- Email: [email protected]
Philosophers versus chemists concerning ‘laws of nature’
0039-3681(94)00017-4
Philosophers versus Chemists Concerning ‘Laws of Nature’ Maureen Chris tie * Abstract ~ The law of definite proportions and the law of multiple proportions are two of the important laws of chemistry associated with the development of the atomic theory in the early nineteenth century. A detailed study of these laws shows that they have characters which cannot be reconciled with philosophers’ accounts of laws of nature. They are non-universal, and one of them is imprecise. Philosophers have approached an account of laws of nature by trying to fit their character to a particular model. Duhem, in particular, who introduces the law of multiple proportions as an example, misrepresents the law to make it fit his conventionalist model. The various models adopted by philosophers have differed widely, but there has been a universal failure even to recognize the possibility of diversity among laws, let alone face its reality. A more liberal and pluralistic view of just what is a law of nature is required. Contrary to standard accounts, laws of nature are a diverse group of dicta, of widely varying character. Unlike philosophers, chemists have recognized this diversity for at least a hundred years. In many ways the differences between the characters of laws are more interesting than the similarities. The analysis will show that some laws are approximations, while others are exact; and that some laws are purely formal, but not all of them. But on a more revolutionary note, it will also show that many quite respectable laws of science are non-universal, and even that there are a few that cannot be formulated as precise propositions. There is a possible escape for the philosophical accounts, in the claim that laws of character inconvenient for a particular model are not really laws. This course will be considered, and found inadvisable. The more appropriate course of action would rather seem to be a recognition of the scientists’ broader notions of scientific law, and acceptance of a wide diversity of character among laws of nature.
Two ‘Laws’ of Chemistry proportions (also known as ‘Proust’s
THE LAW
of definite
expressed: in definite
‘Any pure chemical compound is made up of its constituent and invariant proportions by mass.’
law’) may
be
elements
*School of Philosophy, La Trobe University, Bundoora, 3083, Australia. Received
17 January
Pergamon
1994; in revised form
15 March
1994.
Stud. Hist. Phil. Sci., Vol. 25, No. 4, pp. 613-629, 1994
Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0039-3681/94 $7.00+0.00 613
614
Studies in History and Philosophy
oJ’ Science
While a cook, in preparing a cake, can make an egg-rich or an egg-poor mixture by varying the recipe slightly, the chemist who reacts 1 mass of hydrogen
with 7.94 of oxygen to produce
oxygen-rich proportions. A French
or oxygen-poor chemist,
Joseph
water. Louis
water cannot
The reaction Proust,
vary the recipe to obtain
proceeds
according
was first to express
to exact
and provide
practical verification of the law of definite proportions in 1799.1 Dalton’s atomic theory in 1808 gave a very simple explanation of the law,’ but a long and famous controversy ensued between Proust and Berthollet,’ who argued that there was no essential difference between compounds and solutions which exhibited variable composition (like salt in water). Berthollet saw constant proportions as only rarely and accidentally instanced.4 Proust got the better of the debate with some careful experimental work, which showed that oxidized copper, which Berthollet claimed to exhibit variable proportions, consisted of mixtures of unreacted copper with just two oxides, each of which had definite composition. Proust’s argument was that the sort of combination involved in forming a chemical compound was a stronger and more intimate union than that involved in a solution. Solutions typically showed physical and chemical properties not very different from those of the separate constituents, along with variable composition. With compounds a completely new set of properties was usually obtained, and the constituents reacted in definite proportions. Constituents of solutions can usually be recovered by evaporation, distillation or fractional crystallization; compounds are not so easily separated. When confronted with a series of awkward cases, including glasses and alloys ~ systems that clearly showed variable proportions, but were compound-like in the difficulty of separating their constituents ~ Proust simply pleaded that the current state of knowledge was inadequate for a good description of these systems, and reasserted that there was a difference in kind between the types of combination exhibited in solutions and compounds.5 As chemistry developed through the nineteenth century, the law of definite proportions continued to be seen as central, at least in the fact that textbooks paid homage to it. It is still usually mentioned in present day textbooks, but ‘J. L. Proust, in Ann&s de Chimie 32 (1799), 26-54, as translated and reprinted in part in H. M. Leicester and H. S. Klickstein, A Source Book irr Chemistry 1400-1900 (Cambridge, Mass.: Harvard University Press, 1952), pp. 202-204. ‘L. K. Nash, The Atomic-Moleculur Theory (Cambridge. Mass.: Harvard University Press, 1950), p. 35. 3For a detailed discussion of the Proust -Berthollet controversy, see: Nash, ibid., pp. 33~.35; K. Fujii, ‘The Berthollet-Proust Controversy and Dalton’s Chemical Atomic Theory 1800-1820’; British Journalfbr the History of Science 19 (1986), 177-200. “J. R. Partington, A Short History of Chemistry. 3rd edn (London: Macmillan, 1957), p. 153; Nash, op. cit., note 2, p. 33. . ” ‘3. L. Proust, Journal de Physique 63 (I 806), p. 369, as reprinted in Leicester and Klickstein (eds), op. cit., note 1, p. 204.
615
Philosophers versus Chemists concerning ‘Laws of Nature’ many
chemical
borderline
systems
were
discovered
region between compounds
in that their constituents
were strongly
which
and solutions. joined
could
only
be placed
in a
They were compound-like
together
by chemical
bonds,
but
solution-like in that their proportions could be varied over a small range. The sort of systems that are involved in these cases are known as ‘network solids’. The atoms are chemically bonded, not in discrete clusters as molecules, but each to several neighbours in a network that extends throughout the bulk crystal or glass. Aluminium oxide is such a network solid. It forms a white powder, or a clear and very hard gemstone (corundum). A chromium atom has almost exactly the same size and bonding propensities as an aluminium atom. If between about 1% and 5% of aluminium atoms in aluminium oxide are replaced by chromium atoms (more or less at random), ruby is formed. Is ruby a compound? The aluminium and chromium atoms are chemically bonded to oxygen atoms, and via these oxygen atoms to one another. They cannot be separated without breaking very strong chemical bonds. Or is ruby a solid solution of chromium oxide and aluminium oxide? Most modern chemists would say the latter, but not without some reservation. There are many similar examples, particularly among minerals6 Other systems which produce difficulties for the law of definite proportions include synthetic polymers like nylon or polystyrene. The molecules of these substances consist of large numbers of repetitions (typically 50 to 1000) of a basic structural unit. In most cases the long chains are capped with end groups that differ slightly from those in the middle of the chain ~ the overall structure may be considered to have the form ABBBBBBBB...BBBBBBC. Now any particular sample of polymer will not have a precisely fixed number of units in the chain. A sample of nylon may have some molecules with 164 units and others with 165 units. Moreover, it is possible to produce different grades of nylon with different specifications for the average chain length. Because of the different relative proportion of end groups, these grades will have slightly different composition. They also show differences in physical properties. Nevertheless, it is convenient for chemists to regard nylon as a compound. A strict interpretation-where the only pure compounds in polymer chemistry are those where every molecule has exactly the same chain length, is operationally inappropriate, and has never been adopted. As the awkward cases were increasingly investigated through the nineteenth century, a difference arose between chemists about how to deal with them. It has never been completely resolved. One group of chemists, including Mellor in his Comprehensive Treatise on Inorganic and Theoretical Chemistry (1922), gave the law a formal status, as a 6E.g. in olivine ~ (Mg,Fe),SiO, - and amphibole - Ca,(Mg,Fe),Si,O,,(OH), ~ magnesium and iron atoms may replace one another at random. Once again these two atoms have similar size and bonding propensities.
616
primary
Studies in History and Philosophy of Science taxonomic
device.
A chemical
concoction
cannot
be classified
as a
compound by dejkition unless it has constant composition. As far as Mellor was concerned ‘we refuse to call substances compounds which do not conform with this definition’ (viz. constant composition).7 The other
group
allows
certain
strongly
bonded
concoctions
of variable
composition as compounds, and regards them as exceptions to the law of definite proportions. Linus Pauling in 1947 took this line. Immediately following his introduction of ‘the law of constant proportions’, Pauling says: ‘Recently it has become customary to accept as substances not only those materials that, when purified, show constant composition, but also those that may have a small range of variability in composition.‘8 In an earlier passage he defines ‘substance’ as ‘a homogeneous species of matter with reasonably definite chemical composition’, and digresses on precise and imprecise definitions: ‘The words that are used in describing nature, which is itself complex, may not be capable of precise definition. In giving a definition for such a word the effort is made to describe the accepted usage’!9 These chemists use the terms ‘berthollide’ for ‘compounds of variable composition’ and ‘daltonide’ for ‘compounds of fixed composition’ - a suggestion first made by Kurnakov in 1914.1° The other term frequently used is ‘non-stoichiometric compounds’ii a contradiction in terms if the law of definite proportions is regarded as unexceptioned. Despite Pauling’s ‘recently’, a similar attitude can be found in Mendeleev’s 1869 textbook, where he refers to ‘indefinite compounds’ and ‘definite compounds’.i2 Also, despite Pauling’s ‘small range of variability’, Wadsley uses formulas like ‘Na,WO, (0.93 2 x 2 0.32) and Li,WO, (0.57 2 x 2 0.31)‘.‘3 A variability of a factor of 3 in composition, as in the first case, could hardly be called small. While it could possibly be argued that Pauling sees the law as an unexceptioned approximate law, it is clear that the view of most of this school is that the law is exact and exceptioned. The difference of view as to whether the law is formal and unexceptioned, or contingent and exceptioned, appears to persist to the present. It is hardly an active controversy because it is a matter of choice and usage how the borderline cases are to be regarded, and the law is not used in an explicit sense in modern chemistry. ‘5. W. Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry (London; Longmans, 1922) vol. 1, p. 95. *L. Pauling, General Chemistry (San Francisco: Freeman, 1947) p. 150. ‘Ibid., p. 8. “‘N S Kurnakov, in Bulletin de l’dcadhmie Imp&ale des Sciences de St. PPtersbourg (1914), 321-338, as cited in H. M. Leicester, The Historical Background of Chemistry (New York: Wiley, 1965) p. 153. “A. D. Wadsley, ‘The Crystal Chemistry of Non-Stoichiometric Compounds’, Reviews of Pure and Applied Chemistry 5 (1955), 165-193. “D. I. Mendeltev, The Principles of Chemistry, trans. of the Russian 5th edn by G. Kamensky, ed. A. J. Greenaway (London: Longmans, 1891) vol. 1, p. 32. 13Wadsley, op. cit., note 11, p. 172.
617
Philosophers versus Chemists concerning ‘Laws of Nature’
The
second
law to be considered
is the closely
related
law of multiple
proportions. The law of multiple
proportions
(also
known
as ‘Dalton’s
law’) can be
expressed: ‘If two radicals A and B unite to form more than one compound, then the invariant amounts of B which unite with the same mass of A in the various
compounds
are in the ratio of simple whole numbers.‘14
For example, copper forms two oxides. A portion (100 g) of copper reacts with 12.25 g of oxygen to produce red copper oxide, or with 24.50 g of oxygen to produce black copper oxide. The uptake of oxygen in one case is just double what it is in the first. That is, the ratio 12.25:24.50 is just the ratio 1:2. Proust in an article about his work on sulfurets of iron15 casually remarked that he had been surprised to note that the uptake of sulfur in the second compound was just one and a half times that in the first. He had made similar remarks in other papers, but he did not generalize and formulate a law. The law is ascribed to Dalton, who arrived at it via a different route. Dalton suggested that if compound atoms’6 consisted of combinations of small numbers of simpler atoms, then the result embodied in the law of multiple proportions should apply to the combinations of bulk quantities of simpler substances into compounds. The suggestion was presented purely as a theoretically based speculation. Thomas Thomson17 and William Hyde Wollaston*8 presented confirmation of the law of multiple proportions in 1808. Apparently quite independently of Dalton, Wollaston had observed that whenever an acid and a base combined in more than one ratio a very simple relationship of this form (usually 2:l) applied, and suggested the generalization and investigation of the result. Wollaston’s report is the archetypal example for scientific theory arising from empirical generalization: Dr Thomson has remarked that oxalic acid unites to strontian as well as to potash in two different proportions, and that the quantity of acid combined with each of the bases in their super-oxalates, is just double of that which is saturated by the same quantity of base in their neutral compounds. As I had observed the same law to prevail in various other instances of superacid and subacid salts, I thought it not unlikely that this law might obtain generally in such compounds, and it was my design to have pursued the subject with the hope of discovering the cause to which so regular a relation might be ascribed. “‘Mendeleev, op. cit., note 12, vol. 1, p. 213. “J. L. Proust, Nicholson’s Journal, 8vo series 1 (1802) 269-273. 16Dalton did not use the term ‘molecule’ or the concept in the modern sense, but referred to ‘comnound atoms’ instead. This led to a concentual system of sub-structures, because a ‘compound _ _ atom could itself be made up of simple or compound atoms. “T. Thomson. Philosoohical Transactions of the Roval Societv, 98 (1808). . ,_ 63. 69970, 74, as in Alembic Club Reprints number 2. “W H Wollaston. Philosophical Transactions of the Royal Society 98 (1808), 96102, as in Alembic Club Reprints number 2.
618
Studies in History and Philosophy oJ’ Science
But since the publication of Mr Dalton’s theory of chemical combination, as explained and illustrated by Dr Thomson, the inquiry which I had designed appears to be superfluous. A subtle
change
crept
into
textbook
statements
of the law of multiple
proportions, roughly at the start of the twentieth century. The law, which had previously been understood as also applying to compositions in terms of compound constituents, was narrowed to a law expressed in terms of elemental compositions and binary compounds of elements only. The change is nowhere much remarked upon. The effect was to remove from the law all of its practical importance, except as an illustration of the atomic theory. The classical examples. like Wollaston’s super-acid and sub-acid salts, no longer even came within the scope of the law! This can only be seen as an adjustment to cope with a major shift in the understanding of the atomic theory. No longer was potassium oxalate (K2CZ04) seen as a compound of potash (K,O) and oxalic acid (H,C,O,), but as a compound of potassium, carbon and oxygen. The law of multiple proportions is not a precise proposition. The problem lies with the word ‘simple’ or ‘small’ which appears in its statement. Although most of the time the ratios are very simple indeed ~ 2: 1,3: 1,3:2 - there is no precise size of whole number that represents a cut-off. A chemist cannot say that 7 is a simple number and 8 is not! (By a simple whole number ratio, chemists mean a ratio that reduces to the ratio of small integers.) There are instances of multiple proportions where the numbers are not so simple, but these are always accompanied by other evidence of complexity of at least one of the compounds concerned. The origin of the notion of simple whole number ratios was Dalton’s rule of greatest simplicity. This rule was later largely discredited, because, inter alia, it led Dalton to formulate water and ammonia as HO and NH, respectively, rather than H,O and NH,. In spite of this, Nash’s evaluation is that ‘in its prediction of simple, readily perceived ratios, the rule of greatest simplicity more than justified its existence by stimulating the quest for such ratios. This quest rapidly proved to be very fruitful. ‘I9 Brock suggests that even Dalton himself used the rule as a rule of thumb, without any great belief in its fundamental significance;20 the evidence for this is that Dalton allowed the possibility that water might be ternary ~ either H,O or HO, in his discussion in the ‘New System’. The law of multiple proportions ns understood by chemists, includes ‘simple’ as an essential descriptor of the whole number ratios. The law therefore cannot be formulated as a precise proposition. It is clearly instanced, and exactly instanced, but it also has clear exceptions, and there are cases where it cannot be decided how the law applies. “Nash, op. cit., note 2, p. 38. “W. H. Brock, The Fontana History
of Chemistry
(London:
Fontana,
1992),
p. 138
Philosophers
The hydrocarbons thousands
619
versus Chemists concerning ‘Laws of Nature’
provide
of different
and hydrogen.
If a comparison
ethene (ethylene obviously instanced.
a series of examples
compounds
which contain
is made between
of the difficulty:
there are
just the two elements
carbon
ethyne (acetylene
-
C,H,)
and
C2H4), the law of definite proportions is very simply and A sample of ethene containing the same mass of carbon as
a sample of ethyne always has just exactly twice as much hydrogen as the ethyne, but if we compare pentane (C5Hi2) with ethyne, the ratio is 12:5 rather than the simpler 2:l. We could go on to compare heptane (C,H,,J with butane (C4Hio), obtaining a ratio of 35:32, or even C,,H,, with C,,H,,, which gives 429:425!21 It can be seen that although the first comparison is in the ratio of simple whole numbers, the large range of compounds provides many comparisons which can be chosen to give ratios of almost any desired complexity. Certainly the last comparison could not fairly be regarded as providing an analysis in the ratio of simple whole numbers at all. Both of these laws are of a character very different to those typically quoted as examples in philosophical discussions of scientific laws. The law of definite proportions can be seen either as an exact rule with exceptions (if the Pauling view of the law is followed) or as a purely formal taxonomic device (if the approach of the Mellor school is taken). The law of multiple proportions is not even a precise proposition.
Duhem and the Law of Multiple Proportions the law of multiple In a book written in 1906, 22 Duhem misrepresents proportions by leaving out the word ‘simple’ in ‘ratio of simple whole numbers’. He possibly does this because it is the only way to express the law as a precise proposition, but the inclusion of ‘simple’ is an essential part of the way that chemists
understand
the law. His statement
of the law is as follows:
On Hypotheses whose Statement has no Experimental Meaning . For example, chemical theory rests entirely on the ‘law of multiple proportions’; here is the exact statement of this law: Simple bodies A, B and C may by uniting in various proportions form various compounds M, M’, etc. The masses of the bodies A, B and C combining to form the compound M are to one another as the three numbers a, b and c. Then the masses of the elements A, B and C combining to form the compound M’ will be to one another as the numbers xa, yb and zc (x, y and z being three whole numbers). Is this law perhaps subject to experimental test? Chemical analysis will make us acquainted with the chemical composition of the body M’, not exactly, but with a ‘IThe simplest way to obtain the ratio is to cross-multiply the subscripts. Thus - comparing C,H,, with C,H,,, we obtain 7 x lo:16 x 4=70:64=35:32. 22P. Duhem, The Aim and Structure of Physical Theory, trans. P. P. Wiener (Princeton: Princeton University Press, 1954), pp. 212-214.
620
Studies in History and Philosophy of Science
certain approximation.... whatever the results given by the chemical analysis of the compound M’, we are always sure to find three integers x, y and z thanks to which the law of multiple proportions will be verified with a precision greater than that of experiment. Therefore, no chemical analysis, no matter how refined, will ever be able to show the law of multiple proportions wrong.
Duhem argued that since any ratio can be expressed as the ratio of whole numbers to within any desired precision, the law (as he expressed it) was a truism. Nash, in reference to Dalton’s atomic theory, points out that Dalton’s ‘rule of greatest simplicity definitely suggests that the ratios will always be simple ones, involving only small numbers.23 Wollaston and Thomson were definitely looking specifically at a series of 2:l ratios in their experiments with super-acid and sub-acid salts. Chemistry textbooks from Mendeleev in 1869 to the present have always included ‘simple’ or ‘small’ in describing the whole number ratios predicted by the law. Thus, Duhem’s treatment of the law of multiple proportions is a misrepresentation. Duhem produces the law, asserting that ‘chemical theory rests entirely’ on it. He then claims to give ‘the exact statement of this law’. The statement is interesting in that it is in its twentieth-century form of compositions in terms of elements only (it dates from 1906), and in that it is expressed for ternary compounds rather than the traditional expression in terms of binary compounds. It concludes with ‘x, y and z being three whole numbers’ (where a chemist’s expression ought to have had ‘x, y and z being three small whole numbers’). No other chemist is referenced in this section of his work; the only nearby reference is to his own earlier work (1902) on Mixture and Chemical Combination.24
Duhem’s thesis is that this law is one of several examples of hypotheses whose statement has no experimental meaning. He argues that ‘laws’ like this are purely formal, and their role is to help to provide a conceptual basis for a scientific subject. In particular, he argues, a law like this could never be falsified by experiment, even in principle. The writing of Wollaston, in particular, cries out against Duhem’s interpretation. His apprehension of the law had been based on a ‘truly remarkable regularity’ - specifically, a series of 2: 1 ratios in composition between different salts of the same acid and base. An empirical generalization was made from a series of his own experiments on different systems. From Wollaston’s point of view, Dalton’s atomic theory provided the basis for a theoretical explanation, that his experimental results demanded. Duhem is also wrong about the falsifiability of this particular law. Certainly his own version of the law is purely formal, and not falsifiable, but the law of
Z3Nash, op. cit., note 2, p. 38. Le mixte et la combination chimique: essai SW I’6volution d’une idke (Paris, 1902).
24P. Duhem,
Philosophers
multiple
621
versus Chemists concerning ‘Laws of Nature’
proportions,
other law. The modern
as understood
chemist
by chemists,
is at least as falsifiable
is aware of many cases of widely varying
as any
complexity.
If
cases can be quoted which are exceptions to the law (in that they produce ratios like 429:425 - see earlier), then what could possibly falsify it? How could a case arise that would not just be regarded as another exception? Here is a hypothetical example which shows how the law of multiple proportions, as a law with exceptions, might be falsified. Suppose that two chemical substances, A and B, combine to form two different compounds Ml and M2. Suppose that the other evidence that chemists collect to characterize a compound spectra and the like showed on the usual bases of interpretation that both Ml and M2 had molecular rather than network structures, and fairly simple molecular structures at that, then a ratio of 1.55: 1 (with 1% experimental error) would constitute a clear falsifying violation of the law (and indeed such ratios are not observed in these cases). The ratio is significantly different from 3:2, which is the only simple ratio that even comes close. Ratios of 11:7, 14:9 or 17:11, which might fall within experimental error, are inconsistent with the other evidence of structural simplicity. In this way a falsification of the law could be produced. To regard such a case as a non-falsifying exception would introduce a completely new class of exception, and undermine the utility of the law. Duhem’s more general point is that any inconsistency that is manifest is really only an inconsistency in the larger theoretical edifice used to interpret an experimental result, and that the law is not necessarily the part of the edifice that should or would be abandoned. This aspect of his argument remains intact, of course. Chemists, both early and modern, do think that the statement of the law of multiple proportions has a definite experimental meaning, even though it is not a precise proposition. Perhaps Duhem, as a philosopher, did not like dealing with imprecise propositions. It is likely that part of his programme in producing an ‘exact statement’
of the law was to tidy it up in such a way that it became
a precise proposition. It is also likely that the way he went about this tidying up was largely governed by his preconceived view of laws of nature, as a conventionalist. He then seems to have completed the circle by citing the law as an example to support and illustrate his conventionalist position! Philosophers’ Accounts: Forcing Laws to Fit a Viewpoint? Molnar encapsulates a ‘regularity theory’ to describe laws of nature from a generally Humean viewpoint,25 in terms of the following four requirements: universal quantification, truth, contingency, only non-local empirical predicates 25G. Molnar, in Philosophical Review 78 (1969), 79-89.
622
Studies in History and Philosophy of Science
(presumably meaning kinds or classes of object, rather than particular objects or places). While few, if any, philosophers (including Molnar) argue this exact position, Molnar’s criteria are often cited and used as a departure point for a different
account.26
One thing that all philosophers of science tend to do is to consider laws as a class. Specific laws are cited as examples, and often several rather diverse laws are introduced to show how they all fit into the author’s favoured pattern (as we have already seen with Duhem’s conventionalism). But there is little or no exploration of the possibility that family resemblances between different individual laws might not extend to the issues discussed by the authors. It is possible, and seems likely, that some laws are merely formal and conventional, while others have a genuinely contingent status.*’ It is possible, and seems likely, that some laws are obeyed exactly, while others are framed in terms of ideals which may only be approached and approximated, but never actually achieved by natural systems. It is possible, and seems likely, that some laws have definite exceptions, while others have some sort of claim to universality whether as ideals, conventions or accurate and contingent dicta. Mendeltev, in his 1869 Principles of Chemistry, refers to a ‘class of approximate laws’ and gives examples. ** In so doing, he is clearly taking an implicitly different stand to that of the philosophers. In saying that some specific and named scientific laws expressed approximate relationships, he made a definite implication that he saw others as expressing exact relationships. Recently, some philosophers have argued that no laws are exact, and that all represent unrealized idealizations, notably Cartwright.2’ The desire for a single model to embrace all laws persists. Contrary to Cartwright’s thesis, and parallel to MendelCev’s implication, there is an essential difference of kind between exact laws, like conservation of charge, or even Newton’s law of universal gravitation, and approximate laws, like Boyle’s law or Charles’s law. Exact laws are realized exactly within the precision of most plausible experimental measurements, and some very fine nit-picking is required to show their slight inadequacies. But for an approximate law any careful measurement might routinely be expected to be a few percent away from the predicted the law itself. 26E.g. D. M. Armstrong,
value, by virtue of the approximate
What is a LOW
of Nature? (Cambridge:
Cambridge
nature
University
of
Press,
1983) p. 12.
“The term ‘contingent’, as used in this paper, refers to the notion that a law must not be a trivial statement which arises of logical or semantic necessity. It must make a definite statement about the world. The term carries a positive connotation. Ellis, in particular, uses the term to refer to ‘something that might have been otherwise’, and gives it a negative connotation. For Ellis, a law must be a statement that indicates a connection so strong that it would apply in all legitimate possible worlds. “MendelCev, op. cit., note 12, vol. 1, p. 78. “See N. Cartwright, HOW the Lms of Physics Lie (New York: Oxford University Press, 1983).
Philosophers versus Chemists concerning ‘Laws of Nature’ Ellis, for example,
introduces
his discussion
623
of laws as idealizations,
with the
statement that ‘Physical theory seems largely to be about such things as inertial systems, black body radiators... perfect gases, and so on,‘30 and continues with the notion
that not only blatantly
most fundamental idealization, citing
idealized
systems
of this sort, but also ‘the
theories we have’, contain essentially Cartwright’s general line of argument.
a similar type of But Mendeltev’s
‘class of approximate laws’ (and the implication of at least one other class of laws) is a more appropriate representation. There is an enormous difference between the gas laws and the law of conservation of energy. The difference shows up clearly at an operational level; it should also be seen as a fundamental difference of character. When a chemist or physicist uses the ideal gas laws to deduce volumes or pressures of real gases, there is an expectation that the answer will be approximate - within 1% or so, with possibly a much larger error at high pressures or low temperatures. But when a calculation is made based on conservation of energy, the result is expected to be exact ~ so much so that such calculations are used to calibrate instruments. Ellis argues that ‘since these laws are concerned with the intrinsic natures of the elementary processes of nature, they can apply strictly only to causally isolated processes and therefore ‘apply strictly only to closed and isolated systems’.3’ But this takes only one very specific viewpoint. The law of conservation of energy is often stated in the form ‘Energy cannot be created or destroyed’s2 with minor variations and qualifications. There is no need to refer to any ‘system’, let alone a ‘closed and isolated system’.33 It is a consequence of the law of conservation of energy that if such a thing as a closed and isolated system existed, then no process could alter its total energy. It is also a consequence that no totally internal process can alter the total energy of a system, even if it is not closed and isolated. But the form in which chemists, at least, usually use the law, is in terms of the consequence that the change in total internal energy of any system is equal to the energy flux into or out of it. This is made quite clear by Brady immediately following his introduction of the law: ‘The energy bookkeeping for both heat and work is taken care of by the equation A E=q + w, where q is defined as the heat absorbed by the system from the surroundings when the system undergoes a change, and w is the work done on the system by the surroundings.‘34 3”B D Ellis ‘Idealization in Science’, in C. Dilworth (ed.) Idealization IV: Intelligibility in Science (Amsteidam: Rodopi, 1991), p. 265. “Ibid., p. 280. 32J E. Brady, General Chemistry, 5th edn (New York: Wiley, 1990), p. 455. 33The true nature of Ellis’ objection to the law of conservation of energy becomes clear if we look at the definitions of closed and isolated systems used in chemical thermodynamics: ‘a closed system is one that does not exchange matter with its surroundings, but may exchange energy’; ‘an isolated system is one that exchanges neither energy nor matter with its surroundings’. Incidentally, to refer to a closed and isolated system is a tautology - any isolated system is closed of necessity! s4Brady, op. cit., note 32, p. 456.
624
Studies in History and Philosophy of Science
It is thus exactly true, not an approximation, that energy can be neither created nor destroyed,35 and this law has consequences that can be just as usefully
interpreted
for real systems
as for unrealized
ideal systems.
On this
basis, the claim is that while the ideal gas laws clearly belong to a class of approximate laws that relate to an unrealized ideal, the law of conservation of energy (and others like it) belongs If the argument that such laws which is doubtful, the idealization character.
to a class of laws of quite different
character.
represent idealizations can be sustained, is of a different and much more subtle
Towards a Taxonomy of Laws The distinction between exact and approximate laws is only the first of a number of taxonomic distinctions between different laws of nature that may be worth making. Even among approximate laws, there is a difference in kind between Boyle’s law and the law of Dulong and Petit. Boyle’s law is explained in modern kinetic theory by deriving it for a model gas whose particles (molecules) are negligibly small, and do not have any attraction for one another. It is clearly an idealization. We can therefore have some theoretical notions of which gases, in which circumstances of pressure and temperature, will follow it more closely. The law of Dulong and Petit states that the product of the atomic weight of a solid element and its mass heat capacity relative to water is approximately 6.1 at room temperature. This law is not obviously related to any particular idealization in theory. The claim here is not that the law of Dulong and Petit is a mystery with no sound theoretical basis, it is rather that there is no theory of the ideal solid element, analogous to ideal gas theory. It is not known, for example, whether the molar heat capacity of the ideal solid element is 6.114 or 6.135! There may be a taxonomic subdivision worth making among approximate laws between those that represent idealizations and those that do not. If the Pauling view of the law of definite proportions is taken -~ compounds usually have fixed composition, but in some cases there is variability in composition - then this law is a non-universal law. A IUU~can be non-universal and still represent un expression of’a very us&l generalization, especially if there is some underlying theory which alerts the scientist to the particular types of system or situation where the exceptions may arise (and conversely guarantees that certain other types of system or situation are safe from exceptions). Gases and volatile liquids obey the law of definite proportions without exception. ‘%pecial relativity theory introduces the complication of mass-energy interconversion. This does not usually affect the systems chemists are interested in, and the difficulty can be overcome either by stipulating ‘in the absence of measurable relativistic effects’, which almost invariably applies, or by regarding mass itself as a form of potential energy. J. R. Christie, private communication.
Philosophers
Pauling constant
versus Chemists concerning ‘Laws of Nature’
also mentions
salts, molecular
625
solids and organic
compounds
as having
composition.36
In all of the debate
on ‘natural
laws’, universality
has never been challenged
in quite this way. It has been suggested that laws are approximate, or that they relate to ideal systems that are never quite realized, but the idea of a law that is frequently and exactly instanced, but has particular exceptions, has not been much discussed. Is the law of definite proportions non-contingent, as those who take the conventionalist position imply? The answer is clearly not. The contingency of the law can be demonstrated by the following device. Suppose that we wish to distinguish between solutions and compounds. It can be shown that this is, at the limit, an unsolved problem, and that indeed, there may be no natural distinction. But if the discussion is restricted to gaseous mixtures and compounds, the situation changes enormously. None of the awkward or borderline systems are gases. For gases, there are several different methods and criteria that could be used for the classification, and they all provide the same answers. Gases can therefore be chosen as a clear and easily differentiated subclass of systems which does not contain any of the awkward cases. The property of ‘having a distinctive molecular spectrum’ (B) is one that could be used as a primary method of classifying gaseous concoctions as mixtures or compounds. ‘Having a constant composition’ (C) becomes a contingent property which always occurs whenever property B does (i.e. C may occur without B, but B may not occur without C). ‘If B then C’ is a statement which is universally true, but not true of necessity. ‘Any substance with a distinctive molecular spectrum has fixed composition’ cannot be a convention! It would be possible, but rather more complicated, to define a much larger sub-class for which the law of definite proportions would be both universal and contingent. To be completely accurate, it should be said that what has been shown to be contingent is arguably not the law of definite proportions, but only a ‘sub-law’ which applies exclusively to gases, or a wider sub-law that applies only to the larger sub-class of systems for which both (i) the law of definite proportions clearly universal, and (ii) a reliable alternative means of classification available.
is is
In practice, it is probably fairest to describe the status of the law as a law that is accurate (in that it is widely and exactly instanced), and contingent (in that it does not arise of logical or taxonomic necessity), but not universal (in that there are several very specific types of exception to the rule, and/or ambiguities in the taxonomy). The evidence of recent textbooks is that many modern chemists see the law in these terms, and still consider it to have some validity.” ‘6Pauling, op. cit., note 8, p. 150. “E.g. N. N. Greenwood and A. Earnshaw, pp. 753-156.
Chemistry
ofthe Elements (Oxford:
Pergamon,
19X4),
626
Studies in History and Philosophy
of Science
The alternative Mellor view of the law of definite proportions gives this law a purely formal status. Rather than expressing any fact about nature, it effectively expresses part of our definition of what is meant by ‘compound’. Conventionalists that they represent nature
have argued that all laws of science are purely formal an attempt by humans to impose demarcations and order on
to help our understanding,
where no such demarcations
or order exist in
reality. A rejection of the conventionalist position as such may nonetheless be accompanied by a recognition that some laws of nature do have a purely formal status. The preceding argument about a large sub-class of systems for which several different taxonomic criteria for compounds would concur, does indicate, though, that the law of definite proportions is rather more than a purely formal law. The law of multiple proportions is very strange in being regarded as a law while not even being a precise proposition. I have already argued that Duhem’s attempt to give it precise meaning misrepresents the law. It cannot be seen as a convention that helps to define anything in particular. It is exactly instanced, and clearly exemplified, but it clearly cannot be described as an ‘approximate law’ or as an ‘idealization’ in the usual sense of these terms. There is one other law of chemistry which must be seen as very similar in regard of not being a precise statement: Mendeleev’s formulation of the periodic law ‘the properties of the elements, as well as the forms and properties of their compounds, are in periodic dependence or, expressing ourselves algebraically, form a periodic function of the atomic weights of the elements.‘3x Mendeleev goes on to discuss the fact that the independent variable is a discrete variable, and has no meaning except at the particular atomic weights that correspond to particular elements. More importantly, these discrete values are at irregular intervals. Moreover, as he also points out, many of the most
important
chemical
properties,
as dependent
variables,
are also
discrete. The valencies exhibited by an element in its compounds are integers, for example. These factors qualify the usual meaning of a periodic function. It is apparent from Mendeleev’s discussion that he was not using the concept of a periodic function with its strict algebraic meaning. As a result, the statement of this law is vague in the extreme. While the ‘periodic law’ is little used and seldom quoted in modern chemistry, the periodic table, which arises from it, still plays a central and crucial role. It is possible that both Mendeleev and Newlands, who also used the concept of periodic law, were concentrating on ‘periodic law’ rather than ‘periodic table’, because the notion of ‘law’ fitted in with their desire to see chemistry as a fundamental science, while ‘table’ pointed rather to a descriptive and 38MendelCev, op. cit., note 12, vol. 2, p. 16.
Philosophers
versus Chemists concerning ‘Laws
taxonomic
science -
the very realm
ofNature’
621
from which they were trying
chemistry.39 These are only a few of the examples
that could be chosen
to remove
to illustrate
the
great diversity of character of scientific laws. It is clear that the laws of definite and multiple proportions have characters very different from one another, and from the more acceptable laws typically chosen as examples of scientific laws. It is also clear that they are not alone in these peculiarities, and that there are several quite different classes of scientific law. We have mentioned the law of Dulong and Petit as a law that is not only an approximate law, but also has clear exceptions, and the periodic law as another example of a law embodied in an imprecise proposition. Hooke’s law says that the fractional extension produced in an elastic material is proportional to the applied stress (force per unit area). It applies only to certain materials, and then only at stress values below the ‘elastic limit’. As a law, then, it can be seen as a non-universal contingent law, or it could be seen as a convention which defines one use of the term ‘elastic’. A similar view should be taken of Ohm’s law - that the current flowing through a resistive element in an electrical circuit is proportional to the drop in electrical potential across the element. Again this does not apply to all materials, nor to extremely high voltages. Once again, the law could be seen as a non-universal generalization with clear exceptions, or it could be seen as a convention which defines the use of the term ‘Ohmic resistor’. We can be fairly confident that further research would show that many of the most useful laws of science have characters which are not quite respectable in a variety of similar ways. Is a Statement in Science Known as ‘X’s Law’, a Law of Science? A possible response to much of what has been said in this paper is that these various ‘laws’ are not really scientific laws. One prong of the attack might be that these laws are outdated by new understandings in the area of science. The other would be that they do not have the character or fulfil the criteria to fit in with whichever
of the various
notions
of a scientific
law is being advanced.
Just
because something is called ‘Jones’s law’ by scientists, the argument would go, that does not make it a scientific law in the stricter sense that a philosophical account would require. The argument would be applied with particular vigour to notions like the law of multiple proportions and the periodic law, which cannot even be formulated as precise propositions. The statements of these, and many of the other so-called laws cannot be seen as ‘law-like statements’. Are the laws of definite proportions and multiple proportions outdated, and no longer relevant? Both of these laws are no longer explicitly used in chemistry. They are recognized as an important part of the development of chemistry, ?
am indebted
to a referee for suggesting
this very sensible interpretation.
Studies in History and Philosophy qf’ Science
628
particularly
as they relate to the articulation
of the atomic theory. They are now
introduced development
to chemistry students mainly of this theory, and are vaguely
as illustrations of the historical familiar to most working chemists
only in this role. But the laws are used implicitly every time a chemical or reaction is written down, or an analysis or recipe calculated.
formula
A modern chemist knows that when writing a chemical formula, constant rather than variable subscripts are used. do ‘One must use constant subscripts in chemical formulas’ is in effect a statement of the law of definite proportions. Similarly, in writing such a formula one does not normally use fractional subscripts like FeO,.,,,. ‘One must use small whole number subscripts in chemical formulas’ is a statement of the law of multiple proportions. The laws must be seen as an essential part of the basis of the prevailing theoretical structure of chemistry, in spite of their almost invisible status. Can it then be argued that they ought not to be regarded as laws because of their unacceptable character? While it is clearly possible to take this view, I would consider it undesirable. There are several problems with adopting this attitude. The first is that it would contribute to communication difficulties. An account of ‘laws of nature’ that requires us to consider that Newton’s laws and Boyle’s law are laws of nature, while Dalton’s law and Ohm’s law ure not, will cause confusion at best. At worst. it amounts to Humpty-Dumptyism.41 It could be argued that the practice of scientists in freely labelling such diverse types of statement as ‘laws’ has led to a situation where the notion of a law of science is so broad and diffuse as to be useless. In this case, there may be a call for philosophers to adopt a narrower and more rigid definition of a law of science. But the consequence of this would be that a philosopher could not just introduce X’s law into a discussion as an example, without first going to some trouble to establish its credentials as a respectable law of science according to the narrower definition. Philosophers manifestly do not do this! The second
problem
is an extension
of this same difficulty.
Because
of the
diversity of character discussed earlier, particular laws are likely to be admitted as respectable in one philosopher’s account, while being rejected by another. We cannot move to a narrower definition of what is a law of science until some sort of consensus has been established. A third, and quite different problem, is that a narrow purist’s view of laws of nature is likely to lead to a model where specific laws arise only in physics, and the rest of science is likely to be regarded as a vast anarchy, if not disregarded “‘There are three instances where variable of compounds rather than a single substance, air pollution studies; (ii) when a new substance (iii) when referring to a berthollide as an 0.93 > x > 0.32. “r“‘When I use a word”, Humpty Dumpty choose it to mean - neither more nor less.“’
subscripts are found: (i) when referring to a group as in NO, as a generic term for oxides of nitrogen in has been prepared but is not yet fully characterized; exception to definite proportions, e.g. Na,WO, said in rather a scornful tone, “it means just what I Lewis Carroll, Alice Through the Looking Glass.
Philosophers
altogether. before
versus Chemists concerning ‘Laws of Nature’
As Hutchison
we recognize
has recently warned:
a law of nature,
629
‘If we insist on absolute
we are not going
certainty
to get very many
of
them!‘42 Current treatments of laws of nature concentrate on physics, and particularly on the highly developed areas of physics - mechanics and electromagnetism. When forced to turn to laws of chemistry,
writers come out with something
like
‘gold is a yellow metal with atomic number 79’ as a law of chemistry.43 No chemist would regard this law-like statement as a law. Although gold is a kind among samples of material, it is an individual among elements. It is something a chemist wishes to generalize away from. The alleged law is actually a data statement as far as the chemist is concerned. Chemists do not spend their time and energy checking that one sample of substance X behaves in the same way as another. The laws and relationships that interest them involve such things as how and why the behaviour of substance X is analogous to that of substance Y. The properties of gold, and of other substances, are compiled in volumes with titles like ‘Handbook of Chemical Reference Data’ ~ certainly not in volumes entitled ‘Compilation of Laws of Chemistry’. On the other hand, chemists have numerous dicta that they do refer to as ‘laws’. These laws indicate the connections and analogies between the properties of different substances. Many of them are non-universal. A few are imprecise. By and large they cannot be seen as ‘law-like statements’, as defined by philosophers of science.4 Even physicists in less developed and less quoted areas of their subject - thermodynamics, statics, fluid mechanics, materials are in many respects in a similar situation. Ultimately, the best policy is to define ‘laws of nature’ in such a way as to include most or all of the very diverse dicta that scientists have chosen to regard as laws of their various branches of science. If this is done, we will find that there is not a particular character that one can associate with a law of nature.
Acknowledgements - The author wishes to thank Dr John Christie for extensive discussions help with the more technical Neil Thomason for reading
4*K
Hutchison
aspects of chemistry in this paper. The author earlier drafts of this paper and for a number
‘Is Classical
Mechanics
Really
Time-Reversible
of and also wishes to thank Dr of useful suggestions.
and Deterministic?‘,
British
Journnlfor the Phbosophy of Science 44 (1993), 316. 43E.g, R. M. Chisholm, in Analysis 15 (1955), 101, 103; J. Bigelow, B. D. Ellis and C. Lierse, The World as One ofa Kind (preprint, La Trobe University Philosophy Dept, 1991) p. 23. &E.g. Armstrong, op. cit., note 26, pp. 6-S.
Philosophers versus Chemists Concerning ‘Laws of Nature’ Maureen Chris tie * Abstract ~ The law of definite proportions and the law of multiple proportions are two of the important laws of chemistry associated with the development of the atomic theory in the early nineteenth century. A detailed study of these laws shows that they have characters which cannot be reconciled with philosophers’ accounts of laws of nature. They are non-universal, and one of them is imprecise. Philosophers have approached an account of laws of nature by trying to fit their character to a particular model. Duhem, in particular, who introduces the law of multiple proportions as an example, misrepresents the law to make it fit his conventionalist model. The various models adopted by philosophers have differed widely, but there has been a universal failure even to recognize the possibility of diversity among laws, let alone face its reality. A more liberal and pluralistic view of just what is a law of nature is required. Contrary to standard accounts, laws of nature are a diverse group of dicta, of widely varying character. Unlike philosophers, chemists have recognized this diversity for at least a hundred years. In many ways the differences between the characters of laws are more interesting than the similarities. The analysis will show that some laws are approximations, while others are exact; and that some laws are purely formal, but not all of them. But on a more revolutionary note, it will also show that many quite respectable laws of science are non-universal, and even that there are a few that cannot be formulated as precise propositions. There is a possible escape for the philosophical accounts, in the claim that laws of character inconvenient for a particular model are not really laws. This course will be considered, and found inadvisable. The more appropriate course of action would rather seem to be a recognition of the scientists’ broader notions of scientific law, and acceptance of a wide diversity of character among laws of nature.
Two ‘Laws’ of Chemistry proportions (also known as ‘Proust’s
THE LAW
of definite
expressed: in definite
‘Any pure chemical compound is made up of its constituent and invariant proportions by mass.’
law’) may
be
elements
*School of Philosophy, La Trobe University, Bundoora, 3083, Australia. Received
17 January
Pergamon
1994; in revised form
15 March
1994.
Stud. Hist. Phil. Sci., Vol. 25, No. 4, pp. 613-629, 1994
Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0039-3681/94 $7.00+0.00 613
614
Studies in History and Philosophy
oJ’ Science
While a cook, in preparing a cake, can make an egg-rich or an egg-poor mixture by varying the recipe slightly, the chemist who reacts 1 mass of hydrogen
with 7.94 of oxygen to produce
oxygen-rich proportions. A French
or oxygen-poor chemist,
Joseph
water. Louis
water cannot
The reaction Proust,
vary the recipe to obtain
proceeds
according
was first to express
to exact
and provide
practical verification of the law of definite proportions in 1799.1 Dalton’s atomic theory in 1808 gave a very simple explanation of the law,’ but a long and famous controversy ensued between Proust and Berthollet,’ who argued that there was no essential difference between compounds and solutions which exhibited variable composition (like salt in water). Berthollet saw constant proportions as only rarely and accidentally instanced.4 Proust got the better of the debate with some careful experimental work, which showed that oxidized copper, which Berthollet claimed to exhibit variable proportions, consisted of mixtures of unreacted copper with just two oxides, each of which had definite composition. Proust’s argument was that the sort of combination involved in forming a chemical compound was a stronger and more intimate union than that involved in a solution. Solutions typically showed physical and chemical properties not very different from those of the separate constituents, along with variable composition. With compounds a completely new set of properties was usually obtained, and the constituents reacted in definite proportions. Constituents of solutions can usually be recovered by evaporation, distillation or fractional crystallization; compounds are not so easily separated. When confronted with a series of awkward cases, including glasses and alloys ~ systems that clearly showed variable proportions, but were compound-like in the difficulty of separating their constituents ~ Proust simply pleaded that the current state of knowledge was inadequate for a good description of these systems, and reasserted that there was a difference in kind between the types of combination exhibited in solutions and compounds.5 As chemistry developed through the nineteenth century, the law of definite proportions continued to be seen as central, at least in the fact that textbooks paid homage to it. It is still usually mentioned in present day textbooks, but ‘J. L. Proust, in Ann&s de Chimie 32 (1799), 26-54, as translated and reprinted in part in H. M. Leicester and H. S. Klickstein, A Source Book irr Chemistry 1400-1900 (Cambridge, Mass.: Harvard University Press, 1952), pp. 202-204. ‘L. K. Nash, The Atomic-Moleculur Theory (Cambridge. Mass.: Harvard University Press, 1950), p. 35. 3For a detailed discussion of the Proust -Berthollet controversy, see: Nash, ibid., pp. 33~.35; K. Fujii, ‘The Berthollet-Proust Controversy and Dalton’s Chemical Atomic Theory 1800-1820’; British Journalfbr the History of Science 19 (1986), 177-200. “J. R. Partington, A Short History of Chemistry. 3rd edn (London: Macmillan, 1957), p. 153; Nash, op. cit., note 2, p. 33. . ” ‘3. L. Proust, Journal de Physique 63 (I 806), p. 369, as reprinted in Leicester and Klickstein (eds), op. cit., note 1, p. 204.
615
Philosophers versus Chemists concerning ‘Laws of Nature’ many
chemical
borderline
systems
were
discovered
region between compounds
in that their constituents
were strongly
which
and solutions. joined
could
only
be placed
in a
They were compound-like
together
by chemical
bonds,
but
solution-like in that their proportions could be varied over a small range. The sort of systems that are involved in these cases are known as ‘network solids’. The atoms are chemically bonded, not in discrete clusters as molecules, but each to several neighbours in a network that extends throughout the bulk crystal or glass. Aluminium oxide is such a network solid. It forms a white powder, or a clear and very hard gemstone (corundum). A chromium atom has almost exactly the same size and bonding propensities as an aluminium atom. If between about 1% and 5% of aluminium atoms in aluminium oxide are replaced by chromium atoms (more or less at random), ruby is formed. Is ruby a compound? The aluminium and chromium atoms are chemically bonded to oxygen atoms, and via these oxygen atoms to one another. They cannot be separated without breaking very strong chemical bonds. Or is ruby a solid solution of chromium oxide and aluminium oxide? Most modern chemists would say the latter, but not without some reservation. There are many similar examples, particularly among minerals6 Other systems which produce difficulties for the law of definite proportions include synthetic polymers like nylon or polystyrene. The molecules of these substances consist of large numbers of repetitions (typically 50 to 1000) of a basic structural unit. In most cases the long chains are capped with end groups that differ slightly from those in the middle of the chain ~ the overall structure may be considered to have the form ABBBBBBBB...BBBBBBC. Now any particular sample of polymer will not have a precisely fixed number of units in the chain. A sample of nylon may have some molecules with 164 units and others with 165 units. Moreover, it is possible to produce different grades of nylon with different specifications for the average chain length. Because of the different relative proportion of end groups, these grades will have slightly different composition. They also show differences in physical properties. Nevertheless, it is convenient for chemists to regard nylon as a compound. A strict interpretation-where the only pure compounds in polymer chemistry are those where every molecule has exactly the same chain length, is operationally inappropriate, and has never been adopted. As the awkward cases were increasingly investigated through the nineteenth century, a difference arose between chemists about how to deal with them. It has never been completely resolved. One group of chemists, including Mellor in his Comprehensive Treatise on Inorganic and Theoretical Chemistry (1922), gave the law a formal status, as a 6E.g. in olivine ~ (Mg,Fe),SiO, - and amphibole - Ca,(Mg,Fe),Si,O,,(OH), ~ magnesium and iron atoms may replace one another at random. Once again these two atoms have similar size and bonding propensities.
616
primary
Studies in History and Philosophy of Science taxonomic
device.
A chemical
concoction
cannot
be classified
as a
compound by dejkition unless it has constant composition. As far as Mellor was concerned ‘we refuse to call substances compounds which do not conform with this definition’ (viz. constant composition).7 The other
group
allows
certain
strongly
bonded
concoctions
of variable
composition as compounds, and regards them as exceptions to the law of definite proportions. Linus Pauling in 1947 took this line. Immediately following his introduction of ‘the law of constant proportions’, Pauling says: ‘Recently it has become customary to accept as substances not only those materials that, when purified, show constant composition, but also those that may have a small range of variability in composition.‘8 In an earlier passage he defines ‘substance’ as ‘a homogeneous species of matter with reasonably definite chemical composition’, and digresses on precise and imprecise definitions: ‘The words that are used in describing nature, which is itself complex, may not be capable of precise definition. In giving a definition for such a word the effort is made to describe the accepted usage’!9 These chemists use the terms ‘berthollide’ for ‘compounds of variable composition’ and ‘daltonide’ for ‘compounds of fixed composition’ - a suggestion first made by Kurnakov in 1914.1° The other term frequently used is ‘non-stoichiometric compounds’ii a contradiction in terms if the law of definite proportions is regarded as unexceptioned. Despite Pauling’s ‘recently’, a similar attitude can be found in Mendeleev’s 1869 textbook, where he refers to ‘indefinite compounds’ and ‘definite compounds’.i2 Also, despite Pauling’s ‘small range of variability’, Wadsley uses formulas like ‘Na,WO, (0.93 2 x 2 0.32) and Li,WO, (0.57 2 x 2 0.31)‘.‘3 A variability of a factor of 3 in composition, as in the first case, could hardly be called small. While it could possibly be argued that Pauling sees the law as an unexceptioned approximate law, it is clear that the view of most of this school is that the law is exact and exceptioned. The difference of view as to whether the law is formal and unexceptioned, or contingent and exceptioned, appears to persist to the present. It is hardly an active controversy because it is a matter of choice and usage how the borderline cases are to be regarded, and the law is not used in an explicit sense in modern chemistry. ‘5. W. Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry (London; Longmans, 1922) vol. 1, p. 95. *L. Pauling, General Chemistry (San Francisco: Freeman, 1947) p. 150. ‘Ibid., p. 8. “‘N S Kurnakov, in Bulletin de l’dcadhmie Imp&ale des Sciences de St. PPtersbourg (1914), 321-338, as cited in H. M. Leicester, The Historical Background of Chemistry (New York: Wiley, 1965) p. 153. “A. D. Wadsley, ‘The Crystal Chemistry of Non-Stoichiometric Compounds’, Reviews of Pure and Applied Chemistry 5 (1955), 165-193. “D. I. Mendeltev, The Principles of Chemistry, trans. of the Russian 5th edn by G. Kamensky, ed. A. J. Greenaway (London: Longmans, 1891) vol. 1, p. 32. 13Wadsley, op. cit., note 11, p. 172.
617
Philosophers versus Chemists concerning ‘Laws of Nature’
The
second
law to be considered
is the closely
related
law of multiple
proportions. The law of multiple
proportions
(also
known
as ‘Dalton’s
law’) can be
expressed: ‘If two radicals A and B unite to form more than one compound, then the invariant amounts of B which unite with the same mass of A in the various
compounds
are in the ratio of simple whole numbers.‘14
For example, copper forms two oxides. A portion (100 g) of copper reacts with 12.25 g of oxygen to produce red copper oxide, or with 24.50 g of oxygen to produce black copper oxide. The uptake of oxygen in one case is just double what it is in the first. That is, the ratio 12.25:24.50 is just the ratio 1:2. Proust in an article about his work on sulfurets of iron15 casually remarked that he had been surprised to note that the uptake of sulfur in the second compound was just one and a half times that in the first. He had made similar remarks in other papers, but he did not generalize and formulate a law. The law is ascribed to Dalton, who arrived at it via a different route. Dalton suggested that if compound atoms’6 consisted of combinations of small numbers of simpler atoms, then the result embodied in the law of multiple proportions should apply to the combinations of bulk quantities of simpler substances into compounds. The suggestion was presented purely as a theoretically based speculation. Thomas Thomson17 and William Hyde Wollaston*8 presented confirmation of the law of multiple proportions in 1808. Apparently quite independently of Dalton, Wollaston had observed that whenever an acid and a base combined in more than one ratio a very simple relationship of this form (usually 2:l) applied, and suggested the generalization and investigation of the result. Wollaston’s report is the archetypal example for scientific theory arising from empirical generalization: Dr Thomson has remarked that oxalic acid unites to strontian as well as to potash in two different proportions, and that the quantity of acid combined with each of the bases in their super-oxalates, is just double of that which is saturated by the same quantity of base in their neutral compounds. As I had observed the same law to prevail in various other instances of superacid and subacid salts, I thought it not unlikely that this law might obtain generally in such compounds, and it was my design to have pursued the subject with the hope of discovering the cause to which so regular a relation might be ascribed. “‘Mendeleev, op. cit., note 12, vol. 1, p. 213. “J. L. Proust, Nicholson’s Journal, 8vo series 1 (1802) 269-273. 16Dalton did not use the term ‘molecule’ or the concept in the modern sense, but referred to ‘comnound atoms’ instead. This led to a concentual system of sub-structures, because a ‘compound _ _ atom could itself be made up of simple or compound atoms. “T. Thomson. Philosoohical Transactions of the Roval Societv, 98 (1808). . ,_ 63. 69970, 74, as in Alembic Club Reprints number 2. “W H Wollaston. Philosophical Transactions of the Royal Society 98 (1808), 96102, as in Alembic Club Reprints number 2.
618
Studies in History and Philosophy oJ’ Science
But since the publication of Mr Dalton’s theory of chemical combination, as explained and illustrated by Dr Thomson, the inquiry which I had designed appears to be superfluous. A subtle
change
crept
into
textbook
statements
of the law of multiple
proportions, roughly at the start of the twentieth century. The law, which had previously been understood as also applying to compositions in terms of compound constituents, was narrowed to a law expressed in terms of elemental compositions and binary compounds of elements only. The change is nowhere much remarked upon. The effect was to remove from the law all of its practical importance, except as an illustration of the atomic theory. The classical examples. like Wollaston’s super-acid and sub-acid salts, no longer even came within the scope of the law! This can only be seen as an adjustment to cope with a major shift in the understanding of the atomic theory. No longer was potassium oxalate (K2CZ04) seen as a compound of potash (K,O) and oxalic acid (H,C,O,), but as a compound of potassium, carbon and oxygen. The law of multiple proportions is not a precise proposition. The problem lies with the word ‘simple’ or ‘small’ which appears in its statement. Although most of the time the ratios are very simple indeed ~ 2: 1,3: 1,3:2 - there is no precise size of whole number that represents a cut-off. A chemist cannot say that 7 is a simple number and 8 is not! (By a simple whole number ratio, chemists mean a ratio that reduces to the ratio of small integers.) There are instances of multiple proportions where the numbers are not so simple, but these are always accompanied by other evidence of complexity of at least one of the compounds concerned. The origin of the notion of simple whole number ratios was Dalton’s rule of greatest simplicity. This rule was later largely discredited, because, inter alia, it led Dalton to formulate water and ammonia as HO and NH, respectively, rather than H,O and NH,. In spite of this, Nash’s evaluation is that ‘in its prediction of simple, readily perceived ratios, the rule of greatest simplicity more than justified its existence by stimulating the quest for such ratios. This quest rapidly proved to be very fruitful. ‘I9 Brock suggests that even Dalton himself used the rule as a rule of thumb, without any great belief in its fundamental significance;20 the evidence for this is that Dalton allowed the possibility that water might be ternary ~ either H,O or HO, in his discussion in the ‘New System’. The law of multiple proportions ns understood by chemists, includes ‘simple’ as an essential descriptor of the whole number ratios. The law therefore cannot be formulated as a precise proposition. It is clearly instanced, and exactly instanced, but it also has clear exceptions, and there are cases where it cannot be decided how the law applies. “Nash, op. cit., note 2, p. 38. “W. H. Brock, The Fontana History
of Chemistry
(London:
Fontana,
1992),
p. 138
Philosophers
The hydrocarbons thousands
619
versus Chemists concerning ‘Laws of Nature’
provide
of different
and hydrogen.
If a comparison
ethene (ethylene obviously instanced.
a series of examples
compounds
which contain
is made between
of the difficulty:
there are
just the two elements
carbon
ethyne (acetylene
-
C,H,)
and
C2H4), the law of definite proportions is very simply and A sample of ethene containing the same mass of carbon as
a sample of ethyne always has just exactly twice as much hydrogen as the ethyne, but if we compare pentane (C5Hi2) with ethyne, the ratio is 12:5 rather than the simpler 2:l. We could go on to compare heptane (C,H,,J with butane (C4Hio), obtaining a ratio of 35:32, or even C,,H,, with C,,H,,, which gives 429:425!21 It can be seen that although the first comparison is in the ratio of simple whole numbers, the large range of compounds provides many comparisons which can be chosen to give ratios of almost any desired complexity. Certainly the last comparison could not fairly be regarded as providing an analysis in the ratio of simple whole numbers at all. Both of these laws are of a character very different to those typically quoted as examples in philosophical discussions of scientific laws. The law of definite proportions can be seen either as an exact rule with exceptions (if the Pauling view of the law is followed) or as a purely formal taxonomic device (if the approach of the Mellor school is taken). The law of multiple proportions is not even a precise proposition.
Duhem and the Law of Multiple Proportions the law of multiple In a book written in 1906, 22 Duhem misrepresents proportions by leaving out the word ‘simple’ in ‘ratio of simple whole numbers’. He possibly does this because it is the only way to express the law as a precise proposition, but the inclusion of ‘simple’ is an essential part of the way that chemists
understand
the law. His statement
of the law is as follows:
On Hypotheses whose Statement has no Experimental Meaning . For example, chemical theory rests entirely on the ‘law of multiple proportions’; here is the exact statement of this law: Simple bodies A, B and C may by uniting in various proportions form various compounds M, M’, etc. The masses of the bodies A, B and C combining to form the compound M are to one another as the three numbers a, b and c. Then the masses of the elements A, B and C combining to form the compound M’ will be to one another as the numbers xa, yb and zc (x, y and z being three whole numbers). Is this law perhaps subject to experimental test? Chemical analysis will make us acquainted with the chemical composition of the body M’, not exactly, but with a ‘IThe simplest way to obtain the ratio is to cross-multiply the subscripts. Thus - comparing C,H,, with C,H,,, we obtain 7 x lo:16 x 4=70:64=35:32. 22P. Duhem, The Aim and Structure of Physical Theory, trans. P. P. Wiener (Princeton: Princeton University Press, 1954), pp. 212-214.
620
Studies in History and Philosophy of Science
certain approximation.... whatever the results given by the chemical analysis of the compound M’, we are always sure to find three integers x, y and z thanks to which the law of multiple proportions will be verified with a precision greater than that of experiment. Therefore, no chemical analysis, no matter how refined, will ever be able to show the law of multiple proportions wrong.
Duhem argued that since any ratio can be expressed as the ratio of whole numbers to within any desired precision, the law (as he expressed it) was a truism. Nash, in reference to Dalton’s atomic theory, points out that Dalton’s ‘rule of greatest simplicity definitely suggests that the ratios will always be simple ones, involving only small numbers.23 Wollaston and Thomson were definitely looking specifically at a series of 2:l ratios in their experiments with super-acid and sub-acid salts. Chemistry textbooks from Mendeleev in 1869 to the present have always included ‘simple’ or ‘small’ in describing the whole number ratios predicted by the law. Thus, Duhem’s treatment of the law of multiple proportions is a misrepresentation. Duhem produces the law, asserting that ‘chemical theory rests entirely’ on it. He then claims to give ‘the exact statement of this law’. The statement is interesting in that it is in its twentieth-century form of compositions in terms of elements only (it dates from 1906), and in that it is expressed for ternary compounds rather than the traditional expression in terms of binary compounds. It concludes with ‘x, y and z being three whole numbers’ (where a chemist’s expression ought to have had ‘x, y and z being three small whole numbers’). No other chemist is referenced in this section of his work; the only nearby reference is to his own earlier work (1902) on Mixture and Chemical Combination.24
Duhem’s thesis is that this law is one of several examples of hypotheses whose statement has no experimental meaning. He argues that ‘laws’ like this are purely formal, and their role is to help to provide a conceptual basis for a scientific subject. In particular, he argues, a law like this could never be falsified by experiment, even in principle. The writing of Wollaston, in particular, cries out against Duhem’s interpretation. His apprehension of the law had been based on a ‘truly remarkable regularity’ - specifically, a series of 2: 1 ratios in composition between different salts of the same acid and base. An empirical generalization was made from a series of his own experiments on different systems. From Wollaston’s point of view, Dalton’s atomic theory provided the basis for a theoretical explanation, that his experimental results demanded. Duhem is also wrong about the falsifiability of this particular law. Certainly his own version of the law is purely formal, and not falsifiable, but the law of
Z3Nash, op. cit., note 2, p. 38. Le mixte et la combination chimique: essai SW I’6volution d’une idke (Paris, 1902).
24P. Duhem,
Philosophers
multiple
621
versus Chemists concerning ‘Laws of Nature’
proportions,
other law. The modern
as understood
chemist
by chemists,
is at least as falsifiable
is aware of many cases of widely varying
as any
complexity.
If
cases can be quoted which are exceptions to the law (in that they produce ratios like 429:425 - see earlier), then what could possibly falsify it? How could a case arise that would not just be regarded as another exception? Here is a hypothetical example which shows how the law of multiple proportions, as a law with exceptions, might be falsified. Suppose that two chemical substances, A and B, combine to form two different compounds Ml and M2. Suppose that the other evidence that chemists collect to characterize a compound spectra and the like showed on the usual bases of interpretation that both Ml and M2 had molecular rather than network structures, and fairly simple molecular structures at that, then a ratio of 1.55: 1 (with 1% experimental error) would constitute a clear falsifying violation of the law (and indeed such ratios are not observed in these cases). The ratio is significantly different from 3:2, which is the only simple ratio that even comes close. Ratios of 11:7, 14:9 or 17:11, which might fall within experimental error, are inconsistent with the other evidence of structural simplicity. In this way a falsification of the law could be produced. To regard such a case as a non-falsifying exception would introduce a completely new class of exception, and undermine the utility of the law. Duhem’s more general point is that any inconsistency that is manifest is really only an inconsistency in the larger theoretical edifice used to interpret an experimental result, and that the law is not necessarily the part of the edifice that should or would be abandoned. This aspect of his argument remains intact, of course. Chemists, both early and modern, do think that the statement of the law of multiple proportions has a definite experimental meaning, even though it is not a precise proposition. Perhaps Duhem, as a philosopher, did not like dealing with imprecise propositions. It is likely that part of his programme in producing an ‘exact statement’
of the law was to tidy it up in such a way that it became
a precise proposition. It is also likely that the way he went about this tidying up was largely governed by his preconceived view of laws of nature, as a conventionalist. He then seems to have completed the circle by citing the law as an example to support and illustrate his conventionalist position! Philosophers’ Accounts: Forcing Laws to Fit a Viewpoint? Molnar encapsulates a ‘regularity theory’ to describe laws of nature from a generally Humean viewpoint,25 in terms of the following four requirements: universal quantification, truth, contingency, only non-local empirical predicates 25G. Molnar, in Philosophical Review 78 (1969), 79-89.
622
Studies in History and Philosophy of Science
(presumably meaning kinds or classes of object, rather than particular objects or places). While few, if any, philosophers (including Molnar) argue this exact position, Molnar’s criteria are often cited and used as a departure point for a different
account.26
One thing that all philosophers of science tend to do is to consider laws as a class. Specific laws are cited as examples, and often several rather diverse laws are introduced to show how they all fit into the author’s favoured pattern (as we have already seen with Duhem’s conventionalism). But there is little or no exploration of the possibility that family resemblances between different individual laws might not extend to the issues discussed by the authors. It is possible, and seems likely, that some laws are merely formal and conventional, while others have a genuinely contingent status.*’ It is possible, and seems likely, that some laws are obeyed exactly, while others are framed in terms of ideals which may only be approached and approximated, but never actually achieved by natural systems. It is possible, and seems likely, that some laws have definite exceptions, while others have some sort of claim to universality whether as ideals, conventions or accurate and contingent dicta. Mendeltev, in his 1869 Principles of Chemistry, refers to a ‘class of approximate laws’ and gives examples. ** In so doing, he is clearly taking an implicitly different stand to that of the philosophers. In saying that some specific and named scientific laws expressed approximate relationships, he made a definite implication that he saw others as expressing exact relationships. Recently, some philosophers have argued that no laws are exact, and that all represent unrealized idealizations, notably Cartwright.2’ The desire for a single model to embrace all laws persists. Contrary to Cartwright’s thesis, and parallel to MendelCev’s implication, there is an essential difference of kind between exact laws, like conservation of charge, or even Newton’s law of universal gravitation, and approximate laws, like Boyle’s law or Charles’s law. Exact laws are realized exactly within the precision of most plausible experimental measurements, and some very fine nit-picking is required to show their slight inadequacies. But for an approximate law any careful measurement might routinely be expected to be a few percent away from the predicted the law itself. 26E.g. D. M. Armstrong,
value, by virtue of the approximate
What is a LOW
of Nature? (Cambridge:
Cambridge
nature
University
of
Press,
1983) p. 12.
“The term ‘contingent’, as used in this paper, refers to the notion that a law must not be a trivial statement which arises of logical or semantic necessity. It must make a definite statement about the world. The term carries a positive connotation. Ellis, in particular, uses the term to refer to ‘something that might have been otherwise’, and gives it a negative connotation. For Ellis, a law must be a statement that indicates a connection so strong that it would apply in all legitimate possible worlds. “MendelCev, op. cit., note 12, vol. 1, p. 78. “See N. Cartwright, HOW the Lms of Physics Lie (New York: Oxford University Press, 1983).
Philosophers versus Chemists concerning ‘Laws of Nature’ Ellis, for example,
introduces
his discussion
623
of laws as idealizations,
with the
statement that ‘Physical theory seems largely to be about such things as inertial systems, black body radiators... perfect gases, and so on,‘30 and continues with the notion
that not only blatantly
most fundamental idealization, citing
idealized
systems
of this sort, but also ‘the
theories we have’, contain essentially Cartwright’s general line of argument.
a similar type of But Mendeltev’s
‘class of approximate laws’ (and the implication of at least one other class of laws) is a more appropriate representation. There is an enormous difference between the gas laws and the law of conservation of energy. The difference shows up clearly at an operational level; it should also be seen as a fundamental difference of character. When a chemist or physicist uses the ideal gas laws to deduce volumes or pressures of real gases, there is an expectation that the answer will be approximate - within 1% or so, with possibly a much larger error at high pressures or low temperatures. But when a calculation is made based on conservation of energy, the result is expected to be exact ~ so much so that such calculations are used to calibrate instruments. Ellis argues that ‘since these laws are concerned with the intrinsic natures of the elementary processes of nature, they can apply strictly only to causally isolated processes and therefore ‘apply strictly only to closed and isolated systems’.3’ But this takes only one very specific viewpoint. The law of conservation of energy is often stated in the form ‘Energy cannot be created or destroyed’s2 with minor variations and qualifications. There is no need to refer to any ‘system’, let alone a ‘closed and isolated system’.33 It is a consequence of the law of conservation of energy that if such a thing as a closed and isolated system existed, then no process could alter its total energy. It is also a consequence that no totally internal process can alter the total energy of a system, even if it is not closed and isolated. But the form in which chemists, at least, usually use the law, is in terms of the consequence that the change in total internal energy of any system is equal to the energy flux into or out of it. This is made quite clear by Brady immediately following his introduction of the law: ‘The energy bookkeeping for both heat and work is taken care of by the equation A E=q + w, where q is defined as the heat absorbed by the system from the surroundings when the system undergoes a change, and w is the work done on the system by the surroundings.‘34 3”B D Ellis ‘Idealization in Science’, in C. Dilworth (ed.) Idealization IV: Intelligibility in Science (Amsteidam: Rodopi, 1991), p. 265. “Ibid., p. 280. 32J E. Brady, General Chemistry, 5th edn (New York: Wiley, 1990), p. 455. 33The true nature of Ellis’ objection to the law of conservation of energy becomes clear if we look at the definitions of closed and isolated systems used in chemical thermodynamics: ‘a closed system is one that does not exchange matter with its surroundings, but may exchange energy’; ‘an isolated system is one that exchanges neither energy nor matter with its surroundings’. Incidentally, to refer to a closed and isolated system is a tautology - any isolated system is closed of necessity! s4Brady, op. cit., note 32, p. 456.
624
Studies in History and Philosophy of Science
It is thus exactly true, not an approximation, that energy can be neither created nor destroyed,35 and this law has consequences that can be just as usefully
interpreted
for real systems
as for unrealized
ideal systems.
On this
basis, the claim is that while the ideal gas laws clearly belong to a class of approximate laws that relate to an unrealized ideal, the law of conservation of energy (and others like it) belongs If the argument that such laws which is doubtful, the idealization character.
to a class of laws of quite different
character.
represent idealizations can be sustained, is of a different and much more subtle
Towards a Taxonomy of Laws The distinction between exact and approximate laws is only the first of a number of taxonomic distinctions between different laws of nature that may be worth making. Even among approximate laws, there is a difference in kind between Boyle’s law and the law of Dulong and Petit. Boyle’s law is explained in modern kinetic theory by deriving it for a model gas whose particles (molecules) are negligibly small, and do not have any attraction for one another. It is clearly an idealization. We can therefore have some theoretical notions of which gases, in which circumstances of pressure and temperature, will follow it more closely. The law of Dulong and Petit states that the product of the atomic weight of a solid element and its mass heat capacity relative to water is approximately 6.1 at room temperature. This law is not obviously related to any particular idealization in theory. The claim here is not that the law of Dulong and Petit is a mystery with no sound theoretical basis, it is rather that there is no theory of the ideal solid element, analogous to ideal gas theory. It is not known, for example, whether the molar heat capacity of the ideal solid element is 6.114 or 6.135! There may be a taxonomic subdivision worth making among approximate laws between those that represent idealizations and those that do not. If the Pauling view of the law of definite proportions is taken -~ compounds usually have fixed composition, but in some cases there is variability in composition - then this law is a non-universal law. A IUU~can be non-universal and still represent un expression of’a very us&l generalization, especially if there is some underlying theory which alerts the scientist to the particular types of system or situation where the exceptions may arise (and conversely guarantees that certain other types of system or situation are safe from exceptions). Gases and volatile liquids obey the law of definite proportions without exception. ‘%pecial relativity theory introduces the complication of mass-energy interconversion. This does not usually affect the systems chemists are interested in, and the difficulty can be overcome either by stipulating ‘in the absence of measurable relativistic effects’, which almost invariably applies, or by regarding mass itself as a form of potential energy. J. R. Christie, private communication.
Philosophers
Pauling constant
versus Chemists concerning ‘Laws of Nature’
also mentions
salts, molecular
625
solids and organic
compounds
as having
composition.36
In all of the debate
on ‘natural
laws’, universality
has never been challenged
in quite this way. It has been suggested that laws are approximate, or that they relate to ideal systems that are never quite realized, but the idea of a law that is frequently and exactly instanced, but has particular exceptions, has not been much discussed. Is the law of definite proportions non-contingent, as those who take the conventionalist position imply? The answer is clearly not. The contingency of the law can be demonstrated by the following device. Suppose that we wish to distinguish between solutions and compounds. It can be shown that this is, at the limit, an unsolved problem, and that indeed, there may be no natural distinction. But if the discussion is restricted to gaseous mixtures and compounds, the situation changes enormously. None of the awkward or borderline systems are gases. For gases, there are several different methods and criteria that could be used for the classification, and they all provide the same answers. Gases can therefore be chosen as a clear and easily differentiated subclass of systems which does not contain any of the awkward cases. The property of ‘having a distinctive molecular spectrum’ (B) is one that could be used as a primary method of classifying gaseous concoctions as mixtures or compounds. ‘Having a constant composition’ (C) becomes a contingent property which always occurs whenever property B does (i.e. C may occur without B, but B may not occur without C). ‘If B then C’ is a statement which is universally true, but not true of necessity. ‘Any substance with a distinctive molecular spectrum has fixed composition’ cannot be a convention! It would be possible, but rather more complicated, to define a much larger sub-class for which the law of definite proportions would be both universal and contingent. To be completely accurate, it should be said that what has been shown to be contingent is arguably not the law of definite proportions, but only a ‘sub-law’ which applies exclusively to gases, or a wider sub-law that applies only to the larger sub-class of systems for which both (i) the law of definite proportions clearly universal, and (ii) a reliable alternative means of classification available.
is is
In practice, it is probably fairest to describe the status of the law as a law that is accurate (in that it is widely and exactly instanced), and contingent (in that it does not arise of logical or taxonomic necessity), but not universal (in that there are several very specific types of exception to the rule, and/or ambiguities in the taxonomy). The evidence of recent textbooks is that many modern chemists see the law in these terms, and still consider it to have some validity.” ‘6Pauling, op. cit., note 8, p. 150. “E.g. N. N. Greenwood and A. Earnshaw, pp. 753-156.
Chemistry
ofthe Elements (Oxford:
Pergamon,
19X4),
626
Studies in History and Philosophy
of Science
The alternative Mellor view of the law of definite proportions gives this law a purely formal status. Rather than expressing any fact about nature, it effectively expresses part of our definition of what is meant by ‘compound’. Conventionalists that they represent nature
have argued that all laws of science are purely formal an attempt by humans to impose demarcations and order on
to help our understanding,
where no such demarcations
or order exist in
reality. A rejection of the conventionalist position as such may nonetheless be accompanied by a recognition that some laws of nature do have a purely formal status. The preceding argument about a large sub-class of systems for which several different taxonomic criteria for compounds would concur, does indicate, though, that the law of definite proportions is rather more than a purely formal law. The law of multiple proportions is very strange in being regarded as a law while not even being a precise proposition. I have already argued that Duhem’s attempt to give it precise meaning misrepresents the law. It cannot be seen as a convention that helps to define anything in particular. It is exactly instanced, and clearly exemplified, but it clearly cannot be described as an ‘approximate law’ or as an ‘idealization’ in the usual sense of these terms. There is one other law of chemistry which must be seen as very similar in regard of not being a precise statement: Mendeleev’s formulation of the periodic law ‘the properties of the elements, as well as the forms and properties of their compounds, are in periodic dependence or, expressing ourselves algebraically, form a periodic function of the atomic weights of the elements.‘3x Mendeleev goes on to discuss the fact that the independent variable is a discrete variable, and has no meaning except at the particular atomic weights that correspond to particular elements. More importantly, these discrete values are at irregular intervals. Moreover, as he also points out, many of the most
important
chemical
properties,
as dependent
variables,
are also
discrete. The valencies exhibited by an element in its compounds are integers, for example. These factors qualify the usual meaning of a periodic function. It is apparent from Mendeleev’s discussion that he was not using the concept of a periodic function with its strict algebraic meaning. As a result, the statement of this law is vague in the extreme. While the ‘periodic law’ is little used and seldom quoted in modern chemistry, the periodic table, which arises from it, still plays a central and crucial role. It is possible that both Mendeleev and Newlands, who also used the concept of periodic law, were concentrating on ‘periodic law’ rather than ‘periodic table’, because the notion of ‘law’ fitted in with their desire to see chemistry as a fundamental science, while ‘table’ pointed rather to a descriptive and 38MendelCev, op. cit., note 12, vol. 2, p. 16.
Philosophers
versus Chemists concerning ‘Laws
taxonomic
science -
the very realm
ofNature’
621
from which they were trying
chemistry.39 These are only a few of the examples
that could be chosen
to remove
to illustrate
the
great diversity of character of scientific laws. It is clear that the laws of definite and multiple proportions have characters very different from one another, and from the more acceptable laws typically chosen as examples of scientific laws. It is also clear that they are not alone in these peculiarities, and that there are several quite different classes of scientific law. We have mentioned the law of Dulong and Petit as a law that is not only an approximate law, but also has clear exceptions, and the periodic law as another example of a law embodied in an imprecise proposition. Hooke’s law says that the fractional extension produced in an elastic material is proportional to the applied stress (force per unit area). It applies only to certain materials, and then only at stress values below the ‘elastic limit’. As a law, then, it can be seen as a non-universal contingent law, or it could be seen as a convention which defines one use of the term ‘elastic’. A similar view should be taken of Ohm’s law - that the current flowing through a resistive element in an electrical circuit is proportional to the drop in electrical potential across the element. Again this does not apply to all materials, nor to extremely high voltages. Once again, the law could be seen as a non-universal generalization with clear exceptions, or it could be seen as a convention which defines the use of the term ‘Ohmic resistor’. We can be fairly confident that further research would show that many of the most useful laws of science have characters which are not quite respectable in a variety of similar ways. Is a Statement in Science Known as ‘X’s Law’, a Law of Science? A possible response to much of what has been said in this paper is that these various ‘laws’ are not really scientific laws. One prong of the attack might be that these laws are outdated by new understandings in the area of science. The other would be that they do not have the character or fulfil the criteria to fit in with whichever
of the various
notions
of a scientific
law is being advanced.
Just
because something is called ‘Jones’s law’ by scientists, the argument would go, that does not make it a scientific law in the stricter sense that a philosophical account would require. The argument would be applied with particular vigour to notions like the law of multiple proportions and the periodic law, which cannot even be formulated as precise propositions. The statements of these, and many of the other so-called laws cannot be seen as ‘law-like statements’. Are the laws of definite proportions and multiple proportions outdated, and no longer relevant? Both of these laws are no longer explicitly used in chemistry. They are recognized as an important part of the development of chemistry, ?
am indebted
to a referee for suggesting
this very sensible interpretation.
Studies in History and Philosophy qf’ Science
628
particularly
as they relate to the articulation
of the atomic theory. They are now
introduced development
to chemistry students mainly of this theory, and are vaguely
as illustrations of the historical familiar to most working chemists
only in this role. But the laws are used implicitly every time a chemical or reaction is written down, or an analysis or recipe calculated.
formula
A modern chemist knows that when writing a chemical formula, constant rather than variable subscripts are used. do ‘One must use constant subscripts in chemical formulas’ is in effect a statement of the law of definite proportions. Similarly, in writing such a formula one does not normally use fractional subscripts like FeO,.,,,. ‘One must use small whole number subscripts in chemical formulas’ is a statement of the law of multiple proportions. The laws must be seen as an essential part of the basis of the prevailing theoretical structure of chemistry, in spite of their almost invisible status. Can it then be argued that they ought not to be regarded as laws because of their unacceptable character? While it is clearly possible to take this view, I would consider it undesirable. There are several problems with adopting this attitude. The first is that it would contribute to communication difficulties. An account of ‘laws of nature’ that requires us to consider that Newton’s laws and Boyle’s law are laws of nature, while Dalton’s law and Ohm’s law ure not, will cause confusion at best. At worst. it amounts to Humpty-Dumptyism.41 It could be argued that the practice of scientists in freely labelling such diverse types of statement as ‘laws’ has led to a situation where the notion of a law of science is so broad and diffuse as to be useless. In this case, there may be a call for philosophers to adopt a narrower and more rigid definition of a law of science. But the consequence of this would be that a philosopher could not just introduce X’s law into a discussion as an example, without first going to some trouble to establish its credentials as a respectable law of science according to the narrower definition. Philosophers manifestly do not do this! The second
problem
is an extension
of this same difficulty.
Because
of the
diversity of character discussed earlier, particular laws are likely to be admitted as respectable in one philosopher’s account, while being rejected by another. We cannot move to a narrower definition of what is a law of science until some sort of consensus has been established. A third, and quite different problem, is that a narrow purist’s view of laws of nature is likely to lead to a model where specific laws arise only in physics, and the rest of science is likely to be regarded as a vast anarchy, if not disregarded “‘There are three instances where variable of compounds rather than a single substance, air pollution studies; (ii) when a new substance (iii) when referring to a berthollide as an 0.93 > x > 0.32. “r“‘When I use a word”, Humpty Dumpty choose it to mean - neither more nor less.“’
subscripts are found: (i) when referring to a group as in NO, as a generic term for oxides of nitrogen in has been prepared but is not yet fully characterized; exception to definite proportions, e.g. Na,WO, said in rather a scornful tone, “it means just what I Lewis Carroll, Alice Through the Looking Glass.
Philosophers
altogether. before
versus Chemists concerning ‘Laws of Nature’
As Hutchison
we recognize
has recently warned:
a law of nature,
629
‘If we insist on absolute
we are not going
certainty
to get very many
of
them!‘42 Current treatments of laws of nature concentrate on physics, and particularly on the highly developed areas of physics - mechanics and electromagnetism. When forced to turn to laws of chemistry,
writers come out with something
like
‘gold is a yellow metal with atomic number 79’ as a law of chemistry.43 No chemist would regard this law-like statement as a law. Although gold is a kind among samples of material, it is an individual among elements. It is something a chemist wishes to generalize away from. The alleged law is actually a data statement as far as the chemist is concerned. Chemists do not spend their time and energy checking that one sample of substance X behaves in the same way as another. The laws and relationships that interest them involve such things as how and why the behaviour of substance X is analogous to that of substance Y. The properties of gold, and of other substances, are compiled in volumes with titles like ‘Handbook of Chemical Reference Data’ ~ certainly not in volumes entitled ‘Compilation of Laws of Chemistry’. On the other hand, chemists have numerous dicta that they do refer to as ‘laws’. These laws indicate the connections and analogies between the properties of different substances. Many of them are non-universal. A few are imprecise. By and large they cannot be seen as ‘law-like statements’, as defined by philosophers of science.4 Even physicists in less developed and less quoted areas of their subject - thermodynamics, statics, fluid mechanics, materials are in many respects in a similar situation. Ultimately, the best policy is to define ‘laws of nature’ in such a way as to include most or all of the very diverse dicta that scientists have chosen to regard as laws of their various branches of science. If this is done, we will find that there is not a particular character that one can associate with a law of nature.
Acknowledgements - The author wishes to thank Dr John Christie for extensive discussions help with the more technical Neil Thomason for reading
4*K
Hutchison
aspects of chemistry in this paper. The author earlier drafts of this paper and for a number
‘Is Classical
Mechanics
Really
Time-Reversible
of and also wishes to thank Dr of useful suggestions.
and Deterministic?‘,
British
Journnlfor the Phbosophy of Science 44 (1993), 316. 43E.g, R. M. Chisholm, in Analysis 15 (1955), 101, 103; J. Bigelow, B. D. Ellis and C. Lierse, The World as One ofa Kind (preprint, La Trobe University Philosophy Dept, 1991) p. 23. &E.g. Armstrong, op. cit., note 26, pp. 6-S.