Our general ideas, from those immediately bordering on the concrete
to those which attain pure symbolism, constitute a hierarchy of
ever-increasing simplicity. What value must be assigned to this
thinking by concepts, in proportion as it ascends higher in the scale?
We are all familiar with the debates upon this question, bearing, as
it does, fundamentally upon the _objective_ value of abstraction and
generalisation. Psychology, as the science of facts, is able to ignore
this point, since it is concerned only with the nature of the two
intellectual processes, their variations, and adaptations to multiple
cases. Still, it is reasonable enough that it should assume a position,
at any rate provisionally, and for convenience of discussion.
To recall only the two extreme opinions: On the one side we have
those who maintain that the particular alone exists—for event or
individual—that our general ideas are but a means of maintaining order,
while they teach us nothing as to the nature of things. They are
comparable to a catalogue, or to the card-index of a library which are an
easy indicator to the millions of books, leaving us totally ignorant as
to their contents and value. Hence, the higher we ascend, the farther we
penetrate into the region of the fictitious and the vacant.
On the other hand, there are those who assert that nature has general and
fixed characteristics; in discovering them, we penetrate into the essence
of things. Events and individuals have but a borrowed existence; under
their fleeting appearances, we must seek the enduring; and thus, the
greater the generalisation, the higher we rise in reality and in dignity.
The psychologist can only take up the position of relativity. To him,
general ideas are approximations: they have an objective value, but it is
provisional and momentary, dependent on the variability of phenomena and
on the state of our knowledge.
On the one hand, the similarities that are the substrata of
generalisation are not fictitious. Since, moreover, knowledge of the
laws of nature has a practical value, by enabling us to act upon things,
and since we fail, in ignorance of them,—we are fain, objections
notwithstanding, to attribute to them at least a certain measure of
objective value.
On the other, if there is evolution in nature, there must also be
evolution in our ideas, and the pretension to laws or types that are
fixed unalterably, becomes chimerical. There is no longer the sharp
distinction, as formerly admitted, between “essential” and “accidental,”
i. e., permanent and variable characters. The Primary epoch of our globe
may have obeyed laws which no longer hold for our Quaternary age: all
changes in the course of development. We shall return to this point in
the concluding section.
Without insisting further upon a debate that is of secondary interest
for the psychologist, we may remark that three principal periods can be
distinguished in the development of the Concept of Law: viz., the periods
of generic images, of concrete or empirical laws, and of theoretical or
ideal laws.
It is useless to study the first phase in detail, since it interests
us only as an embryonic form, a germ, or essay. It consists in the
mechanical conception of regularity for a very restricted number of
events. Resulting from the constant or frequent repetition of certain
cycles (the course of the sun, moon, seasons, etc.) it is organised in
the mind by a process of semi-passive assimilation, that of generic
images. Many men have had, and still have, only this shadow, this
simulacrum of law, resting upon pure association, upon practical habit,
upon the unreflecting expectation of an often-perceived recurrence.
Humble as it is, this notion was nevertheless useful in the education of
humanity, for it checked the exuberant tendency of the imagination to
people the world with capricious causes, obedient to no law. It prevented
the establishment of a rule of universal contingency; it was the first
affirmation of a faith in regular order. The progress of reflexion, and
methodical research, have done the rest.
We owe to Wundt (_Philosophische Studien_, 1886, III., p. 195 et seq.) an
observation of great interest to any one concerned in the development of
the idea of law. To-day this word is current in all the sciences; indeed
its most rigorous acceptance is in mathematics and chemical physics.
This was not always the case. In antiquity, the word was employed
almost exclusively in a social, juristic, moral sense. The concept of
natural law, regarded as a sort of order, a police-force, was only very
slowly formed and established. Copernicus and Kepler employed the word
“hypothesis.” Galileo calls the fundamental laws of nature “axioms,” and
those derived from them “theorems,” following the terminology of the
mathematicians. Descartes begins his Philosophy of Nature by laying down
certain _Regulæ sive leges naturales_. Newton says: _Axiomata sive leges
motus_. The extension of the word law is due apparently to the need of
establishing a clear distinction between the purely abstract axioms of
mathematics, and the principles to which we attribute an objective value,
an existence in nature. Montesquieu’s celebrated definition, “Laws are
the necessary relations derived from the nature of things,” exhibits
this concept in its highest degree of generalisation. We may note, in
passing, that in the enquiry referred to above (ch. IV.), nearly all the
answers indicate that images of the social juristic order were evoked,
although the scientific acceptance of the word was perfectly familiar to
a large number of the subjects: showing that the primitive signification
preponderates in the vulgar conscience.
In another article, entitled _Wer ist der Gesetzgeber der Naturgesetze?_
(_loc. cit._, pp. 493 et seq.), the same author maintains an opinion,
which, notwithstanding its paradoxical appearance, seems to me perfectly
valid. Descartes called the laws of nature “rules,” inasmuch as they
explain phenomena to us; “laws,” inasmuch as God constituted them _ab
initio_ as properties of matter. At a later period, nature takes the
place of God, which is still the survival of a pantheistic conception
of the world. Still later, the preponderating tendency is to call laws
by the names of their inventors: Mariotte, Gay-Lussac, Dulong and
Petit, Avogadro, Ohm, Weber, etc. “In the seventeenth century it was
God who established the laws of nature; in the eighteenth it was Nature
herself; in the nineteenth it is the affair of the scientists.” This
thesis agrees with what was said above, of the approximate character of
laws, of the mixture of objective and subjective elements that obtain in
their formulæ, and it is no paradox to assert that the state of mind of
a Mariotte, a Gay-Lussac, a Weber, etc., when they discover their law,
represents this approximation at a given moment.
I. Empirical laws correspond, broadly speaking, with the intermediate
forms of abstraction and of generalisation. They consist in the reduction
of a large number of facts to a single formula, but without any rational
explanation. In the course of events we discover a constant relation of
co-existence or of succession between two or several facts; we mentally
detach this regular relation from the total which includes it, and extend
it to other cases. Constancy is not even necessary for empirical laws,
frequency suffices: at least one often has to be content with it. These
laws abound in the half-sciences, and in embryo science: they are useful,
they give order and simplification.
Their first characteristic is that they are identical with fact. Laws
and facts are only two aspects of the same thing. To pass from facts to
their empirical law, is merely replacing simple and homogeneous cognition
by abstraction, multiple and heterogeneous cognition by perception.
Hence the empirical law is rightly compared to a general fact, and it
is legitimate in psychology to say the law of association or the general
fact of association. On the other hand (in virtue of the natural tendency
to anthropomorphism) vulgarisms such as “laws govern facts,” and the
like, encourage in many minds the illusion of an ideal world of law
superposed upon the world of facts, external to experience, and acting
upon it like a government.
A second characteristic, which though frequent is not universal, is
complexity. Necessarily objective, since it is a simple notation of
observed facts, the empirical law does not always succeed in embracing
the results of abstraction in one short and simple formula. Sometimes
it does so; sometimes it is confronted with a multiplicity that cannot
be reduced to a single proportion; in many cases it has to distribute
itself, and resignedly to employ a long formula. Ex.: in physiology,
Pflüger’s law (or the laws of reflexes), in linguistics, the laws
of Grimm, etc. Here there is a summary description, reduced to the
principal facts. It often has to cover a great number of details, as in
Listing’s law (of the rotation of the ocular globe). Plenty of examples
are to be found in the sciences that are in process of formation, and
ill-constituted: psychology,[128] ethics, sociology, etc. Empirical
law could only be further simplified by changing its nature, namely by
transforming it into theoretical law.
Empirical law is thus the type of law that is immanent, contained in the
facts, invoking their representation directly and indirectly by means of
intermediate abstraction, involving ascending degrees of abstraction,
that, at their highest level, bring it insensibly very near to ideal law.
II. Theoretical, or ideal, law corresponds with the higher forms of
abstraction. It exhibits increasingly approximative constructions of
the mind, in proportion as these ascend, and are farther removed from
experience. Empirical laws are the material whence they are derived, and
the transformation is accomplished at the moment, and in the degree, in
which description gives place to explanation. To minds accustomed to the
discipline of the strict sciences, this conception of law alone is valid,
and they are prone to treat with disdain or defiance the formulæ that are
a simple summing-up of the results of experience, judging them unworthy
of the name of laws. To the psychologist, the position is quite other:
empirical concept and theoretical concept are two forms, two aspects of
the same intellectual process: there is no constitutional difference
between them. Nevertheless, in its higher form, the concept of law has
its proper and special characteristics which must be noted.
1. Simplicity, as contrasted with the complexity of empirical laws; this
is the necessary corollary of the operation that gives rise to it, since
it is an abstraction of abstractions, the final result of a long series
of eliminations. Compare with the long, vague, entangled formulæ, charged
with details, of which examples were given above, the enunciation of the
higher laws, which are usually short and invariably precise. And, it may
be added, invariably lucid, at least to the scientist who is in the habit
of dealing with them, because he knows exactly what they cover. In this
connexion a saying of D’Alembert deserves to be recalled and considered,
because it discloses, better than any commentary, the psychology of
abstract minds: “The most abstract notions, such as the majority of
mankind regard as the most inaccessible, are often those which carry with
them the greatest elucidating power: our ideas seem to be blotted out by
obscurity in proportion as, in any object, we examine into its sensible
properties.”
2. Quantitative determination. The higher laws alone can assume a
numerical form, and it is a truism to say that the perfection of any
science is measured by the quantity of mathematics which it involves.
Not that mathematical formulæ imply or confer any magical virtue, but
they are the sign of reduction to clear and simple relations, and are
frequently an instrument of further progress. It is true that in the
domain of empirical law, there are many processes which attempt to
imitate quantitative determination: graphic records, curves, statistics,
percentages, etc. Yet these are often a very poor substitute for the
equation, or worse—for they offer an illusory preciseness, and are
fallacious.
3. It is well to insist upon the ideal character of these laws, because
one is apt to forget that, in virtue of their very abstraction, they can
be approximate only; and can but be applied, and reduced from theory
to practice, by means of rectifications and additions. It has been said
that “physical laws are general truths that are invariably more or less
falsified for each particular case.” All scientific men, and there are
many, who have reflected on the subject, bring out this character of
approximation.[129]
Thus—it is not absolutely true that a movement is uniform and
rectilinear. The theoretic law of the oscillation of a pendulum is
unrealisable, because there is no non-resisting medium, no totally rigid
and inextensible bar, no suspending apparatus capable of turning without
friction. A planet could only describe an exact ellipse if it alone were
turning round the sun: but as, in point of fact, there are several which
act and react upon one another, Kepler’s law remains ideal. It is known
by very accurate researches that Mariotte’s law of the relations between
the density of a gas, and the pressure which it bears, is not strictly
accurate for either; but the differences between theory and reality are
so slight that, in ordinary cases, they are negligible. The laws of
thermodynamics (conservation of energy, correlation of forces) which are
so much used in the present day because of their character of generality,
and are held by some to be the ultimate principle of phenomena, have
no absolute value. It is not, e. g., correct to say that all change
generates a change which can be re-transformed without loss or addition.
The first moment of enthusiasm passed, there was no lack of criticism and
of reservation on this point. And so in other instances, _ad infinitum_.
In brief, the concept of law, whenever it is more than a vague term in
the mind, corresponds either to a direct condensation of facts (empirical
laws), or to an ideal simplification (theoretical laws); but, imperfect
or perfect, the mental process is the same in the two cases. They differ
only in the degree of simplification attainable by analysis for any
given material or datum. If empirical law, which is in strict relation
with experience, has not been idolised, this distinction and misfortune
has frequently befallen the other categories. It has been forgotten
that, in the sciences as in the arts, the ideal is only an ideal,
although it is here attained by different means, viz., elimination,
voluntary omission for the sake of preciseness, a more or less artificial
reduction to unity. Consequently many have fallen into the strange
illusion of believing that, in manipulating experience by the labor of an
ever-growing abstraction, the absolute can be brought out.[130]