes in multiple sets of ratios? Dalton's response was that elements combine in simple, integer multiples of their characteristic weights because there are integral bits of these same elements that remain undivided in chemical reactions. Configurations that are chemically stable (i.e., chemical compounds) will always manifest integer proportions because of the integral bits that remain intact underneath the chemical change. Dalton's atomism also explained what happens in chemical reactions: there are least parts of chemical elements that remain undivided in such reactions but that separate from each other and recombine in a new arrangement (see Dalton Reference Dalton1808, 212). Dalton's explanation helps us to understand why it should be possible to break down a chemical compound and later build it back up again: there are least parts of each element that remain intact throughout the entire process.Footnote ²

3.2. Chemical Compounds versus Solutions

The background for another of Needham's criticisms of Dalton's atoms comes from Joseph Proust's work in the early nineteenth century, which established a distinction between compounds and solutions. Both compounds and solutions were considered “homogeneous mixtures.” Proust showed that, independent of temperature, pressure, and the process by which they are synthesized, compounds are made up of constant proportions of elements. Solutions, in contrast, contained varying proportions of elements. In light of Proust's result, Needham proposes that any explanation of the law of constant proportions in compounds must also be an explanation of the difference between compounds and solutions. Needham claims that Dalton's atoms did not provide such an explanation (Reference Needham2004a, 1040–41).

However, Dalton did make a distinction that is directly relevant to the difference between compounds and solutions. His distinction was between a pure elastic fluid and a mixed elastic fluid. A pure elastic fluid is “one, the constituent particles of which are all alike, or in no way distinguishable” (Dalton Reference Dalton1808, 145). These identical constituent particles could be either simple atoms or compound atoms (Dalton's term for “molecule”). A mixed elastic fluid, however, is one in which the particles of two or more pure elastic fluids mechanically diffuse through one another in the same space but do not unite chemically (150). If two or more elastic fluids are mixed and the various types of particles are present in certain specific proportions, the different types of particles will unite (i.e., chemically combine) such that they form new compound particles (169). What was originally a mixed elastic fluid will have become a pure elastic fluid because its constituent particles are now all alike.Footnote ³

Using his theory of the constitution of mixed elastic fluids, Dalton also attempted an explanation of the law of partial pressures (i.e., the additivity of the pressure of mixed gases). He proposed a hypothesis in which there is a force of repulsion specific to each distinct type of atom (simple or compound) and where each type of atom was immune to the repulsive forces of other types. Since each distinct fluid pushed against the containing surface with its own force of repulsion, the various forces of repulsion present in any container simply added together to produce a total pressure (Reference Dalton1801, 242–43; Reference Dalton1802, 536). This same hypothesis also explained why gases in mixtures do not separate out according to their specific weights. According to the hypothesis, the particles of each distinct type in a given volume arranged themselves independently of all other types in the same volume, as if the other types were not present at all.Footnote ⁴

Dalton's distinction between pure and mixed elastic fluids and his hypothesis about selective repulsion give answers to several why-questions: (1) Why are compounds subject to the laws of constant proportions and multiple proportions while solutions are not? It is because of the differing arrangement of atoms in the two cases. (2) Why do the pressures of gases in a mixture simply add to produce the total pressure, and (3) why do the various gases in a mixture not separate out into layers according to density? These last two questions are answered by his theory of the selective repulsion of each distinct type of particle.

Dalton does not, however, give us an answer to a particularly troubling question: What is it that causes two particles to combine? Why should two particles combine, rather than remain separate? Needham objects to the fact that “Dalton offers no account of what draws unlike atoms together in molecules” (Reference Needham2004a, 1046). I agree with Needham that Dalton's explanation of chemical combination is less than satisfying in this sense. Although Dalton distinguished between chemical and mechanical effects, he did not explain the nature of chemical combination or any underlying reason for the tendency of atoms to combine in some cases but not in others. Furthermore, the meager account that Dalton provided for chemical combination gave no ability to predict which kinds of atoms might have the tendency to combine and in what arrangements and proportions they might do so.

Although Dalton gives us very little indication of the nature of chemical combination, he does hint that, if two bodies are to combine, they must be “disposed” to do so (see Dalton Reference Dalton1808, 192, 213). It seems then, if we dare to read between the lines, that the “disposition” of a chemical substance to combine with another is an inherent chemical property of that substance. If so, such a disposition, particular to each type of atom, would be no more (or less) mysterious than Newton's gravitational force.Footnote ⁵ On my view, the concept of a chemical disposition as something distinct from mechanical interaction constitutes an explanation inasmuch as it is a small step forward in understanding chemical combination. There is, however, an important sense in which the explanation is less than satisfactory because it leaves a why-question unanswered: In what does this chemical disposition or property consist?

4.1. Duhem's Antiatomistic Chemistry

In 1892, Duhem published an essay (Reference Duhem1892/2000) that contains a fascinating account of how chemistry can be done without atoms, and how, furthermore, the entire history of the science can be told without atoms.Footnote ⁶ In this section, I will explain how this can be done, on Duhem's view.

For Duhem, the science of chemistry is built on the solid foundation of observables—the proportional weights of the various elements in chemical compounds—and “they alone … represent the experimental givens of chemical analysis” (Reference Duhem1892/2000, 130; emphasis mine). Derivative from these proportional weights are the proportional numbers that chemists choose, by convention, to assign to each element. In order to establish these conventions, chemists collate the many instances in which a particular element (e.g., nitrogen) is found in a compound and note that its proportional weight in these compounds is generally very close to a small multiple of a particular whole number (e.g., 14 for nitrogen).Footnote ⁷ The collection of instances of a given element in compounds, together with a consideration of the analogies between the various compounds to which the element belongs and other compounds to which it does not, helps chemists to collectively fix the most reasonable standard of equivalent weights of various elements. With a system of equivalent weights in place, crude chemical formulas with symbols and superscripts take on a particular meaning; the letter symbol for each element represented the equivalent weight of that element, and the superscript in the formula represents the number of “equivalents” represented. An “equivalent” for Duhem is simply a certain amount, by weight, of an element in proportion to the weight of other elements making up a compound.

Duhem then shows that these crude formulas can be refined by a study of the way in which some elements substitute for others in analogous compounds. Refined formulas not only express the number of equivalents for each element but also group the symbols in such a way as to make apparent the more cohesive (and substitutable) parts of the compound. For example, the crude formula for grain alcohol is C²H⁶O, but if we wish to regard it as water in which an equivalent of hydrogen is replaced by an ethyl group (C²H⁵), then we might represent it by the formula (C²H⁵)HO (Reference Duhem1892/2000, 149).

Even more subtlety in representation can be gained; certain elements or basic subgroups can be swapped not only one for one in analogous compounds but also two for one or three for one. For example, one PO group is substitutable for three equivalents of hydrogen in HCl or H²O (Reference Duhem1892/2000, 156). Duhem explains that the notion of valency is simply a method of accounting for interchangeable groups. Consideration of each element's involvement in various compounds and subgroups allows for a standardization of valencies for each element. Constitutional formulas can be drawn in which connective lines indicate the number of valencies that are “exchanged” among elements. Using this notation, all of the relationships in a compound can be shown at once, making all of the derivative properties of these relationships evident at first glance.

In the entire foregoing account of the science of chemistry, Duhem is very careful and pointed in his use of the word “equivalents” instead of “atoms,” and his use of the word “valency” instead of “atomicity.” According to him, all of chemistry at his time (including classification of chemicals and prediction of their properties) could be done without reference to atoms.

4.2. Duhem's Resistance to the Atomic Interpretation

Although Duhem avoided all mention of atoms when writing as a chemist, he had no qualms about passing a verdict on atomism when writing as a philosopher interpreting chemistry. In fact, Duhem spent a large segment of his 1892 article—a total of 11 pages—discussing how well (or how poorly) atomistic theories explain.Footnote ⁸ By the time he wrote the article, chemical atomism had expanded to include a great many addenda and modifications to Dalton's original basic postulates. Duhem had several complaints about the inconsistencies and problems with these addenda, but of Dalton's original basic theory, he had only praise for its explanatory power: “The nature and number of atoms juxtaposed to form a molecule are characteristic of the properties of the compound. From that, as Dalton showed, it is easy to deduce the fundamental laws of chemistry” (Reference Duhem1892/2000, 168–69). Duhem's reference to the “fundamental laws of chemistry” here included the law of definite proportions, the law of multiple proportions, and the “law of isomorphism” (i.e., chemical analogy due to similarities in molecular structure; 169). Duhem showed how, when we ask why each of these laws hold, Dalton's atomism can provide a satisfying answer. In his other work on the same topic, Duhem even referred to the atomic theory as a “plausible and appealing interpretation” of the law of multiple proportions (Reference Duhem and Needham1902/2002, 93).

So why did Duhem reject atomism? At the end of the passage in which he discussed the strong points of Dalton's theory, Duhem concluded with the following words: “This is Dalton's atomic hypothesis. It agrees well with the primary laws and the primary notions of chemistry. The concern now is to complete it” (Reference Duhem1892/2000, 170). It is at this point that Duhem began to take issue not with Dalton but with Duhem's own contemporaries who attempted to give atomic explanations of chemical combination and atomicity (i.e., valency). His main objections are as follows:

1. 1. No viable explanation has been given for the atomicity property of atoms, and thus it is difficult to explain chemical combination (i.e., what holds atoms together). Also, atoms of the same element do not always have the same atomicity for all compounds into which they enter (see Duhem Reference Duhem1892/2000, 171–73; Reference Duhem and Needham1902/2002, 88–91).

2. 2. There are compounds with very different formulas that have very similar macroscopic properties such as crystal structure. This is a problem if compositional formulas are taken to represent the arrangement of atoms in a molecule (see Duhem Reference Duhem1892/2000, 175–76).Footnote ⁹

3. 3. After Dalton, some compounds were found to require large (rather than small) whole-number ratios of masses, which seemed to weaken the significance of the law of multiple proportions. To make matters worse, Duhem showed that the law cannot be empirically verified in principle. No measurement technique can ascertain the exact ratio of the masses of two elements in a compound; it can only say that the ratio lies within certain limits. Because there is an infinity of possible numbers—both commensurable and incommensurable—within these limits, there is a possibility that the true ratio is actually incommensurable (see Duhem Reference Duhem and Needham1902/2002, 92–93).Footnote ¹⁰

After discussing the above problems in some depth, Duhem concluded, “It is apparent that the atomic notation as ordinarily explained faces certain difficulties which have their source in experience” (Reference Duhem1892/2000, 176). It appears that Duhem's main reason for his rejection of atomism was not that it did not explain anything but that it did not explain well enough to be accepted as an interpretation of chemistry.