We had originally intended, in this first number ofThe Monist, to present to our readers a comprehensive statement of the courses announced by American Universities in the departments of Philosophy, Ethics, and Psychology; first, in order to supply students proposing to pursue these studies and others interested, with information at first-hand, and secondly to give the non-academic world, which is considerable, an insight into what our higher professional schools are doing in these branches.
Since thenThe American Journal of Psychologyhas published a very full and gratifying account of the state of psychological research in our Universities, made up of the reports of the professors at the head of these departments; and we therefore refer our readers for information regarding this branch to the article entitled "Psychology in American Universities," published in Vol. III, No. 2, of that ably-conducted magazine.
It was also difficult to obtain the required information: most of our professors, in the last few months, having been absent from the university towns.
But reports from the most representative universities in different parts of the country have been obtained. They are intended merely to exhibit the general nature and extent of philosophical instruction in America and do not profess to be complete.
* * * * *
A review of the Registers, Catalogues, and Programmes of a large number of our colleges has led us to the conviction that the acquiring in America of a broad philosophical training is not the fault of theprofessionsof our academical authorities. The courses offered are set forth in our college catalogues at very great length; they are very exhaustive; and their specification is accompanied with analyses of the work of the various departments and with bibliographical schedules that in point of thoroughness leave nothing to be desired. This fulness of exposition is noticeable in all the departments.
But under the obligatory system of study, the separate departments, or rather the professions of the separate departments, must certainly conflict: and the question arises in the mind of the observing outsider, To which is justice done?
And, except where a specialty is exclusively followed, wherein under the professed conditions, does the elective system differ from the obligatory? Only that in the one case, the student is made the author of his embarrassment, and in the other the victim of it. However, in the absence of a decided educational sentiment in our nation, and in the lack of a uniformity of opinion as to what must bedemandedof our schools instead of a submissive acquiescence in what they give us, the question whether a college has fulfilled what it has professed, must be left to the faithful individual student who is forced to devote the best years of his life to the solution of it. It seems impossible to determine it otherwise. And yet, except in the case of our foremost institutions, to which all of us cannot go, this is true.
We have observed, too, that the extension of the departments of philosophy proper is not keeping pace with that of many other departments—as, for instance, the departments of history and economics.
Perhaps this is inevitable; the last-mentioned sciences having been until of late very much neglected.
But the tendency threatens to overbalance the curriculum; and where pretensions to universality are made, it is not justified.
On the other hand, the firm hold that experimental psychology has obtained in some of our foremost schools, is gratifying; though enthusiasm may also lead too far in this direction.
Lack of co-operation in cognate branches is, with very few notable exceptions, universal. Preparatory training is not emphasised. At least, where so much is said of the character and method of instruction, and where the elective system prevails, we should expect some mention of it. But it is not found.
Philosophy would seem to be something that is to be obtained only in the lecture-rooms of the "philosophical department," and in most cases it is sought nowhere else. The study of Mathematics, Physics, Natural Science, and Philology, is greatly neglected. Philosophy becomes an aim and a means in itself, and the student at the close of his course often discovers himself in the quest of philosophy, but with no means of finding it.
This necessity of co-operation has been fully recognised, for instance, at Harvard. "When a student applies for Honors," says Professor Palmer, "we require from him not merely an acquaintance with technical philosophy butalso with the subjects most nearly adjacent to the special philosophical field he has chosen."
And so it is in other of our advanced and enlightened schools. Yet in the majority of cases, thefoundationsof philosophical culture are not insisted upon, but left to chance and the uncertainties of a universal elective curriculum.
Lastly, philosophy at some institutions exhibits a sectarian and theological complexion.
This, one thinks, might be left to the theological seminaries. But it is not.
We have Baptist Philosophy, and Presbyterian Philosophy, and denominational philosophies of divers other descriptions.
A president of a prominent Eastern University, (a gentleman to whom the philosophic spirit of this country is greatly indebted for inspiration and expansion,) has taken,—let it be remarked in this connection,—a much more liberal step, and urged the necessity of establishing a school ofAmericanPhilosophy.
This is laudable; and in harmony with the present resuscitation ofAmerican patriotism in——matters of learning.
It was this spirit that dictated the witty proposition of a Chicago gentleman to found a "school" of AmericanGeometry.
* * * * *
We hope that the appended syllabuses of courses in philosophy will afford a general idea of the scope of philosophical teaching in America. The professors who have supplied us with the information we requested, we thank for their courtesy and obligingness.
The Philosophical Courses of the University of Michigan may be conveniently classified under three heads:—
1. ELEMENTARY LOGIC, in which there are two courses, one general covering the rudiments of syllogistic and deductive logic in which Jevons is used as the basis, the other in inductive logic, intended especially for scientific students, in which Fowler is used.
2. ELEMENTARY PSYCHOLOGY. The main facts regarding modern scientific researches and methods, and the various attempts at their philosophic interpretation. Dewey's Psychology is the book used in connection with this course.
3. INTRODUCTION TO PHILOSOPHY. A course of lectures on the main problems and principles of the theory of knowledge and reality. Each of the foregoing courses is for one semester.
1. HISTORY OF PHILOSOPHY. Ancient and Modern. Lectures and readings designed to give information regarding both the historical development of thought, and the main problems developed in its course. The department of philosophy owns a large number of copies of the chief thinkers in modern philosophy, Locke, Descartes, etc., etc., and these are assigned to members of the class for readings and reports. Each student thus becomes acquainted with at least half-a-dozen of the leading writers at first-hand.
The course runs through the year.
2. ETHICS, THEORETICAL (one-half year) AND SOCIAL (Political Philosophy, one-half year also). The theoretical course attempts to arrive at an account of the ethical ideal by means of a critical consideration of the principal modern ethical theories, especial attention being paid to Utilitarianism, Evolutionary Ethics, and Kantianism. The second division of the course discusses the ethical basis and value of society and the state, law and rights, in connection with an account of the political theories of Plato, Aristotle, Grotius, Hobbes, Locke, Kant, Rousseau, Hegel, etc.
3. ÆSTHETICS. This course, like the previous one, unites the historical and theoretical treatment of æsthetic doctrines and results. It is designed largely to aid students in the interpretation and criticism of literature. It is a half-year course, and is followed by a half-year course (given in the English Department) on the Principles and Methods of Literary Criticism.
4. PHYSIOLOGICAL PSYCHOLOGY. Lectures, assigned readings and elementary experiments, and demonstrations. There is established, as yet, no separate psycho-physical laboratory, but the new-equipped physiological laboratory of the University is, through the courtesy of the Professor of Physiology, at the disposal of students in this line. Half-year course.
5. SCIENCE AND PHILOSOPHY OF RELIGION. Lectures, readings, etc., designed to give an account of the chief methods employed and results achieved in the modern historical and comparative study of religions. And also an account of the principal theoretical interpretations of religion. Half-year course.
1. KANT'S CRITIQUE OF PURE REASON. A study of Kant's masterpiece at first-hand. This is accompanied by a shorter subsidiary course, treating of the development of the Kantian system, and criticisms upon it. Caird's Critical Philosophy of Kant, is read and discussed in connection with the latter course. Half-year course.
2. HEGEL'S LOGIC. A study of Wallace's translation of the lesser Logic of Hegel. Half-year course.
3. THE LOGIC OF SCIENTIFIC METHODS. A lecture course taking up the study of the Logic of Science, and intended to make the hearers acquainted with the standpoint and spirit of such authors as Lotze, Sigwart, Wundt, Mill, Jevons, Bradley, Bosanquet, and the modern movement in logic generally. Half-year course.
4. PROBLEMS IN HIGHER ÆSTHETICS. A brief course for graduate students in Æsthetics.
5. SEMINARY IN ETHICS. Discussion of the treatment of some main ethical problems by the chief modern ethical writers.
The Elementary courses are conducted mainly by text-books and recitations; the Intermediate courses by lectures and assigned readings, reports and essay-writings. The Advanced courses are pursued by class discussions, conversations, etc. on basis of work done independently by the student.
The teaching is carried on by John Dewey, J. H. Tufts, and F. N. Scott.
The courses at Harvard are, we believe, the most complete offered in any American University. They consist (for 1890-91) of four groups:
Including lectures on COMPARATIVE RELIGION, GREEK PHILOSOPHY,DESCARTES-SPINOZA-LEIBNITZ, ENGLISH PHILOSOPHY FROM HOBBES TO HUME, THEMOVEMENT OF GERMAN THOUGHT FROM 1770-1830, CONTEMPORARY SYSTEMS ANDAPPLIED ETHICS.
Including the Psychological, Metaphysical, and Ethical Seminaries. These do not include the additional and auxilliary courses in other subjects, which are required for Honors.
"Holding that there is one best way for the young student to begin his philosophical study," says Prof. G. H. Palmer, "we have planned a single introductory course and have given it variety by setting three instructors to teach it. When these elementary matters have been mastered, we offer the student a choice among half-a-dozen dogmatic courses, or among as many more historical. These last two sets of courses are open alike to graduates and to undergraduates. For graduate specialists three or four lines of Seminary work are provided, with a view to giving the most advanced students ample opportunity to develop their individual powers…. But the chief aim of our Honors is to test powers rather than acquirement."
In Harvard there are six instructors engaged in the department of philosophy alone: Prof. G. H. Palmer, Prof. C. C. Everett, Prof. W. James, Prof. F. G. Peabody, Prof. J. Royce, and Dr. G. Santayana. A dozen or more courses of philosophical content are offered, and acquaintance with auxilliary branches is necessary to take Honors.
The instruction given in the various branches of philosophy at this institution is conducted according to the following scheme:
1. PROPÆDEUTIC TO PHILOSOPHY. Empirical psychology, including formal logic, deductive and inductive. Four times a week.
2. INTRODUCTION TO PHILOSOPHY. History of European philosophy, in outline. Four times a week.
3. ELEMENTARY ETHICS, INCLUDING CIVIL POLITY. Sketch of the history of ethical and political theories; critique of the conflict between perfectionism and hedonism, freedom and necessity, optimism and pessimism; investigation of the nature of a state, and of its bearing on the limits of liberty and allegiance. Four times a week.
4. FIRST ALTERNATING COURSE. Exposition of some principal movement or conflict in the history of philosophy, by a critical study of its leading participants; or the like, the subject being changed from year to year. Twice a week.
5. SECOND ALTERNATING COURSE. Some additional topic, similar to that of Course IV., and similarly changed, but drawn, preferably, from the field of practical philosophy. Four times a week.
6. GRADUATE COURSE. First-hand study of certain philosophic masterpieces, such as Plato'sParmenides,TheætetusandSophist, Aristotle'sDe Anima, Kant'sKritiken, or Hegel'sPhænomenologie des Geistes; etc. Four times a week throughout the year.
Courses 1, 2, and 3, in this scheme are permanent, and are repeated from year to year in substantially the same form; Course 4 is continued throughout a whole year; the rest throughout a single term. Courses 4 and 5 are projected with the intention of furnishing a variety of topics, a new one being usually presented each year; though a subject is sometimes continued, if it proves to excite the special interest or meet the particular wants of the incoming Senior class. Course 6, provided for graduate students only, is sufficiently described in its sub-title.
The specific subjects for the ensuing year 1890-91, under these courses with varying topics, will be as follows:
Course 4. PHILOSOPHY FROM KANT TO HEGEL. The Development of Rationalistic Idealism, from its negative and partial to its complete and positive form. Twice a week.
Text-Books: (1) Watson's Philosophy of Kant; (2) Everett's Fichte's Science of Knowledge; (3) Watson's Schelling's Transcendental Idealism; (4) Caird's Hegel; (5) Hegel's Logic, translated by Wallace. With the standard works of reference.
Course 5. HIGHER ETHICS. Based on a criticism of Sidgwick andMartineau. Four times a week during the second term.
Text-Books: (1) Sidgwick's Methods of Ethics; (2) Martineau's Types ofEthical Theory.
Course 6. GRADUATE COURSE. The Dialektik and Methodenlehre in Kant's Kritik, followed by Hegel's Lesser Logic in Wallace's translation. Four times a week throughout the year.
From this statement it will be seen that some important text covering each topic is in the hands of each student. The object of this is to furnish an actual historical basis for the discussion of the subject, which is conducted by the professor's lectures. These proceed from a criticism, partly appreciative, partly destructive, of the texts chosen, to a constructive and positive presentation of the subject, according to the reasoned views of the lecturer.
The interest in philosophical studies is steadily increasing in this institution. The instruction in them was opened in the academic year 1884-85, and the growth of interest is well indicated by the fact that the number of students now annually electing these courses is more than double the number during the first and second year.
The Courses offered in Logic, Psychology, Ethics, and Philosophy, at this institution for the year 1890-91, are as follows:
1. A ELEMENTARY COURSE IN LOGIC. Two hours a week.
2. THE ELEMENTS OF PSYCHOLOGY. One hour a week.
3. SCIENTIFIC METHODS IN PSYCHOLOGY. Lectures with Laboratory Work. Two hours.
4. EXPERIMENTAL PSYCHOLOGY. Lectures with Laboratory Work. Two hours.
5. A COURSE IN ETHICS. Two hours.
6. A COURSE ON THE PHILOSOPHY OF ETHICS. One hour.
7. A COURSE ON THE HISTORY OF PHILOSOPHY. Two hours.
8. A COURSE ON THE DEVELOPMENT OF IDEALISM. Two hours.
1. COMPARATIVE, SOCIAL, AND ABNORMAL PSYCHOLOGY. Two hours.
2. SPECIAL PSYCHOLOGICAL PROBLEMS. Lectures with Laboratory Work. Two hours.
3. ADVANCED PSYCHOLOGY. Two hours.
4. ETHICAL THEORIES. One hour.
5. HISTORY OF MODERN PHILOSOPHY. Two hours.
Each course of undergraduate lectures will extend through half the year. Courses 1, 2, 3, and 7, will be delivered during the first term; Courses 4, 5, 6, and 8 during the second. Of the graduate lectures, Courses 1 and 2 will be given during the first and second terms respectively. Courses 3, 4, and 5 will extend throughout the year. The psychological laboratory is open at all hours to students engaged in special researches.
In addition to these courses, mention may be made of those delivered on Physiological, Abnormal, and Comparative Psychology in the Biological and Medical Schools of the University; and of the numerous courses, more or less directly ethical, which are delivered in the field of Sociology. In several of these there is a purposed effort to bring out the significance for ethics of the subject treated.
From the well-classified and thorough courses offered at ClarkUniversity, (conducted by Dr. Hall, Prof. Donaldson, Dr. Sanford, Dr.Boas, Dr. Cook, Dr. Strong, and others,) we select, for its uniqueness,an account of the instruction at that institution in—
Under this head, come among others, the different forms of abnormal and pathological humanity. The most extreme form is treated of in Criminal Anthropology, which takes up the study of man as criminal. As an introduction, the acts that would be considered criminal in man's case, are investigated, as they appear in the whole realm of nature. This division we call Criminal Embryology.
The other divisions to be considered in the lectures are: the Anthropometry, Craniology, Physiognomy, Cerebrology, Psychology, Sociology, Teratology, and Prophylaxis of criminals; also criminality in relation to Psychiatry and Psychiatrical Anthropology. The general relation of Ethics to Criminal Anthropology, is one of degree; crime being an exaggerated form of wrong. We can illustrate the method of application in this way: If a nerve of a normal organism is cut, the organs in which irregularities are produced, are those which the nerve controls. In this way the office of a nerve in the normal state may be discovered. The criminal is, so to speak, the severed-nerve of society; and the study of him is a very practical way (though indirect) of studying normal men. And since the criminal is seven-eights like other men, such a study is also a direct inquiry into normal humanity.
The lesser degrees of abnormal and pathological cases will be discussed under the head of Charitology. These are represented by the different kinds of benevolent institutions, such as almshouses, asylums for the insane, imbecile, and epileptic; for the deaf, dumb, and blind; hospitals, dispensaries, and infirmaries; homes for truants, orphans, and for the friendless and aged.
The characteristics of inmates of such institutions and the methods of treatment and prevention, will be the main considerations. The facts gathered, and the principles underlying such institutions, will be utilised in an attempt to give a scientific basis to ethics. The problems of right, duty and freedom, will be carefully considered.
Accepting the sociological truism, that the community is more important than any individual in it, the ethical standpoint of the lecturer is:that the idea of wrong depends upon the moral, intellectual, physical or financial danger or injury, which a thought, feeling, willing or acting, brings to humanity.
The decision, as to what thoughts, feelings, actions, etc., are dangerous or injurious, will depend upon the results from the application of the scientific method to the different departments of knowledge.
The direct practical object of the course, will be the study of preventatives, based on a thorough diagnosis.
Visitations and practical investigations of charitable and penal institutions will be made as occasion shall offer.
The lectures will be delivered in the latter part of the year.
Besides the comprehensive courses in psychology, the following are offered:
1. HISTORY OF GREEK PHILOSOPHY. A brief survey of the development of philosophical thought in Greece. Zeller's Hand-book of Greek Philosophy is the reference book. Twice a week. Elective. (Prof. Jastrow.)
2. THE HISTORY OF MODERN ENGLISH PHILOSOPHY. Three times a week. Elective. (Prof. Stearns.)
3. ETHICS. Four times a week. Elective. (Prof. Stearns.)
4. ÆSTHETICS. In addition to the study of the physiological and psychological basis of æsthetics an elementary knowledge of the history of art and the principles of art criticism is given by lectures and discussions. Five times a week. Elective. (Prof. Stearns.)
5. ELEMENTARY LOGIC, DEDUCTIVE AND INDUCTIVE. The analysis of arguments, the construction and elaboration of syllogisms; the symbolic and diagrammatic methods of representing logical operations, and modern and ancient systems of logic will form the main topics of the deductive logic; while in inductive logic special emphasis will be laid upon the methods of scientific reasoning, the logic of chance, the detection of fallacies, and the estimation of evidence. Daily in winter term. (Prof. Jastrow.)
6. ADVANCED LOGIC. Special attention paid to the logic of the sciences; to mathematical logic as introduced by Boole and developed by Venn, Peirce, Schroeder and others; to the theory of probabilities, and the history of logical doctrines. Twice weekly. Elective. (Prof. Jastrow.)
7. MILL'S LOGIC. A general course upon the philosophy of reasoning and the principles of inductive science. Killick's Handbook to Mill's Logic used. Three times weekly. (Prof. Jastrow.) Each course extends over a single term only.
In Ethics an effort is made to introduce the students to three phases of the subject, the historical, theoretical, and practical. The first is at present limited to a brief review, by lectures, of the chief English ethical theories. In the second Prof. Fowler's Progressive Morality is made the basis of the instruction. The third is pursued chiefly in the form of topics, relating generally to current ethical questions, which are assigned for special study to members of the class, and their presentation is, when desirable, made the basis of general discussion.
The following are the courses for the present year, at BostonUniversity, under the direction of Prof. B. P. Bowne and DeanHuntington.
PSYCHOLOGY. Thought studied as a fact; its forms and laws investigated;Current Theories expounded and criticised. Five hours.
LOGIC. Thought studied not as a fact, but as an instrument of knowledge. Investigation of the laws, forms, aims, and methods of mental activity. Five hours.
THEORY OF KNOWLEDGE. The study of thought as a process supplemented by the study of knowledge as its product. Knowledge defined, and the conditions, subjective and objective, of its validity investigated. The claims of scepticism, agnosticism, etc., considered at length. Three hours.
METAPHYSICS. Modifications of ontological and cosmological ideas in the light of rational criticism. Four hours.
PHILOSOPHY OF THEISM. The logical value and foundation of Theism considered. Four hours.
HISTORY OF ETHICAL THOUGHT. Christian Ethics. Text-book and lectures.Five hours.
PHILOSOPHY OF ETHICS. Critical and constructive review of ethical theories. Psychological questions as to the nature and origin of moral faculty ruled out as irrelevant. Two hours.
HISTORY OF PHILOSOPHY. From Descartes to the present time. Five hours.
The Philosophical Club, organised in 1886, has since that time maintained stated meetings for the furtherance of its members in philosophical studies.
Last year, under the auspices of the University, a special course of five lectures on Educational Psychology was given before large audiences by William T. Harris, LL. D. The topics treated were as follows:
1. Introspection contrasted with external Sense Perception.
2. Mental PicturesversusGeneral Ideas.
3. The Logical Constitution of Sense Perception.
4. Physiological Psychology.
5. The Psychology of Mathematics, Æsthetics, and Ethics.
The courses are for single terms only.
The Undergraduate instruction in philosophy provides five hours a week of required work for one year:
The courses are unified and thorough. A voluntary course in the History of Philosophy is given; and advanced courses will be offered this year in Modern Philosophy from Descartes to Kant, and in English Ethics from Hobbes to Stephen. The instructors are Professors Griffin and Emmot.
MIND. July 1890. No. LIX.
OUR SPACE-CONSCIOUSNESS. A Reply. ByHerbert Spencer.
VOLKMANN'S PSYCHOLOGY (I). ByThomas Whittaker.
THE LOGIC OF THE ETHIC OF EVOLUTION. ByWilliam Mitchell.
THE ANTINOMY OF THOUGHT. ByAlexander F. Shand.
MENTAL TESTS AND MEASUREMENTS. By Prof.J. McK. Cattell.
DISCUSSION: 1) The Evolution of Inductive Thought. ByHiram M.Stanley.2) The Genesis of the Cognition of Physical Reality. ByJuliusPikler.
CRITICAL NOTICES: "Fouillée's L'Avenir de la Métaphysique fondéesur l'Expérience"; Tarde's "Lois de l'Imitation"; Bæumker's"Das Problem der Materie in der Griechischen Philosophie."
SOME NEWLY-DISCOVERED LETTERS OF HOBBES. By theEditor.
Our Space-Consciousness.In this article Mr. Herbert Spencer replies to criticisms, by adherents of Kantian doctrine, of objections contained in §§ 326-335 ofThe Principles of Psychology. He objects that the disciples of Kant "cannot imagine how it is possible that our space-consciousness can have arisen out of that which was not originally a space-consciousness."
Volkmann's Psychology.Shows that the really important point in Volkmann's doctrine of "psychological mechanism" is its theory of the interaction of contemporaneous presentations, and of the existence among them of unconscious presentations. Herbartian psychology is strictly scientific system, but when its superfluous mechanism is cleared away, its explanations become those of associationism.
InThe Logic of the Ethic of Evolution, Mr. William Mitchell points out that the two conditions of an ethical end are that it be the motive of individual action, and that it furnish a critical system of universal laws; and further that those conditions are fulfilled by the end variously propounded in the ethic of evolution only if it be represented, not as an external limit forcing itself on men, but as presenting a more desirable character and medium to the individual than any other. The end and means of moral progress given by the Ethic of Evolution are perfectly true, but they do not express the essence of the matter.
The Antinomy of Thought.This paper investigates an antinomy which infects all our thought of reality that is not intuitive. The source of error is the confusion of the judgment with the consciousness or intuition of reality.
In the article onMental Tests and Measurements, Prof. J. McK. Cattell describes certain tests which are used in the Psychological Laboratory of the University of Pennsylvania, with the object of providing data for the discovery of the rules which govern the constancy of mental processes, their interdependence, and their variations under different circumstances.
The Evolution of Inductive Thought.A primary element in all experience is its inductive quality. The struggle of existence awakens experience to the thought-stage where it knows and directs itself, but this very slowly. Development precedes self-development, and this precedes a self-development which is self-conscious. This conclusion is confirmed by some analyses of thought in the divisions of conception, judgment, and reasoning.
The Genesis of the Cognition of Physical Reality.This is a criticism by Mr. Julius Pikler of Mr. Stout's criticism on Mill, which appeared in the January number ofMind. His opinion is that Mr. Strong's statements are simply negations of Mill's theory, and as such prove nothing.
Some newly-discovered Letters of Hobbes.These letters, seventeen in number, were written to the French physician Sorbière, and have been discovered by Dr. F. Tönnies in the National Library at Paris. All of them, with related letters of Sorbière and others, are given at length in theArchiv f. Gesch. d. Phil.iii. 58-71, 192-232, and the first nine, which are the only ones of real importance, are set out in this number ofMind. They have reference to the important period of Hobbes's life and work that led up toLeviathanin 1651. (London: Williams & Norgate.)
REVUE PHILOSOPHIQUE. No. 175. July 1890.
L'HOMOGENEITE MORALE. ByG. Fonsegrive.
CONTRIBUTIONS PSYCHO-PHYSIQUES A L'ETUDE ESTHETIQUE (fin). ByG.Sorel.
LA FOLIE DE J. J. ROUSSEAU. ByH. Joly.
LA PERCEPTION DES LONGUEURS ET DES NOMBRES CHEZ QUELQUES PETITSENFANTS. ByAlfred Binet.
M. Fonsegrive inL'Homogénéité moralepoints out the necessity of a proper system of education for developing in the mind of the young a moral homogeneity to replace the heterogeneity which psychologists find in the nature of man.
InContributions psycho-physiques a l'Etude esthétique, M. G. Sorel continues his studies on the psychology of æsthetics, and concludes that experimental psychology and especially psycho-physics form the base of practical æsthetics.
M. H. Joly inLa Folie de J. J. Rousseaupoints out that the problem of the agreement of genius with insanity, so far as concerns Rousseau, is reduced to small dimensions.
La Perception des Longueurs et des Nombres ches quelques petits Enfantsby M. Alfred Binet, describes certain original experiments which indicate that young children have an accurate perception of differences in length, but that their perception of number is very limited. (Paris: F. Alcan.)
REVUE PHILOSOPHIQUE. No. 176. August 1890.
LES ORIGINES DE LA TECHNOLOGIE. ByA. Espinas.
L'INHIBITION DANS LES PHÉNOMENES DE CONSCIENCE. ByA. Binet.
LA GÉOMÉTRIE GÉNÉRALE ET LES JUGEMENTS SYNTHÉTIQUES A PRIORI. ByG. Lechalas.
CORRESPONDANCE: "Les Manuscrits de M. de Biran."
InLes Origines de la TechnologieM. Espinas aims at giving a history of philosophy in action. The present paper is devoted to physico-theological technology, and concludes with the observation that it was undoubtedly a progress to conceive the technical arts as a whole, as a divine gift in like manner as the fruits of the earth and the beneficent phenomena ofnature, since this conception by opposition gave rise to the idea ofart, that is of human initiative acting differently according to diversity of circumstances.
InL'Inhibition dans les Phénomènes de ConscienceM. Alfred Binet explains certain phenomena by showing that under various circumstances certain images and sensations cannot coexist with others in the same field of consciousness; the presence of one excludes that of another. Antagonism and exclusion are the two simple facts which explain the phenomena in question.
La Géométrie Générale et les Jugements Synthétiques a prioriis a reply by M. G. Lechalas to an article by M. Renouvier in theCritique Philosophiquecriticising M. Calinon's theory of geometrical spaces embodied in the system of "general geometry." While showing that spaces with three dimensions are rationally included in a space with four dimensions, M. Lechalas recognises the impossibility of establishing such a geometry, seeing that we have no figure that answers to what a four-dimensional space would be, as well as the purely formal character of the presentations of non-Euclidian figures. (Paris: F. Alcan.)
ZEITSCHRIFT FÜR PSYCHOLOGIE UND PHYSIOLOGIE DER SINNESORGANE. Vol. I,No. 2.
UEBER DIE WAHRNEHMUNG UND LOKALISATION VON SCHWEBUNGEN UNDDIFFERENZTÖNEN. ByCarl L. Schaefer.
DIE ASSOCIATION SUCCESSIVER VORSTELLUNGEN. ByH. Münsterberg.
BRIEFE VON G. TH. FECHNER: UEBER NEGATIVE EMPFINDUNGSWERTE.(Concluded.) Edited byW. Preyer.
The results of Mr. Schaefer's researches are that for the localisation of the vibrations of two tones, in the case of their unequal relative intensity, the direction and distance of the relatively louder tone are determinate. If the relative intensity of the primary tones is equal, the vibrations are heard to proceed from the region between the two sounding points. Differential tones are heard between the ears, when the sounding sources are in the median plane; but when both primary tones come from the same side, in or immediately before the ear on that side; and in case of unequal intensity, when both come from different sides, on the side of the softer sound.
Prof. Münsterberg concludes that there is nosuccessiveassociation of ideas; when successively appearing, they are received singly into the memory.
The letters of Fechner are continued from No. 1.
ZEITSCHRIFT FÜR PSYCHOLOGIE UND PHYSIOLOGIE DER SINNESORGANE. Vol. I,No. 3.
UEBER DIE KLEINSTEN WAHRNEHMBAREN GESICHTSWINKEL IN DENVERSCHIEDENEN TEILEN DES SPEKTRUMS. ByW. Uhthoff.
DIE ÆSTHETISCHEN GEFUEHLE. ByA. Döring.
BESPRECHUNGEN: (1) A. Mosso's und A. Maggiora's "Ueber dieGesetze der Ermüdung." (2) Münsterberg's "Beitraege zurExperimentellen Psychologie."
Dr. Uhthoff, in order to determine the least visual angle of perception, has employed a grating in a pure-monochromatic spectral field. His results were that the angles in the different parts of the spectrum are essentially equal.
Æsthetic emotions, Mr. Döring contends, proceed from the unhindered play of the functions of psychical faculties; their contrary, from the inhibition of the same.
This periodical is edited by H. Ebbinghaus and A. König, with H. Aubert, S. Exner, H. v. Helmholtz, E. Hering, J. v. Kries, Th. Lipps, G. E. Müller, W. Preyer, and C. Stumpf as collaborators. It appears every two months. The review of the literature of its special department of research is very comprehensive. (Hamburg and Leipsic: L. Voss.)
RAGIONI E IDEALI. ByLa Direzione.
LA SENSAZIONE E LA SUA CONOSCIBILITA. ByR. Ardigo.
J. E. ALAUX'S LE PROBLEME RELIGIEUX AU XIX^e SIÈCLE. ByA.Torre.
ECONOMIA SCIENTIFICA ED ECONOMIA UTOPISTA. ByA. Loria.
P. LEROY-BEAULIEU'S L'ETAT MODERNE ET SES FONCTIONS. ByF. S.Nitti.
C. JANNET'S LE SOCIALISME D'ETAT ET LA REFORME SOCIALE. ByF. S.Nitti.
LOMBROSO'S AND LASCHI'S IL DELITTO POLITICO E LE RIVOLUZIONI. ByG. Fioretti.
A. Angiulli—A. Saffi—F. Petruccelli della Gattina. (MEMORIE.)ByA. Torre.
QUESTIONI E PROBLEMI. La responsabilità filosofica, secondoPaolo Janet.
This is the first number ofLa Nuova Filosofiawhich is established, under the editorship of Dr. Andrea Torre, to diffuse in Europe and America the best results of contemporary culture, in relation especially to the life and development of society. (Naples: Dr. Andrea Torre, Vico Lungo Avvocata, 66.)
Cut exhibiting modifications that affect the accessory nucleus. Referred to on page 26 of this number ofThe Monist, in M. Binet's article "The Immortality of Infusoria."
[Illustration: CONJUGATION OF CHILODON CUCULLULUS.]
A, beginning of conjugation;b, mouth;n, nucleus;nu, nucleolus;v. c., multiple contracticle vesicles.
B, division of the nucleolus into two segments,nu',nu'; the nucleusnbegins to show signs of regression.
C, each of the two individuals in conjugation contains two nucleolar segments, brought near together, of which one probably comes from the individual opposite by course of exchange, and will fuse with the segment not exchanged, to form a compound segment (Maupas).
D, division of the segment into two portions which grow to unequal sizes; the larger,nn, will become the new nucleus, the smaller, the nucleolus of the new formation,nun.
E, the old nucleus,n, reduced to a small pale and rumpled mass, is replaced by the new nucleusnn, near by which is seen the new nucleolusnun.
Of the fifty or hundred systems of philosophy that have been advanced at different times of the world's history, perhaps the larger number have been, not so much results of historical evolution, as happy thoughts which have accidently occurred to their authors. An idea which has been found interesting and fruitful has been adopted, developed, and forced to yield explanations of all sorts of phenomena. The English have been particularly given to this way of philosophising; witness, Hobbes, Hartley, Berkeley, James Mill. Nor has it been by any means useless labor; it shows us what the true nature and value of the ideas developed are, and in that way affords serviceable materials for philosophy. Just as if a man, being seized with the conviction that paper was a good material to make things of, were to go to work to build apapier mâchéhouse, with roof of roofing-paper, foundations of paste-board, windows of paraffined paper, chimneys, bath tubs, locks, etc., all of different forms of paper, his experiment would probably afford valuable lessons to builders, while it would certainly make a detestable house, so those one-idea'd philosophies are exceedingly interesting and instructive, and yet are quite unsound.
The remaining systems of philosophy have been of the nature of reforms, sometimes amounting to radical revolutions, suggested by certain difficulties which have been found to beset systems previously in vogue; and such ought certainly to be in large part the motive of any new theory. This is like partially rebuilding a house. The faults that have been committed are, first, that the dilapidations have generally not been sufficiently thoroughgoing, and second, that not sufficient pains has been taken to bring the additions into deep harmony with the really sound parts of the old structure.
When a man is about to build a house, what a power of thinking he has to do, before he can safely break ground! With what pains he has to excogitate the precise wants that are to be supplied! What a study to ascertain the most available and suitable materials, to determine the mode of construction to which those materials are best adapted, and to answer a hundred such questions! Now without riding the metaphor too far, I think we may safely say that the studies preliminary to the construction of a great theory should be at least as deliberate and thorough as those that are preliminary to the building of a dwelling-house.
That systems ought to be constructed architectonically has been preached since Kant, but I do not think the full import of the maxim has by any means been apprehended. What I would recommend is that every person who wishes to form an opinion concerning fundamental problems, should first of all make a complete survey of human knowledge, should take note of all the valuable ideas in each branch of science, should observe in just what respect each has been successful and where it has failed, in order that in the light of the thorough acquaintance so attained of the available materials for a philosophical theory and of the nature and strength of each, he may proceed to the study of what the problem of philosophy consists in, and of the proper way of solving it. I must not be understood as endeavoring to state fully all that these preparatory studies should embrace; on the contrary, I purposely slur over many points, in order to give emphasis to one special recommendation, namely, to make a systematic study of the conceptions out of which a philosophical theory may be built, in order to ascertain what place each conception may fitly occupy in such a theory, and to what uses it is adapted.
The adequate treatment of this single point would fill a volume, but I shall endeavor to illustrate my meaning by glancing at several sciences and indicating conceptions in them serviceable for philosophy. As to the results to which long studies thus commenced have led me, I shall just give a hint at their nature.
We may begin with dynamics,—field in our day of perhaps the grandest conquest human science has ever made,—I mean the law of the conservation of energy. But let us revert to the first step taken by modern scientific thought,—and a great stride it was,—the inauguration of dynamics by Galileo. A modern physicist on examining Galileo's works is surprised to find how little experiment had to do with the establishment of the foundations of mechanics. His principal appeal is to common sense andil lume naturale. He always assumes that the true theory will be found to be a simple and natural one. And we can see why it should indeed be so in dynamics. For instance, a body left to its own inertia, moves in a straight line, and a straight line appears to us the simplest of curves. Initself, no curve is simpler than another. A system of straight lines has intersections precisely corresponding to those of a system of like parabolas similarly placed, or to those of any one of an infinity of systems of curves. But the straight line appears to us simple, because, as Euclid says, it lies evenly between its extremities; that is, because viewed endwise it appears as a point. That is, again, because light moves in straight lines. Now, light moves in straight lines because of the part which the straight line plays in the laws of dynamics. Thus it is that our minds having been formed under the influence of phenomena governed by the laws of mechanics, certain conceptions entering into those laws become implanted in our minds, so that we readily guess at what the laws are. Without such a natural prompting, having to search blindfold for a law which would suit the phenomena, our chance of finding it would be as one to infinity. The further physical studies depart from phenomena which have directly influenced the growth of the mind, the less we can expect to find the laws which govern them "simple," that is, composed of a few conceptions natural to our minds.
The researches of Galileo, followed up by Huygens and others, led to those modern conceptions ofForceandLaw, which have revolutionised the intellectual world. The great attention given to mechanics in the seventeenth century soon so emphasised these conceptions as to give rise to the Mechanical Philosophy, or doctrine that all the phenomena of the physical universe are to be explained upon mechanical principles. Newton's great discovery imparted a new impetus to this tendency. The old notion that heat consists in an agitation of corpuscles was now applied to the explanation of the chief properties of gases. The first suggestion in this direction was that the pressure of gases is explained by the battering of the particles against the walls of the containing vessel, which explained Boyle's law of the compressibility of air. Later, the expansion of gases, Avogadro's chemical law, the diffusion and viscosity of gases, and the action of Crookes's radiometer were shown to be consequences of the same kinetical theory; but other phenomena, such as the ratio of the specific heat at constant volume to that at constant pressure require additional hypotheses, which we have little reason to suppose are simple, so that we find ourselves quite afloat. In like manner with regard to light, that it consists of vibrations was almost proved by the phenomena of diffraction, while those of polarisation showed the excursions of the particles to be perpendicular to the line of propagation; but the phenomena of dispersion, etc., require additional hypotheses which may be very complicated. Thus, the further progress of molecular speculation appears quite uncertain. If hypotheses are to be tried haphazard, or simply because they will suit certain phenomena, it will occupy the mathematical physicists of the world say half a century on the average to bring each theory to the test, and since the number of possible theories may go up into the trillions, only one of which can be true, we have little prospect of making further solid additions to the subject in our time. When we come to atoms, the presumption in favor of a simple law seems very slender. There is room for serious doubt whether the fundamental laws of mechanics hold good for single atoms, and it seems quite likely that they are capable of motion in more than three dimensions.
To find out much more about molecules and atoms, we must search out a natural history of laws of nature, which may fulfil that function which the presumption in favor of simple laws fulfilled in the early days of dynamics, by showing us what kind of laws we have to expect and by answering such questions as this: Can we with reasonable prospect of not wasting time, try the supposition that atoms attract one another inversely as the seventh power of their distances, or can we not? To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. That a pitched coin should sometimes turn up heads and sometimes tails calls for no particular explanation; but if it shows heads every time, we wish to know how this result has been brought about. Law ispar excellencethe thing that wants a reason.
Now the only possible way of accounting for the laws of nature and for uniformity in general is to suppose them results of evolution. This supposes them not to be absolute, not to be obeyed precisely. It makes an element of indeterminacy, spontaneity, or absolute chance in nature. Just as, when we attempt to verify any physical law, we find our observations cannot be precisely satisfied by it, and rightly attribute the discrepancy to errors of observation, so we must suppose far more minute discrepancies to exist owing to the imperfect cogency of the law itself, to a certain swerving of the facts from any definite formula.
Mr. Herbert Spencer wishes to explain evolution upon mechanical principles. This is illogical, for four reasons. First, because the principle of evolution requires no extraneous cause; since the tendency to growth can be supposed itself to have grown from an infinitesimal germ accidentally started. Second, because law ought more than anything else to be supposed a result of evolution. Third, because exact law obviously never can produce heterogeneity out of homogeneity; and arbitrary heterogeneity is the feature of the universe the most manifest and characteristic. Fourth, because the law of the conservation of energy is equivalent to the proposition that all operations governed by mechanical laws are reversible; so that an immediate corollary from it is that growth is not explicable by those laws, even if they be not violated in the process of growth. In short, Spencer is not a philosophical evolutionist, but only a half-evolutionist,—or, if you will, only a semi-Spencerian. Now philosophy requires thoroughgoing evolutionism or none.
The theory of Darwin was that evolution had been brought about by the action of two factors: first, heredity, as a principle making offspring nearly resemble their parents, while yet giving room for "sporting," or accidental variations,—for very slight variations often, for wider ones rarely; and, second, the destruction of breeds or races that are unable to keep the birth rate up to the death rate. This Darwinian principle is plainly capable of great generalisation. Wherever there are large numbers of objects, having a tendency to retain certain characters unaltered, this tendency, however, not being absolute but giving room for chance variations, then, if the amount of variation is absolutely limited in certain directions by the destruction of everything which reaches those limits, there will be a gradual tendency to change in directions of departure from them. Thus, if a million players sit down to bet at an even game, since one after another will get ruined, the average wealth of those who remain will perpetually increase. Here is indubitably a genuine formula of possible evolution, whether its operation accounts for much or little in the development of animal and vegetable species.
The Lamarckian theory also supposes that the development of species has taken place by a long series of insensible changes, but it supposes that those changes have taken place during the lives of the individuals, in consequence of effort and exercise, and that reproduction plays no part in the process except in preserving these modifications. Thus, the Lamarckian theory only explains the development of characters for which individuals strive, while the Darwinian theory only explains the production of characters really beneficial to the race, though these may be fatal to individuals.[33] But more broadly and philosophically conceived, Darwinian evolution is evolution by the operation of chance, and the destruction of bad results, while Lamarckian evolution is evolution by the effect of habit and effort.
[33] The neo-Darwinian, Weismann, has shown that mortality would almost necessarily result from the action of the Darwinian principle.
A third theory of evolution is that of Mr. Clarence King. The testimony of monuments and of rocks is that species are unmodified or scarcely modified, under ordinary circumstances, but are rapidly altered after cataclysms or rapid geological changes. Under novel circumstances, we often see animals and plants sporting excessively in reproduction, and sometimes even undergoing transformations during individual life, phenomena no doubt due partly to the enfeeblement of vitality from the breaking up of habitual modes of life, partly to changed food, partly to direct specific influence of the element in which the organism is immersed. If evolution has been brought about in this way, not only have its single steps not been insensible, as both Darwinians and Lamarckians suppose, but they are furthermore neither haphazard on the one hand, nor yet determined by an inward striving on the other, but on the contrary are effects of the changed environment, and have a positive general tendency to adapt the organism to that environment, since variation will particularly affect organs at once enfeebled and stimulated. This mode of evolution, by external forces and the breaking up of habits, seems to be called for by some of the broadest and most important facts of biology and paleontology; while it certainly has been the chief factor in the historical evolution of institutions as in that of ideas; and cannot possibly be refused a very prominent place in the process of evolution of the universe in general.
Passing to psychology, we find the elementary phenomena of mind fall into three categories. First, we have Feelings, comprising all that is immediately present, such as pain, blue, cheerfulness, the feeling that arises when we contemplate a consistent theory, etc. A feeling is a state of mind having its own living quality, independent of any other state of mind. Or, a feeling is an element of consciousness which might conceivably override every other state until it monopolised the mind, although such a rudimentary state cannot actually be realised, and would not properly be consciousness. Still, it is conceivable, or supposable, that the quality of blue should usurp the whole mind, to the exclusion of the ideas of shape, extension, contrast, commencement and cessation, and all other ideas, whatsoever. A feeling is necessarily perfectly simple,in itself, for if it had parts these would also be in the mind, whenever the whole was present, and thus the whole could not monopolise the mind.[34]
[34] A feeling may certainly be compound, but only in virtue of a perception which is not that feeling nor any feeling at all.
Besides Feelings, we have Sensations of reaction; as when a person blindfold suddenly runs against a post, when we make a muscular effort, or when any feeling gives way to a new feeling. Suppose I had nothing in my mind but a feeling of blue, which were suddenly to give place to a feeling of red; then, at the instant of transition there would be a shock, a sense of reaction, my blue life being transmuted into red life. If I were further endowed with a memory, that sense would continue for some time, and there would also be a peculiar feeling or sentiment connected with it. This last feeling might endure (conceivably I mean) after the memory of the occurrence and the feelings of blue and red had passed away. But thesensationof reaction cannot exist except in the actual presence of the two feelings blue and red to which it relates. Wherever we have two feelings and pay attention to a relation between them of whatever kind, there is the sensation of which I am speaking. But the sense of action and reaction has two types: it may either be a perception of relation between two ideas, or it may be a sense of action and reaction between feeling and something out of feeling. And this sense of external reaction again has two forms; for it is either a sense of something happening to us, by no act of ours, we being passive in the matter, or it is a sense of resistance, that is, of our expending feeling upon something without. The sense of reaction is thus a sense of connection or comparison between feelings, either,A, between one feeling and another, orB, between feeling and its absence or lower degree; and underBwe have, First, the sense of the access of feeling, and Second, the sense of remission of feeling.
Very different both from feelings and from reaction-sensations or disturbances of feeling are general conceptions. When we think, we are conscious that a connection between feelings is determined by a general rule, we are aware of being governed by a habit. Intellectual power is nothing but facility in taking habits and in following them in cases essentially analogous to, but in non-essentials widely remote from, the normal cases of connections of feelings under which those habits were formed.
The one primary and fundamental law of mental action consists in a tendency to generalisation. Feeling tends to spread; connections between feelings awaken feelings; neighboring feelings become assimilated; ideas are apt to reproduce themselves. These are so many formulations of the one law of the growth of mind. When a disturbance of feeling takes place, we have a consciousness of gain, the gain of experience; and a new disturbance will be apt to assimilate itself to the one that preceded it. Feelings, by being excited, become more easily excited, especially in the ways in which they have previously been excited. The consciousness of such a habit constitutes a general conception.
The cloudiness of psychological notions may be corrected by connecting them with physiological conceptions. Feeling may be supposed to exist, wherever a nerve-cell is in an excited condition. The disturbance of feeling, or sense of reaction, accompanies the transmission of disturbance between nerve-cells or from a nerve-cell to a muscle-cell or the external stimulation of a nerve-cell. General conceptions arise upon the formation of habits in the nerve-matter, which are molecular changes consequent upon its activity and probably connected with its nutrition.
The law of habit exhibits a striking contrast to all physical laws in the character of its commands. A physical law is absolute. What it requires is an exact relation. Thus, a physical force introduces into a motion a component motion to be combined with the rest by the parallelogram of forces; but the component motion must actually take place exactly as required by the law of force. On the other hand, no exact conformity is required by the mental law. Nay, exact conformity would be in downright conflict with the law; since it would instantly crystallise thought and prevent all further formation of habit. The law of mind only makes a given feelingmore likelyto arise. It thus resembles the "non-conservative" forces of physics, such as viscosity and the like, which are due to statistical uniformities in the chance encounters of trillions of molecules.
The old dualistic notion of mind and matter, so prominent in Cartesianism, as two radically different kinds of substance, will hardly find defenders to-day. Rejecting this, we are driven to some form of hylopathy, otherwise called monism. Then the question arises whether physical laws on the one hand, and the psychical law on the other are to be taken—
(A) as independent, a doctrine often calledmonism, but which I would nameneutralism; or,
(B) the psychical law as derived and special, the physical law alone as primordial, which ismaterialism; or,
(C) the physical law as derived and special, the psychical law alone as primordial, which isidealism.
The materialistic doctrine seems to me quite as repugnant to scientific logic as to common sense; since it requires us to suppose that a certain kind of mechanism will feel, which would be a hypothesis absolutely irreducible to reason,—an ultimate, inexplicable regularity; while the only possible justification of any theory is that it should make things clear and reasonable.
Neutralism is sufficiently condemned by the logical maxim known as Ockham's razor, i. e., that not more independent elements are to be supposed than necessary. By placing the inward and outward aspects of substance on a par, it seems to render both primordial.
The one intelligible theory of the universe is that of objective idealism, that matter is effete mind, inveterate habits becoming physical laws. But before this can be accepted it must show itself capable of explaining the tridimensionality of space, the laws of motion, and the general characteristics of the universe, with mathematical clearness and precision; for no less should be demanded of every Philosophy.
Modern mathematics is replete with ideas which may be applied to philosophy. I can only notice one or two. The manner in which mathematicians generalise is very instructive. Thus, painters are accustomed to think of a picture as consisting geometrically of the intersections of its plane by rays of light from the natural objects to the eye. But geometers use a generalised perspective. For instance, in the figure letObe the eye, letA B C D Ebe the edgewise view of any plane, and leta f e D cbe the edgewise view of another plane. The geometers draw rays throughOcutting both these planes, and treat the points of intersection of each ray with one plane as representing the point of intersection of the same ray with the other plane. Thus,erepresentsE, in the painter's way.Drepresents itself.Cis represented byc, which is further from the eye; andAis represented byawhich is on the other side of the eye. Such generalisation is not bound down to sensuous images. Further, according to this mode of representation every point on one plane represents a point on the other, and every point on the latter is represented by a point on the former. But how about the pointfwhich is in a direction fromOparallel to the represented plane, and how about the pointBwhich is in a direction parallel to the representing plane? Some will say that these are exceptions; but modern mathematics does not allow exceptions which can be annulled by generalisation. As a point moves fromCtoDand thence toEand off toward infinity, the corresponding point on the other plane moves fromctoDand thence toeand towardf. But this second point can pass throughftoa; and when it is there the first point has arrived atA. We therefore say that the first point has passedthrough infinity, and that every line joins in to itself somewhat like an oval. Geometers talk of the parts of lines at an infinite distance as points. This is a kind of generalisation very efficient in mathematics.
[Illustration]
Modern views of measurement have a philosophical aspect. There is an indefinite number of systems of measuring along a line; thus, a perspective representation of a scale on one line may be taken to measure another, although of course such measurements will not agree with what we call the distances of points on the latter line. To establish a system of measurement on a line we must assign a distinct number to each point of it, and for this purpose we shall plainly have to suppose the numbers carried out into an infinite number of places of decimals. These numbers must be ranged along the line in unbroken sequence. Further, in order that such a scale of numbers should be of any use, it must be capable of being shifted into new positions, each number continuing to be attached to a single distinct point. Now it is found that if this is true for "imaginary" as well as for real points (an expression which I cannot stop to elucidate), any such shifting will necessarily leave two numbers attached to the same points as before. So that when the scale is moved over the line by any continuous series of shiftings of one kind, there are two points which no numbers on the scale can ever reach, except the numbers fixed there. This pair of points, thus unattainable in measurement, is called the Absolute. These two points may be distinct and real, or they may coincide, or they may be both imaginary. As an example of a linear quantity with a double absolute we may take probability, which ranges from an unattainable absolute certaintyagainsta proposition to an equally unattainable absolute certaintyforit. A line, according to ordinary notions, we have seen is a linear quantity where the two points at infinity coincide. A velocity is another example. A train going with infinite velocity from Chicago to New York would be at all the points on the line at the very same instant, and if the time of transit were reduced to less than nothing it would be moving in the other direction. An angle is a familiar example of a mode of magnitude with no real immeasurable values. One of the questions philosophy has to consider is whether the development of the universe is like the increase of an angle, so that it proceeds forever without tending toward anything unattained, which I take to be the Epicurean view, or whether the universe sprang from a chaos in the infinitely distant past to tend toward something different in the infinitely distant future, or whether the universe sprang from nothing in the past to go on indefinitely toward a point in the infinitely distant future, which, were it attained, would be the mere nothing from which it set out.
The doctrine of the absolute applied to space comes to this, at either—
First, space is, as Euclid teaches, bothunlimitedandimmeasurable, so that the infinitely distant parts of any plane seen in perspective appear as a straight line, in which case the sum of the three angles of a triangle amounts to 180°; or,