CHAPTER V.. Evolution of the Principal Concepts.

EVOLUTION OF THE PRINCIPAL CONCEPTS.

Section I.—The Concept of Number.

Return to lower phases: concrete and abstract.—Formation of idea of unity. Hypotheses as to its experimental origin: touch, sight, hearing, internal sensations, attention. Unity the result of decomposition, an abstract.—The series of numbers. Process of construction.—Function of signs: discussions of this subject 137

Section II.—The Concept of Space.

Extension as a concrete fact. Variable and relative characteristics.—Transition to concrete-abstract period.—Space (abstract): the current popular conception the result of imagination. Idle problems.—The true concept is the result of dissociation.—The notion of “function.”—Imagination of an infinite space.—Works on ideal geometry: constructive power of the mind; reinforcement of distinction between space as perceived and conceived 146

Section III.—The Concept of Time.

Real (concrete) duration: the present, its reality; its experimental determination: maximum and minimum. Reproduction of duration; experiments; indifferent point.—Variable and relative characteristics.—Origin of concrete notion of time: different hypotheses: external and internal sensations: presumption in favor of the latter.—Abstract duration (time). First stage, depends on memory and imagination only: corresponds (1) to generic images (representation of duration among the higher animals), and (2) to the concrete-abstract period (intermediate forms of abstraction). Primitive races. Why has time (and not space) been personified.—Second stage depends upon abstraction. Function of the astronomers: measure of time.—Infinite time.—Current hypotheses as to the psychologic process which constitutes the notion of time: sensations and consecutive images: sensations which are feelings of tension, of effort. “Temporal signs.”—Full and empty time 159

Section IV.—The Concept of Cause.

Psychical elements constituting the concept.—Experiential origin of the idea of cause: different solutions have all a common basis.—Its primitive individual character. Its extension.—Subjective and anthropomorphic period of generic images.—Period of reflexion, partial elimination of its subjective character, reduction to an invariable relation.—The notion of universal causality is acquired and remains a postulate.—Two ideas have hindered the development of this last notion: that of miracles and that of chance.—Transformation of the notion of cause. Rule of scientific research: its position is exterior. Identity of cause and effect.—Present form of the principle of universal causality.—Two quite distinct notions of cause (force, invariable relation), one of which is alone a concept 180

Section V.—The Concept of Law.

Objective value of general ideas. Two contrary theories. Mere approximations to the psychologist.—Three periods in the development of the notion of law.—Period of generic images. Primitive sense of the word law.—Period of empirical laws, corresponding with the intermediate forms of abstraction. Characteristics: identity of fact and law; complexity.—Period of theoretical or ideal laws, corresponding to medium forms of abstraction. Its features: simplicity, quantitative determination, ideal formula 194

Section VI.—The Concept of Species.

Its value: contemporaneous discussion of this subject. Component elements of the concept of species: resemblance, filiation. Difficulties resulting from polymorphism, from alternate generation.—Races, varieties.—Temporary and provisional objectivity.—Genera. Theories of Linnæus and Agassiz.—Shifting character of the classifications above the species.—One common point between transformists and their opponents: practical value of concepts. Not realities, nor fictions, but approximations.—Laws and species dependent on conditions of existence and varying with them 203