Chapter V: 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

CHAPTER VI.

CONCLUSION.

How was the faculty of abstracting and of generalising
constituted? Two principal causes: utility, appearance of
inventors.—How has it developed? Three principal directions:
practical, speculative, scientific.—_Résumé_: necessary
co-operation of two factors: the one conscious, the other
unconscious 216