SCIENTIFIC EXPLANATION george gale

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SCIENTIFIC EXPLANATION 

george gale 

1. INTRODUCTION 

The great French philosopher-historian of science Emile Meyerson (1859–1933) 

began his 1929 Encyclopedia Britannica article ‘Explanation’ with the following 

words: 

What is meant by explaining a phenomenon? There is no need to insist on the importance 

of this question. It is obvious that the entire structure of science will necessarily depend 

upon the reply given. (Meyerson 1929: 984) 

Meyerson’s conclusion would be difficult to overstate: the structure of any given 

science – indeed, of science itself – is developed around the ideal of explanation 

peculiar to it. Explanations in physics differ formally and materially from those 

in biology; and both differ from explanations provided by geologists and sociologists; 

even more generally, explanations in science differ widely from those 

given in, say, law or religion. 

2. MEYERSON ON THE TWO MODES OF EXPLANATION 

From the publication of the 1908 first edition (of three) of his monumental 

Identité et Realité (Identity and Reality) until his death in 1933, Emile Meyerson 

was not only France’s dominant philosopher of science, he was one of the 

most important philosophers of science throughout the Western world. In the 

opening chapter of Identity and Reality, Meyerson speaks of two sharply opposed 

modes of explanation: the ‘mode of law’, and the ‘mode of cause’. Each mode has 

ancient philosophical roots. Law-explanations may with some justice be traced 

to Heraclitus’s dictum that everything changes except the law of change itself. 

Cause-explanations, according to Meyerson, trace back through atomic theory 

all the way to Parmenides’s notion of the unchanging self-identity of being. 

In his own era, Meyerson identified himself with the philosophical lineage 

that espoused cause-explanations; as his opposition he identified most especially 

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Scientific explanation 607 

Comte, Mach, and their followers in positivism, among whom he numbered 

his contemporary Pierre Duhem and the members of the Vienna Circle. 

To speak very roughly, the two forms of explanation may be characterised 

as follows. Law-explanations show that phenomena are related in dependable 

patterns. Meyerson quotes Berkeley’s view as paradigmatic: 

For the laws of nature being once ascertained, it remains for the philosopher to show 

that each thing necessarily follows in conformity with these laws; that is, that every 

phenomenon necessarily results from these principles. (Berkeley 1901: §37) 

Taine puts it even more simply: ‘A stone tends to fall because all objects tend 

to fall’ (Taine 1897: 403–4). An adequate law-explanation, then, is produced 

by showing that some target phenomenon is a consequence of an accepted 

rule, or, best, of a well-established law of nature. For the most part, French 

philosophers of our period – with the exception of Duhem and also Poincaré – 

were not legalistes (supporters of law-explanations). It was among the Anglo- 

Saxons, including Russell, Bridgeman, Carnap, and others of the Vienna Circle, 

that the law-explanation was brought to its highest perfection, as we will see 

below. 

Meyerson links modern cause-explanation to Leibniz’s principle of sufficient 

reason, most especially its dynamical statement that ‘the whole effect can reproduce 

the entire cause or its like’ (Leibniz 1860: 439). Underlying this, Meyerson 

notes, ‘we see that the principle of Leibniz comes back to the well-known formula 

of the scholastics, causa aequat effectum’ (Meyerson 1908 [1930]: 29). Thus, 

‘the principle of causality is none other than the principle of identity applied to 

the existence of objects in time’ (Meyerson 1908 [1930]: 43). Although murky as 

here stated, when cashed out in practice the principle is clear enough: ‘according 

to the causal principle’, in an adequate explanation ‘the original properties plus 

the change of conditions must equal the transformed properties.’ (Meyerson 

1908 [1930]: 41). In other words, an adequate cause-explanation necessarily entrains 

an object or objects, and describes how these objects preserve relevant 

aspects of their identity throughout the change. Prototypical examples of this 

type of explanation would include chemical equations which exhibit the conservation 

of mass and energy at the level of the atom, ion, or molecule. Since 

Meyerson was a trained chemist, his choice of prototype is not in the least odd. 

Underlying Meyerson’s distinction between the two forms of explanation 

is his analysis of the goals of science. Science, he says, has two separate and 

distinct goals. The first is a utilitarian one, namely, science serves to make our 

lives easier, or better, or, in some cases, possible at all. This it does through 

prediction: ‘foresight is indispensable for action’ and ‘action for any organism 

of the animal kingdom is an absolute necessity’ (Meyerson 1962: 22). Thus,


608 George Gale 

the dog, when pursuing the rabbit, is able to foresee – to predict – the path of 

his quarry. Humanity’s science, according to proponents of law-explanation, is 

nothing less than an exquisite means to satisfy this necessity. Meyerson quotes 

Poincaré with satisfaction: ‘“Science” as H. Poincaré has so well said, “isarule 

of action which succeeds”’ (Meyerson 1908 [1930]: 20; Poincaré 1902a: 265). 

Proponents of law-explanation justify their choice by arguing that science’s goal 

is prediction alone. 

On the other hand, underlying cause-explanation is the deeply human need 

to understand: Meyerson again cites Poincaré, who ‘says: “In my view knowledge 

is the end, and action is the means [and] Aristotle had already said: ‘All 

men by nature are actuated by the desire for knowledge’.”’ (Meyerson 1908 

[1930]: 42; Poincaré 1902a: 266). Referring again to Leibniz’s version of the 

principle of cause-explanation, Meyerson remarks: ‘wherever we establish it, 

the phenomenon becomes rational, adequate to our reason: we understand it 

and we can explain it. This thirst for knowledge, for understanding, is felt by 

each one of us’ (Meyerson 1908 [1930]: 42). 

Scientific reasoning, indeed, scientific rationality, is not in principle different 

from ordinary, common sense, human reasoning and rationality. In ordinary 

reasoning, a phenomenon is made understandable, ‘rational’, when it has been 

linked to an object, its properties, and its behaviour. Science, according to 

Meyerson, is nothing more than the extension of ‘common sense’ into new 

domains: in this role, science creates, invents, discovers new sorts of objects 

which can act as the causes of phenomena which are beyond ordinary experience. 

Thus, the ordinary concept of ‘boiling’ and an object’s ‘boiling point’ is 

linked to the disappearance of a spot of a new substance, gasoline (Meyerson 

1908 [1930]: 45). 

3. OTHER EPISTEMOLOGISTES 

Léon Brunschvicg (1869–1944) was not a philosopher of science in the same 

measure as Meyerson: although Brunschvicg based his thought in the history of 

science (as well as in the history of Western philosophy), his focus upon science 

was as means, and not as end. Brunschvicg’s goal was to understand how reason 

contributed to human experience, and, in so doing, became ever more conscious 

of itself over time. Since, like Meyerson, Brunschvicg believed that the history 

of science captured some of the finest examples of the powers and behaviours of 

human reason at work, analysis of the history of science would serve his goal of 

understanding reason and its works. Brunschvicg, again like Meyerson, believed 

that the mind itself made a significant contribution to the world as it was finally 

known: ‘Positive science goes from the mind to matter, and not from matter



to the mind’ (Brunschvicg 1931: 144). Yet, his idealism was not unalloyed; in 

the end knowledge was a product both of the mind and of matter, working 

together, in an essentially dialectical interaction. Most importantly, Brunschvicg 

viewed science as a dynamic process, an open-ended creative action, that not 

only exhibited the speculative freedom of the mind, but also assured humanity’s 

practical liberty. 

Brunschvicg’s ideas about scientific theorising and explanation were less dramatic. 

A hypothesis or explanation was true just in case it was intelligible. Over 

time, the dialectic between scientific reasoning and matter ‘gives to thought 

an increasing approximation to reality’ (Brunschvicg 1905: 12). It is evident 

that both the spirit of Brunschvicg’s thought, as well as some of its particular 

doctrines, were influential during the period between the wars. After all, 

he occupied the chair of general philosophy at the Sorbonne for thirty years: 

1909–39. One philosopher of science who came especially under his influence 

was Gaston Bachelard. 

Bachelard (1884–1962) was a late bloomer: he started his work life as a postman; 

later, in 1913, he got a teaching certificate and taught secondary-school 

science for fourteen years. Then, in 1927, he got his doctorate and in 1930 

became professor of philosophy in Dijon. His experiences as a science teacher 

directly affected his philosophy of science. At the time when he was teaching, 

the ministry of education kept extremely tight reins on what would be taught in 

science, and how. In particular, the strictures forced an ontology-free positivism: 

‘One was directed not to speak the word “atom”. One always thought about 

it; but one could never speak about it. Some authors . . . gave a short history 

of atomist doctrines, but always after a totally positivist exposition’ (Bachelard 

1933: 93). As far as Bachelard was concerned, this was all wrong: ‘In actual fact, 

as Meyerson has proved, science usually postulates a reality’ (Bachelard 1969: 13; 

Jones 1991: 24). But, except for the usual focus upon the knower, and agreement 

about foundations in history of science, this was one of the few points where 

Bachelard’s philosophy agreed with that of his older colleague, Meyerson. 

From Brunschvicg, Bachelard got the idea of the open-endedness of the task 

of scientific reasoning. He communicates this notion in a particularly evocative 

way: ‘The scientist leaves his laboratory in the evening with a program of work 

in mind, and he ends the working day with this expression of faith, which is 

daily repeated: “Tomorrow, I shall know”’ (Bachelard 1973: 177; Jones 1991: 

59). Bachelard’s doctoral thesis was entitled Essai sur la connaissance approchée 

(Essay on the Approach on Knowledge) (1969); this connotes (at least in French) the 

notion of knowledge as approximate, ‘being approached only as a limit’, perhaps 

even, ‘under construction’. Again, the root of the idea is found in Brunschvicg: 

knowledge is a product, a synthesis produced by the mutual interaction between



the mind and the world. Although Bachelard himself does not use the term 

‘dialectic’ to refer to this interaction, Brunschvicg would not have so hesitated; 

neither should we: knowledge is produced by two compelling, albeit contradictory, 

impulses: ‘rationalism’ and ‘realism’. In practice, these two metaphysics 

play out simply enough: ‘if scientific activity is experimental, then reasoning will 

be necessary; if it is rational, then experiment will be necessary’ (Bachelard 1973: 7; 

Jones 1991: 48). Obviously, what is involved here is mutual interaction between 

mind and matter in producing knowledge. But mutuality is not equality: in 

the end, at least in post-Einsteinian science, it is the rationality of mathematics 

which will prove most significant over against the matter of experimental 

reality: 

Mathematical realism, in some shape, form, or function, will sooner or later come along 

and give body to thought, making it psychologically permanent, ...revealing, here as 

everywhere else, the dualism of the subjective and the objective. (Bachelard 1973: 8; 

Jones 1991: 49; author’s italics) 

This remark shows two important ways in which Bachelard differs from 

Meyerson. In the first place, Bachelard believed that Einstein’s relativity theory 

represented so great a divergence from earlier theories – mostly because it raised 

to an unprecedented level the ontological creative power of mathematicisation – 

that it required a ‘break’ (= rupture) in philosophy of science, a rupture of the 

classical from the modern. Meyerson argued, in opposition, that relativity theory 

in fact represented the triumph of classical mechanics. The two thinkers 

fought it out in book-length form: Meyerson’s La Déduction relativiste 1925 versus 

Bachelard’s La Valeur inductive de la relativité (1929). The opposition between 

Meyerson’s ‘deduction’ and Bachelard’s ‘induction’ in their respective book-titles 

is especially salient: after Einstein, Bachelard believed, all attempts to use deductive 

logic in scientific explanations are fruitless. Meyerson believed precisely the 

opposite. 

The second issue dividing the two men follows directly on the first. According 

to Meyerson, scientific reasoning – most particularly, scientific explanation – 

is not different in kind from reasoning in ordinary common affairs. Reason’s 

activities were then, are now, and will always be the same. Bachelard denied this 

flat out. Because post-relativity scientific thinking mathematicises the world in 

an entirely new way, the world as newly mathematicised reaches back into the 

thinking apparatus and re-shapes it; thus the new explanatory achievements 

produce a psychologically ‘permanent’ change, an epistemological rupture in 

the manner of thinking itself (Bachelard 1973: 59). It follows from this that 

scientific thinking in general, and scientific explaining in particular, is different 

from what it once was; most especially, it is and can no longer be, deductive.



It is obvious from even this short discussion that these French thinkers have 

had enormous influence throughout the twentieth century. Meyerson’s historical 

approach, plus his conclusion that scientific theories and explanations necessarily 

include ontologies, were taken up intact by Kuhn, as he himself admitted. 

Brunschvicg and Bachelard adopted historical approaches as well, and added 

to Meyerson’s thinker-centred idealism the notion of the open-ended ‘project’ 

of constructing scientific knowledge. This latter view is now, sixty years later, 

one of the major themes in end-of-the-century science studies. Clearly, the 

French causalistes held significance far beyond their own times. But France did 

not hold a monoply on cause-explanation proponents. 

4. NORMAN CAMPBELL 

Norman Campbell (1880–1949) was an English physicist who, after reflecting 

deeply upon his practice, developed and propounded an influential philosophy of 

science. Like Meyerson, he believed that explanation in science was contiguous 

with explanation in ordinary life; moreover, again similarly to Meyerson, he 

held that explanations necessarily entrained causes: objects, their properties, 

and interactions. Finally, writing of the positivists, and most certainly Mach in 

particular, he wrote: ‘I cannot understand how anybody can find any interest 

in science, who thinks that its task is completed with the discovery of laws’ 

(Campbell 1921: 89). 

Laws, of course, are part of a scientific theory. But, thought Campbell, they 

are not the important part; indeed, almost invariably, discoverers of laws ‘have 

no claim to rank among the geniuses of science’ (Campbell 1921: 92). On the 

other hand, every important explanatory theory ‘is associated with some man 

whose scientific work was notable apart from that theory’ either because of 

other important discoveries or because of their ‘greatly above average work’ 

(Campbell 1921: 92). Explanations do their work by reducing the unfamiliar to 

the ‘familiar’ (Campbell 1921: 77). The reduction takes place when the objects, 

properties, or interactions in the unfamiliar system are placed in analogy with 

objects, properties, or interactions in a familiar system: 

The explanation offered by a theory . . . is always based on an analogy and the system 

with which an analogy is traced is always one of which the laws are known. (Campbell 

1921: 96) 

Moreover, the familiar system ‘is always one of those systems which form part 

of that external world’ which science studies (Campbell 1921: 96). Analogies, 

therefore, inevitably make claims about what exists in the external world.



Campbell’s prototypical case involves gases. The laws of the behaviour of 

gases – Boyle’s Law and Gay-Lussac’s Law are his examples – are well known. 

But what makes these laws intelligible, what provides an explanation, is the 

Dynamical Theory of Gases: ‘a gas consists of an immense number of very 

small particles, called molecules, flying about in all directions, colliding with 

each other and with the wall of the containing vessel ...etc.’ (Campbell 1921: 

81). The phenomena described by the two laws – pressure, for example – are 

explained by the movements and interactions of the molecules. But the reason 

this explanation succeeds is simply the fact that the movements of the molecules 

are analogous to motions in the ordinary world: 

the behaviour of moving solid bodies is familiar to every one; every one knows roughly 

what will happen when such bodies collide with each other or with a solid wall ...Movement 

is just the most familiar thing in the world...Andsobytracing a relation between 

the unfamiliar changes which gases undergo when their temperature or volume is altered, 

and the extremely familiar changes which accompany the motions and mutual reactions 

of solid bodies, we are rendering the former more intelligible; we are explaining them. 

(Campbell 1921: 84) 

With Campbell we reach the last cause-explanation advocate of the period from 

1915 to 1945. We now turn to an examination of the other side of the controversy 

and examine the views of those who argued that scientific explanations are 

provided by applications of laws, those philosophers called positivists. 

5. POSITIVISM 

positivism began as a reform movement, an attempt to bring philosophical salvation 

to wayward science (Gale 1984: 491). Two names are especially associated 

with the origins of positivism, those of the French mathematician and social 

scientist Auguste Comte (1798–1857), and the German physicist Ernst Mach 

(1838–1916). As all reform movements must, positivism contained both an attack 

upon a perceived evil, and a manifesto proclaiming the correct way forward. The 

attack focused upon the metaphysical proclivities of then-contemporary science. 

Explanatory hypotheses such as atomic theory and, for Mach especially, energy, 

and absolute space and time, were taken to be speculative excesses, unverifiable 

postulates about forever-hidden structures of Reality. The problem with 

causal explanations, according to positivism, is that they tend to be wrong, and, 

once new theories are proposed, old hypotheses must be discarded along with 

the commitments of the scientists who believe them. A major case in point 

was Lavoisier’s revolution in chemistry, during which the substance ‘phlogiston’



went out of existence, only to be replaced by the substance ‘oxygen’. Science, 

according to the positivists, simply had no need to become involved with such 

illusory entities. 

What behoved science was to stick to its ‘positive’ (hence the name) contributions: 

the well-verified laws which tended to remain constant even through 

a drastic revolution, such as Lavoisier’s. Moreover, according to the positivists, 

laws satisfied the most important goal of science, its utilitarian promise to provide 

prevision, prediction, of the future course of events. Although elimination 

of cause-explanation would leave unattained humankind’s desire for intellectual 

satisfaction – the goal of science according to Meyerson, Bachelard, et al. – 

law-explanation and its attendant prediction was a safe and eminently satisfiable 

goal. 

Underlying the safety of law-explanation and prediction was a thoroughgoing 

empiricism, a commitment to exclude from science all notions, concepts, and 

words which could not, one way or another, be tied to entities apparent to 

the senses. Thus, following Hume, in order for a term to have any meaning at 

all, it must be tied to some observable entity. For example, ‘pressure of a gas’ 

could be tied to the felt elasticity of a balloon, or, perhaps, the visible reading 

of a manometer. But since ‘an atom’ provided no such empirically observable 

concomitant, the term had no meaning at all; hence the concept, and its verbal 

expression, must be discarded from science. The ultimate sought-for goal was the 

reformulation of all scientific theories in meaningful terms, terms with direct ties 

to empirical observation. This would be accompanied by the elimination of all 

meaningless terms, that is, all those terms such as ‘atom’, ‘energy’, and ‘absolute 

space and time’, which referred to entities hidden or otherwise unavailable to 

empirical observation. 

Two French thinkers added significant elements to the positivist tradition. 

These are the physicists Henri Poincaré(1854–1912) and Pierre Duhem (1861– 

1916). For both men the only acceptable theory is one which is strictly mathematical; 

this because, as Poincare notes, the sole end of theory ‘is to co-ordinate 

the physical laws which experience makes known to us, but which, without 

the help of mathematics, we could not even state’ (Poincaré 1889: 1). Duhem, 

Meyerson remarks, ‘affirms in the same way that the mathematical theory is 

not an explanation, but a system of mathematical propositions; it classifies laws’ 

(Meyerson 1962: 52). Duhem was a genuinely talented historian of physics; he 

knew full well that ‘several of the geniuses to whom we owe modern physics 

have constructed their theories in the hope of giving an explanation of natural 

phenomena’ (Duhem 1906: 46). Yet, as Meyerson remarks, Duhem’s ‘own ideas 

are diametrically opposed to this manner of thinking’ (Meyerson 1908 [1930]:



53). Duhem’s heroically steadfast rejection of metaphysics, directly in the face of 

his own thorough grounding in the history of his subject, served as an inspiration 

to later positivists. 

Poincaré’s contribution was more direct. Although both he and Duhem were 

strictly committed to mathematicised theories in physics, just as Mach before 

them, this commitment, when carefully examined, represented a sharp 

challenge to their equally strict empiricist beliefs. Although ‘pressure of a gas’ 

and ‘volume of a gas’ are concepts which can be cashed in via empirical observations, 

what can be made of the mathematical operations contained in, say, 

Boyle’s law that the pressure multiplied by the volume of a given container of 

gas has a constant product throughout changes in either? That is, what is one to 

make of the ‘×’ and the ‘=’ in the law p1 × v1 = p2 × v2? At least prima facie, 

multiplication signs and equal signs do not signify anything genuinely empirical. 

Poincaré made a very sensible response to this difficulty. He proposed that 

mathematical operations referred to the behaviour of physicists; that is, through 

convention, physicists had come to agree to use multiplication and equality 

as procedures during instances of Boyle’s Law applications. Thus, if one were 

to observe a physicist doing a Boyle’s Law application, one would observe the 

physicist measuring the pressure of the gas, then measuring the volume of the gas 

and then multiplying the measurements. The physicists’ ‘multiplying the measurements’ 

is just as empirically observable as their ‘measuring the volume’. 

This conventionalist analysis extended to all mathematical operations; indeed, 

as we shall see, it applied to all formal manipulations, including those of formal 

logic. 

Poincaré’s solution became a permanent part of the positivist view. At about 

the same time, however, a development of equal significance to the development 

of positivism was taking place in England. I refer, of course, to Russell and 

Whitehead’s development of symbolic logic (Whitehead and Russell 1910–13). 

6. ADDING LOGIC TO POSITIVISM 

Philosophical concern to impose logical methods on scientific thinking is an 

ancient and honorable endeavour. It was Aristotle himself who laid it down 

that deductive logical structure is a necessary condition for any discipline to call 

itself ‘scientific’. Descartes and Leibniz reaffirmed this demand during the early 

stages of modern science. But none of these projects fully succeeded. What was 

missing was a sufficiently rich, powerful, and precise logical apparatus. Deductive 

syllogisms produced from the syntax and semantics of everyday speech just 

could not do the job capturing the richness of scientific language. Whitehead 

and Russell’s axiomatic system for symbolic logic, the logic of quantifiers and



predicates with identity, made available for the first time a language which 

seemed to offer the potential to allow the empiricist re-formulation so desired 

by the positivists. Thus did the positivists become the ‘logical’ positivists (or, in 

some camps, and for obvious reasons, the ‘logical’ empiricists). 

Rudolf Carnap (1891–1970) presented the first mature interpretation of logical 

positivism in his 1928 Der logische Aufbau der Welt. Carnap, true to Mach’s 

empiricism, employs as his central concept Zurückführbarkeit, or‘reducibility’, a 

process through which one concept is reformulated in terms of other(s). A concept 

x is said to be reducible to a set of concepts Y if every sentence concerning 

x can be reformulated in sentences concerning concepts belonging to Y, with 

no loss of truth. The reformulation is carried out according to a ‘constitutional 

definition’, one side of which is ultimately – perhaps through more reformulations 

– linked to a ‘basis’, a set of basic objects. For Carnap, at this stage of 

development staying close and true to Mach’s sensationalism, the basic objects 

were mental objects: a certain kind of experience. During the reformulation 

process, the number of, and number of kinds of, concepts was sizeably reduced, 

with the result that the final product, the concepts of the basis, would be both 

simplest and minimum in number. 

Carnap’s basic concepts got their meaning by being cashed into statements 

about mental experiences. Although this procedure certainly satisfies most 

empiricist criteria of meaning (including the very one Carnap used, which 

he called ‘Wittgenstein’s principle of verifiability’), it did not satisfy Carnap’s 

Vienna Circle colleagues, in particular, Otto Neurath, who was a thoroughgoing 

physicalist. After some argument, Neurath convinced Carnap that basic concepts 

should be defined in physicalist terms, that is, by reference to quantitative descriptions 

of events occurring at definite spatio-temporal locations. Neurath preferred 

this physicalist language because it allowed for agreement among observers 

about the occurrence or non-occurrence of the event referred to (Neurath 

1932). Moreover, since the language symbolised the events of physics, it would 

serve to capture all other sciences which, presumably, would be reducible to 

physics. Thus, for example, theories in chemistry or biology would be formulatable 

in terms of the physicalist basis concepts.When fully implemented, the 

physicalist basis would accomplish once and for all that long-sought Holy Grail of 

all empiricist proponents of law-explanation, the elimination from science of the 

metaphysical excesses hypothesised by the cause-explainers. This achievement 

was duly announced by Carnap in his article ‘Überwindung der Metaphysik 

durch logische Analyse der Sprache’ (‘The Elimination of Metaphysics through 

the Logical Analysis of Language’) (Carnap 1932). 

A final fillip was added to physicalist empiricism by the Nobel-prize-winning 

American physicist: W. Bridgman (1882–1961). Bridgman held that Einstein’s



brilliant achievement in discovering relativity theory did not come through a 

disclosure of facts or by showing something new about nature. Rather, Einstein’s 

discovery dramatically highlighted the value of sound conceptual analysis: after 

an analysis of then-current notions of time, and the operations used in measuring 

it, Einstein, according to Bridgman, saw that the concept of time, as generally 

understood, was severely flawed (Bridgman 1936). 

For example, Einstein saw that there was no possible way to measure whether 

two spatially separated events were simultaneous or not. Hence ‘simultaneity 

of occurrence’ was a temporal concept that could not be given a meaning in 

terms of a measuring operation. But since this very concept was fundamental in 

Newtonian theory, Einstein’s analysis suggested that Newtonian theory was fundamentally 

flawed, and needed to be replaced. Based upon this case, Bridgman 

argued forcefully for elimination from physics of all concepts which could not 

be defined in terms of operations, actual measurements, carried out by actual 

physicists. 

The empiricist bent of this, not to mention its positivist reformational spirit, 

will not go unnoticed. Although not all logical positivists adopted Bridgman’s 

emendation, many did. Moreover, scientists in psychology (e.g., Skinner) and 

linguistics (e.g., Bloomfield) called for operationalist reform. With Bridgman’s 

contribution, logical positivism was finally in a position to provide a canonical 

formulation of its view on scientific theories. This is what it looked like: 

A theory is an axiomatised deductive system formulated in a symbolic language 

having the following elements: 

1. The theory is formulated in a first-order mathematical logic with equality, L 

2. The nonlogical terms or constants of L are divided into three disjoint classes called 

vocabularies: 

a. The logical vocabulary consisting of logical and mathematical constants. 

b. The observation vocabulary, V0 containing observation terms. 

c. The theoretical vocabulary, VT containing theoretical terms. 

3. The terms in V0 are interpreted as referring to directly observable physical objects or 

directly observable attributes of physical objects. 

4. There is a set of theoretical postulates T whose only nonlogical terms are from VT. 

5. The terms in VT are given an explicit definition in terms of V0 by correspondence rules 

C – that is, for every term ‘F’ in VT, there must be a definition for it of the form 

‘(∀x)(Fx ≡ Ox)’ where ‘Ox’ is an expression of L containing symbols only from V0 

and possibly the logical vocabulary. 

(But it must be kept in mind that various aspects of the positivist view on theories 

were in nearly constant change from the first moment of their publication 

in 1928; most of the changes concerned clauses 2 and 5, particularly where their 

content involved the logic of the conditional.)



An example of this approach applied to the theory of metals might look 

something like this: 

Observation vocabulary, Vo: 

conducts electricity, is ductile, expands, is heated 

Theoretical vocabulary, VT: 

is a metal 

In accordance with clause 5, the predicate ‘is a metal’ would thus be introduced 

by a correspondence rule, in this case: 

(∀x)[x is a metal ≡ (x is ductile &xconducts electricity)] 

that is, metals are things which are ductile and conduct electricity. Laws of 

Nature presumably would be postulates (or, in some cases, axioms or theorems) 

of the theory. The following might be taken to be a plausible example of a Law 

of Nature: 

(∀x)[(x is a metal &xisheated) → x expands] 

i.e. metals expand when heated. 

7. PREDICTION, EXPLANATION AND 

THE COVERING-LAW MODEL 

As noted earlier, law-explainers typically take prediction to be science’s goal. 

For the most part, the logical positivists agree with this position, but with a 

very interesting twist. The logical positivist account of explanation is embedded 

in the view of theories and laws given just now, and one of its features is the 

symmetry of explanation and prediction. According to this view, an explanation 

and a prediction have exactly the same logical form, but with reversed timesignatures. 

Thus, an explanation is a ‘prediction’ of the past (sometimes called a 

‘retrodiction’), and a prediction is an ‘explanation’ of the future! What lies at the 

center of the doctrine is the single logical form which serves both explanations 

and predictions; let us therefore examine the logical form of explanations. 

In this account, L stands for a suitable Law; and C stands for an initial (factual) 

condition. The form of an explanation is: 

L1,...,Ln, C1,...,Cn (Explanans) 

E (Explanandum) 

Thus the Law(s) in conjunction with the initial conditions – the ‘explanans’ – 

are sufficient to imply logically the explanandum, that is, the phenomenon 

needing to be explained. The name ‘covering law model’ of explanation comes



from the fact that laws are used to ‘cover’ all the cases needing explanation. Here 

is a simple example: 

Phenomenon / Query: ‘Why did the copper penny (p) expand when heated?’ 

Explanans: 

Law: (∀x) [(x is a metal & x is heated) → x expands] 

Conditions: p is a metal & p was heated 

Explanandum: 

p expands 

It is clear that such explanations function as deductive arguments. In justifying 

a prediction exactly the same form would obtain, but the initial query and the 

verb tense would be different: 

Query: What would happen if I heated this copper penny? 

Prediction: Given that this copper penny is metal, if it were heated it would 

expand. 

It should be noted that the account presented here was never given as such 

by any particular logical positivist thinker, especially as regards its rendering in 

logical symbols. However, given what many of these thinkers stated, remarked, 

and argued at various time during the 25-year history of this model, they would 

be hard put to provide an account materially different from that presented here. 

8. CONCLUSION 

After a brief hiatus during the Second World War, philosophers of science resumed 

work on the problems of scientific explanation. For the most part, the 

Anglophone community counted itself among the legalistes, more particularly, 

especially in America, as logico-empirico-positivists. Yet opposition from the 

causalistes never entirely disappeared. By the 1960s, the legalist model of explanation 

was under serious attack, from both within and without. Harré and Hesse, 

for example, continued the Meyersonian-Campbellian tradition of emphasis 

upon the role of analogies and models, with their attendant causal ontologies. 

Indeed, Hesse’s (1966) dialogue featured a legalist called ‘The Duhemist’ pitted 

against a causalist called, naturally enough, ‘The Campbellian’. Kuhn, with explicit 

reference to Meyerson, opposed an historical methodology to the logical 

perspective of the positivists, with devastating results. 

In the end, what is perhaps surprising is that the entire century’s agenda 

for philosophical controversy about scientific explanation was effectively set, in 

France, by the argument in 1908 between Poincaré and Duhem – the legalists – 

and Meyerson – the causalist. In a very real sense, much of the following ninetytwo 

years of philosophical controversy are footnotes to that argument.

SCIENTIFIC EXPLANATION george gale

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