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Rh of the meaning of propositions and functions. For Frege the propositions of logic were names and their arguments the indices of these names.

The truth-functions can be ordered in series. That is the foundation of the theory of probability.

The truth-functions of every number of elementary propositions can be written in a schema of the following kind: {{smaller block| (T T T T) (p, q) Tautology (if p then p, and if q then q) [p$$\supset $$ p q$$\supset $$q] (F T T T) (p, q) in words: Not both p and q. [ $$\sim $$(p.q)] (T F T T) (p, q) „ „ If q then p. [q$$\supset $$p] (T T F T) (p, q) „ „ If p then q. [p$$\supset $$q] (T T T F) (p, q) „ „ p or q. [p$$\or $$q] (F F T T) (p, q) „ „ Not q. [p$$\or $$q] (F T F T) (p, q) „ „ Not p [p$$\or $$p] (F T T F) (p, q) „ „ p or q, but not both. [p. $$\or $$q : v : q. $$\or $$p] (T F F T) (p, q) „ „ If p then q ; and if q, then p [p$$\equiv $$q] {T F T F) (p, q) „ „ p (T T F F) (p, q) „ „ q (F F F T) (p, q) „ „ Neither p nor q. [$$\or $$p. $$\or $$q or p|q] (F F T F) (p, q) „ „ p and not q. [p. $$\or $$q] (F T F F) (p, q) „ „ q and not p [q. $$\or $$p] (T F F F) (p, q) „ „ p and q. [p.q] (F F F F) (p, q) Contradiction (p and notp and q and not q.)[p. $$\or $$p.q. $$\or $$q] }} Those truth-possibilities of its truth-arguments, which verify the proposition, I shall call its truth-grounds.

If the truth-grounds which are common to a number of propositions are all also truth-grounds of some one proposition, we say that the truth of this proposition follows from the truth of those propositions.

In particular the truth of a proposition p follows from that of a proposition q, if all the truth-grounds of the second are truth-grounds of the first. Rh


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 sounds he had ever heard. Though greatly surprised and terrified, he ventured to look through a window of the building, when he was amazed to see a large assembly of cats, who, arranged in solemn order, were lamenting over the corpse of one of their own species, which lay in state, and was surrounded with the various emblems of sovereignty.—Alarmed and terrified at this extraordinary spectacle, he hastened from the place with greater eagerness than he approached it; and arriving, some time after, at the house of a gentleman who never turned the wanderer from his gate, the impressions of what he had seen were so visible on his countenance, that his friendly host enquired into the cause of his anxiety. He accordingly told his story, and, having finished it, a large family cat, who had lain, during the narrative, before the fire, immediately started up, and very articulately exclaimed, “Then I am King of the Cats!” and, having thus announced its new dignity, the animal darted up the chimney and was seen no more.

Now, the man, who seriously repeated this strange and singular history, was a peer of the realm, had been concerned in the active scenes of life, and was held in high esteem

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 and veneration among mankind for his talents, wisdom, and Christian piety. After this information, which I give you as a serious fact, what have you to say? It is impossible but you must immediately withdraw your charge of infidelity against a period which could produce one such implicit believer.

As for myself, I will readily confess to you that I am neither a skeptick nor a believer.—I have enough of skepticism to prevent the throwing my share of faith away: at the same time I feel within me that there is something, which I cannot very well explain, the belief whereof I ought to cultivate, and from whence I should derive much satisfaction and contentment, could I but frame my mind to the purpose. If, however, after all my reasoning, you should still continue to fix a skeptical character upon the present age, I trust that you will at least discard it from your own breast, while I assure you of the great regard with which I am

Your most sincere, humble servant.


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Rh The truth-grounds of q are contained in those of p; p follows from q.

If p follows from q, the sense of "p" is contained in that of "q".

If a god creates a world in which certain propositions are true, he creates thereby also a world in which all propositions consequent on them are true. And similarly he could not create a world in which the proposition "p" is true without creating all its objects.

A proposition asserts every proposition which follows from it.

"p.q" is one of the propositions which assert "p" and at the same time one of the propositions which assert "q".

Two propositions are opposed to one another if there is no significant proposition which asserts them both.

Every proposition which contradicts another, denies it.

That the truth of one proposition follows from the truth of other propositions, we perceive from the structure of the propositions.

If the truth of one proposition follows from the truth of others, this expresses itself in relations in which the forms of these propositions stand to one another, and we do not need to put them in these relations first by connecting them with one another in a proposition; for these relations are internal, and exist as soon as, and by the very fact that, the propositions exist.

When we conclude from pvq and ~p to q the relation between the forms of the propositions "pvq" and "~p" is here concealed by the method of symbolizing. But if we write, e.g. instead of "pvq" "p|q .|. p|q" and instead of "~p" "p|p" (p|q = neither p nor q), then the inner connexion becomes obvious. Rh


text: Letters of the Late Lord Lyttleton/Letter XXXIX


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Rh (The fact that we can infer fa from (x)fx shows that generality is present also in the symbol "(x).fx".

If p follows from q, I can conclude from qp to p; infer p from q.

The method of inference is to be understood from the two propositions alone.

Only they themselves can justify the inference.

Laws of inference, which—as in Frege and Russell—are to justify the conclusions, are senseless and would be superfluous.

All inference takes place a priori.

From an elementary proposition no other can be inferred.

In no way can an inference be made from the existence of one state of affairs to the existence of another entirely different from it.

There is no causal nexus which justifies such an inference.

The events of the future cannot be inferred from those of the present.

Superstition is the belief in the causal nexus. The freedom of the will consists in the fact that future actions cannot be known now. We could only know them if causality were an inner necessity, like that of logical deduction.—The connexion of knowledge and what is known is that of logical necessity.

("A knows that p is the case*' is senseless if p is a tautology.)

If from the fact that a proposition is obvious to us it does not follow that it is true, then obviousness is no justification for our belief in its truth.

If a proposition follows from another, then the latter says more than the former, the former less than the latter. Rh


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The Encyclopedia Americana (1920)/Education, Elementary

EDUCATION, Elementary. — In all the elementary schools of the United States, public and private, there were enrolled in the year 1914 over 19,000,000 pupils, — 17,500,000 of these in public schools. The average number of days attended by each pupil enrolled in the public or common schools and including rural schools was 115.6 days, and the average length of the school term 158.1 days. The total expenditure per pupil was $38.31 for sites, buildings, salaries and all other purposes as compared with $15.91 for the same items in 1875.

Rural Schools. — By the increasing concentration of industrial and commercial life and the concurrent growth of railways and other modes of rapid transportation during the past 50 years, the suburbs of cities were greatly extended, the urban population vastly increased and the rural population diminished. Rural schools suffered correspondingly. Within later years, however, a reaction has set in favor of agricultural life by which rural schools have begun to profit. There still are rural schools in sparsely settled districts that continue the old practice of holding winter schools with limited sessions of SO to 90 days and taught by ill-prepared makeshift teachers. Yet lingering shortcomings are steadily yielding to the establishment of union schools, to the consequent more generous extension of school terms and to increasingly successful efforts to secure more adequate preparation of prospective teachers through special normal courses in State and county normal schools and in high schools. In the union schools a number of districts are consolidated; the children are conveyed to these at public expense; the courses of instruction are graded; the teachers comparatively well prepared and more permanent. Moreover, they offered rallying points for the people of the community for lectures, entertainments, discussions, exhibitions, institutes, social gatherings, etc. In a number of instances, increased interest in education was stimulated and led to the establishment of township and county high schools. Township high schools are common in New England and in some of the Middle Atlantic and Middle Western States; Kansas and Oklahoma and several of the Middle Western States have county high schools.

Much fresh stimulus, too, has come from the extension and increased stringency of compulsory school attendance laws. Since 1899 such laws have been passed or amended in the direction of greater stringency by all the States save two, and 28 of these require attendance during the full school year for from 6 to 9 years. The beneficial effect of such legislation will appear in the fact that the percentage of illiteracy has sunk from 7.1 per cent in 1900 to 4.1 per cent in 1910. Furthermore, it appears that out of 100 persons enrolled, approximately 92 pursue elementary studies, 6 are enrolled in

secondary schools, and 2 are in higher institutions.

From the general character of courses of study, it is fair to assume that the average schooling in all but the most backward rural district ts sufficient to secure for each normal person enough to enable the future citizen to read and write and cipher within the practical needs of life, and to enjoy in addition some geographical knowledge, some acquaintance with the history and political organization of his country and, in many instances, some skill in singing, in drawing and other handwork, and a measure of literary taste

Trained Teachers. — Consideration of the reasons for increasing the length of the term of the elementary school and the adoption of a graded course of study, reveals the most important item of improvement in the recent history of American schools, namely the introduction of professionally trained teachers. The first normal school in the United States was established at Lexington. Mass., in 1339. The number of normal schools supported by state or municipal governments has increased since that year to 235; in addition there are 46 private normal schools and a number of courses for the training of teachers in high schools and colleges. The advantage of professionally educated teachers above others lies in the fact that they have learned to use methods and devices intelligently and in thoughtful adjustment to the needs and interests of children. They have learned to distinguish between the essential and the accessory in the subjects of instruction and know how to lead the pupil to inspiring uses of his knowledge in deliberate research and in successful application to varied purposes of achievement.

But much is yet to be done, if teaching is to become a profession with adequate permanence of tenure on the part of its votaries. Thus, with regard to rural schools, Harold W. Foght, rural school specialist of the United States Bureau of Education, reports that the average rural school teacher remains in the profession less than four years of 140 days each. “This means that the entire personnel must be renewed every four years or that about 92,000 new teachers must be provided annually.” Now, the normal schools of the country had enrolled in 1913-14, 94,455 students and graduated only 19,438. The burden of providing for the largest immediate supply of rural teachers falls upon the training departments of high schools and upon county and township training schools in some of the States. Nor do these sources seem to be adequate in view of the fact that in 1913, according to the commissioner's report, there were in the teachers' training courses of public and private high schools only 3,767 boys and 23,284 girls. Nor is the dearth of satisfactorily trained teachers confined to rural schools; for of 1,350 cities reporting to the Bureau of Education in 1914 only 474 require elementary teachers to be normal school graduates, 630 require only a high school education, and the remainder fail to specify what qualifications are demanded.

Probably the most serious obstacle to the professionalizing of teachers is to be found in the comparatively low salaries paid them. In 1914 the average wage of elementary teachers

in cities of 25,000 and less than 50,000 inhabitants was $641; in cities of 5,000 and less than 10,000 inhabitants the average wage was $533; both wholly inadequate to secure normal graduates and continuous tenure. With similar import, the investigations of the National Education Association committee on teachers' salaries discloses the fact that the annual wage of farm laborers in 1913 was $257, while the average wage for rural teachers was but slightly more, although the exact figure was not available. At the same time, the average wage of rural mail carriers was $1,150. The average salary of elementary teachers in cities of 100,000 and fewer than 250,000 population in the same year was $791, and in cities of 5,000 and fewer than 10,000 population the average salary reached only $533.

Under such conditions permanence of tenure and the choice of teaching as a life work become almost unthinkable. One-third of the men and one-half of the women engaged in teaching are under 24 years of age. One-half of the teachers have had but four or fewer years of experience, and one-fourth can claim only one year of experience. At the same time, because of the more varied and wider opportunities for profitable vocational employment, men are more and more turning to other pursuits and leaving the field of teaching to women. Thus it has happened that the percentage of men teachers, which in 1870-71 amounted to 41, has steadily declined so that in 1911-12 it had fallen to 20.9, leaving practically four-fifths of the field to women. Unfortunately, this situation is still further complicated by the fact that, all but universally, married women are excluded from eligibility. Consequently, to the characteristic of the great majority of elementary teachers there has to be added the qualification that they are unmarried women. This qualification each teacher, up to a certain age, hopes to escape, thus adding a new factor to the uncertainty of tenure and a new limitation to the growth of professional spirit

Sex Problem. — The modern reorganization of the elementary school which will be discussed later on in full, presents among other welcome features the fact that it brings into the life of the child at an earlier period the influence of men teachers. The value of this cannot be overestimated. It furnishes the boy realizable ideals and examples he can emulate, and to the girl it furnishes the opportunity to gain respect for the masculine factors in life on the ground of merit. I direct attention to this without prejudice to the equally valuable influence of women in the school; for I am aware of the fact that the all but exclusive employment of men as teachers in former days had as weakening an influence upon the effectiveness of schools as their excessive feminization has upon the schools of to-day. As in the ideal family we find mother and father, sister and brother, so in the school both elements should be found in vital proportion, if the children are to grow into ideal relationships in a social organization involving both women and men.

Under the circumstances indicated, it is evident that small rural districts cannot secure professionally trained teachers. Such, indeed, find ready employment in cities and villages;

for these, too, as a whole cannot show in their graded schools an average of more than one teacher in three that holds the diploma of a normal school.

Urban Schools. — Another great advantage belongs to the schools of the village or city. They are graded schools, have a regular course of study, proper classification of pupils and uniformity of textbooks. In the small district school 15 to 40 pupils are brought together under one teacher. Their ages vary from 4 to 20, and their degree of advancement ranges from beginners to those who have attended for 10 or 12 winters and attempt secondary studies. It still may happen that there is no un i formity of textbooks except, perhaps, in the speller and reader, each pupil bringing such arithmetic, geography or grammar as his family may possess. This was the case universally in the old time district school — such as existed in 1790, when 29 out of 30 of the population lived in rural districts, and 50 years later when only 1 in 12 lived in a city. As the railroad has caused villages to grow into cities, so it has virtually moved into a city a vast population living near railway stations in the country by giving them the morning newspaper and rapid transportation. In 1890 one-third of the population was living in cities of not less than 8,000 inhabitants. But the suburban populations made urban by the railroad swell the city population to one-half of the whole nation. Hence the great change now taking place in methods of building schoolhouses and in organizing schools.

With this change in the condition of the population, the method of individual instruction was supplanted by class instruction. The individual did not gain much under the old plan, for the reason that his teacher had only 5 or 10 minutes to examine him on his daily work. In the graded school each teacher has her grade divided into two sections and hears one recite while the other prepares a new lesson. All pupils learn more by such class recitation than by individual recitations, for in the class each can see the lesson reflected in the minds of others, and understand the teacher's views much better when drawn out in the form of a running commentary on the recitation.

Textbook and Oral Teaching. — It is supposed that the chief work of the pupil is the mastery of textbooks containing treatises that give the elements of branches of learning taught. The evil of memorizing words without understanding their meaning or verifying the statements made in the book is incident to this method, and is perhaps the most widely prevalent defect in teaching to be found in the schools of the United States. The oral method escapes this evil almost entirely, but encounters another. The pupils taught by the oral method exclusively are apt to lack power to master the printed page and to get from it the full meaning; they need the teacher to explain technical phrases and definitions. The American method of textbook instruction, it is claimed, throws the children upon the printed page and holds them responsible for its mastery. The pupil is taught to assume a critical attitude toward the statements of the book and to test and verify them or to disprove them by appeal to other authorities or by actual experiment. It is evident that this system of instruction is feasible only in

graded village and city schools and can find no place in the ungraded small rural school. Where such schools have made the attempt to classify their pupils, e.g., in arithmetic or geography, they were obliged to unite in one class children of very different degrees of attainment with unavoidable injury to the dull by overpressure, to the gifted by neglect, and with but doubtful benefit to the average.

The chief objections to this method of work in graded schools has been found in its tendency to degenerate even in the hands of well-equipped teachers into spiritless “machine” work and mass-teaching with their disregard and suppression of individual needs and interests, as well as of the claims of spontaneous social intro-ordination. It proved to be economical financially, it is true, but wasteful educationally. The shortcoming is further emphasized in 24 States by the fact that these have made uniform textbooks mandatory. In some of these States the adopted books must be used as basic texts in all schools, elementary and secondary, and in all districts; in others, high schools are permitted to select for themselves; and in still others, city districts and special tax districts may adopt whatever books they may desire. In a few instances, where the State prints its own texts and modifies them from time to time on the basis of advancing professional insight, possible evils of the measure are greatly mitigated.

A concomitant of the “machine” work and mass-teaching to which large graded schools have been subject is found in so-called discipline or government. The establishment of order, regularity, silence, concerted action and general obedience to authority offered great difficulties and invited measures that seem arbitrary, out of relation with the object in view, and without even indirect appeal to the children's good will and insight.

The New Pedagogy. — However, under the inspirations of Frœbel and Herbart, of Spencer and Wundt, of Dewey and Hall, and many others, a new psychology and a new pedagogy are coming to the rescue. More and more, in the life of the school, the needs of the child with reference to his individual and social development are coming to the front. The treatment of subjects of instruction is learning to adjust itself to these needs; the very textbooks, more especially in elementary schools, reflect the new tendencies, place stress upon touching interest on the basis of the learner's experience, upon stirring the desire for independent research, upon utilizing new knowledge in fresh individual achievement or generous social endeavor. Similarly, disciplinary measures are judged more and more by these considerations. Incentives are adapted to individual nature and need. Encouragement is taking the place of relentless pedantic criticism. Good will, insight and self-respect are appealed to and, in growing proportion, deliberate self-control and even organized pupil-government take the place of ostentatiously vigilant government by teachers.

Much is due in the gradual reorganization of the elementary school to the influence of the kindergarten, of manual training, drawing and certain phases of nature study. In all of these the value of the hand as man's chief organ in exploring his world and in adjusting it to his needs is fully revealed. With their

the motto, “learn by doing and in order to do,” acquired appreciable meaning. At last, the whole diild — hand, head and heart of him — went to school. The liberal and the practical lost their antagonism, became indeed the two indispensable poles of full culture which carries men, as Gœthe has it, “from” the useful, through the true, to the beautiful. The progress of the kindergarten as a factor in elementary education has been quite rapid. The first public school kindergarten was established in Saint Louis in 1873. In 1892 the Commissioner of Education reported 459 public and 852 private kindergartens in the United States. In 1898 there were in 389 cities of 8,000 inhabitants or over 1,365 kindergartens supported by public funds. The number of teachers employed in these was 2,532, and under their care were 95,867 children. At the same time, information had been obtained concerning 2,998 private kindergartens, with 6,405 kindergartners and 93,737 children. Thus the total number of kindergartens, public and private, in this year was 4,363 with 8,937 teachers and 389,604 children. Kindergartens were authorized in 14 States, but a number of cities had established kindergartens through powers conferred in their charters. For 1914 the commissioner reports that in all States but one the establishment and maintenance of kindergartens is either required by law under certain conditions, specially permitted by law, or permitted under general authorizations. There were reported in this year 7,254 public kindergartens in 1,135 cities with an enrollment of 391,143 children. In addition there were reported in 677 cities and villages 1,571 private kindergartens with an enrolment of 74,725 children; yielding for this year a grand total of 8,825 kindergartens with an enrolment of 465,868 children.

It is the general consensus of opinion on the part of superintendents, principals and primary teachers that the kindergarten child has advantages over the non-kindergarten child, other things equal, in good school and life habits, in wealth of ideas and power of expression, in powers of observation and concentration, in perseverance in a task once begun, in control of the hand in manual work, in social co-operation and sense of responsibility in common work, in responsiveness and obedience and a number of other minor points. So beneficial, indeed, has been the influence of the kindergarten upon the spirit and work of the primary school that deliberate movements for the mutual adjustment or even coalescence of the two are becoming more and more urgent. It is proposed — and sporadically carried out — that the transition from one to the other be made less abrupt and that in normal schools student teachers for the kindergarten and others for primary work be taught together in all essential things; in short, that the kindergarten be no longer treated as a separate department, but be made an integral part of primary instruction.

A further development brought to the elementary school by the kindergarten is found in the fact that it directed favorable attention to the value and need of modeling, drawing and other forms of constructive and creative handwork in connection with the educative activities of the school. This prepared the way for slojd and other forms of manual training which later on came to the upper grammar

grades and to secondary schools, largely under the pressure of the growing industrial needs of the country.

Certain of these forms of manual training had been advocated long ago by Locke and Franke, by Rousseau and Pestalozzi; but the recognition of its full value as a factor in education was reserved for Frœbel. He, first, fully and clearly revealed the law that the end of mental activity is not knowledge, but the use of knowledge in some sort of self-expression or doing; that as the acquisition of knowledge rests largely upon the activity of the exploring hand, so the application of knowledge to the needs of life is largely dependent upon the activity of the achieving hand; and, furthermore, that full normal interest in learning can be stimulated only by the achievements it serves. To Frœbel, the manual training he had in mind was not a new subject of instruction, nor was it a concession to the industrial need of the time, but an immanent factor in every part of the educational work, adding meaning to intellectual effort, substance to ethical and esthetic aspiration. In a measure, then, it includes all the workshop and sketching-room, the kitchen and sewing-room features of current manual training departments of the elementary school, but it also includes the manual work of the kindergarten and of the modern primary school, the laboratory, the studio and the schoolgarden. In a broader sense, looking upon the hand as the symbol of deliberate muscular activity, it even may include the new attitude of the school to physical training, to play and playgrounds, to dramatization, to song and rhythmic motion.

Inspiration for manual training of a technical and industrial character came to European countries from Finland and the Scandinavian countries. To Uno Cygnæus, whom his countrymen fondly name “father of the school,” belongs the honor of first introducing work of a technical character in the urban schools and slojd in the rural schools of Finland in 1866. Similar and almost simultaneous movements for the extension of slojd and home industries in the schools of the people were carried on successfully in Sweden and Norway and more particularly in Denmark. In our own country, what goes by the specific name of manual training is traced to an exhibit of a Russian institution at the Centennial Exposition in Philadelphia in 1876. The value of the system of manual training, there suggested, appealed to such men as John D. Runkle and C. M. Woodward who introduced it into the institutions under their charge and became forcible advocates of its value. The advanced technical features of this phase of manual training — including various forms of woodwork and ironwork — are confined to high schools and, in some instances, to the upper grades of the grammar schools. The manual training of grades below the 7th deals with extended kindergarten material, with paper and cardboard work, plastic material, raffia, bookbinding, simple forms of slojd, etc.

Industrial Vocational Training. — Within recent years the problem of manual training has been much complicated by movements for the establishment of courses for industrial and vocational training which involve more or less complete preparation for distinct callings,

coupled with the opportunity for the pupil to find under so-called vocational guidance what particular vocation or group of vocations it is most profitable for him to choose. While in the original manual training, which still persists in elementary schools, the stress is upon its cultural value, industrial and vocational training emphasize the distinctively practical outcome in fitting the pupil for some definite calling, for some domestic, agricultural or other industrial work. In 1898 manual training was an important feature in the public school course of 149 cities. In 359 institutions other than city schools, there was training that partook more or less of the nature of manual training. These institutions embraced almost every class known to American education, and the manual features varied from the purely educational manual training of the Teachers' College in New York city to the specific trade instruction of the apprentice school. In 1914 there were approximately 1,200 public high schools that offered courses in manual or technical training, in agriculture, and domestic economy. No reports are available as to the extent of educational or other hand-training in the elementary schools at this time.

Within the last two decades, the attention of legislative activity has been directed to the importance of hand-training, more especially with reference to industrial and vocational needs. To Massachusetts belongs the honor of leading the way in this matter in a law 20 years old, requiring every city of 20,000 inhabitants or over to maintain manual training courses in both elementary and high schools. Later on, Massachusetts again led in legislation aiding the establishment of industrial and vocational schools. By 1915 24 States and the District of Columbia had found it necessary to pass laws providing for courses in a variety of vocational work: for continuation schools, evening schools, trade schools, special classes, etc. Thus, by way of illustration, New York provides for courses in agriculture and home-making in her consolidated rural schools, for continuation schools, for trade schools, and for evening vocational schools; New Jersey provides for all-day industrial schools for boys over 14, household-arts schools for girls over 14, part-time continuation schools for boys over 14 employed as apprentices, evening industrial classes for boys or girls over 16 who are employed as apprentices, evening household-art classes for girls over 17, and vocational agricultural classes. Indiana makes provision for “fitting each individual in the State for some useful form of work” in the public school work of the State; for this purpose, the law requires that elementary instruction in domestic science and in the industrial arts be given as a part of the regular course of instruction in all the schools — in the 7th and 8th grades and in the high schools — of the State. Moreover, the law provides for vocational departments and schools conducted for the sole purpose of preparing for efficient and productive work in the shop, in the home, and on the farm.

The highly organized graded school of to-day is quite young. The War of Independence and the subsequent need for organizing and extending the new territory and of establishing means of intercommunication and other economic facilities had deflected attention to the scanty

provisions for public education. At the same time immigration brought many poor and ignorant families, and illiteracy was growing apace. A new enthusiasm and an intensely popular movement, however, set in when in 1837 Horace Mann and Henry Barnard began their educational work, the one in Massachusetts, the other in Connecticut and later (1843) in Rhode Island. From these beginnings and within less than 80 years, the elementary division of our public school system has been evolved. Within the past 40 years, there have come to our public elementary schools among many other commendable features grouping by grades, trained teachers, enrichment of studies, care for the health of the children and for their general well-being. The most significant steps in the functional reorganization of the elementary school came within recent years: in the first place through efforts of the college to shorten the time required for college graduation by reducing the elementary school period to six years instead of eight or nine; and, subsequently, to free the public school generally from its all but exclusive subservience to college ideals in order that it might be enabled to serve also the needs of industrial, commercial, agricultural and domestic life. With this in view, the course of the elementary school is being more and more generally shortened to six years, to be followed by an intermediate course of two or three years and by a high school course of four or three years.

Six-three-and-three Plan. — Among the various plans proposed and set in operation for the purpose indicated, the six-three-and-three plan is probably the most favored. It reduces the elementary school to six years, establishes an intermediate school, or “Junior High School,” of three years and a full-fledged high school of three years. In both the intermediate and the high school the courses are flexible and promotion is by subjects not by grades. Instruction throughout is departmental and in the hands of persons who combine the qualities of the teacher with those of the expert. The curriculum of this intermediate school affords much opportunity for differentiation. All, it is true, share in pursuits that reveal the duties of citizenship and open avenues to the appreciation of the refinements of life. Yet, for each one there is opportunity to emphasize what talent, genius, necessity, or even inclination may demand. This flexibility of the course with its wealth of opportunity enables the student under the teacher's guidance to “find himself,” his capacities and enthusiasms with reference to the choice of a life-career. Thus the intermediate schools of Los Angeles offer five distinct courses: the literary-scientific course, the engineering preparatory course, the mechanic arts course, the home economics course, and the commercial course. Aside from its many internal advantages, this coming intermediate school confers the great boon of holding the children under instruction for a longer period and of bridging the fatal chasm between the elementary and the high school, leading a greater number of children into the high school proper in its academic, scientific, technical, commercial and other quasi-professional departments. The work assigned to the elementary grades remains practically the same. Courses of study deal with reading, writing, arithmetic, spelling,

the use of the vernacular, nature study, the history of our country (biographical and chronological), some geography, hygiene, physical culture, music, drawing, and some phases of manual work, mostly in connection with other subjects of instruction or with the plays of the pupils.

Problems. — The problems of truancy, retardation and varying endowment are destined to became important factors in the reorganization of the elementary school. These problems became urgent with the sincere and consistent enforcement of compulsory education laws about 1890. It soon became evident that the physical and mental conditions of children are not uniform and that individual differences in children demand serious consideration in their education. The fact that children vary widely in their natural gifts and inclinations and the clear discovery of eye, ear and motor-mindedness in children, forced upon the school demands of greater flexibility in method and organization. At first, the attention was chiefly upon mere truancy and certain disciplinary faults. Then, and until quite lately, the stress was upon the needs of laggards; ungraded rooms, so-called industrial schools, special help devices, shorter promotion intervals and promotion by subjects came to be applied as remedies; for abnormal children special schools were established. At last it has come to be fully realized that retardation is an individual matter, that it threatens the specially gifted through lack of interest as much as it falls to the lot of the less favored through lack of ability, and that it was necessary to make provision for all the various phases of individual capacity. In 1911, therefore, it became possible for the Commissioner of Education to report that provisions for backward children had been made in 220 cities, for mentally defective children in 99 cities, and for exceptionally gifted children in 54 cities. Prominent among the last were Baltimore, Indianapolis, Lincoln, Rochester, and Worcester. The provisions of all these cities were based upon the desire to furnish these children opportunity in the 7th and 8th grades to do advanced work for which they could receive credit when entering the high school. Many educators, however, doubt the wisdom of singling out such children and separating them from the classes of normal children. They emphasize the social value of joint training upon the development of character. They point out the fact that children have likenesses as well as differences and that in the school they should learn to work together as they will have to do subsequently in life; that, therefore, they should be trained together, although each in his own way and according to his ability in common work. Teachers are deeply interested in the problems involved, since from their study valuable contributions to the progressive reorganization of the elementary school cannot fail to flow.

Gary Plan. — A new departure in school management which is attracting much attention proceeds from Gary, Ind., under the direction of Superintendent William A. Wirt. The city of Gary is located on the shore of Lake Michigan, about 30 miles southeast of Chicago. When it was founded in June 1906 the site was a waste of shifting sand dunes dotted with marshes. To-day it is a flourishing city of approximately 50,000 inhabitants, with all the public utilities

and aspirations of a modern city. In 1906 four teachers taught 120 pupils in its first schoolhouse; in 1916 the number of teachers had risen to nearly 200 and that of pupils to more than 6,000. The Gary plan of a school plant is “a playground, garden, workshop, social centre, library and traditional school combined under one management.” For these purposes the new Frœbel School, erected at a cost of $350,000, stands upon a tract of 10 acres; one-half of this is used for playgrounds, two acres for schoolgardens, and three acres for park. There are also two conservatories for nature-study work, the botany work in the high school, and for supplying plants for the schoolrooms. Among the striking features of the work, the following are the most noteworthy:

1. The schools are open the year round, or for four quarters of 12 weeks each. Pupils are held to attend school for three of these quarters, choosing for vacation the one that suits them and the home best. During the free quarter the pupil may attend voluntarily any of the activities of the school or, with the help of the school, find employment in the industrial life of the city.

2. The elementary school and the high school are in the same building. This, it is claimed, removes the chasm between the two departments and tends to hold pupils in the school for longer periods. Moreover, it establishes the same standard of discipline for all grades, increasing sense of responsibility on the part of the older pupils and stimulating worthy ideals on the part of the younger.

3. Throughout, the teaching is departmental. This renders it possible to promote pupils by subjects, to employ skilled special teachers and to do away with supervisors.

4. The school plant is open on Saturdays. Pupils come and go as they please, work or play as they choose under teachers who receive extra pay for this work. The responsibility placed upon pupils who avail themselves of this stimulates initiative and has a tendency to “transform the play impulse into the work impulse.”

5. Similarly, certain schools are open four evenings per week for continuation school work and for "social and recreational centre" activities.

6. Constant utilization of the school plant by double the number of classes as compared with the number of available classrooms. This involves the constant use by successive classes of the auditorium, the basements, the library, the gymnasium, and various portions of the playgrounds in such a way that no part of the plant is ever idle during the entire schoolday.

Other phases of the work, still in progress of evolution promise equally valuable contributions to school management. Indeed, the results already attained by Superintendent Wirt have induced a number of cities to seek at least partial enjoyment of the benefits of the Gary plan. Prominent among these is New York which is making extensive experiments with it under the direction of Superintendent Wirt, not without prospects of success.

Among a number of other features in the progressive development of schools within the past two decades, a prominent place belongs to increasing attention to sanitation, to the care for atypical children, the organization of

associations, the use of schools as community centres.

Sanitation. — With reference to sanitation, it is reported that in 1914 there were over 500 open-air schools in the United States and that throughout open-window ventilation is gaining ground. Forty States have enacted laws relative to the sanitation of school plants, involving the inspection of schools and approval of plans for new buildings, and the right to compel improvements. In a number of instances, these laws extend to rural schools empowering the county superintendent to condemn faulty structures and to inspect and pass on plans for new buildings. Medical inspection laws relate to compulsory health supervision of school children; to examination of teachers and janitors and to regular inspection of buildings, premises and drinking water in order to insure sanitary conditions; inspection to control contagious diseases; annual tests for sight and hearing; provision for the employment of school nurses; penal i ties or other provisions for the enforcement of the laws. That steady gain is being made in cities appear, from a summary of returns made by 1,406 cities to a questionaire, sent out by the Bureau of Education in 1914. These returns show, among other things, that 750 of these cities have some form of medical inspection; that 570 have inspection of ears, eyes and teeth, 62 of ears and eyes only, 90 of eyes only, and 29 of teeth only; that 268 have school nurses, and that in all 923 school nurses are reported; that 130 cities have dental clinics and 195 treat the teeth of school children through other agencies; that 74 have general clinics and 33 psychological clinics under expert direction. On the other hand, the sanitary condition of rural schools still is described as deplorable. Indeed, it is pointed out on the basis of comparative statistics concerning defects of school children of the cities and rural districts of five of the older States that for all defects except two, the prevalence of defect was much greater among the children of the rural schools. This is attributed largely to low architectural and sanitary standards in rural regions; ignorance regarding the physical, mental, social, and moral effects of unattractive and insanitary school buildings; false economy of school boards; and lack of State supervision and assistance. However, as indicated above, inroads are being made by means of suitable legislation, by normal schools and educational associations, so that improvement cannot tarry long.

Surveys. — The tendency to secure improvement of schools in both rural and urban districts through the agency of careful surveys of existing conditions and needs is steadily extending. In tracing the development of the movement in an address delivered in 1915, Dr. Leonard P. Ayres, director of the division of education of the Russell Sage Foundation, gave an account of the important features of the 30 surveys made up to the time. The following data are culled from this report. These surveys were carried on: seven by individuals, six by universities, five by bureaus of municipal research, three by State departments of education, three by foundations, two by the United States Bureau of Education, two by municipal departments, and two by national societies. The directors of the surveys were professors of education, 13; special investigators, 11;

of foundations, four; the United States Commissioner of Education, one; superintendent of schools, one. The cost figures for the different surveys varied from $500 (Montclair, N. J.) to $125,000 (New York city). The time required varied from three months to two years and two months. From 1 to 12 individuals were engaged in each survey; and the published reports varied from six pages to 2,573 pages in size. Much good has come to the systems thus surveyed in the relation of supervising and teaching forces to each other and to boards of education; in the vitalizing of courses of study and methods of work; in securing minimum standards for drill work, notably in the three R's, setting free much time for work of greater value. As a result many new surveys are being called for by city and rural school authorities. A number of cities, indeed, have established permanent bureaus of efficiency. Notable among these are Boston, Detroit, Kansas City, New Orleans, New York and Oakland.

Parent-teachers' Asociations. — Ideally, the public school is an organic factor of our democracy. By it the coming citizens are to be fitted in knowledge and character for the performance of their duties. On its work depends the political and economic welfare of the state, as well as the individual and social welfare of each coming citizen. It is obvious, therefore, that fathers and mothers should feel a direct and personal interest and civic responsibility in the organization and work of the school, an interest and responsibility that cannot wholly be delegated to representatives. To such considerations the school owes the organization within recent years of mothers' clubs, parents' guilds and parent-teachers' associations which by their very existence have been and are exerting a highly beneficial influence upon the progressive development of the school. In a general way, the object of these associations is co-operation between the home and the school, to induce the school to consider in its work the needs of the home and to induce the home to aid the school in its attempts to meet new conditions and civic needs. In a city of 100,000 inhabitants in the Middle West such associations provided pianos, valuable art objects, stereoscopic lanterns and slides, and other physical apparatus, thereby declaring emphatically and in most amiable fashion that in the opinion of the people music, art and science had a legitimate place in the curriculum. Elsewhere the schools owe to such organizations in a large measure the establishment of kindergartens, the teaching of domestic arts, the enrichment of school libraries, the introduction of school luncheons, the encouragement of schoolgardens, of school festivals and school exhibits. They arrange for round table discussions of topics relating to the children's health, their conduct in and out of school, the nature and value of play, the influence of environment and every phase of child-study (q.v.). They invite experts to lecture on similar and other timely topics.

Social Centres. — Of deep significance for the further development of the elementary as well as for the other departments of the public school is a correlated movement of recent origin, namely, the wider use of school buildings for “social centre” and “community centre” activities. Aside from the fact that it utilizes the costly school plants for worthy purposes of

public import at times when they are not needed for the direct purposes of the school, this movement means that the people are begining to realize the deeper fact that the school has not completed its work when it has dismissed its pupils to enter upon some way to earn a living and that these young people still need opportunity for further social and character development as well as for additional instruction under wholesome conditions. The movement originated in efforts to vitalize the work of rural schools by a variety of social occasions interesting to parents and in the needs of parent-teachers associations in cities; but within less than a decade it has assumed wider proportions. In 1915 the Bureau of Education received reports from 603 cities of 5,000 inhabitants and over, detailing the more or less extended adoption or admission of social, civic and educative activities in their schools. Among the activities mentioned the following are prominent: meeting of mothers' clubs, parent-teachers' associations, women's civic clubs, musical organizations, art clubs, Chautauqua circles, Boy Scouts, Campfire Girls, gymnastic clubs, dramatic and literary clubs, debating societies, lectures, evening schools for a variety of purposes. Already 18 States have secured legislation permitting the use of schools for the purposes indicated.

The management of these activities still is in an inchoate condition. In Youngstown, Ohio, the local playground association provides for supervisor and supports social centres in the schools. In Trenton, N. J., it is the Social Centre League, assisted by the principals and teachers. In Plainfield, N. J., there is a citizens' committee on evening recreations in which the Board of Education is represented by its president and the superintendent of schools. In Grand Rapids, Mich., the park and school boards together maintain a department of municipal recreation. Philadelphia has a municipal recreation commission and in Kansas City, Mo., the public welfare board co-operates with the board of education. Quite steadily, however, the responsibility is passing into the hands of school-boards and its employees. Thus, in Pittsburgh, Pa., the direction is in the hands of the director of evening schools; Cincinnati has a special director of social centres; in Boston, a similar official works directly under the superintendent of schools and has the advisory assistance of the Women's Municipal League; in Milwaukee, a special department of school extension controls the after-school activities.

Increasingly, too, we find in new elementary school plans adaptations to the new uses of the buildings. Prominent among these are auditoriums, gymnasiums, lunchrooms, plunges, library rooms, swimming pools, in one case a pair of bowling alleys. In the equipment movable the Women's Municipal League; in Milwaukee, the social centre directors are provided with amply furnished private offices; many of the rooms intended for recreational work are in the basement and have been made attractive through the use of paint, pictures, book cabinets and a supply of suitable chairs and tables. The assembly rooms are provided with large electric lamps of high power and stoutly screened to adapt the room for basket ball and similar games. In most of these large rooms there are

also trough footlights and sliding curtains, as well as motion picture booths.

Bibliography. — Bunker, Frank Forest, “Reorganization of the Public School System” (Bulletin of the Bureau of Education, 1916, No. 8); Bulletins of the Bureau of Education: 1911, Nos. 4 and 14; 1912, Nos. 16 and 21; 1913, Nos. 13, 31, 39; 1914, Nos. 2, 4, 6, 18, 48; 1915, Nos. 24, 28, 36, 41; 1916, Nos. 3 and 8; Reports of the Commissioner of Education for the years 1910-15. Cole, Percival A., “Industrial Education in the Elementary School” (1915); Eliot Charles W., “The Tendency to the Concrete and Practical in Modern Education” (1916); Hanus, Paul H., “School Efficiency”; Weeks, Ruth Mary, “The People's School” (1915).

Rural Schools: Betts, Herbert George, “New Ideals in Rural Schools” (1913); Dexter, Edwin Grant, “A History of Education in the United States” (1914); Cubberly, Elwood P., “The Improvement of Rural Schools” (1912); Bulletins of the Bureau of Education: 1912, Nos. 21 and 28; 1913, Nos. 2, 8, 32, 42; 1914, Nos. 12, 25, 27, 28, 30, 44, 49; 1915, No. 20; 1916, Nos. 2 and 8; Reports of the Commissioner of Education for the years 1910-15.


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Rh If p follows from q and q from p then they are one and the same proposition.

A tautology follows from all propositions: it says nothing.

Contradiction is something shared by propositions, which no proposition has in common with another. Tautology is that which is shared by all propositions, which have nothing in common with one another.

Contradiction vanishes so to speak outside, tautology inside all propositions.

Contradiction is the external limit of the propositions, tautology their substanceless centre.

If Tr is the number of the truth-grounds of the proposition "r", Trs the number of those truth-grounds of the proposition "s" which are at the same time truth-grounds of "r", then we call the ratio Trs:Tr the measure of the probability which the proposition "r" gives to the proposition "s".

Suppose in a schema like that above in No. 5.101 Tr is the number of the "T"'s in the proposition r, Trs the number of those "T"'s in the proposition s, which stand in the same columns as "T"'s of the proposition r; then the proposition r gives to the proposition s the probability Trs: Tr.

There is no special object peculiar to probability propositions.

Propositions which have no truth-arguments in common with one another we call independent.

Two elementary propositions give to one another the probability ½.

If p follows from q, the proposition q gives to the proposition p the probability 1. The certainty of logical conclusion is a limiting case of probability.

(Application to tautology and contradiction.)

A proposition is in itself neither probable nor Rh


text: Author:William Nicholas Hailmann

title: Author:William Nicholas Hailmann


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Rh improbable. An event occurs or does not occur, there is no middle course.

In an urn there are equal numbers of white and black balls (and no others). I draw one ball after another and put them back in the urn. Then I can determine by the experiment that the numbers of the black and white balls which are drawn approximate as the drawing continues.

So this is not a mathematical fact.

If then, I say, It is equally probable that I should draw a white and a black ball, this means, All the circumstances known to me (including the natural laws hypothetically assumed) give to the occurrence of the one event no more probability than to the occurrence of the other. That is they give—as can easily be understood from the above explanations—to each the probability ½.

What I can verify by the experiment is that the occurrence of the two events is independent of the circumstances with which I have no closer acquaintance.

The unit of the probability proposition is: The circumstances—with which I am not further acquainted—give to the occurrence of a definite event such and such a degree of probability.

Probability is a generalization. It involves a general description of a propositional form. Only in default of certainty do we need probability.

If we are not completely acquainted with a fact, but know something about its form.

(A proposition can, indeed, be an incomplete picture of a certain state of affairs, but it is always a complete picture.) Rh


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 good work for "Modern Painters," one he had meant to do himself but for which he will not now have time a bit of the fir boughs in Turner's "Crossing the Brook," now at South Kensington.

I told him about you, about my visit, about your work among the men how lovely I thought it, and how fresh. He was very much pleased, and told me about the daughter of a friend of his, who does much the same to whom it seems he has sent several of my drawings for her men to use.

We got at last upon the subject of the education of working women ; and he asked much about it, seemed greatly interested. I told him many anecdotes, and something of what I said in my article on the subject. He was much interested about the question of fiction. He hopes to publish the fifth volume in the spring. I was with him an hour and a quarter. When I came away he said, "We'd quite a nice chat" ; he "wasn't so horridly busy as usual." January 8th, 1860. . In a description of a gathering at the Working Men's College she says : "I was much interested in an earnest young countryman of the name of Cooke, who had presented a collection of butterflies and moths, etc., to the College. As every scrap of natural history is eagerly learnt by me, to be repeated wherever I go, and lovingly remembered, I got him to tell me some of their names and habits. . ..

"I was delighted to hear Mr. Dickinson (whose portrait of Mr. Maurice you may remember) praising Mr. Ward's drawings. . . It was very nice to see old faces back again and to feel as if I never should have done


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Rh The probability proposition is, as it were, an extract from other propositions.

The structures of propositions stand to one another in internal relations.

We can bring out these internal relations in our manner of expression, by presenting a proposition as the result of an operation which produces it from other propositions (the bases of the operation).

The operation is the expression of a relation between the structures of its result and its bases.

The operation is that which must happen to a proposition in order to make another out of it.

And that will naturally depend on their formal properties, on the internal similarity of their forms.

The internal relation which orders a series is equivalent to the operation by which one term arises from another.

The first place in which an operation can occur is where a proposition arises from another in a logically significant way; i.e. where the logical construction of the proposition begins.

The truth-functions of elementary proposition, are results of operations which have the elementary propositions as bases. (I call these operations, truth-operations.)

The sense of a truth-function of p is a function of the sense of p.

Denial, logical addition, logical multiplication, etc. etc., are operations.

(Denial reverses the sense of a proposition.)

An operation shows itself in a variable; it shows how we can proceed from one form of proposition to another.

It gives expression to the difference between the forms.


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 the papyrus and other aquatic plants. But according to Wilson the most general appelation is simply Nyanza, that is, the "lake" in a superlative sense.

South of Ukerewe a large bay penetrating far inland has by Stanley been named after Speke, his precursor in the exploration of equatorial Africa. The stagnant pools and lagoons fringing this inlet are infested by crocodiles of enormous size. Others, which frequent the reedy banks of the Tanguré, are by the natives regarded as demi-gods, personifying the tutelar deity of the stream. Some of the islands are in the undisputed possession of fierce hippopotami, grouped in regular tribes and families, which tolerate the presence of no other large animals in their respective territories. For the capture of these monsters the natives have constructed boats of a peculiar build; but such hunting expeditions are always attended with great risk.

The coastlands, which apart from a thousand small indentations have a circumference of over 720 miles, present an endless variety of landscape. Along the rocky shores the prevailing formations are everywhere gneiss, granite, or basalts. But in some places the riverain tracts spread out in level, treeless plains, while elsewhere the margin of the lake is skirted by high hills and even mountains diversified with patches of verdure and enlivened by groups of villages. Between

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 shaking hands. ... its joy consisted so much in the momentary grasp of a hand, in the sudden sight of a face which owed all its preciousness to the thought of natures I had learnt to know in sad moments or hard working days. . . . Does it not seem to you one of the main things we long for in heaven that every strong affection for visible things will have some answer? ... I often feel so sure that the love of places, employments, books, as well as people, is not to perish, but to be justified." January 29th, 1860. . Yesterday I saw Ruskin. "Do you come by appointment?" the servant asked me, "because Mr. Ruskin said he would see no one." "Mr. Ruskin fixed the day, I named the hour ; but if he is busy——." The servant, however, seemed sure that I was to be admitted, and I was shown into the study, where Ruskin greeted me with the words, "I'm very glad to see you." I saw he was ill, and found he had been suffering from toothache, and awake all night. I begged him, therefore, not to attend to my work. However he would do it. I shall not readily forget the afternoon. He was not busy, and showed me the loveliest things, exquisite copies of illuminations, wonderful sketches by Mr. Bunney (one of his College pupils), sketches which Ruskin said he had seen nothing like them except Turner. . . . And then Ruskin showed me two of Turner's loveliest small drawings, one of Solomon's pools, and beyond their square basins, and the battlements, amidst which the light gleamed, the sun was setting ; and clouds gathered about him, because, Ruskin said, the clouds gathered about


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 Solomon's wisdom. Oh that sky palpitating with colour, changing on every thousandth inch !

Kuskin asked me if I'd been reading anything lately ; and we talked about Tennyson. I said he was so very sad. He said, "You see far more to make you sad than I do ; but I don't think Tennyson a bit too sad. I haven't found that he sees far enough." "He knows, however," Ruskin said, "how far he does see, and that is more than other people do." I told him how years ago Tennyson's words had distressed me, because I believed that good was then and always, and that we it is who mar it all ; I forgot that what had distressed me most of all was Tennyson's apparent uncertainty about the fact at all. "So runs my dream," etc.

Ruskin said, "Do you think that good is coming now to bad people?" "Yes," I replied, "and that their greatest sin is in refusing it." "But how much more that is than most people see," he went on. "Oh, yes, I see that now," I agreed, smiling ; "I am amused now that I did not know that then."

We spoke about the wickedness of rich and poor people. Ruskin spoke of the little children like angels he saw running about the dirty streets, and thought how they were to be made wicked. I spoke about the frightful want of feeling in all classes ; but added that I thought rich people were now waking up to a sense of their duties. "Yes," he said, "I'm glad that you and I have probably a good deal of life still to come. I think we may live to see some great changes in society." "I hope at least," I said, "to see some great changes in individuals before I die." "Oh, no," he said, " that's quite hopeless ; people are always the same. You can't alter natures."

We talked a good deal about it ; but not quite


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 the Kalonga and Tanguré rivers the coast is generally low, and here the shallow water nowhere exceeds a few feet in depth for two or three miles from the land. But farther south the shore is fringed by bare cliffs, varied with strips of red or orange lichens, giving them the appearance of blocks of iron, and several have in fact been found to consist of ferruginous ores.

The most charming prospects are displayed towards the north-west in the territory of U-Ganda. Here the inlets along the coast appear to be divided by the intervening wooded headlands into lakelets of unequal size. Limpid streams are everywhere seen sparkling amid the dense masses of verdure; down every dell flows a silvery rivulet fringed with tall grasses or shrubs, above which are interlaced the branches of forest trees. Probably no other region in Central Africa enjoys a more equable climate or a richer soil than this land of U-Ganda. The plants of the temperate zone recently introduced by Europeans thrive well.

Off the coast of U-Ganda an archipelago of four hundred islands, of which the largest group bears the name of Sessé, stretches in a continuous chain between the high sea and the creeks along the shore. The scenery of this insular world is even more diversified and its vegetation more exuberant than on the opposite mainland. Here magnificent timber clothes the slopes of the hills down to the beach, which is everywhere bordered by masses of papyrus. Towards the west the basalt island of Bukerebé, Stanley's Alice Island, raises its blackish walls over 300 feet above the lake. But of all the insular masses lining the shores of Nyanza, the most remarkable is that to which Stanley has given the name of "Bridge Island." This rock, which lies not far from the north-east corner of the lake, consists of two basaltic columns connected by an irregular elliptical arch with a spring of about twenty-four and a depth of twelve feet. Trees have struck their roots deep into the interstices of the rocks, which, overgrown with brushwood and tall grass, leave nothing visible except two columnar masses of verdure hanging in graceful festoons down to the water. Through this archway of tropical vegetation a glimpse is afforded of the hazy coast-range bounding the horizon on the opposite mainland.

The beauty of the Nyanza scenery is enhanced by the native craft which enliven its waters, and which are at times grouped in large fleets. Some of the surrounding communities have sailing-boats; the traders have launched vessels of considerable size, resembling the dhows of the Zanzibari Arabs, and the European missionaries have constructed sloops on the English model. But most of the skiffs are still of a primitive type, mere barges with round stems sunk deep in the water, and sharp prows projecting clean above the surface and adorned with two antelope horns and a bunch of feathers. From a distance they present the appearance of an animal raising its neck above the water in search of prey. These boats, manned by crews of from ten to forty-eight hands, carry neither mast nor sail, and are propelled only by the paddle. Rudely constructed of trunks of trees lashed together with flexible branches, and caulked with a mixture of bark and mud, they offer but a slight resistance to the waves; hence accidents are frequent, although they seldom venture far from the shore.

Before the arrival of the Europeans the fleets of the king of U-Ganda seldom

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text: 1911 Encyclopædia Britannica/Nicholas (King of Montenegro)


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 decisively. I see we quite agree that you can only call out and make living that which is in a nature. Kuskin meant a great truth when he said, "I can never alter myself. I think I had better make the best of myself as I am." When I said, "I am very much altered during the last few years," he laughed very kindly, saying, "Oh, no, you're not ; you're just the same as ever ; only you know more."

But it does make all the difference in the world whether we are fully developing all that we are meant to be, conquering all bad passions, or not. 103, Milton Street, February 5th, 1860. .

I am afraid that it is long since I wrote to you ; but of course I am always thinking of you both, dears, and longing to have you home again, that you may really know all our doings and lives. Mine lately you would assuredly consider rather of the dissipated kind. I've been giving some book-keeping lessons to Miss J. B. She is a bright, spirited, brave, generous young lady living alone in true bachelor style. It took me three nights to teach her, and she begged me to come to dinner each time. . . . She has a friend, who is killing herself by hard work to support her younger sisters. ... I gather she would gladly give her friend help, for she speaks most sadly of the "modern fallacy" "that the money must be earned." She thinks it might be given when people are dear friends ; she says they've given the most precious thing ; and what difference can a little money make? I am so very happy about my work, now that I've finished nine drawings altogether for the " Modern Painters." Oh,


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Rh (And that which is common to the bases, and the result of an operation, is the bases themselves.)

The operation does not characterize a form but only the difference between forms.

The same operation which makes "q" from "p", makes "r" from "q", and so on. This can only be expressed by the fact that "p", "q", "r", etc., are variables which give general expression to certain formal relations.

The occurrence of an operation does not characterize the sense of a proposition.

For an operation does not assert anything; only its result does, and this depends on the bases of the operation.

(Operation and function must not be confused with one another.)

A function cannot be its own argument, but the result of an operation can be its own basis.

Only in this way is the progress from term to term in a formal series possible (from type to type in the hierarchy of Russell and Whitehead). (Russell and Whitehead have not admitted the possibility of this progress but have made use of it all the same.)

The repeated application of an operation to its own result I call its successive application ("O' O' O' a" is the result of the threefold successive application of "O' ξ" to "a").

In a similar sense I speak of the successive application of several operations to a number of propositions.

The general term of the formal series a, O', a, O' O' a, ... I write thus: "[a, x, O' x]". This expression in brackets is a variable. The first term of the expression is the beginning of the Rh


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 you old Mirry, what a person you are for a joke ! I've found you out ! How came you to write that I'd received 6d. from Lord Palmerston, and spent 6d. in seven birds' nests ! Impertinent old thing ! I came upon the entries in looking thro' my cash book ; and I think Mama will never forget it. February 26th, 1860. .

Gertrude, Octavia and Minnie went to a party at Mrs. Shaw's. Gertrude and Minnie say Octavia looked "perfectly lovely." She had a high white dress, a grand scarlet sash and scarlet net. . . . Ockey, tho' looking so ill, is unusually nice, genial and merry. She has met with some amusing people lately, and it is as good as a play to hear her relate her dealings with them. She attracts an unusual share of confidence. Even strangers go to her for advice. Ladies at S. Kensington read their letters to her tell her their history. She could not help laughing one day ; she said a lady, a perfect stranger, told her all about herself, even to the time she went to bed. April 1st, 1860. ,

,

As to those old days I owe more to those visits than I can ever express. I remember now that strange imagination of yours that peopled the world for us with wonderful and beautiful beings, and I am sure we always went on happily together. (She also speaks of the impression of Mrs. Howitt's loving, cheerful look.)


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 April 15th, 1860. .

Yesterday we took Miss Baumgartner to see Ruskin's Turners. . . . Ruskin says lie does not mean to write any more for ten years, but to teach more. . . . He said he did not want to write any letters to people. He wanted Ockey's advice, as to what excuse he should make. She said he should think what was the truth, and try if he could not say that. Then he began talking about truth, saying it was difficult to speak the truth ; but to convey a truthful impression was almost impossible. That those who speak the truth are often the most misunderstood. O. asked him if he had read Mrs. Browning's new poems. He called them beautiful but absurd. O. said, "Why absurd ? Because she trusts Louis Napoleon?" "No," he said ; "I hold it is right to trust a man till he does something which proves him wrong. But mind, you're not to say I'm wrong if he turns out treacherous." Ruskin said that the taking of Savoy did not implicate Napoleon's character, because it was no pecuniary advantage to him, "not much larger than my garden and very poor." Do you think an ambitious man would spend thousands of men and money for that? He takes it just to pacify the French, who want some substantial proof that they were conquerors. To me personally it was a great blow, because it was so nice and dirty and tumble-down, and those wretched French will go and put it all to rights. It will be much better for the people, but I shall get no lore sketching."


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Rh formal series, the second the form of an arbitrary term x of the series, and the third the form of that term of the series which immediately follows x.

The concept of the successive application of an operation is equivalent to the concept "and so on". One operation can reverse the effect of another. Operations can cancel one another.

Operations can vanish (e.g. denial in "~ ~ p". ~ ~ p = p).

All propositions are results of truth-operations on the elementary propositions.

The truth - operation is the way in which a truth - function arises from elementary propositions. According to the nature of truth-operations, in the same way as out of elementary propositions arise their truth-functions, from truth-functions arises a new one. Every truth-operation creates from truth-functions of elementary propositions another truth-function of elementary propositions, i.e., a proposition. The result of every truth-operation on the results of truth-operations on elementary propositions is also the result of one truth-operation on elementary propositions.

Every proposition is the result of truth-operations on elementary propositions.

The Schemata No. 4.31 are also significant, if "p", "q", "r", etc. are not elementary propositions.

And it is easy to see that the propositional sign in No. 4.42 expresses one truth-function of elementary propositions even when "p" and "q" are truth-functions of elementary propositions.

All truth-functions are results of the successive Rh


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 103, Milton Street, April 29th, 1860. . At last I've returned to my old proper habit of writing once a fortnight to you, I hope. I've been gadding about in the idlest way possible, and yet with my time quite full. You ask me about Good Friday. My dear sister, I'm far more afraid of your plaguing and torturing your conscience than of your doing wrong.

Mr. Maurice and Mr. Da vies seem to me decidedly to think it a mistake to treat going to church as always a duty ; of course you must do whatever you think right. I shouldn't hesitate to give up going to church on one day, or even fifty, for one of you. You dear old thing, I wish I had you here to give you a thorough good rest, and rousing, and refreshing. How I should enjoy it ! I'm as merry as a grig. I greatly enjoyed Miss Baumgartner's visit. Miss J. B. and I are great companions. I'm always doing things with her. You know she's teaching me Euclid. We went to see Holman Hunt's picture. It is very wonderful, in some respects extremely beautiful, exquisitely beautiful as to colour. But I don't feel as if the picture had thrown much light on the subject for me. I have taken a class in the night-school for girls here for three weeks, during the absence of Miss C. S. I am so glad at last to get into parish work. Miss Sterling and Miss J. B. give me almost unlimited money help for poor people ; the only question is how to use it wisely. . ..

We have been twice to Spitalfields and seen much poverty there among the weavers, besides making the acquaintance of a most nice Ragged School master there. He went round with us to the people's houses


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 quite gladly, after his hard day's work ; and it was so very nice to see the welcome all the people gave him, but especially the children. He told us such an interesting story about a pupil of his, a very desperate bad character, about 16, who gambled in school, and only came with the avowed intention of having "a lark," i.e., pouring out the ink, and upsetting the forms. At last this schoolmaster spoke to him, told him he had no children of his own, and that he should be one to him, if he would. The boy was deeply touched. He always sat by the master and studied hard. To quote Mr. S., "I assure you, and I'm not ashamed to own it, he distanced me out and out. He was a first-rate mathematician ; he solved some of the greatest problems of the age (?). 'There, old 'un,' he used to say, showing me his slate in triumph, ' do you know anything about that ? '"

"And what became of him at last ? " we asked. " He died at twenty-one," Mr. S. answered, his eyes filling with tears as he went on "He died a peaceful and triumphant Christian. My wife and I never left his bed for three days and nights. That's his portrait; he'd long promised it to me, and on the Thursday (he died on Tuesday) he said, ; Old fellow, if you don't have it now, you'll never Jiave it.' I never could break him of his rough way of speaking. He'd come in here to the last and say, ' Well, old 'un, have you got anything to eat ? ' He wanted to come over from his father's house, and die in my easy chair ; and the little wife and I would have given him his wish. But the doctor forbade it. Yes, I do miss him."

Maggie Yarnall is now on her voyage to England, which gives me the faintest most precious hope that Mary Harris may possibly come to London.


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Rh application of a finite number of truth-operations to elementary propositions.

Here it becomes clear that there are no such things as "logical objects" or "logical constants" (in the sense of Frege and Russell).

For all those results of truth-operations on truth-functions are identical, which are one and the same truth-function of elementary propositions.

That ∨, ⊃ etc., are not relations in the sense of right and left, etc., is obvious.

The possibility of crosswise definition of the logical "primitive signs" of Frege and Russell shows by itself that these are not primitive signs and that they signify no relations.

And it is obvious that the "⊃" which we define by means of "~" and "∨" is identical with that by which we define "∨" with the help of "~", and that this "∨" is the same as the first, and so on.

That from a fact p an infinite number of others should follow, namely ~ ~p, ~ ~ ~ ~p etc., is indeed hardly to be believed, and it is no less wonderful that the infinite number of propositions of logic (of mathematics) should follow from half a dozen "primitive propositions". But all propositions of logic say the same thing. That is, nothing.

Truth-functions are not material functions.

If e.g. an affirmation can be produced by repeated denial, is the denial—in any sense—contained in the affirmation?

Does "~ ~p" deny ~p, or does it affirm p; or both? The proposition "~ ~p" does not treat of denial as an object, but the possibility of denial is already prejudged in affirmation.

And if there was an object called "~", then Rh


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 103, Milton Street, Dorset Square, August 16th, 1860. . Your sweet and kind letter gave me a great deal of pleasure. I have written to Florence, as you will probably see. I am glad that you asked me to do so. I have a great deal to tell you. I do not know how you think or feel about Portman Hall school. You know that I do not think the omission of all religious teaching a sufficient reason, for disapproval to counter-balance the immense good which I consider they are doing there, especially as the teacher and three of the monitors are earnest believers in our Lord ; and I do believe more is taught indirectly than directly. I teach my drawing class there, and heartily wish the school success ; tho' I confess I look to a day when we shall have as liberal views about education carried out by members of the Church. I would not give my whole or main strength to the school unless I were obliged ; but I would and do very willingly help. You will wonder why I write all this. It is because they are trying to find a lady to help there ; and I have mentioned you to them. They could not meet with what they wanted, and had just made arrangements for extra lessons instead until spring, when my note proposing your taking the work next spring arrived. I mentioned Mrs. Malleson as able to say what she thought of your fitness for the post ; and, since communicating with her, Mme. Bodichon is very anxious to arrange it in the spring when she again returns from Algiers. They first wanted a person's entire time for ₤100 ; but now they have resolved to divide their fund, and would probably like to have you for about two or three hours daily except Saturday. I do think


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Rh "~ ~p" would have to say something other than "p". For the one proposition would then treat of ~, the other would not. This disappearance of the apparent logical constants also occurs if "$$~ (\exists x) ~ fx$$" says the same as "$$~ (x) ~ fx$$", or "$$~ (\exists x).fx.x=a$$" the same as fa. If a proposition is given to us then the results of all truth-operations which have it as their basis are given with it.

If there are logical primitive signs a correct logic must make clear their position relative to one another and justify their existence. The construction of logic out of its primitive signs must become clear.

If logic has primitive ideas these must be independent of one another. If a primitive idea is introduced it must be introduced in all contexts in which it occurs at all. One cannot therefore introduce it for one context and then again for another. For example, if denial is introduced, we must understand it in propositions of the form "~p" just as in propositions like "~(pvq)", "$$~ (\exists x). ~ fx$$" and others. We may not first introduce it for one class of cases and then for another, for it would then remain doubtful whether its meaning in the two cases was the same, and there would be no reason to use the same way of symbolizing in the two cases.

(In short, what Frege ("Grundgesetze der Arithmetik") has said about the introduction of signs by definitions holds, mutatis mutandis, for the introduction of primitive signs also.)

The introduction of a new expedient in the symbolism of logic must always be an event full of consequences. No new symbol may be introduced in logic in brackets or in the margin—with, so to speak, an entirely innocent face. Rh


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 that a permanent work of this sort, and among that class of children, would be deeply interesting ; that it would make a nice change from private pupils ; that you would find Mme. Bodichon and Mrs. Malleson delightful people to work under ; you would have such power to carry out what you thought best ; and, dearest Andy, it is not the least part of the pleasure of the thought to me that it does seem to me it would make it so safe for you both to return, so certain that you would, if you had the prospect of this daily work. I must tell you that Miss Sterling appears, from the short talk we have had, to think that it is not a good thing to do, only a nice thing to have a certainty ; but she herself confesses, and I am sure it is true, she does not know about it. Nothing has to be, or can be, settled yet, but I should like to know how you feel about it. I mean to learn what Mr. Maurice thinks. Oh, darling, you must come home in spring somehow. We are on Mr. Davies' side of the street, two doors nearer to the New Road. I am doing such a glorious illumination round a photograph of Raphael's Madonna della Seggiola, with the words, "For unto us a child is born, etc." It reminds me of the glorious chorus. Milton Street, August 19th, 1860. . Yes, I am really back again, and so hard at work that our glorious tour only comes to me at moments as a precious bright possession that nothing can take away, and interpreting splendidly one passage after another in this glorious volume of Ruskin (which I have at last obtained to read). . ..


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 If you had any notion of my state of mind just now ! Everything I want to do seems delayed. One girl, a darling protegee of mine, says her mistress starves her, will not try another place, insists upon going home. Oh such a home ! irreligious, dirty, cruel, impoverished ; and the girl has just had two years' training. Well ! she must just try her home, and God bring her safe out of it. ... We hope to have my dearest sisters home next spring. I have been offered some delicious teaching for Andy, in a school near here, Just the kind of work, and among the class of children that she would enjoy ; and the supporters of the school are earnest generous people. There is, however, no religious teaching given in the school ; wherefore, say many wise people to me, you as a Christian should not accept it at all. So I have not thought ; but I suppose I hardly feel sure enough about whether I ought to give my sister advice, however strong my conviction may be, when wise good people think differently. ... I never have stopped, I hope I never shall stop, to consider what set or sect of people are at work, if I thoroughly and entirely approve of the work. I may think the work incomplete ; but, if it comes in my way, and I think it good, as far as it goes, I do help it with the little power I have. Above all I would not, in this age, refuse help to a society because it did not state that it was working in Christ's cause. I do believe we want all generous and good work recognised as Christ's, whether conscious or unconscious. I think the tendency is very much for doubters to think the best work is done by benevolent unbelievers ; to think our faith cramps our labours and narrows our hearts. I would like, so far as in me lies, to show them we care for men as men, we care for good as good. I never would deny


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 faith. I care very little to express it anywhere but in life. . . . How much these people lose by their omission I believe they will one day know. I think the time will come when all this round world will seem to them mainly precious, because it was made by a Father and redeemed by His Son. October 30th, 1860. .

In these days, when so many conscientious people seem to be seeking over the whole world for some new good work, and cannot see the holiness of that which lies near them, it is very delicious to find people owning their home work as first and most blessed. At the same time, I cannot feel that I should join your Society further than I have joined it already. It feels to me that all people who are obeying the best part of the nature that has been given them, do, more or less, belong to it ; that those, who know from Whom the light proceeds " that lighteth every man that cometh into the world," know themselves to be bound into a society by that gift, by being children of God and heirs of Christ.

Do, dear Maggie, believe that I feel it the greatest honour to have been asked to join your Society, and have great sympathy with you about it.

.

How the real bond of family re-asserts itself, dominant over fancy, attraction, yes even perhaps, in a measure, over friendship itself ! as tho' it would teach us how tremendous is the botod of duty. Certainly we have duties to our friends too ; but they seem to have more relation to what we feel instinctive longing to do,


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 innate capacity for doing,—to stand more by virtue of relations we have chosen for ourselves, than solely, wholly on the command of God. I suppose it must be because He is our Father. November 15th, 1860. .

I have spoken to Mr. Maurice about Portman Hall ; and he decidedly thinks you ought not to undertake it. He says, what one sees at once, that you could not bind yourself not to speak to the children in any way that seemed best to you. He said that he believes those who are acting up to all they know will learn more ; but those who habitually ignore what they know, lose it. He was so good, and took a great interest in all our plans. November, 1860. .

I begin not to wonder that men of business look forward to leaving off work, when they get old. I think it would be very delicious to have done with the bustle, and be able to see people one loves, and think a little in peace. However, 1 daresay it's all right ; and it certainly is a glorious life ; but lists of things one has to do, and machinery to keep things going, never can be as interesting as writing to my darling sister. December 17th, 1860. ,

Account of the taking of the lease of 14, Nottingham Place.

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All has been arranged about the house at last. I am very thankful indeed about it ; and we are all


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 thoroughly pleased with the house. . . . Ruskin was very kind indeed about it.

We had a delicious talk afterwards about my life and life in general, and cultivated affection, its duties, practicability ; whether or not the cultivation of it deteriorated natures and how.

Ruskin spoke of his own father and mother. He quite willingly wrote what he imagined would satisfy Mr. Harlowe, and so did Mr. Maurice ; but in the meantime Miss Wodehouse had most kindly offered a guarantee. She was perfectly convinced of the success of the plan, and was anxious that Miss Jex Blake should have her rooms.

I had such a glorious talk with Ruskin, stayed till 2.20 ; had to take a cab, and to drive furiously to College, where I was ten minutes late, and recovered from shame and remorse for it, by finding everyone in a state of alarm about me ; only so thankful I was safe, my unpunctuality being unprecedented. I was a little proud, and vastly amused.


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130 Enormous revenues flowed into various monasteries and churches in all parts of Europe from relics noted for their healing powers. The ecclesiastics perceived that the physician would interfere with these revenues and gifts of the shrines, and deemed it the will of God to persecute and condemn physicians. St. Ambrose declared, "The precepts of medicine are contrary to celestial science, watching and prayer." St. Augustine declared, "All diseases of Christians are to be ascribed to these demons, chiefly do they torment fresh baptized Christians, yea, even the guiltless, new-born babe." Gregory of Nazianzus declared that bodily pains are provoked by demons, and that medicines are useless, but that they are often cured by the laying on of consecrated hands. St. Niles and St. Gregory of Tours gave examples to show the sinfulness of resorting to medicine instead of trusting to the intercession of saints.

Even as late as 1517, Pope Leo X, for a consideration, issued tickets bearing a cross and the following inscription, "This cross measured forty times makes the height of Christ in His humanity. He who kisses it is preserved for seven days from falling sickness, apoplexy, and sudden death."

The Council of Le Mons, in 1248, forbade monks to engage in surgery. At the beginning of the twelfth century, the Council of Rheims forbade monks to study medicine; and shortly after the middle of the twelfth century, Pope Alexander III forbade monks to study or practice medicine. In the thirteenth century, the Dominican Order forbade all ecclesiastics to have any connection with medicine; and when we remember that the policy of the Church had made it impossible for any learned man to enter any other profession, the only resource left for a scholar was the Church; so effectively did the Church kill all scientific endeavors.


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 dared to approach the island of U-Vuma. The islanders, armed with nothing but a knife, would swim towards the boats, dive under the keels, and sever the connecting wooden ropes. Presently the frail craft were swamped and their crews struggling in the water. Those and other dangers of the navigation insure for the divinities of the lake the respect of all the surrounding populations. The water-gods, who dwell on the islands, condescend to communicate with mortals only through their envoys, who dare not be approached by empty-handed votaries. But the steam launches must ere long deprive these local deities of their prestige and reduce them to the level of ordinary mortals. When the American Chaillé-Long wanted to embark on the lake, the king of U-Ganda struck off the heads of seven wizards who had hitherto been both worshipped and hated as the evil genii of Nyanza. By this summary process he hoped to ensure the safety of his guest. Storms and waterspouts are frequent on the lake. "Wilson has also determined the existence of a current, which sets steadily from Speke Bay parallel with the coast westwards. It is caused by the south-east trade winds, which prevail throughout the greater part of the year.

The superfluous waters of the inland sea flow gently through a broad opening on the north coast over against the island of U-Vuma. This emissary, forming the head of the Nile properly so called, gradually narrows its banks to the proportions of a river, when its liquid contents are precipitated over a tremendous cascade, to which Speke has given the name of the Ripon Falls. A group of boulders, on which a few trees have taken root, stands nearly in the centre of the stream, which is here about 1,300 feet broad. Other less elevated blocks divide the current right and left, which lower down is studded with other reefs and rocks scarcely rising above the surface of the seething waters. Hence the expression Jinja, or "Stones," applied by the natives to these falls. Although they have a vertical height of 13 feet, hundreds of fishes crowding the lower reach are able to leap the rapids and pass to the upper stream, which a short distance higher up is gentle enough to be crossed by a ferry. Here the view of the lake is to a great extent concealed by a wooded headland, while the line of separation between the gulf and the course of the river is marked by a low peninsula crowned with a clump of palms. The hills of the mainland merge farther on in the verdant isles of the lake.

According to Stanley, the Kivira, as the Nile is here called, is about a third larger than the Tanguré, the chief affluent of Nyanza. It flows with a mean breadth of 550 yards, at first towards the north-west, and after passing a few smaller rapids, spreads out right and left in vast reedy lagoons. But even here its normal depth is maintained, and some 60 miles below the falls it enters the Gita-Nzigé, another lake, to which the name of Ibrahim has been given by Chaillé-Long, who discovered it in 1875. Compared with the other equatorial basins, it is of small extent, having an area of probably not more than 200 square miles. In this region the Nile receives a number of tributaries, including the Luajerri, which

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