## 1. Substances, Elements, and Chemical Combination



Our contemporary understanding of chemical substances is elemental and
atomic: All substances are composed of atoms of elements such as
hydrogen and oxygen. These atoms are the building blocks of the
microstructures of compounds and hence are the fundamental units of
chemical analysis. However, the reality of chemical atoms was
controversial until the beginning of the 20th century and
the phrase "fundamental building blocks" has always
required careful interpretation. So even today, the claim that all
substances are composed of elements does not give us sufficient
guidance about the ontological status of elements and how the elements
are to be individuated.



In this section, we will begin with the issue of elements.
Historically, chemists have offered two answers to the question
"What is it for something to be an element?"


1. An element is a substance which can exist in the isolated state
and which cannot be further analyzed (hereafter the *end of
analysis* thesis).
2. An element is a substance which is a component of a composite
substance (hereafter the *actual components* thesis).



These two theses describe elements in different ways. In the first,
elements are explicitly identified by a procedure. Elements are simply
the ingredients in a mixture that can be separated no further. The
second conception is more theoretical, positing elements as
constituents of composite bodies. In the pre-modern Aristotelian
system, the end of analysis thesis was the favored option. Aristotle
believed that elements were the building blocks of chemical
substances, only potentially present in these substances. The modern
conception of elements asserts that they are actual components,
although, as we will see, aspects of the end of analysis thesis
linger. This section will explain the conceptual background behind
chemistry's progression from one conception to the other. Along the
way, we will discuss the persistence of elements in chemical
combination, the connection between element individuation and
classification, and criteria for determining pure substances.



### 1.1 Aristotle's Chemistry



The earliest conceptual analyses concerning matter and its
transformations come in the Aristotelian tradition. As in modern
chemistry, the focus of Aristotle's theories was the nature of
substances and their transformations. He offered the first systematic
treatises of chemical theory in *On Generation and Corruption*
(*De Generatione et Corruptione*), *Meteorology*, and
parts of *Physics* and *On the Heavens* (*De
Caelo*).



Aristotle recognized that most ordinary, material things are composed
of multiple substances, although he thought that some of them could be
composed of a single, pure substance. Thus, he needed to give a
criterion of purity that would individuate a single substance. His
criterion was that pure substances are *homoeomerous*: they are
composed of like parts at every level. "[I]f combination has
taken place, the compound *must* be uniform--any part of
such a compound is the same as the whole, just as any part of water is
water" (*De Generatione et Corruptione*,
henceforth *DG*, I.10,
328a10ff).[1] So
when we encounter diamond in rock, oil in water, or smoke in air,
Aristotelian chemistry tells us that there is more than one substance
present.



Like some of his predecessors, Aristotle held that the elements Fire,
Water, Air, and Earth were the building blocks of all substances. But
unlike his predecessors, Aristotle established this list from
fundamental principles. He argued that "it is impossible for the
same thing to be hot and cold, or moist and dry ... Fire is hot
and dry, whereas Air is hot and moist ...; and Water is cold and
moist, while Earth is cold and dry" (*DG* II.3,
330a30-330b5). Aristotle supposed hot and moist to be maximal
degrees of heat and humidity, and cold and dry to be minimal degrees.
Non-elemental substances are characterized by intermediate degrees of
the primary qualities of warmth and humidity.



Aristotle used this elemental theory to account for many properties of
substances. For example he distinguished between liquids and solids by
noting the different properties imposed by two characteristic
properties of elements, moist and dry. "[M]oist is that which,
being readily adaptable in shape, is not determinable by any limit of
its own; while dry is that which is readily determinable by its own
limit, but not readily adaptable in shape" (*DG* II.2,
329b30f.). Solid bodies have a shape and volume of their own, liquids
only have a volume of their own. He further distinguished liquids from
gases, which don't even have their own volume. He reasoned that while
water and air are both fluid because they are moist, cold renders
water liquid and hot makes air gas. On the other hand, dry together
with cold makes earth solid, but together with hot we get fire.



Chemistry focuses on more than just the building blocks of substances:
It attempts to account for the transformations that change substances
into other kinds of substances. Aristotle also contributed the first
important analyses of this process, distinguishing between
*transmutation*, where one substance overwhelms and eliminates
another and *proper mixing*. The former is closest to what we
would now call change of phase and the latter to what we would now
call chemical combination.



Aristotle thought that proper mixing could occur when substances of
comparable amounts are brought together to yield other substances
called
 'compounds.'[2]
 Accordingly, the substances we typically encounter are compounds, and
all compounds have the feature that there are some ingredients from
which they could be made.



What happens to the original ingredients when they are mixed together
to form a compound? Like modern chemists, Aristotle argued that the
original ingredients can, at least in principle, be obtained by
further transformations. He presumably knew that salt and water can be
obtained from sea water and metals can be obtained from alloys. But he
explains this with a conceptual argument, not a detailed list of
observations.



Aristotle first argues that heterogeneous mixtures can be
decomposed:



> 
> Observation shows that even mixed bodies are often divisible into
> homoeomerous parts; examples are flesh, bone, wood, and stone. Since
> then the composite cannot be an element, not every homoeomerous body
> can be an element; only, as we said before, that which is not
> divisible into bodies different in form (*De caelo*, III.4,
> 302b15-20).
> 



He then goes on to offer an explicit definition of the concept of an
element in terms of simple bodies, specifically mentioning recovery in
analysis. 



> 
> An element, we take it, is a body into which other bodies may be
> analyzed, present in them potentially or in actuality (which of these
> is still disputable), and not itself divisible into bodies different
> in form. That, or something like it, is what all men in every case
> mean by element (*De caelo*, III.3, 302a15ff).
> 



The notion of simplicity implicit here is introduced late in
*DG* where in book II Aristotle claims that "All the
compound bodies ... are composed of all the simple bodies"
(334b31). But if all simple bodies (elements) are present in all
compounds, how are the various compounds distinguished? With an eye to
more recent chemistry, it is natural to think that the differing
degrees of the primary qualities of warmth and humidity that
characterize different substances arise from mixing different
proportions of the elements. Perhaps Aristotle makes a fleeting
reference to this idea when he expresses the uniformity of a product
of mixing by saying that "the part exhibit[s] the same ratio
between its constituents as the whole" (*DG* I.10,
328a8-9 and again at *DG* II.7, 334b15).



But what does "proportions of the elements" mean? The
contemporary laws of constant and multiple proportions deal with a
concept of elemental proportions understood on the basis of the
concept of mass. No such concept was available to Aristotle. The
extant texts give little indication of how Aristotle might have
understood the idea of elemental proportions, and we have to resort to
speculation (Needham 2009a).



Regardless of how he understood elemental proportions, Aristotle was
quite explicit that while recoverable, elements were not actually
present in compounds. In *DG* I.10 he argues that the original
ingredients are only potentially, and not actually, present in the
resulting compounds of a mixing process.



There are two reasons why in Aristotle's theory the elements are not
actually present in compounds. The first concerns the manner in which
mixing occurs. Mixing only occurs because of the primary powers and
susceptibilities of substances to affect and be affected by other
substances. This implies that all of the original matter is
*changed* when a new compound is formed. Aristotle tells us
that compounds are formed when the opposing contraries are neutralized
and an intermediate state results:



> 
> since there are differences in degree in hot and cold, ... [when]
> both by combining destroy one another's excesses so that there exist
> instead a hot which (for a hot) is cold and a cold which (for a cold)
> is hot; then there will exist ... an intermediate. ... It is
> thus, then, ... that out of the elements there come-to-be flesh
> and bones and the like--the hot becoming cold and the cold
> becoming hot when they have been brought to the mean. For at the mean
> is neither hot nor cold. The mean, however, is of considerable extent
> and not indivisible. Similarly, it is in virtue of a mean condition
> that the dry and the moist and the rest produce flesh and bone and the
> remaining compounds. (*DG* II.7, 334b8-30)
> 



The second reason has to do with the homogeneity requirement of pure
substances. Aristotle tells us that "if combination has taken
place, the compound *must* be uniform--any part of such a
compound is the same as the whole, just as any part of water is
water" (*DG* I.10, 328a10f.). Since the elements are
defined in terms of the extremes of warmth and humidity, what has
intermediate degrees of these qualities is not an element. Being
homogeneous, every part of a compound has the same intermediate
degrees of these qualities. Thus, there are no parts with extremal
qualities, and hence no elements actually present. His theory of the
appearance of new substances therefore implies that the elements are
not actually present in compounds.



So we reach an interesting theoretical impasse. Aristotle defined the
elements by conditions they exhibit in isolation and argued that all
compounds are composed of the elements. However, the properties
elements have in isolation are nothing that any part of an actually
existing compound could have. So how is it possible to recover the
elements?



It is certainly not easy to understand what would induce a compound to
dissociate into its elements on Aristotle's theory, which seems
entirely geared to showing how a stable equilibrium results from
mixing. The overwhelming kind of mixing process doesn't seem to be
applicable. How, for example, could it explain the separation of salt
and water from sea water? But the problem for the advocates of the
actual presence of elements is to characterize them in terms of
properties exhibited in *both* isolated and combined states.
The general problem of adequately meeting this challenge, either in
defense of the potential presence or actual presence view, is the
*problem of mixture* (Cooper 2004; Fine 1995, Wood &
Weisberg 2004).



In summary, Aristotle laid the philosophical groundwork for all
subsequent discussions of elements, pure substances, and chemical
combination. He asserted that all pure substances were homoeomerous
and composed of the elements air, earth, fire, and water. These
elements were not actually present in these substances; rather, the
four elements were potentially present. Their potential presence could
be revealed by further analysis and transformation.


### 1.2 Lavoisier's Elements



Antoine Lavoisier (1743-1794) is often called the father of
modern chemistry, and by 1789 he had produced a list of the elements
that a modern chemist would recognize. Lavoisier's list, however, was
not identical to our modern one. Some items such as hydrogen and
oxygen gases were regarded as compounds by Lavoisier, although we now
know regard hydrogen and oxygen as elements and their gases as
molecules.



Other items on his list were remnants of the Aristotelian system which
have no place at all in the modern system. For example, fire remained
on his list, although in the somewhat altered form of caloric. Air is
analyzed into several components: the respirable part called oxygen
and the remainder called azote or nitrogen. Four types of earth found
a place on his list: lime, magnesia, barytes, and argill. The
composition of these earths are "totally unknown, and, until by
new discoveries their constituent elements are ascertained, we are
certainly authorized to consider them as simple bodies" (1789,
p. 157), although Lavoisier goes on to speculate that "all the
substances we call earths may be only metallic oxyds" (1789, p.
159).



What is especially important about Lavoisier's system is his
discussion of how the elemental basis of particular compounds is
determined. For example, he describes how water can be shown to be a
compound of hydrogen and oxygen (1789, pp. 83-96). He
writes:



> 
> When 16 ounces of alcohol are burnt in an apparatus properly adapted
> for collecting all the water disengaged during the combustion, we
> obtain from 17 to 18 ounces of water. As no substance can furnish a
> product larger than its original bulk, it follows, that something else
> has united with the alcohol during its combustion; and I have already
> shown that this must be oxygen, or the base of air. Thus alcohol
> contains hydrogen, which is one of the elements of water; and the
> atmospheric air contains oxygen, which is the other element necessary
> to the composition of water (1789, p. 96).
> 



The metaphysical principle of the conservation of matter--that
matter can be neither created nor destroyed in chemical
processes--called upon here is at least as old as Aristotle
(Weisheipl 1963). What the present passage illustrates is the
employment of a criterion of conservation: the preservation of mass.
The total mass of the products must come from the mass of the
reactants, and if this is not to be found in the easily visible ones,
then there must be other, less readily visible reactants.



This principle enabled Lavoisier to put what was essentially
Aristotle's notion of simple substances (302a15ff., quoted in section
1.1) to much more effective experimental use. Directly after rejecting
atomic theories, he says "if we apply the term
*elements*, or *principles of bodies*, to express our
idea of the last point which analysis is capable of reaching, we must
admit, as elements, all the substances into which we are capable, by
any means, to reduce bodies by decomposition" (1789, p. xxiv).
In other words, elements are identified as the smallest components of
substances that we can produce experimentally. The principle of the
conservation of mass provided for a criterion of when a chemical
change was a decomposition into simpler substances, which was decisive
in disposing of the phlogiston theory. The increase in weight on
calcination meant, in the light of this principle, that calcination
was not a decomposition, as the phlogiston theorists would have it,
but the formation of a more complex compound.



Despite the pragmatic character of this definition, Lavoisier felt
free to speculate about the compound nature of the earths, as well as
the formation of metal oxides which required the decomposition of
oxygen gas. Thus, Lavoisier also developed the notion of an element as
a theoretical, last point of analysis concept. While this last point
of analysis conception remained an important notion for Lavoisier as
it was for Aristotle, his notion was a significant advance over
Aristotle's and provided the basis for further theoretical advance in
the 19th century (Hendry 2005).


### 1.3 Mendeleev's Periodic Table



Lavoisier's list of elements was corrected and elaborated with the
discovery of many new elements in the 19th century. For example,
Humphrey Davy (1778-1829) isolated sodium and potassium by
electrolysis, demonstrating that Lavoisier's earths were actually
compounds. In addition, caloric disappeared from the list of accepted
elements with the discovery of the first law of thermodynamics in the
1840s. Thus with this changing, but growing, number of elements,
chemists increasingly recognized the need for a systematization. Many
attempts were made, but an early influential account was given by John
Newlands (1837-98) who prepared the first periodic table showing
that 62 of the 63 then known elements follow an "octave"
rule according to which every eighth element has similar
properties.



Later, Lothar Meyer (1830-95) and Dmitrij Mendeleev
(1834-1907) independently presented periodic tables covering all
63 elements known in 1869. In 1871, Mendeleev published his periodic
table in the form it was subsequently acclaimed. This table was
organized on the idea of periodically recurring general features as
the elements are followed when sequentially ordered by relative atomic
weight. The periodically recurring similarities of chemical behavior
provided the basis of organizing elements into groups. He identified 8
such groups across 12 horizontal periods, which, given that he was
working with just 63 elements, meant there were several holes.



![periodic table](periodic-table.png)
Figure 1.
The International Union of Pure and Applied Chemistry's Periodic
Table of the Elements.




The modern Periodic Table depicted in Figure 1 is based on Mendeleev's
table, but now includes 92 naturally occurring elements and some dozen
artificial elements (see Scerri 2006). The lightest element,
hydrogen, is difficult to place, but is generally placed at the top of
the first group. Next comes helium, the lightest of the noble gases,
which were not discovered until the end of the 19th
century. Then the second period begins with lithium, the first of the
group 1 (alkali metal) elements. As we cross the second period,
successively heavier elements are first members of other groups until
we reach neon, which is a noble gas like helium. Then with the next
heaviest element sodium we return to the group 1 alkali metals and
begin the third period, and so on.



On the basis of his systematization, Mendeleev was able to correct the
values of the atomic weights of certain known elements and also to
predict the existence of then unknown elements corresponding to gaps
in his Periodic Table. His system first began to seriously attract
attention in 1875 when he was able to point out that gallium, the
newly discovered element by Lecoq de Boisbaudran (1838-1912),
was the same as the element he predicted under the name eka-aluminium,
but that its density should be considerably greater than the value
Lecoq de Boisbaudran reported. Repeating the measurement proved
Mendeleev to be right. The discovery of scandium in 1879 and germanium
in 1886 with the properties Mendeleev predicted for what he called
"eka-bor" and "eka-silicon" were further
triumphs (Scerri 2006).



In addition to providing the systematization of the elements used in
modern chemistry, Mendeleev also gave an account of the nature of
elements which informs contemporary philosophical understanding. He
explicitly distinguished between the end of analysis and actual
components conceptions of elements and while he thought that both
notions have chemical importance, he relied on the actual components
thesis when constructing the Periodic Table. He assumed that the
elements remained present in compounds and that the weights of
compounds is the sum of the weights of their constituent atoms. He was
thus able to use atomic weights as the primary ordering property of
the Periodic
 Table.[3]



Nowadays, chemical nomenclature, including the definition of the
element, is regulated by The International Union of Pure and Applied
Chemistry (IUPAC). In 1923, IUPAC followed Mendeleev and standardized
the individuation criteria for the elements by explicitly endorsing
the actual components thesis. Where they differed from Mendeleev is in
what property they thought could best individuate the elements. Rather
than using atomic weights, they ordered elements according to
*atomic number*, the number of protons and of electrons of
neutral elemental atoms, allowing for the occurrence of
*isotopes* with the same atomic number but different atomic
weights. They chose to order elements by atomic number because of the
growing recognition that electronic structure was the atomic feature
responsible for governing how atoms combine to form molecules, and the
number of electrons is governed by the requirement of overall
electrical neutrality (Kragh 2000).


### 1.4 Complications for the Periodic System



Mendeleev's periodic system was briefly called into question with the
discovery of the inert gas argon in 1894, which had to be placed
outside the existing system after chlorine. But William Ramsay
(1852-1916) suspected there might be a whole group of chemically
inert substances separating the electronegative halogen group 17 (to
which chlorine belongs) and the electropositive alkali metals, and by
1898 he had discovered the other noble gases, which became group 18 on
the modern Table.



A more serious challenge arose when the English radiochemist Frederick
Soddy (1877-1956) established in 1913 that according to the
atomic weight criterion of sameness, positions in the periodic table
were occupied by several elements. Adopting Margaret Todd's
(1859-1918) suggestion, Soddy called these elements
'isotopes,' meaning "same place." At the same
time, Bohr's conception of the atom as comprising a positively charged
nucleus around which much lighter electrons circulated was gaining
acceptance. After some discussion about criteria (van der Vet 1979),
delegates to the 1923 IUPAC meeting saved the Periodic Table by
decreeing that positions should be correlated with atomic number
(number of protons in the nucleus) rather than atomic weight.



Correlating positions in the Periodic Table with whole numbers finally
provided a criterion determining whether any gaps remained in the
table below the position corresponding to the highest known atomic
number. The variation in atomic weight for fixed atomic number was
explained in 1932 when James Chadwick (1891-1974) discovered the
neutron--a neutral particle occurring alongside the proton in
atomic nuclei with approximately the same mass as the proton.



Contemporary philosophical discussion about the nature of the elements
begins with the work of Friedrich Paneth (1887-1958), whose work
heavily influenced IUPAC standards and definitions. He was among the
first chemists in modern times to make explicit the distinction
between the last point of analysis and actual components analyses, and
argued that the last point in analysis thesis could not be the proper
basis for the chemical explanation of the nature of compounds.
Something that wasn't actually present in a substance couldn't be
invoked to explain the properties in a real substance. He went on to
say that the chemically important notion of element was
"transcendental," which we interpret to mean "an
abstraction over the properties in compounds" (Paneth
1962).



Another strand of the philosophical discussion probes at the
contemporary IUPAC definition of elements. According to IUPAC, to be
gold is to have atomic number 79, regardless of atomic weight. A
logical and intended consequence of this definition is that all
isotopes sharing an atomic number count as the same element. Needham
(2008) has recently challenged this identification by pointing to
chemically salient differences among the isotopes. These differences
are best illustrated by the three isotopes of hydrogen: protium,
deuterium and tritium. The most striking chemical difference among the
isotopes of hydrogen is their different rate of chemical reactions.
Because of the sensitivity of biochemical processes to rates of
reaction, heavy water (deuterium oxide) is poisonous whereas ordinary
water (principally protium oxide) is not. With the development of more
sensitive measuring techniques, it has become clear that this is a
general phenomenon. Isotopic variation affects the rate of chemical
reactions, although these effects are less marked with increasing
atomic number. In view of the way chemists understand these
differences in behavior, Needham argues that they can reasonably be
said to underlie differences in chemical substance. He further argues
that the criteria of sameness and difference provided by
thermodynamics also suggest that the isotopes should be considered
different substances. However, notwithstanding his own view, the
places in Mendeleev's periodic table were determined by atomic number
(or nuclear charge), so a concentration on atomic weight would be
highly revisionary of chemical classification (Hendry 2006a). It can
also be argued that the thermodynamic criteria underlying the view
that isotopes are different substances distinguish among substances
more finely than is appropriate for chemistry (Hendry 2010c).


### 1.5 Modern Problems about Mixtures and Compounds



Contemporary theories of chemical combination arose from a fusion of
ancient theories of proper mixing and hundreds of years of
experimental work, which refined those theories. Yet even by the time
that Lavoisier inaugurated modern chemistry, chemists had little in
the way of rules or principles that govern how elements combine to
form compounds. In this section, we discuss theoretical efforts to
provide such criteria.



A first step towards a theory of chemical combination was implicit in
Lavoisier's careful experimental work on water. In his *Elements of
Chemistry*, Lavoisier established the mass proportions of hydrogen
and oxygen obtained by the complete reduction of water to its
elements. The fact that his results were based on multiple repetitions
of this experiment suggests that he assumed compounds like water are
always composed of the same elements in the same proportions. This
widely shared view about the constant proportions of elements in
compounds was first explicitly proclaimed as the *law of constant
proportions* by Joseph Louis Proust (1754-1826) in the first
years of the 19th century. Proust did so in response to Claude Louis
Berthollet (1748-1822), one of Lavoisier's colleagues and
supporters, who argued that compounds could vary in their elemental
composition.



Although primarily a theoretical and conceptual posit, the law of
constant proportions became an important tool for chemical analysis.
For example, chemists had come to understand that atmospheric air is
composed of both nitrogen and oxygen and is not an element. But was
air a genuine compound of these elements or some looser mixture of
nitrogen and oxygen, that could vary at different times and in
different places? The law of constant proportions gave a criterion for
distinguishing compounds from genuine mixtures. If air was a compound,
then it would always have the same proportion of nitrogen and oxygen
and it should further be distinguishable from other compounds of
nitrogen and oxygen such as nitrous oxide. If air was not a genuine
compound, then it would be an example of a *solution*, a
homogenous mixture of oxygen and nitrogen that could vary in
proportions.



Berthollet didn't accept this rigid distinction between solutions and
compounds. He believed that whenever a substance is brought into
contact with another, it forms a homogeneous union until further
addition of the substance leaves the union in excess. For example,
when water and sugar are combined, they initially form a homogenous
union. At a certain point, the affinities of water and sugar for one
another are saturated, and a second phase of solid sugar will form
upon the addition of more sugar. This point of saturation will vary
with the pressure and temperature of the solution. Berthollet
maintained that just as the amount of sugar in a saturated solution
varies with temperature and pressure, the proportions of elements in
compounds are sensitive to ambient conditions. Thus, he argued, it is
not true that substances are always composed of the same proportions
of the element and this undermines the law of constant proportions.
But after a lengthy debate, chemists came to accept that the evidence
Proust adduced established the law of constant proportions for
compounds, which were thereby distinguished from solutions.



Chemists' attention was largely directed towards the investigation of
compounds in the first half of the 19th century, initially with a view
to broadening the evidential basis which Proust had provided. For a
time, the law of constant proportions seemed a satisfactory criterion
of the occurrence of chemical combination. But towards the end of the
19th century, chemists turned their attention to solutions.
Their investigation of solutions drew on the new science of
thermodynamics, which said that changes of state undergone by
substances when they are brought into contact were subjected to its
laws governing energy and entropy.



Although thermodynamics provided no sharp distinction between
compounds and solutions, it did allow the formulation of a concept for
a special case called an *ideal solution*. An ideal solution
forms because its increased stability compared with the separated
components is entirely due to the entropy of mixing. This can be
understood as a precisification of the idea of a purely mechanical
mixture. In contrast, compounds were stabilized by interactions
between their constituent components over and above the entropy of
mixing. For example, solid sodium chloride is stabilized by the
interactions of sodium and chlorine, which react to form sodium
chloride. The behavior of real solutions could be compared with that
of an ideal solution, and it turned out that non-ideality was the rule
rather than the exception. Ideality is approached only in certain
dilute binary solutions. More often, solutions exhibited behavior
which could only be understood in terms of significant chemical
interactions between the components, of the sort characteristic of
chemical combination.



Long after his death, in the first decades of the 20th century,
Berthollet was partially vindicated with the careful characterization
of a class of substances that we now call Berthollides. These are
compounds whose proportions of elements do not stand in simple
relations to one another. Their elemental proportions are not fixed,
but vary with temperature and pressure. For example, the mineral
wustite, or ferrous oxide, has an approximate compositional
formula of FeO, but typically has somewhat less iron than oxygen.



From a purely macroscopic, thermodynamic perspective, Berthollides can
be understood in terms of the minimization of the thermodynamic
function called the Gibbs free energy, which accommodates the
interplay of energy and entropy as functions of temperature and
pressure. Stable substances are ones with minimal Gibbs free energy.
On the microscopic scale, the basic microstructure of ferrous oxide is
a three-dimensional lattice of ferrous (Fe2+) and oxide
(O2-) ions. However, some of the ferrous ions are replaced
by holes randomly distributed in the crystal lattice, which generates
an increase in entropy compared with a uniform crystal structure. An
overall imbalance of electrical charge would be created by the missing
ions. But this is countered in ferrous oxide by twice that number of
ions from those remaining being converted to ferric (Fe3+)
ions. This removal of electrons requires an input of
energy, which would make for a less stable structure were it not for
the increased entropy afforded by the holes in the crystal structure.
The optimal balance between these forces depends on the temperature
and pressure, and this is described by the Gibbs free energy function.




Although the law of constant proportions has not survived the
discovery of Berthollides and more careful analyses of solutions
showed that chemical combination or affinity is not confined to
compounds, it gave chemists a principled way of studying how elements
combine to form compounds through the 19th century. This
account of Berthollides also illustrates the interplay between
macroscopic and microscopic theory which is a regular feature of
modern chemistry, and which we turn to in the next section.



Chemistry has traditionally distinguished itself from classical
physics by its interest in the division of matter into different
substances and in chemical combination, the process whereby substances
are held together in compounds and solutions. In this section, we have
described how chemists came to understand that all substances were
composed of the Periodic Table's elements, and that these elements are
actual components of substances. Even with this knowledge,
distinguishing pure substances from heterogeneous mixtures and
solutions remained a very difficult chemical challenge. And despite
chemists' acceptance of the law of definite proportions as a criterion
for substancehood, chemical complexities such as the discovery of the
Berthollides muddied the waters.


## 2. Atomism



Modern chemistry is thoroughly atomistic. All substances are thought
to be composed of small particles, or atoms, of the Periodic Table's
elements. Yet until the beginning of the 20th century, much
debate surrounded the status of atoms and other microscopic
constituents of matter. As with many other issues in philosophy of
chemistry, the discussion of atomism begins with Aristotle, who
attacked the coherence of the notion and disputed explanations
supposedly built on the idea of indivisible constituents of matter
capable only of change in respect of position and motion, but not
intrinsic qualities. We will discuss Aristotle's critiques of atomism
and Boyle's response as well as the development of atomism in the 19th
and 20th centuries.


### 2.1 Atomism in Aristotle and Boyle



In Aristotle's time, atomists held that matter was fundamentally
constructed out of atoms. These atoms were indivisible and uniform, of
various sizes and shapes, and capable only of change in respect of
position and motion, but not intrinsic qualities. Aristotle rejected
this doctrine, beginning his critique of it with a simple question:
What are atoms made of? Atomists argue that they are all made of
uniform matter. But why should uniform matter split into portions not
themselves further divisible? What makes atoms different from
macroscopic substances which are also uniform, but can be divided into
smaller portions? Atomism, he argued, posits a particular size as the
final point of division in completely ad hoc fashion, without giving
any account of this smallest size or why atoms are this smallest
size.



Apart from questions of coherence, Aristotle argued that it was
unclear and certainly unwarranted to assume that atoms have or lack
particular properties. Why shouldn't atoms have some degree of warmth
and humidity like any observable body? But if they do, why shouldn't
the degree of warmth of a cold atom be susceptible to change by the
approach of a warm atom, in contradiction with the postulate that
atoms only change their position and motion? On the other hand, if
atoms don't possess warmth and humidity, how can changes in degrees of
warmth and humidity between macroscopic substances be explained purely
on the basis of change in position and motion?



These and similar considerations led Aristotle to question whether the
atomists had a concept of substance at all. There are a large variety
of substances discernible in the world--the flesh, blood and bone
of animal bodies; the water, rock, sand and vegetable matter by the
coast, etc. Atomism apparently makes no provision for accommodating
the differing properties of these substances, and their
interchangeability, when for example white solid salt and tasteless
liquid water are mixed to form brine or bronze statues slowly become
green. Aristotle recognized the need to accommodate the creation of
new substances with the destruction of old by combination involving
the mutual interaction and consequent modification of the primary
features of bodies brought into contact. In spite of the weaknesses of
his own theory, he displays a grasp of the issue entirely lacking on
the part of the atomists. His conception of elements as being few in
number and of such a character that all the other substances are
compounds derived from them by combination and reducible to them by
analysis provided the seeds of chemical theory. Ancient atomism
provided none.



Robert Boyle (1627-1691) is often credited with first breaking
with ancient and medieval traditions and inaugurating modern chemistry
by fusing an experimental approach with mechanical philosophy. Boyle's
chemical theory attempts to explain the diversity of substances,
including the elements, in terms of variations of shape and size and
mechanical arrangements of what would now be called sub-atomic atoms
or corpuscles. Although Boyle's celebrated experimental work attempted
to respond to Aristotelian orthodoxy, his theorizing about atoms had
little impact on his experimental work. Chalmers (1993, 2002)
documents the total absence of any connection between Boyle's atomic
speculations and his experimental work on the effects of pressure on
gases. This analysis applies equally to Boyle's chemical experiments
and chemical theorizing, which was primarily driven by a desire to
give a mechanical philosophy of chemical combination (Chalmers 2009,
Ch. 6). No less a commentator than Antoine Lavoisier (1743-1794)
was quite clear that Boyle's corpuscular theories did nothing to
advance chemistry. As he noted towards the end of the next century,
"... if, by the term *elements*, we mean to express
those simple and indivisible atoms of which matter is composed, it is
extremely probable we know nothing at all about them" (1789, p.
xxiv). Many commentators thus regard Boyle's empirically-based
criticisms of the Aristotelian chemists more important than his own
atomic theories.


### 2.2 Atomic Realism in Contemporary Chemistry



Contemporary textbooks typically locate discussions of chemical
atomism in the 19th century work of John Dalton
(1766-1844). Boyle's ambitions of reducing elemental minima to
structured constellations of mechanical atoms had been abandoned by
this time, and Dalton's theory simply assumes that each element has
smallest parts of characteristic size and mass which have the property
of being of that elemental kind**.** Lavoisier's elements
are considered to be collections of such characteristic atoms. Dalton
argued that this atomic hypothesis explained the law of constant
proportions (see section 1.5).



Dalton's theory gives expression to the idea of the real presence of
elements in compounds. He believed that atoms survive chemical change,
which underwrites the claim that elements are actually present in
compounds. He assumed that atoms of the same element are alike in
their weight. On the assumption that atoms combine with the atoms of
other elements in fixed ratios, Dalton claimed to explain why, when
elements combine, they do so with fixed proportions between their
weights. He also introduced the *law of multiple proportions*,
according to which the elements in distinct compounds of the same
elements stand in simple proportions. He argued that this principle
was also explained by his atomic theory.



Dalton's theory divided the chemical community and while he had many
supporters, a considerable number of chemists remained anti-atomistic.
Part of the reason for this was controversy surrounding the empirical
application of Dalton's atomic theory: How should one estimate atomic
weights since atoms were such small quantities of matter? Daltonians
argued that although such tiny quantities could not be measured
absolutely, they could be measured relative to a reference atom (the
natural choice being hydrogen as 1). This still left a problem in
setting the ratio between the weights of different atoms in compounds.
Dalton assumed that, if only one compound of two elements is known, it
should be assumed that they combine in equal proportions. Thus, he
understood water, for instance, as though it would have been
represented by HO in terms of the formulas that Berzelius was to
introduce (Berzelius, 1813). But Dalton's response to this problem
seemed arbitrary. Finding a more natural solution became pressing
during the first half of the nineteenth century as more and more
elements were being discovered, and the elemental compositions of more
and more chemical substances were being determined qualitatively
(Duhem 2002; Needham 2004; Chalmers 2005a, 2005b, and 2008).



Dalton's contemporaries raised other objections as well. Jacob
Berzelius (1779-1848) argued that Daltonian atomism provided no
explanation of chemical combination, how elements hold together to
form compounds (Berzelius, 1815). Since his atoms are intrinsically
unchanging, they can suffer no modification of the kind Aristotle
thought necessary for combination to occur. Lacking anything like the
modern idea of a molecule, Dalton was forced to explain chemical
combination in terms of atomic packing. He endowed his atoms with
atmospheres of caloric whose mutual repulsion was supposed to explain
how atoms pack together efficiently. But few were persuaded by this
idea, and what came later to be known as Daltonian atomism abandoned
the idea of caloric shells altogether.



The situation was made more complex when chemists realized that
elemental composition was not in general sufficient to distinguish
substances. Dalton was aware that the same elements sometimes give
rise to several compounds; there are several oxides of nitrogen, for
example. But given the law of constant proportions, these can be
distinguished by specifying the combining proportions, which is what
is represented by distinct chemical formulas, for example
N2O, NO and N2O3 for different oxides
of nitrogen. However, as more organic compounds were isolated and
analyzed, it became clear that elemental composition doesn't uniquely
distinguish substances. Distinct compounds with the same elemental
composition are called *isomers*. The term was coined by
Berzelius in 1832 when organic compounds with the same composition,
but different properties, were first recognized. It was later
discovered that isomerism is ubiquitous, and not confined to organic
compounds.



Isomers may differ radically in "physical" properties such
as melting points and boiling points as well as patterns of chemical
reactivity. This is the case with dimethyl ether and ethyl alcohol,
which have the *compositional formula*
C2H6O in common, but are represented by two
distinct *structural formulas*: (CH3)2O
and C2H5OH. These formulas identify different
*functional groups,* which govern patterns of chemical
reactivity. The notion of a structural formula was developed to
accommodate other isomers that are even more similar. This was the
case with a subgroup of *stereoisomers* called *optical*
isomers, which are alike in many of their physical properties such as
melting points and boiling points and (when first discovered) seemed
to be alike in chemical reactivity too. Pasteur famously separated
*enantiomers* (stereoisomers of one another) of tartaric acid
by preparing a solution of the sodium ammonium salt and allowing
relatively large crystals to form by slow evaporation. Using tweezers,
he assembled the crystals into two piles, members of the one having
shapes which are mirror images of the shapes of those in the other
pile. Optical isomers are so called because they have the
distinguishing feature of rotating the plane of plane polarized light
in opposite directions, a phenomenon first observed in quartz crystals
at the beginning of the 19th century. These isomers are
represented by three-dimensional structural formulas which are mirror
images of one another as we show in Figure 2.



![tartaric acid](tartaric-acid.png)
Figure 2.
The enantiomers of tartaric acid. D-tartaric acid is on the
left and L-tartaric acid is on the right. The dotted vertical line
represents a mirror plane. The solid wedges represent bonds coming out
of the plane, while the dashed wedges represent bonds going behind the
plane. These molecular structures are mirror images of one another.




Although these discoveries are often presented as having been
explained by the atomic or molecular hypothesis, skepticism about the
status of atomism persisted throughout the 19th century. Late 19th
century skeptics such as Ernst Mach, Georg Helm, Wilhelm Ostwald, and
Pierre Duhem did not see atomism as an adequate explanation of these
phenomena, nor did they believe that there was sufficient evidence to
accept the existence of atoms. Instead, they advocated non-atomistic
theories of chemical change grounded in thermodynamics (on Helm and
Ostwald, see the introduction to Deltete 2000).



Duhem's objections to atomism are particularly instructive. Despite
being represented as a positivist in some literature (e.g. Fox 1971),
his objections to atomism in chemistry made no appeal to the
unobservability of atoms. Instead, he argued that a molecule was a
theoretical impossibility according to 19th century physics, which
could say nothing about how atoms can hold together but could give
many reasons why they couldn't be stable entities over reasonable
periods of time. He also argued that the notion of valency attributed
to atoms to explain their combining power was simply a macroscopic
characterization projected into the microscopic level. He showed that
chemical formulae could be interpreted without resorting to atoms and
the notion of valency could be defined on this basis (Duhem 1892,
1902; for an exposition, see Needham 1996). Atomists failed to meet
this challenge, and he criticized them for not saying what the
features of their atoms were beyond simply reading into them
properties defined on a macroscopic basis (Needham 2004). Duhem did
recognize that an atomic *theory* was developed in the 19th
century, the vortex theory (Kragh 2002), but rejected it as
inadequate for explaining chemical phenomena.



Skeptics about atomism finally became convinced at the beginning of
the 20th century by careful experimental and theoretical
work on *Brownian motion*, the fluctuation of particles in an
emulsion. With the development of kinetic theory it was suspected that
this motion was due to invisible particles within the emulsion pushing
the visible particles. But it wasn't until the first decade of the
20th century that Einstein's theoretical analysis and Perrin's
experimental work gave substance to those suspicions and provided an
estimate of Avogadro's number, which Perrin famously argued was
substantially correct because it agreed with determinations made by
several other, independent, methods. This was the decisive argument
for the existence of microentities which led most of those still
skeptical of the atomic hypotheses to change their views (Einstein
1905; Perrin 1913; Nye 1972; Maiocchi 1990).



It is important to appreciate, however, that establishing the
existence of atoms in this way left many of the questions raised by
the skeptics unanswered. A theory of the nature of atoms which would
explain how they can combine to form molecules was yet to be
formulated. And it remains to this day an open question whether a
purely microscopic theory is available which is adequate to explain
the whole range of chemical phenomena. This issue is pursued in
Section 6 where we discuss reduction.


## 3. The Chemical Revolution



As we discussed in Section 1, by the end of the 18th century the
modern conception of chemical substances began to take form in
Lavoisier's work. Contemporary looking lists of elements were being
drawn up and also the notion of mass was introduced into chemistry.
Despite these advances, chemists continued to develop theories about
two substances which we no longer accept: caloric and phlogiston.
Lavoisier famously rejected phlogiston, but he accepted caloric. It
would be another 60 years until the notion of caloric was finally
abandoned with the development of thermodynamics.


### 3.1 Caloric



In 1761, Joseph Black discovered that heating a body doesn't always
raise its temperature. In particular, he noticed that heating ice at
0degC converts it to liquid at the same temperature. Similarly,
there is a latent heat of vaporization which must be supplied for the
conversion of liquid water into steam at the boiling point without
raising the temperature. It was some time before the modern
interpretation of Black's ground-breaking discovery was fully
developed. He had shown that heat must be distinguished from the state
of warmth of a body and even from the changes in that state. But it
wasn't until the development of thermodynamics that heating was
distinguished as a process from the property or quality of being warm
without reference to a transferred substance.



Black himself was apparently wary of engaging in hypothetical
explanations of heat phenomena (Fox 1971), but he does suggest an
interpretation of the latent heat of fusion of water as a chemical
reaction involving the combination of the heat fluid with ice to yield
the new substance water. Lavoisier incorporated Black's conception of
latent heat into his caloric theory of heat, understanding latent heat
transferred to a body without raising its temperature as caloric fluid
bound in chemical combination with that body and not contributing to
the body's degree of warmth or temperature. Lavoisier's theory thus
retains something of Aristotle's, understanding what we would call a
phase change of the same substance as a transformation of one
substance into another.



Caloric figures in Lavoisier's list of elements as the "element
of heat or fire" (Lavoisier 1789, p. 175), "becom[ing]
fixed in bodies ... [and] act[ing] upon them with a repulsive
force, from which, or from its accumulation in bodies to a greater or
lesser degree, the transformation of solids into fluids, and of fluids
to aeriform elasticity, is entirely owing" (1789, p. 183). He
goes on to define 'gas' as "this aeriform state of
bodies produced by a sufficient accumulation of caloric." Under
the list of binary compounds formed with hydrogen, caloric is said to
yield hydrogen gas (1789, p. 198). Similarly, under the list of binary
compounds formed with phosphorus, caloric yields phosphorus gas (1789,
p. 204). The Lavoisian element base of oxygen combines with the
Lavoisian element caloric to form the compound oxygen gas. The
compound of base of oxygen with a smaller amount of caloric is oxygen
liquid (known only in principle to Lavoisier). What we would call the
phase change of liquid to gaseous oxygen is thus for him a change of
substance. Light also figures in his list of elements, and is said
"to have a great affinity with oxygen, ... and contributes
along with caloric to change it into the state of gas" (1789, p.
185).


### 3.2 Phlogiston



Another substance concept from roughly the same period is phlogiston,
which served as the basis for 18th century theories of processes that
came to be called oxidation and reduction. Georg Ernst Stahl
(1660-1734) introduced the theory, drawing on older theoretical
ideas. Alchemists thought that metals lose the mercury principle under
calcination and that when substances are converted to slag, rust, or
ash by heating, they lose the sulphur principle. Johann Joackim Becher
(1635-82) modified these ideas at the end of the 17th century,
arguing that the calcination of metals is a kind of combustion
involving the loss of what he called the principle of flammability.
Stahl subsequently renamed this principle 'phlogiston' and
further modified the theory, maintaining that phlogiston could be
transferred from one substance to another in chemical reactions, but
that it could never be isolated.



For example, metals were thought to be compounds of the metal's calx
and phlogiston, sulphur was thought to be a compound of sulphuric acid
and phlogiston, and phosphorus was thought to be a compound of
phosphoric acid and phlogiston. Substances such as carbon which left
little or no ash after burning were taken to be rich in phlogiston.
The preparation of metals from their calxes with the aid of wood
charcoal was understood as the transfer of phlogiston from carbon to
the metal.



Regarding carbon as a source of phlogiston and no longer merely as a
source of warmth was a step forward in understanding chemical
reactions (which Ladyman 2011 emphasizes in support of his structural
realist interpretation of phlogiston chemistry). The phlogiston theory
suggested that reactions could involve the replacement of one part of
a substance with another, where previously all reactions were thought
to be simple associations or dissociations.



Phlogiston theory was developed further by Henry Cavendish
(1731-1810) and Joseph Priestley (1733-1804), who both
attempted to better characterize the properties of phlogiston itself.
After 1760, phlogiston was commonly identified with what they called
'inflammable air' (hydrogen), which they successfully
captured by reacting metals with muriatic (hydrochloric) acid. Upon
further experimental work on the production and characterizations of
these "airs," Cavendish and Priestley identified what we
now call oxygen as 'dephlogisticated air' and nitrogen as
'phlogiston-saturated air.'



As reactants and products came to be routinely weighed, it became
clear that metals gain weight when they become a calx. But according
to the phlogiston theory, the calx involves the loss of phlogiston.
Although the idea that a process involving the loss of a substance
could involve the gain of weight seems strange to us, phlogiston
theorists were not immediately worried. Some phlogiston theorists
proposed explanations based on the 'levitation' properties
of phlogiston, what Priestly later referred to as phlogiston's
'negative weight.' Another explanation of the phenomenon
was that the nearly weightless phlogiston drove out heavy, condensed
air from the pores of the calx. The net result was a lighter product.
Since the concept of mass did not yet play a central role in
chemistry, these explanations were thought to be quite reasonable.



However, by the end of the 1770s, Torbern Olaf Bergman
(1735-1784) made a series of careful measurements of the weights
of metals and their calxes. He showed that the calcination of metals
led to a gain in their weight equal to the weight of oxygen lost by
the surrounding air. This ruled out the two explanations given above,
but interestingly, he took this in his stride, arguing that, as metals
were being transformed into their calxes, they lost weightless
phlogiston. This phlogiston combines with the air's oxygen to form
ponderable warmth, which in turn combines with what remains of the
metal after loss of phlogiston to form the calx. Lavoisier simplified
this explanation by removing the phlogiston from this scheme. This
moment is what many call the Chemical Revolution.


## 4. Structure in Chemistry



Modern chemistry primarily deals with microstructure, not elemental
composition. This section will explore the history and consequences of
chemistry's focus on structure. The first half of this section
describes chemistry's transition from a science concerned with
elemental composition to a science concerned with structure. The
second half will focus on the conceptual puzzles raised by
contemporary accounts of bonding and molecular structure.


### 4.1 Structural Formulas



In the 18th and early 19th centuries, chemical
analyses of substances consisted in the decomposition of substances
into their elemental components. Careful weighing combined with an
application of the law of constant proportions allowed chemists to
characterize substances in terms of the mass ratios of their
constituent elements, which is what chemists mean by the composition
of a compound. During this period, Berzelius developed a notation of
compositional formulas for these mass ratios where letters stand for
elements and subscripts stand for proportions on a scale which
facilitates comparison of different substances. Although these
proportions reflect the proportion by weight in grams, the simple
numbers are a result of reexpressing gravimetric proportions in terms
of chemical equivalents. For example, the formulas
'H2O' and 'H2S' say that
there is just as much oxygen in combination with hydrogen in water as
there is sulphur in combination with hydrogen in hydrogen sulphide.
However, when measured in weight, 'H2O'
corresponds to combining proportions of 8 grams of oxygen to 1 gram of
hydrogen and 'H2S' corresponds to 16 grams of
sulphur to 1 of hydrogen in weight.



By the first decades of the 19th century, the nascent
sub-discipline of organic chemistry began identifying and synthesizing
ever increasing numbers of compounds (Klein 2003). As indicated in
section 2.2, it was during this period that the phenomenon of
isomerism was recognized, and structural formulas were introduced to
distinguish substances with the same compositional formula that differ
in their macroscopic properties. Although some chemists thought
structural formulas could be understood on a macroscopic basis, others
sought to interpret them as representations of microscopic entities
called molecules, corresponding to the smallest unit of a compound as
an atom was held to be the smallest unit of an element.



In the first half of the nineteenth century there was no general
agreement about how the notion of molecular structure could be
deployed in understanding isomerism. But during the second half of the
century, consensus built around the structural theories of August
Kekule (1829-1896). Kekule noted that carbon
tended to combine with univalent elements in a 1:4 ratio. He argued
that this was because each carbon atom could form bonds to four other
atoms, even other carbon atoms (1858 [1963], 127). In later papers,
Kekule dealt with apparent exceptions to carbon's valency of
four by introducing the concept of double bonds between carbon atoms.
He extended his treatment to aromatic compounds, producing the famous
hexagonal structure for benzene (see Rocke 2010), although this was to
create a lasting problem for the universality of carbon's valency of 4
(Brush 1999a, 1999b).



Kekule's ideas about bonding between atoms were important steps
toward understanding isomerism. Yet his presentations of structure
theory lacked a clear system of diagrammatic representation so most
modern systems of structural representation originate with Alexander
Crum Brown's (1838-1932) paper about isomerism among organic
acids (1864 [1865]). Here, structure was shown as linkages between
atoms (see Figure 3).



![Ethane and Formic Acid](ethane-formic-acid.png)
Figure 3. Depictions of ethane and formic acid in Crum Brown's graphic
notation. (1864 [1865], 232)




Edward Frankland (1825-1899) simplified and popularized Crum
Brown's notation in successive editions of his *Lecture Notes for
Chemical Students* (Russell 1971; Ritter 2001). Frankland was
also the first to introduce the term 'bond' for the
linkages between atoms (Ramberg 2003).



The next step in the development of structural theory came when James
Dewar (1842-1943) and August Hofmann (1818-1892) developed
physical models corresponding closely to Crum Brown's formulae
(Meinel 2004). Dewar's molecules were built from carbon atoms
represented by black discs placed at the centre of pairs of copper
bands. In Hofmann's models, atoms were colored billiard balls (black
for carbon, white for hydrogen, red for oxygen etc.) linked by bonds.
Even though they were realized by concrete three-dimensional
structures of croquet balls and connecting arms, the
three-dimensionality of these models was artificial. The medium itself
forced the representations of atoms to be spread out in space. But did
this correspond to chemical reality?



Kekule, Crum Brown, and Frankland were extremely cautious when
answering this question. Kekule distinguished between the
apparent atomic arrangement which could be deduced from chemical
properties, which he called "chemical structure," and the
true spatial arrangement of the atoms (Rocke 1984, 2010). Crum Brown
made a similar distinction, cautioning that in his graphical formulae
he did not "mean to indicate the physical, but merely the
chemical position of the atoms" (Crum Brown, 1864, 232).
Frankland noted that "It must carefully be borne in mind that
these graphic formulae are intended to represent neither the shape of
the molecules, nor the relative position of the constituent
atoms" (Biggs et al. 1976, 59).



One way to interpret these comments is that they reflect a kind of
anti-realism: Structural formulae are merely theoretical tools for
summarizing a compound's chemical behavior. Or perhaps they are simply
agnostic, avoiding definite commitment to a microscopic realm about
which little can be said. However, other comments suggest a realist
interpretation, but one in which structural formulae represent only
the *topological* structure of the spatial arrangement:



> 
> The lines connecting the different atoms of a compound, and which
> might with equal propriety be drawn in any other direction, provided
> they connected together the same elements, serve only to show the
> definite disposal of the bonds: thus the formula for nitric acid
> indicates that two of the three constituent atoms of oxygen are
> combined with nitrogen alone, whilst the third oxygen atom is combined
> both with nitrogen and hydrogen (Frankland, quoted in Biggs et al.
> 1976, 59; also see Hendry 2010b).
> 



The move towards a fully spatial interpretation was advanced by the
simultaneous postulation in 1874 of a tetrahedral structure for the
orientation of carbon's four bonds by Jacobus van 't Hoff
(1852-1911) and Joseph Achille Le Bel (1847-1930) to
account for optical isomerism (see Figure 4 and section 2.2). When
carbon atoms are bonded to four different constituents, they cannot be
superimposed on their mirror images, just as your left and right hands
cannot be. This gives rise to two possible configurations of
*chiral* molecules, thus providing for a distinction between
distinct substances whose physical and chemical properties are the
same except for their ability to rotate plane polarized light in
different directions. 



van 't Hoff and Le Bel provided no account of the mechanism by which
chiral molecules affect the rotation of plane polarized light
(Needham 2004). But by the end of the century, spatial structure was
being put to use in explaining the aspects of the reactivity and
stability of organic compounds with Viktor Meyer's (1848-1897)
conception of steric hindrance and Adolf von Baeyer's
(1835-1917) conception of internal molecular strain (Ramberg
2003).



![tetrahedral carbon diagram](tetrahedracarbon.png)
Figure 4. A schematic representation of the tetrahedral arrangement of
substituents around the carbon atom. Compare the positions of
substituents Y and Z.




Given that these theories were intrinsically spatial, traditional
questions about chemical combination and valency took a new direction:
What is it that holds the atoms together in a particular spatial
arrangement? The answer, of course, is the *chemical bond*.


### 4.2 The Chemical Bond



As structural theory gained widespread acceptance at the end of the
19th century, chemists began focusing their attention on
what connects the atoms together, constraining the spatial
relationships between these atoms. In other words, they began
investigating the chemical bond. Modern theoretical accounts of
chemical bonding are quantum mechanical, but even contemporary
conceptions of bonds owe a huge amount to the classical conception of
bonds developed by G.N. Lewis at the very beginning of the
20th century.


#### The Classical Chemical Bond



G.N. Lewis (1875-1946) was responsible for the first influential
theory of the chemical bond (Lewis 1923; see Kohler 1971, 1975 for
background). His theory said that chemical bonds are pairs of
electrons shared between atoms. Lewis also distinguished between what
came to be called *ionic* and *covalent* compounds,
which has proved to be remarkably resilient in modern chemistry.



Ionic compounds are composed of electrically charged ions, usually
arranged in a neutral crystal lattice. Neutrality is achieved when the
positively charged ions (cations) are of exactly the right number to
balance the negatively charged ions (anions). Crystals of common salt,
for example, comprise as many sodium cations (Na+) as there
are chlorine anions (Cl[?]). Compared to the isolated
atoms, the sodium cation has lost an electron and the chlorine anion
has gained an electron.



Covalent compounds, on the other hand, are either individual molecules
or indefinitely repeating structures. In either case, Lewis thought
that they are formed from atoms bound together by shared pairs of
electrons. Hydrogen gas is said to consist of molecules composed of
two hydrogen atoms held together by a single, covalent bond; oxygen
gas, of molecules composed of two oxygen atoms and a double bond;
methane, of molecules composed of four equivalent carbon-hydrogen
single bonds, and silicon dioxide (sand) crystals of indefinitely
repeating covalently bonded arrays of SiO2 units.



An important part of Lewis' account of molecular structure concerns
directionality of bonding. In ionic compounds, bonding is
electrostatic and therefore radially symmetrical. Hence an individual
ion bears no special relationship to any one of its neighbors. On the
other hand, in covalent or non-polar bonding, bonds have a definite
direction; they are located between atomic centers.



The nature of the covalent bond has been the subject of considerable
discussion in the recent philosophy of chemistry literature (Berson
2008; Hendry 2008; Weisberg 2008). While the chemical bond plays a
central role in chemical predictions, interventions, and explanations,
it is a difficult concept to define precisely. Fundamental
disagreements exist between classical and quantum mechanical
conceptions of the chemical bond, and even between different quantum
mechanical models. Once one moves beyond introductory textbooks to
advanced treatments, one finds many theoretical approaches to bonding,
but few if any definitions or direct characterizations of the bond
itself. While some might attribute this lack of definitional clarity
to common background knowledge shared among all chemists, we believe
this reflects uncertainty or maybe even ambivalence about the status
of the chemical bond itself.


### 4.3 The Structural Conception of Bonding and its Challenges



The new philosophical literature about the chemical bond begins with
the *structural conception of chemical bonding* (Hendry 2008).
On the structural conception, chemical bonds are sub-molecular,
material parts of molecules, which are localized between individual
atomic centers and are responsible for holding the molecule together.
This is the notion of the chemical bond that arose at the end of the
19th century, which continues to inform the practice of
synthetic and analytical chemistry. But is the structural conception
of bonding correct? Several distinct challenges have been raised in
the philosophical literature.



The first challenge comes from the incompatibility between the
ontology of quantum mechanics and the apparent ontology of the
chemical bonds. Electrons cannot be distinguished in principle
 (Identity and Individuality in Quantum Theory)
 and hence quantum mechanical descriptions of bonds cannot depend on
the identity of particular electrons. If we interpret the structural
conception of bonding in a Lewis-like fashion, where bonds are
composed of specific pairs of electrons donated by particular atoms,
we can see that this picture is incompatible with quantum mechanics. A
related objection notes that both experimental and theoretical
evidence suggest that electrons are *delocalized*,
"smeared out" over whole molecules. Quantum mechanics
tells us not to expect pairs of electrons to be localized between
bonded atoms. Furthermore, Mulliken argued that pairing was
unnecessary for covalent bond formation. Electrons in a hydrogen
molecule "are more firmly bound when they have two hydrogen
nuclei to run around than when each has only one. The fact that two
electrons become paired ... seems to be largely incidental"
(1931, p. 360). Later authors point to the stability of the
H2+ ion in support of this contention.



Defenders of the structural conception of bonding respond to these
challenges by noting that G.N. Lewis' particular structural account
isn't the only possible one. While bonds on the structural conception
must be sub-molecular and directional, they need not be electron
pairs. Responding specifically to the challenge from quantum ontology,
they argue that bonds should be individuated by the atomic centers
they link, not by the electrons. Insofar as electrons participate
physically in the bond, they do so not as individuals. All of the
electrons are associated with the whole molecule, but portions of the
electron density can be localized. To the objection from
delocalization, they argue that all the structural account requires is
that *some* part of the total electron density of the molecule
is responsible for the features associated with the bond and there
need be no assumption that it is localized directly between the atoms
as in Lewis' model (Hendry 2008, 2010b).



A second challenge to the structural conception of bonding comes from
computational chemistry, the application of quantum mechanics to make
predictions about chemical phenomena. Drawing on the work of quantum
chemist Charles Coulson (1910-1974), Weisberg (2008) has argued
that the structural conception of chemical bonding is not robust in
quantum chemistry. This argument looks to the history of quantum
mechanical models of molecular structure. In the earliest quantum
mechanical models, something very much like the structural conception
of bonding was preserved; electron density was, for the most part,
localized between atomic centers and was responsible for holding
molecules together. However, these early models made empirical
predictions about bond energies and bond lengths that were only in
qualitative accord with experiment.



Subsequent models of molecular structure yielded much better agreement
with experiment when electron density was "allowed" to
leave the area between the atoms and delocalize throughout the
molecule. As the models were further improved, bonding came to be seen
as a whole-molecule, not sub-molecular, phenomenon. Weisberg argues
that such considerations should lead us to reject the structural
conception of bonding and replace it with a molecule-wide conception.
One possibility is the *energetic* conception of bonding that
says that bonding is the energetic stabilization of molecules.
Strictly speaking, according to this view, chemical bonds do not
exist; bonding is real, bonds are not (Weisberg 2008; also see
Coulson 1952, 1960).



The challenges to the structural view of bonding have engendered
several responses in the philosophical and chemical literatures. The
first appeals to chemical practice: Chemists engaged in synthetic and
analytic activities rely on the structural conception of bonding.
There are well over 100,000,000 compounds that have been discovered or
synthesized, all of which have been formally characterized. How can
this success be explained if a central chemical concept such as the
structural conception of the bond does not pick out anything real in
nature?  Throughout his life, Linus Pauling
(1901-1994) defended this view.



Another line of objection comes from Berson (2008), who discusses the
significance of very weakly bonded molecules. For example, there are
four structural isomers of 2-methylenecyclopentane-1,3-diyl. The most
stable of the structures does not correspond to a normal bonding
interaction because of an unusually stable singlet state, a state
where the electron spins are parallel. Berson suggests that this is a
case where "the formation of a bond actually produces a
destabilized molecule." In other words, the energetic conception
breaks down because bonding and molecule-wide stabilization come
apart.



Finally, the "Atoms in Molecules" program (Bader 1991;
see Gillespie and Popelier 2001, Chs. 6 & 7 for an exposition)
suggests that we can hold on to the structural conception of the bond
understood functionally, but reject Lewis' ideas about how electrons
realize this relationship. Bader, for example, argues that we can
define 'bond paths' in terms of topological features of
the molecule-wide electron density. Such bond paths have physical
locations, and generally correspond closely to classical covalent
bonds. Moreover they partially vindicate the idea that bonding
involves an increase in electron density between atoms: a bond path is
an axis of maximal electron density (leaving a bond path in a
direction perpendicular to it involves a decrease in electron
density). There are also many technical advantages to this approach.
Molecule-wide electron density exists within the ontology of quantum
mechanics, so no quantum-mechanical model could exclude it. Further,
electron density is considerably easier to calculate than other
quantum mechanical properties, and it can be measured empirically
using X-ray diffraction techniques.



![Argon in Buckyball diagram](ArC60.png)
Figure 5. Too many bonds? 60 bond paths from each carbon atom in
C60 to a trapped Ar atom in the interior.




Unfortunately, Bader's approach does not necessarily save the day for
the structural conception of the bond. His critics point out that his
account is extremely permissive and puts bond paths in places that
seem chemically suspect. For example, his account says that when you
take the soccer-ball shaped buckminster fullerene molecule
(C60) and trap an argon atom inside it, there are 60 bonds
between the carbon atoms and the argon atom as depicted in Figure 5
(Cerpa et al. 2008). Most chemists would think this implausible
because one of the most basic principles of chemical combination is
the fact that argon almost never forms bonds (see Bader 2009 for a
response).



A generally acknowledged problem for the delocalized account is the
lack of what chemists call transferability. Central to the structural
view, as we saw, is the occurrence of functional groups common to
different substances. Alcohols, for example, are characterized by
having the hydroxyl OH group in common. This is reflected in the
strong infra red absorption at 3600cm-1 being taken
as a tell-tale sign of the OH group. But ab initio QM treatments just
see different problems posed by different numbers of electrons, and
fail to reflect that there are parts of a molecular structure, such as
an OH group, which are transferable from one molecule to another, and
which they may have in common (Woody 2000, 2012).



A further issue is the detailed understanding of the cause of chemical
bonding. For many years, the dominant view, based on the
Hellman-Feynman theorem, has been that it is essentially an
electrostatic attraction between positive nuclei and negative electron
clouds (Feynman 1939). But an alternative, originally suggested by
Hellman and developed by Rudenberg, has recently come into
prominence. This emphasizes the quantum mechanical analogue of the
kinetic energy (Needham 2014). Contemporary accounts may draw on a
number of subtle quantum mechanical features. But these details
shouldn't obscure the overriding thermodynamic principle governing
the formation of stable compounds by chemical reaction. As Atkins puts
it,



> 
> Although ... the substances involved have dropped to a lower
> energy, this is not the reason why the reaction takes place. Overall
> the energy of the Universe remains constant; ... All that has
> happened is that some initially localized energy has dispersed.
> *That is the cause of chemical change: in chemistry as in physics,
> the driving force of natural change is the chaotic, purposeless,
> undirected dispersal of energy.* (Atkins 1994, p. 112)
> 



The difficulties faced by this and every other model of bonding have
led a number of chemists and philosophers to argue for pluralism.
Quantum chemist Roald Hoffmann writes "A bond will be a bond by
some criteria and not by others ... have fun with the concept and
spare us the hype" (Hoffmann 2009, Other Internet Resources).


### 4.4 Molecular Structure and Molecular Shape



While most of the philosophical literature about molecular structure
and geometry is about bonding, there are a number of important
questions concerning the notion of molecular structure itself. The
first issue involves the correct definition of molecular structure.
Textbooks typically describe a molecule's structure as the equilibrium
position of its atoms. Water's structure is thus characterized by
104.5o angles between the hydrogen atoms and the oxygen atom. But
this is a problematic notion because molecules are not static
entities. Atoms are constantly in motion, moving in ways that we might
describe as bending, twisting, rocking, and scissoring. Bader
therefore argues that we should think of molecular structure as the
topology of bond paths, or the relationships between the atoms that
are preserved by continuous transformations (Bader 1991).



A second issue concerning molecular structure is even more
fundamental: Do molecules have the kinds of shapes and directional
features that structural formulas represent? Given the history we have
discussed so far it seems like the answer is obviously yes. Indeed, a
number of indirect experimental techniques including x-ray
crystallography, spectroscopy, and product analysis provide converging
evidence of not only the existence of shape, but specific shapes for
specific molecular species.



Despite this, quantum mechanics poses a challenge to the notion of
molecular shape. In quantum mechanical treatments of molecular
species, shape doesn't seem to arise unless it is put in by hand.
(Woolley 1978; Primas 1981; Sutcliffe & Woolley 2012).



This tension the between the familiar theories of chemical structure
and quantum- mechanical accounts of molecules might be resolved in
several ways. One might embrace eliminativism about molecular
structure: Quantum mechanics is a more fundamental theory, we might
argue, and its ontology has no place for molecular structure.
Therefore, molecular structure doesn't exist. No philosopher or
chemist that we are aware of has endorsed this option. Another
possible response makes a different appeal to the underlying physics.
Something must be breaking the wavefunction symmetries and giving
atoms locations in molecules. This might be interactions with other
molecules or interactions with measuring devices. Thus, molecular
shape is partially constituted by interaction and is a relational, not
intrinsic property (Ramsey 1997).



A related option is a kind of pragmatism. Hans Primas argues that,
strictly speaking, a quantum mechanical description of a molecule has
to be a whole-universe description. No matter how we draw the
boundaries of interest around some target molecular system, in
reality, the system is open and interacting with everything else in
the universe. Thus the shape of any particular molecule could be the
result of its interactions with anything else in the universe. We only
get the paradox of molecules having no shape when we treat systems as
closed--say a single methane molecule alone in the universe. It
is fine to treat open systems as closed for pragmatic purposes, but we
should always understand that this is an idealization. We shouldn't
treat our idealizations, such as open systems being closed, as
veridical. Hence there is no incompatibility between quantum mechanics
and molecular shape (Primas 1981).



So despite the ubiquity of structural representations of molecules, it
turns out that even the notion of molecular shape is not ambiguous.
Primas' approach, which points to the idealization in many quantum
mechanical models, is accepted by many chemists. But there is nothing
like a consensus in the philosophical literature about how to
understand molecular shape.


### 4.5 Microessentialism: Is Water H2O?



In the final part of this section about structure, we consider a
favorite example of philosophers: the thesis that "Water is
H2O." This thesis is often taken to be
uncontroversially true and is used as evidence for semantic
externalism and for essentialism about natural kinds (Kripke 1980;
Putnam 1975, 1990). Since general theses about the theory of reference
and semantic externalism are beyond the scope of this article, we
focus narrowly on chemical essentialism. Is having a common essential
microstructure sufficient to individuate chemical kinds and explain
their general features? And if so, is "being
H2O" sufficient to individuate water?



The essentialist thesis is often stylized by writing "water =
H2O" or "(all and only) water is
H2O". Ignoring the issue of whether the identity
makes sense (Needham 2000) and of understanding what the predicates
apply to in the second formulation (Needham 2010a), it is not clear
that either formulation expresses the kind of thesis that
essentialists intend. "H2O" is not a
description of any microstructure. Rather,
"H2O" is a compositional formula, describing
the combining proportions of hydrogen and oxygen to make water.



A reasonable paraphrase of the standard formulation would be
"Water is a collection of H2O molecules."
However, although the expression "H2O molecule"
describes a particular microentity, it by no means exhausts the kinds
of microparticles in water, and says nothing of the
micro*structure* by which they are related in water. Describing
the microstructure of water completely involves elaborating the
details of this interconnected structure, as well as detailing how
they depend on temperature and pressure, and how they change over time
(Finney 2004).



Like many other substances, water cannot simply be described as a
collection of individual molecules. Here are just a few examples of
the complexities of its microstructure: water self-ionizes, which
means that hydrogen and hydroxide ions co-exist with H2O
molecules in liquid water, continually recombining to form
H2O molecules. At the same time, the H2O
molecules associate into larger polymeric species. Mentioning these
complexities isn't just pedantic because they are often what give rise
to the most striking characteristics of substances. For example, the
electrical conductivity of water is due to a mechanism in which a
positive charge (hydrogen ion) attaches at one point of a polymeric
cluster, inducing a co-ordinated transfer of charge across the
cluster, releasing a hydrogen ion at some distant point. The effect is
that charge is transferred from one point to another without a
transfer of matter to carry it. The hydrogen bonding underlying the
formation of clusters is also at the root of many other distinctive
properties of water including its high melting and boiling points and
its increase in density upon melting. As van Brakel has argued (1986,
2000), water is practically the poster child for such
"non-molecular" substances.



Maybe water isn't simply a collection of H2O molecules, but
it certainly has a microstructure and perhaps the essentialist thesis
could be recast along the lines of "Water is whatever has its
microstructure," writing in the information that would save this
from tautology. But this thesis still endorses the idea that
"water" is a predicate characterized by what Putnam calls
stereotypical features. This neglects the importance of macroscopic,
yet scientifically important, properties such as boiling points,
specific heats, latent heats, and so on, from which much of the
microstructure is actually inferred. Indeed, many of the criteria that
chemists use to determine the sameness and purity of substances are
macroscopic, not microscopic. In fact, international standards for
determining the purity of substances like water depend on the careful
determination of macroscopic properties such as the triple-point, the
temperature and pressure where liquid, gaseous, and solid phases exist
simultaneously (Needham 2011).



So is water H2O? In the end, the answer to this question
comes down to how one interprets this sentence. Many chemists would be
surprised to find out that water wasn't H2O, but perhaps
this is because they read "H2O" as a shorthand
(Weisberg 2005) or as a compositional formula in the manner we
discussed in the opening of this section. Water is actually
characterized by making reference to both its microstructural and
macroscopic features, so this can't on its own provide a justification
for microessentialism.



For these reasons, microessentialist claims would need to be grounded
in chemical classification and explanation: the systems of
nomenclature developed by IUPAC are based entirely on microstructure,
as are theoretical explanations of the chemical and spectroscopic
behaviour of substances (see Hendry 2016). On the other hand,
H2O content fails to track usage of the term
"water" by ordinary-language speakers, who seem to have
different interests to chemists (Malt 1994). Pluralism is one
response to these tensions: Hasok Chang (2012) urges that even within
science, water's identity with H2O should be left open;
Julia Bursten (2014) tries to reconcile the special role of
microstructure in chemistry with the failure of microessentialism; and
Joyce Havstad (2018) argues that chemists' use of substance concepts
is just as messy and disunified as biologists' use of various species
concepts.


## 5. Mechanism and Synthesis



Our discussion so far has focused on "static" chemistry:
accounts of the nature of matter and its structure. But much of
chemistry involves the transformation of matter from one form to
another. This section describes the philosophical issues surrounding
the synthesis of one substance from another, as well as chemical
mechanisms, the explanatory framework chemists use to describe these
transformations.


### 5.1 Mechanistic Explanations in Chemistry



There has been a profusion of discussion in the literatures of
philosophy of biology and philosophy of neuroscience about the notion
of mechanisms and mechanistic explanations (e.g., Machamer, Darden,
& Craver 2000). Yet the production of mechanisms as explanatory
schemes finds its original home in chemistry, especially organic
chemistry. Chemical mechanisms are used to classify reactions into
types, to explain chemical behavior, and to make predictions about
novel reactions or reactions taking place in novel circumstances
(Weininger 2014).



Goodwin (2012) identifies two notions of chemical mechanism at play in
chemistry. The first or *thick* notion of mechanism is like a
motion picture of a chemical reaction. Such a mechanism traces out the
positions of all of the electrons and atomic cores of some set of
molecules during the course of a reaction, and correlates these
positions to the potential energy or free energy of the system. One
might think of this as an ideal reaction mechanism, as it would
contain all information about the time course of a chemical
reaction.



In contrast, the *thin* notion of a reaction mechanism focuses
on a discrete set of steps. In each step, a set of reactive
intermediates are generated. These intermediates are quasi-stable
molecular species that will ultimately yield the products of the
reaction. For example, the much studied biomolecular nucleophilic
substitution (SN2) reaction is said to have a single
reactive intermediate with the incoming nucleophile and outgoing
leaving group both partially bonded to the reactive carbon center (see
Figure 6). Such a description of the reaction mechanism is not only
abstract in that it leaves out much detail, but it is also highly
idealized. Reactions do not take actually place as a series of
discrete steps, each of which generates a quasi-stable reaction
intermediate.



![Broman SN2 reaction](BromoethaneSN2reaction.png)
Figure 6. Thin reaction mechanism for the SN2 reaction.




While most textbook treatments of reaction mechanisms begin by
mentioning the thick notion, the details nearly always turn to thin
notions of mechanism. At the same time, formal theoretical treatments
of reaction mechanisms deal exclusively with the thick notion. Such
treatments often attempt to calculate the potential energy function
for the reaction from quantum mechanics. Given the importance of the
thick notion to formal chemical theorizing, why does the thin notion
dominate the practice of chemistry and find expression in textbooks
and research articles?



Part of the reason that thin reaction mechanisms are widely used is
that determining thick reaction mechanisms is essentially impossible
experimentally, and extremely difficult theoretically. But this cannot
be the whole story because when necessary, chemists have been able to
produce relevant portions of the thick mechanism.



Alternatively, Goodwin (2012, p. 311) has argued that, given the
explanatory and predictive goals of chemists, not all of the thick
mechanism is needed. In fact, only a characterization of specific
structures, the transition state and stable reactive intermediates,
are necessary to produce chemical explanations and predictions.
Constructing mechanisms as a discrete series of steps between stable
and reactive structures allows the chemist:



> 
> ... to identify or specify which of those standard changes is
> acting as a "bottleneck" (or in chemical parlance, the
> "rate determining step") for the progression of the
> reaction ... make it obvious where alternatives paths are and are
> not available ... [and] to infer something about the structures
> of the important intermediates in the particular reaction whose
> mechanism is being proposed (Goodwin 2012, p. 314).
> 



So chemists' explanatory goals require that specific features of
reaction mechanisms can be identified. The rest of the thick mechanism
wouldn't necessarily add any explanatorily relevant detail to the
explanation.


### 5.2 Confirmation of Reaction Mechanisms



Chemists typically do not engage in philosophical discussions about
their work. Yet, when discussing the confirmation of reaction
mechanisms, it is not uncommon to see mention of philosophical issues
surrounding confirmation. So why does the study of reaction mechanisms
make chemists more philosophically reflective?



For one thing, almost all studies aimed at elucidating reaction
mechanisms rely on indirect techniques. Ideally, elucidating a
reaction mechanism would be like doing experiments in biomechanics.
Slow motion video could give direct information about the movement of
parts and how these movements give rise to the motion of the whole.
But we have nothing like a video camera for chemical reactions.
Instead, after an experimental determination of the reaction products
and possible isolation of stable intermediate species, chemists rely
on measurements of reaction rates in differing conditions,
spectroscopy, and isotopic labeling, among other techniques. These
techniques help eliminate candidate reaction mechanisms, but do not
themselves directly suggest new ones. This emphasis on eliminating
possibilities has led some chemists to endorse a Popperian,
falsificationist analysis of reaction mechanism elucidation (e.g.,
Carpenter 1984).



Although some chemists have been attracted to a falsificationist
analysis, a better analysis of reaction mechanism elucidation is the
account of confirmation known as *eliminative induction.* This
account shares falsification's emphasis on trying to reject
hypotheses, but argues that the hypotheses not rejected receive some
degree of confirmation. So in the case of reaction mechanisms, we
might see eliminative induction as a processes whereby chemists:


1. Enumerate reasonable candidates for the reaction mechanism.
2. Consider the experimental consequences of these mechanisms,
drawing up lists of reaction conditions under which the mechanism
could be tested.
3. Devise experiments which differentially evaluate at least two
hypotheses for a given set of background conditions.
4. Perform these experiments, rejecting reaction mechanisms
hypotheses that are shown to be inconsistent with the experimental
results.



In following this procedure, chemists do more than simply falsify:
they add confirmatory power to the mechanisms that haven't been
eliminated. Indeed, in discussing similar issues, biochemist John
Platt (1964) argued that good scientific inference is *strong
inference*, whereby the goal in an experiment is to eliminate one
or more hypotheses. Several contemporary philosophers have endorsed
the role of eliminative induction in science (e.g., Bird 2010, Dorling
1995, Kitcher 1993, Norton 1995). It is easy to see how it can be
modeled in Bayesian and other quantitative frameworks for
confirmation. Specifically, as particular candidate reaction
mechanisms are eliminated, the probability that one of the remaining
mechanisms is correct goes up (see Earman 1992 for details).



One difficulty with eliminative induction is the source of the
relevant alternative hypotheses, in this case reaction mechanisms.
There is no algorithmic procedure for generating these mechanisms, and
there is always the possibility that the correct mechanism has not
been considered at all. This is a genuine problem, and we believe that
it is the very issue that motivates chemists to turn towards
falsification when thinking about mechanisms; all they can do is
evaluate the plausible mechanisms that they have thought of. However,
we see eliminative induction as a more plausible reflection of the
epistemic situation of mechanistic chemists. This problem is not
uncertainty about mechanisms compatible with
experiments--chemists have evidence that weighs in favor of
those. Rather, the problem is with unconceived alternatives. Structure
offers one way to delineate such mechanistic possibilities: Hoffmann
(1997, Chapter 29) provides a beautiful example of explicitly
eliminative reasoning in his discussion of how H. Okabe and J. R.
McNesby used isotopic labelling to eliminate two out of three possible
mechanisms for the photolysis of ethane to ethylene. But this is an
issue in all parts of science, not just mechanistic chemistry, and
eliminative induction has always played a role in chemists' reasoning
about structure. How did van 't Hoff argue for the tetrahedral
carbon atom? He argued first that it was possible to account for the
observed number and variety of the isomers of certain organic
substances only by taking into account the arrangement of atoms in
space. He then defended a tetrahedral geometry for the carbon atom by
rejecting a square planar arrangement: if carbon's geometry were
square planar, there would be more isomers of substituted methane than
are observed. Thus, for instance, disubstituted methane (of the form
CH2X2) should have two separable isomers if it
is square planar, whereas only one can be found. Assuming a
tetrahedral arrangement, in contrast, would be in accord with the
observed number of isomers (Brock 1992).


### 5.3 Logics of Discovery in Chemistry



In his classic discussion, Hans Reichenbach distinguished between the
*context of discovery* and the *context of
justification*. His distinction was intended to highlight the fact
that we could have a logical analysis of scientific justification in
the form of confirmation theory, but there could never be a logical
procedure for generating hypotheses. Hypothesis generation is the
creative part of science, while confirmation is the logical part. This
distinction has been challenged in recent years by those that see the
path of discovery contributing to justification. But chemistry
provides a more interesting challenge to Reichenbach: It apparently
gives us logics of discovery.



There are two subfields in which chemists sometimes speak of logics or
procedures for discovery. The first is synthetic chemistry. E.J. Corey
(Corey & Cheng 1989) has proposed that the synthesis of organic
molecules can be rationally planned according to the logic of
*retrosynthetic analysis*. Systematizing a long tradition in
synthetic organic chemistry, Corey shows how one can reason backwards
from a target molecule by finding a series of
"disconnections," bonds which one knows how to make. The
resulting tree of disconnections gives potential pathways for
synthesis that can then be evaluated by plausibility, or simply tried
out in the laboratory.



Another area where chemists have developed a logic for discovery is in
the area of drug design. Murray Goodman (Goodman & Ro 1995), for
example, proposed a four-step procedure for developing candidate
molecules for new medication. Say that you were interested in making a
drug that would more effectively target one of the morphine receptors
in the brain. You start by making a molecular analogue of morphine,
perhaps with a more constrained structure. After successful synthesis,
you study the molecule's three-dimensional structure by spectroscopy
and computer simulation. You then test your molecule in a biological
assay to see if you have successfully targeted the receptor and to
what extent. Then based on the information you get, you modify the
structure, hopefully improving in each iteration.



These examples from chemistry put pressure on Reichenbach's claim that
there cannot be a logic of discovery. Moreover, they illustrate how,
when a science is concerned with creating new things, procedures for
discovery may become essential.


## 6. Chemical Reduction



One of the perennial topics in philosophy of science concerns
inter-theoretic relations. In the course of debating whether biology
is reducible to the physical sciences or whether psychology is
reducible to biology, many philosophers assume that chemistry has
already been reduced to physics. In the past, this assumption was so
pervasive that it was common to read about
"physico/chemical" laws and explanations, as if the
reduction of chemistry to physics was complete. Although most
philosophers of chemistry would accept that there is no conflict
between the sciences of chemistry and physics (Needham 2010b), many
would reject a stronger unity thesis. Most believe that chemistry has
not been reduced to physics nor is it likely to be (see Le Poidevin
2005, for the opposite view, and Hendry & Needham 2007, for a
rejoinder).



When thinking about the question of reducibility in chemistry, it is
useful to break this question into two parts: The first, and more
familiar one to philosophers, concerns the relationship between
elements, atoms, molecules, and the fundamental particles of physics.
We might ask, "Are atomic and molecular species reducible to
systems of fundamental particles interacting according to quantum
mechanics?" A second, less familiar question concerns the
relationship between the macroscopic and microscopic descriptions of
chemical substances. "Are chemical substances reducible to
molecular species?" Here, the main question is whether all
chemical properties that have been defined macroscopically can be
redefined in terms of the properties of atoms, molecules, and their
interactions.


### 6.1 Reduction of Molecular Species to Quantum Mechanics



Bogaard (1978), Scerri (1991, 1994) and Hendry (1998) have all
questioned the possibility of fully reducing chemical theories about
atoms and molecules to quantum mechanics. Bogaard argues that many key
chemical concepts such as valence and bonding do not find a natural
home in quantum mechanics. In a similar spirit, Scerri points out that
the quantum mechanical calculations of atomic spectra standardly
presented in chemistry textbooks make highly idealized assumptions
about the structure of many-electron systems. These approximations are
well-motivated on pragmatic grounds. However, they do not allow
quantum mechanics to "approximately reduce" chemical
facts, because the errors introduced by these approximations cannot be
estimated (Scerri 1991, 1994). Further, one of the most important
chemical trends, the length of periods in the Periodic Table, cannot
be derived from quantum mechanics, unless experimentally derived
chemical information is specifically introduced (Scerri 1997).
Drawing on the work of Woolley (1978) and Primas (1981), Hendry (1998)
argues that there are principled difficulties in accommodating
molecular shape within quantum mechanics: the Born-Oppenheimer
approximation effectively adds structure by hand. Although quantum
chemistry can be extremely illuminating, these authors argue that it
has not reduced chemistry to physics.



If one thinks that reduction means deriving the phenomenon of the
higher level exclusively from the lower level, then these arguments
should settle the question of reduction. More than 80 years after the
discovery of quantum mechanics, chemistry has not been reduced to it.
But there are two possible reductionist responses to this
argument.



First, reductionists can argue that there are no principled reasons
that chemical phenomena have not been derived from quantum mechanics.
The problem is a lack of computational power and appropriate
approximation schemes, not anything fundamental. Schwarz (2007) has
made this argument against Scerri, claiming that the electronic
structure of atoms, and hence the Periodic Table, is in principle
derivable from quantum mechanics. He believes that quantum chemistry's
inability to reduce chemical properties is simply a manifestation of
the problems shared by all of the computationally complex sciences.
Debate then turns to the plausibility of such "reducibility in
principle" claims.



There are also arguments that focus, at least implicitly, on
chemistry's ontology. A well-known strand of contemporary metaphysics
defends *physicalism*, the doctrine that everything in the
universe is physical (see the entry on
 physicalism).
 According to the physicalist, chemistry is "nothing but"
physics, even though chemical explanations and theories are not
derivable from physics. The physical world is simply composed of the
fundamental particles of physics. Chemical entities and their
properties have no independent reality.



The status of arguments for physicalism and the supervenience of
everything on the physical are contentious within metaphysics proper,
but beyond the scope of this entry. Yet we think that the failure of
chemical theory to be fully derivable from physics raises interesting
questions about the doctrine of physicalism. Minimally, it points to
longstanding worries that the domain of the physical is not
well-defined. If chemical entities such as molecules and ions end up
being part of the physical ontology, one might argue that this was not
a case of the reduction of chemistry to physics at all but simply the
expansion of the ontology of physics to encompass the ontology of
chemistry.



Independent studies of the ontology of chemistry on the basis of
mereology have been undertaken by several authors (Earley 2005,
Harre and Llored 2011, Needham 2010a). In disputing Scerri's
(2000, 2001) argument against claims (Zuo et al. 1999) that orbitals
have been observed, Mulder (2010) appeals to a general ontological
distinction between entities, which can appropriately be said to
exist, and states which don't exist independently but are features of
entities that exist. Ostrovsky (2005) and Schwarz (2006) take issue
with the role of approximations in Scerri's argument.



More controversially, some philosophers of chemistry have argued that
chemical properties may constrain the behavior of physical systems,
something akin to what philosophers of mind call strong emergence, or
downwards causation (Kim 1999). While acknowledging the central role
of quantum mechanics in understanding structure, Hendry argues that in
some cases, molecular structure is an unexplained explainer. The issue
arises when we consider the quantum-mechanical description of
structural isomers, molecules with the same atoms, but with different
molecular structures. For example, dimethyl ether and ethanol share a
Hamiltonian, the quantum mechanical description of their physical
states. Nevertheless, they are very different molecules. Ethanol is
extremely soluble in water, whereas dimethyl ether is only partially
soluble in water. Ethanol boils at 78.4degC, while dimethyl ether
boils at 34.6degC. Drinking ethanol leads to intoxication, while
dimethyl ether is toxic in quite different ways. Quantum mechanics can
show how each of these structures is energetically stable, and
illuminate how they interact with other molecules and radiation to
explain the chemical and spectroscopic behaviour of ethanol and
dimethyl ether, but the different structures are introduced as
unexplained initial conditions. While he acknowledges that these facts
are not incompatible with the claim that structure is reducible,
Hendry argues that strong emergence is just as plausible an
interpretation as reduction of the explanatory relationship between
chemistry and quantum mechanics (2006b, 2010a).


### 6.2 Reduction of Substances to Molecular Species



So far we have considered intertheoretic relationships between
chemistry and physics. What about within chemistry itself? Do the
macroscopic and microscopic theories of chemistry align perfectly? Are
all macroscopic properties of substances ultimately reducible to
microscopic properties? In other words, if we have a macroscopic
description of matter and a thermodynamic theory about how it behaves,
can all of this be reduced to a molecular description? The answer has
seemed to be "yes" to many philosophers and chemists, but
philosophers of chemistry have urged caution here.



Consider first the relatively simple case of gas temperature, which
has often been supposed reducible to the average kinetic energy of the
gas's molecules (cf. Nagel 1961, p. 343). A particular average
kinetic energy of the molecules is only a necessary condition for
having a given temperature, however. Only gases at equilibrium have a
definite temperature, when all the spatial parts have the same
temperature as the whole (reflecting the fact that temperature is an
intensive property). A sufficient condition would need to complement
the average kinetic energy with a microscopic correlate of the
macroscopic condition of being at thermodynamic equilibrium.
Statistical mechanics specifies the relevant correlative condition as
that of the energy being distributed over the gas molecules in
accordance with the Boltzmann distribution. But the Boltzmann
distribution is expressed as a function of the temperature, and its
derivation from Boltzmann's microscopic construal of entropy appeals
to the thermodynamic law connecting entropy with temperature.
Accordingly, the necessary and sufficient microscopic condition for
gas temperature becomes circular when construed as a reduction of the
concept of temperature (Needham 2009b; Bishop 2010)



Although the reduction of temperature to microscopic properties is
problematic, it is a relatively easy candidate for reduction.
Properties concerned with chemical changes such as phase transitions,
solubility, and reactivity, are considerably more complex. As we
discussed in Section 4.5, a purely microscopic description of matter
is not coextensive with all chemical properties. Solubility, for
example, is not fully explained by microscopic properties. While we
can explain in rough qualitative fashion that substances dissolve when
their ions or molecules have more affinity for the solvent than they
do for each other, this doesn't recover the subtle, quantitative
features of solubility. It also leaves the solubility of nonionic
substances untouched. Predicting these features requires appeals to
thermodynamics, and the alleged reduction of thermodynamics to
statistical mechanics is considered highly contentious (Sklar
1993).



As we have seen in this case, even very fruitful applications of
physical and chemical theory at the microscopic level are often
insufficient to reduce chemically important properties. Whether the
general notion of chemical substance, or the property of being a
particular substance for each of the millions of known substances, can
be reduced to microstructure needs to be demonstrated and not merely
assumed. While there is no in-principle argument that reductions will
always be impossible, essential reference is made back to some
macroscopically observable chemical property in every formal attempt
of reduction that we are aware of. In the absence of definite
arguments to the contrary, it seems reasonable to suppose that
chemistry employs both macroscopic and microscopic concepts in
detailed theories which it strives to integrate into a unified view.
Although plenty of chemistry is conducted at the microscopic level
alone, macroscopic chemical properties continue to play important
experimental and theoretical roles throughout chemistry.



In the background of all of these debates about chemical reduction are
issues concerning the criteria for successful reduction. All of the
literature that we have discussed make explicit or implicit reference
to Nagel's influential account of reduction. Beyond the philosophy of
chemistry literature, this account has also been presupposed by
critics of particular reductionist theses (e.g. Davidson 1970), even
when making points about the inapplicability of Nagel's account to
particular sciences (Kitcher 1984). But Nagel's account of reduction
is thought by many to be unrealistic and inapplicable to actual
science because of the logical requirements it assumes.



Perhaps part of the anti-reductionist consensus in the philosophy of
chemistry literature is driven by the stringent demands of Nagel's
account. But even if Nagel's account is weakened to allow
approximative arguments (as Hempel modified his DN model of
explanation), as some advocates of reductionism have urged (e.g.,
Schaffner 1967; Churchland 1985), this still doesn't circumvent the
problem of the appeal to macroscopic properties in the explanation of
microscopic properties. Current chemical theory makes essential
reference to both microscopic and macroscopic chemical concepts with
both chemical and quantum mechanical origins. We know of no convincing
substantial examples where either of these aspects have been entirely
excised.


## 7. Modeling and Chemical Explanation



Almost all contemporary chemical theorizing involves modeling, the
indirect description and analysis of real chemical phenomena by way of
models. From the 19th century onwards, chemistry was
commonly taught and studied with physical models of molecular
structure. Beginning in the 20th century, mathematical
models based on classical and quantum mechanics were successfully
applied to chemical systems. This section discusses some of the
philosophical questions that arise when we consider modeling in
chemistry more directly.


### 7.1 Physical Modeling



Chemistry's modeling tradition began with physical models of atoms and
molecules. In contemporary chemical education, much emphasis is placed
on the construction and manipulation of such models. Students in
organic chemistry classes are often required to purchase plastic
molecular modeling kits, and it is not uncommon to see complex
molecular structures built from such kits in professional laboratory
settings.



The use of molecular models gained special prominence in the middle of
the 19th, helping chemists to understand the significance
of molecular shape (Brock 2000). While such structures could be
represented on paper, physical models gave an immediacy and an ease of
visualization that sketches alone did not provide. In the middle of
the twentieth century, the discovery of the double helical structure
of DNA was aided by the manipulation of physical models (Watson
1968).


### 7.2. Mathematical Modeling



While physical modeling has been important historically, and is still
a central part of chemical education and some investigations in
stereochemistry, contemporary chemical models are almost always
mathematical. Families of partially overlapping, partially
incompatible models such as the *valence bond, molecular
orbital*, and *semi-empirical* models are used to explain
and predict molecular structure and reactivity. *Molecular
mechanical* models are used to explain some aspects of reaction
kinetics and transport processes. And *lattice* models are used
to explain thermodynamic properties such as phase. These and other
mathematical models are ubiquitous in chemistry textbooks and
articles, and chemists see them as central to chemical theory.



Chemists are very permissive about which kinds of mathematical
structures can serve as models. But while just about any kind of
mathematical structure can serve as a chemical model, different types
of systems lend themselves to particular kinds of mathematical
structures used in modeling. For example, the most common kinds of
mathematical structures employed in quantum chemistry are state
spaces, which typically correlate sub-molecular particle distances
with the total energy of chemical systems. Other parts of chemical
modeling are dynamic, hence they employ trajectory spaces, which can
represent the course of a reaction over time. Still other kinds of
mathematical structures such as graphs and groups can be employed to
model molecular structure and symmetry.



The purpose of many exercises in chemical modeling is to learn about
real systems. In these cases, the model must bear certain
relationships to real-world systems. But these relationships needn't
always be of extremely high fidelity. For example, Linus Pauling
(1939) and early proponents of the simple valence bond model believed
that this model captured the essential physical interactions that give
rise to chemical bonding. This method is closely related to Lewis'
conception of bonding, treating molecules as composed of atomic cores
(nuclei together with inner-shell electrons) and valence electrons
which give rise to localized bonds. It stands in contrast to the
molecular orbital method, which doesn't localize the bonding electrons
to any particular part of the molecule. Modern quantum chemists think
of the valence bond model as a template for building models of greater
complexity. Thus if a modern quantum chemist deploys the simple
valence bond model to study a real molecule, she does so with a much
lower standard of fidelity than Pauling would have. Her use of the
model is only intended to give a first approximation to the most
important features of the system.


### 7.3. Modeling and Explanation



Much of contemporary theoretical research in chemistry involves the
application of quantum mechanics to chemistry. While exact solutions
to the quantum mechanical descriptions of chemical phenomena have not
been achieved, advances in theoretical physics, applied mathematics,
and computation have made it possible to calculate the chemical
properties of many molecules very accurately and with few
idealizations. The approach of striving for ever more accurate
calculations with decreasing levels of idealization is endorsed by
many quantum chemists. For example, the development team of Gaussian,
one of the leading packages for doing quantum chemical calculations,
explicitly endorses this position. While they admit that there are
many considerations that enter into the choice of the degree of
approximation or "level of theory" for any calculation,
the goal is to de-idealize the models as much as possible. They argue
that quantum chemical calculations which are arbitrarily close to the
exact solutions are the "limit to which all approximate methods
strive" (Foresman & Frisch 1996).



This method of developing chemical theory relies on a systematic
refinement of theories, attempting to bring them closer to the truth.
Philosophers of science have called this process *Galilean
idealization*, because as in Galileo's work, idealizations are
introduced for reasons of tractability and are removed as soon as
possible (McMullin 1985; Weisberg 2007b). But not all chemists have
shared this focus on ever more accurate calculations. Reflecting on
why he didn't choose this path in his own career, theorist Roald
Hoffmann wrote:



> 
> I took a different turn, moving from being a calculator ... to
> being an explainer, the builder of simple molecular orbital models
> ... [and] I feel that actually there is a deeper need than before
> for [this] kind of work ... analyzing a phenomenon within its own
> discipline and seeing its relationship to other concepts of equal
> complexity (1998).
> 



Elsewhere in this article, Hoffmann admits that quantum chemistry is
enormously successful in its predictive power, and continues to give
us better approximations to the fundamental theory. Yet the attitude
expressed in this paragraph seems to be that simple, idealized models
are needed for chemical theorizing. Thus, the central philosophical
question arises: Given the availability of models that are closer to
the truth, why work with idealized ones?



One answer is given by Felix Carroll, a physical organic chemist:



> 
> Why then do not we just talk about high-level theoretical calculations
> and ignore the simple theory? We must choose the model that is
> sufficiently accurate for our computational purposes, yet still simple
> enough that we have some understanding of what the model describes.
> Otherwise, the model is a black box, and we have no understanding of
> what it does, perhaps even no idea whether the answers it produces are
> physically reasonable (Carroll 1998).
> 



Carroll does not elaborate on these issues, but this passage contains
the central message: Simple models prevent our theories from having a
"black-box" character, meaning that they will not simply
be a recipe for calculating without giving any physical insight.
Carroll claims that simple models are necessary in order to expose the
mechanisms by which chemical phenomena come about. High-level
theoretical calculations are not capable of showing us these
mechanistic relationships, even though they are based on the quantum
mechanical principles that describe the fundamental physics of the
system. Or, as Hoffmann puts the point: "[I]f understanding is
sought, simpler models, not necessarily the best in predicting all
observables in detail, will have value. Such models may highlight the
important causes and channels" (Hoffmann, Minkin, &
Carpenter 1996).



Why should it be the case that simple models have less black-box
character than others? One explanation appeals to our cognitive
limitations. We can only hold a couple of steps of an argument in our
mind at once. Modern, high-level calculations can take hours or days
to compute using fast computers. Even if every step was made explicit
by the computer, it would be impossible to hold the calculational
steps in mind and hence hard to understand the reason for the result,
even if one was convinced that the answer was correct. Paul Humphreys
has called this the *epistemic opacity* of simulations
(2004).



There is a second reason for employing simple, more highly idealized
models in chemistry, which stems from the explanatory traditions of
chemistry. In developing this point, Hoffmann argues that there are
two modes of explanation that can be directed at chemical systems:
*horizontal* and *vertical* (Hoffmann 1997). Vertical
explanations are what philosophers of science call *deductive
nomological* explanations. These explain a chemical phenomenon by
deriving its occurrence from quantum mechanics. Calculations in
quantum chemistry are often used to make predictions, but insofar as
they are taken to explain chemical phenomena, they follow this
pattern. By showing that a molecular structure is stable, the quantum
chemist is reasoning that this structure was to be expected given the
underlying physics.



In contrast with vertical mode, the horizontal mode of explanation
attempts to explain chemical phenomena with chemical concepts. For
example, all first year organic chemistry students learn about the
relative reaction rates of different substrates undergoing the
SN2 reaction. An organic chemist might ask "Why does
methyl bromide undergo the SN2 reaction faster than methyl
chloride?" One answer is that "the leaving group
Br[?] is a weaker base than Cl[?], and
all things being equal, weaker bases are better leaving groups."
This explains a chemical reaction by appealing to a chemical property,
in this case, the weakness of bases.



Hoffmann doesn't say much about the differing value of the horizontal
and vertical explanations, but one important difference is that they
give us different kinds of explanatory information. Vertical
explanations demonstrate that chemical phenomena can be derived from
quantum mechanics. They show that, given the (approximate) truth of
quantum mechanics, the phenomenon observed had to have happened.
Horizontal explanations are especially good for making
*contrastive* explanations, which allows the explanation of
trends. Consider again our example of the rate of an SN2
reaction. By appealing to the weakness of Br[?] as a
base, the chemist invokes a chemical property, shared across other
molecules. This allows her to explain methyl bromide's reactivity as
compared to methyl chloride, and also methyl fluoride, methyl iodide,
etc. Insofar as chemists want to explain trends, they make contrastive
explanations using chemical concepts.



Reflecting on the nature of chemical theorizing, the eminent chemical
theorist Charles Coulson (1910-1974) makes a similar point. He
wrote:



> 
> [T]he role of quantum chemistry is to understand these concepts and
> show what are the essential features in chemical behavior. [Chemists]
> are anxious to be told ... why the H-F bond is so strong,
> when the F-F bond is so weak. They are content to let
> spectroscopists or physical chemists make the measurements; they
> expect from the quantum mechanician that he will explain why the
> difference exists. ... So the explanation must not be that the
> computer shows that [the bonds are of different length], since this is
> not an explanation at all, but merely a confirmation of experiment
> (Coulson 1960, p. 173).
> 



Although Coulson, Carroll, and Hoffmann defend the use of simple,
idealized models to generate horizontal explanations, it is not clear
that quantum calculations can never generate contrastive explanations.
Although single vertical explanations are not contrastive, a theorist
can conduct multiple calculations and in so doing, generate the
information needed to make contrastive explanations. Many of the best
examples of quantum chemistry have this character: a series of closely
related calculations, attempting to get at chemically relevant
trends.