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Logical positivism: Logical positivism, a philosophical movement that arose in Vienna in the 1920s and was characterized by the view that scientific knowledge is the only kind of factual knowledge and that all traditional metaphysical doctrines are to be rejected as meaningless. A brief treatment of logical positivism

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Constructivism is a learning theory found in psychology which explains how people might acquire knowledge and learn. It therefore has direct application to education. The theory suggests that humans construct knowledge and meaning from their experiences. Constructivism is not a specific pedagogy. Piaget's theory of Constructivist learning has had wide ranging impact on learning theories and teaching methods in education and is an underlying theme of many education reform movements. Research support for constructivist teaching techniques has been mixed, with some research supporting these techniques and other research contradicting those results.

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How to design student-centered constructivist learning activities

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Constructivism is a learning theory found in psychology which explains how people might acquire knowledge and learn. It therefore has direct application to education. The theory suggests that humans construct knowledge and meaning from their experiences. Constructivism is not a specific pedagogy.

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Frederick W. Taylor was a mechanical engineer whose writings on efficiency and scientific management were widely read. The founder of "systems engineering," the selection below is from a collection of his essays published in 1911. The essays were translated into several languages, giving his ideas an influence around the world

INTRODUCTION

PRESIDENT ROOSEVELT, in his address to the Governors at the White House, prophetically remarked that "The conservation of our national resources is only preliminary to the larger question of national efficiency."

The whole country at once recognized the importance of conserving our material resources and a large movement has been started which will be effective in accomplishing this object. As yet, however, we have but vaguely appreciated the importance of "the larger question of increasing our national efficiency."

We can see our forests vanishing, our water-powers going to waste, our soil being carried by floods into the sea; and the end of our coal and our iron is in sight. But our larger wastes of human effort, which go on every day through such of our acts as are blundering, ill-directed, or inefficient, and which Mr. Roosevelt refers to as a lack of" national efficiency," are less visible) less tangible, and are but vaguely appreciated.

We can see and feel the waste of material things. Awkward, inefficient, or ill-directed movements of men, however, leave nothing visible or tangible behind them. Their appreciation calls for an act of memory, an effort of the imagination. And for this reason, even though our daily loss from this source is greater than from our waste of material things, the one has stirred us deeply, while the other has moved us but little.

As yet there has been no public agitation for "greater national efficiency," no meetings have been called to consider how this is to be brought about. And still there are signs that the need for greater efficiency is widely felt.

The search for better, for more competent men, from the presidents of our great companies down to our household servants, was never more vigorous than it is now. And more than ever before is the demand for competent men in excess of the supply.

What we are all looking for, however, is the ready made, competent man; the man whom some one else has trained. It is only when we fully realize that our duty, as well as our opportunity, lies in systematically cooperating to train and to make this competent man, instead of in hunting for a man whom some one else has trained, that we shall be on the road to national efficiency.

In the past the prevailing idea has been well expressed in the saying that "Captains of industry are born, not made"; and the theory has been that if one could get the right man, methods could be safely left to him. In the future it will be, appreciated that our leaders must be trained right as well as born right, and that no great man can (with the old system of personal management) hope to compete with a number of ordinary men who have been properly organized so as efficiently to cooperate.

In the past the man has been first; in the future the system must be first. This in no sense, however, implies that great men are not needed. On the contrary, the first object of any good system must be that of developing first-class men; and under systematic management the best man rises to the top more certainly and more rapidly than ever before.

This paper has been written:

First. To point out, through a series of simple illustrations, the great loss which the whole country is suffering through inefficiency in almost all of our daily acts.

Second. To try to convince the reader that the remedy for this inefficiency lies in systematic management, rather than in searching for some unusual or extraordinary man.

Third. To prove that the best management is a true science, resting upon clearly defined laws, rules, and principles, as a foundation. And further to show that the fundamental principles of scientific management are applicable to all kinds of human activities, from our simplest individual acts to the work of our great corporations, which call for the most elaborate cooperation. And, briefly, through a series of illustrations, to convince the reader that whenever these principles are correctly applied, results must follow which are truly astounding.

This paper was originally prepared for presentation to The American Society of Mechanical Engineers. The illustrations chosen are such as, it is believed, will especially appeal to engineers and to managers of industrial and manufacturing establishments, and also quite as much to all of the men who are working in these establishments. It is hoped, however, that it will be clear to other readers that the same principles can be applied with equal force to all social activities: to the management of our homes; the management of our farms; the management of the business of our tradesmen, large and small; of our churches, our philanthropic institutions, our universities, and our governmental departments.
The Principles of Scientific Management
CHAPTER I

FUNDAMENTALS OF SCIENTIFIC MANAGEMENT

THE principal object of management should be to secure the maximum prosperity for the employer, coupled with the maximum prosperity for each employee.

The words "maximum prosperity" are used, in their broad sense, to mean not only large dividends for the company or owner, but the development of every branch of the business to its highest state of excellence, so that the prosperity may be permanent.

In the same way maximum prosperity for each employ, means not only higher wages than are usually received by men of his class, but, of more importance still, it also means the development of each man to his state of maximum efficiency, so that he may be able to do; generally speaking, the highest grade of work for which his natural abilities fit him, and it further means giving him, when possible, this class of work to do.

It would seem to be so self-evident that maximum prosperity for the employer, coupled with maximum prosperity for the employee, ought to be the two leading objects of management, that even to state this fact should be unnecessary. And yet there is no question that, throughout the industrial world, a large part of the organization of employers, as well as employees, is for war rather than for peace, and that perhaps the majority on either side do not believe that it is possible so to arrange their mutual relations that their interests become identical.

The majority of these men believe that the fundamental interests of employees and employers are necessarily antagonistic. Scientific management, on the contrary, has for its very foundation the firm conviction that the true interests of the two are one and the same; that prosperity for the employer cannot exist through a long term of years unless it is accompanied by prosperity for the employee and vice versa; and that it is possible to give the workman what he most wants-high wages-and the employer what he wants-a low labor cost-for his manufactures.

It is hoped that some at least of those who do not sympathize with each of these objects may be led to modify their views; that some employers, whose attitude toward their workmen has been that of trying to get the largest amount of work out of them for the smallest possible wages, may be led to see that a more liberal policy toward their men will pay them better; and that some of those workmen who begrudge a fair and even a large profit to their employers, and who feel that all of the fruits of their labor should belong to them, and that those for whom they work and the capital invested in the business are entitled to little or nothing, may be led to modify these views.

No one can be found who will deny that in the case of any single individual the greatest prosperity can exist only when that individual has reached his highest state of efficiency; that is, when he is turning out his largest daily output.

The truth of this fact is also perfectly clear in the case of two men working together. To illustrate: if you and your workman have become so skillful that you and he together are making two pairs of shoes in a day, while your competitor and his workman are making only one pair, it is clear that after selling your two pairs of shoes you can pay your workman much higher wages than your competitor who produces only one pair of shoes is able to pay his man, and that there will still be enough money left over for you to have a larger profit than your competitor.

In the case of a more complicated manufacturing establishment, it should also be perfectly clear that the greatest permanent prosperity for the workman, coupled with the greatest prosperity for the employer, can be brought about only when the work of the establishment is done with the smallest combined expenditure of human effort, plus nature's resources, plus the cost for the use of capital in the shape of machines, buildings, etc. Or, to state the same thing in a different way: that the greatest prosperity can exist only as the result of the greatest possible productivity of the men and machines of the establishment-that is, when each man and each machine are turning out the largest possible output; because unless your men and your machines are daily turning out more work than others around you, it is clear that competition will prevent your paying higher wages to your workmen than are paid to those of your competitor. And what is true as to the possibility of paying high wages in the case of two companies competing close beside one another is also true as to whole districts of the country and even as to nations which are in competition. In a word, that maximum prosperity can exist only as the result of maximum productivity. Later in this paper illustrations will be given of several companies which are earning large dividends and at the same time paying from 30 per cent. to 100 per cent. higher wages to their men than are paid to similar men immediately around them, and with whose employers they are in competition. These illustrations will cover different types of work, from the most elementary to the most complicated.

If the above reasoning is correct, it follows that the most important object of both the workmen and the management should be the training and development of each individual in the establishment, so that he can do (at his fastest pace and with the maximum of efficiency) the highest class of work for which his natural abilities fit him.

These principles appear to be so self-evident that many men may think it almost childish to state them. Let us, however, turn to the facts, as they actually exist in this country and in England. The English and American peoples are the greatest sportsmen in the world. Whenever an American workman plays baseball, or an English workman plays cricket, it is safe to say that he strains every nerve to secure victory for his side. He does his very best to make the largest possible number of runs.The universal sentiment is so strong that any man who fails to give out all there is in him in sport is branded as a"quitter," and treated with contempt by those who are around him.

When the same workman returns to work on the following day, instead of using every effort to turn out the largest possible amount of work, in a majority of the cases this man deliberately plans to do as little as he safely can-to turn out far less work than he is well able to do-in many instances to do not more than one-third to one-half of a proper day's work. And in fact if he were to do his best to turn out his largest possible day's work, he would be abused by his fellow-workers for so doing,even more than if he had proved himself a "quitter" in sport. Underworking, that is, deliberately working slowly so as to avoid doing a full day's work, "soldiering," as it is called in this country, "hanging it out," as it is called in England, "ca canae," as it is called in Scotland, is almost universal in industrial establishments, and prevails also to a large extent in the building trades; and the writer asserts without fear of contradiction that this constitutes the greatest evil with which the working-people of both England and America are now afflicted.

It will be shown later in this paper that doing away with slow working and "soldiering" in all its forms and so arranging the relations between employer and employ,that each workman will work to his very best advantage and at his best speed, accompanied by the intimate cooperation with the management and the help (which the workman should receive) from the management, would result on the average in nearly doubling the output of each man and each machine. What other reforms, among those which are being discussed by these two nations, could do as much toward promoting prosperity, toward the diminution of poverty, and the alleviation of suffering?America and England have been recently agitated over such subjects as the tariff, the control of the large corporations on the one hand, and of hereditary power on the other hand, and over various more or less socialistic proposals for taxation, etc. On these subjects both peoples have been profoundly stirred, and yet hardly a voice has been raised to call attention to this vastly greater and more important subject of "soldiering," which directly and powerfully affects the wages, the prosperity, and the life of almost every working-man, and also quite as much the prosperity of every industrial establishment in the nation.

The elimination of "soldiering" and of the several causes of slow working would so lower the cost of production that both our home and foreign markets would be greatly enlarged, and we could compete on more than even terms with our rivals. It would remove one of the fundamental causes for dull times, for lack of employment,and for poverty, and therefore would have a more permanent and far-reaching effect upon these misfortunes than any of the curative remedies that are now being used to soften their consequences. It would insure higher wages and make shorter working hours and better working and home conditions possible.

Why is it, then, in the face of the self-evident fact that maximum prosperity can exist only as the result of the determined effort of each workman to turn out each day his largest possible day's work, that the great majority of our men are deliberately doing just the opposite, and that even when the men have the best of intentions their work is in most cases far from efficient?

There are three causes for this condition, which may be briefly summarized as:

First. The fallacy, which has from time immemorial been almost universal among workmen, that a material increase in the output of each man or each machine in the trade would result in the end in throwing a large number of men out of work.

Second. The defective systems of management which are in common use, and which make it necessary for each workman to soldier, or work slowly,in order that he may protect his own best interests.

Third. The inefficient rule-of-thumb methods, which are still almost universal in all trades, and in practicing which our workmen waste a large part of their effort.

This paper will attempt to show the enormous gains which would result from the substitution by our workmen of scientific for rule-of-thumb methods.

To explain a little more fully these three causes:

First. The great majority of workmen still believe that if they were to work at their best speed they would be doing a great injustice to the whole trade by throwing a lot of men out of work, and yet the history of the development of each trade shows that each improvement, whether it be the invention of a new machine or the introduction of a better method, which results in increasing the productive capacity of the men in the trade and cheapening the costs, instead of throwing men out of work make in the end work for more men.

The cheapening of any article in common use almost immediately results in a largely increased demand for that article. Take the case of shoes, for instance. The introduction of machinery for doing every element of the work which was formerly done by hand has resulted in making shoes at a fraction of their former labor cost, and in selling them so cheap that now almost every man,woman, and child in the working-classes buys one or two pairs of shoes per year, and wears shoes all the time,whereas formerly each workman bought perhaps one pair of shoes every five years, and went barefoot most of the time, wearing shoes only as a luxury or as a matter of the sternest necessity. In spite of the enormously increased output of shoes per workman, which has come with shoe machinery, the demand for shoes has so increased that there are relatively more men working in the shoe industry now than ever before.

The workmen in almost every trade have before the man object lesson of this kind, and yet, because they are ignorant of the history of their own trade even, they still firmly believe, as their fathers did before them, that it is against their best interests for each man to turn out each day as much work as possible.

Under this fallacious idea a large proportion of the workmen of both countries each day deliberately work slowly so as to curtail the output. Almost every labor union has made, or is contemplating making, rules which have for their object curtailing the output of their members, and those men who have the greatest influence with the working-people, the labor leaders as well as many people with philanthropic feelings who are helping them, are daily spreading this fallacy and at the same time telling them that they are overworked.

A great deal has been and is being constantly said about "sweat-shop" work and conditions. The writer has great sympathy with those who are overworked. but on the whole a greater sympathy for those who are under paid. For every individual,however, who is overworked, there are a hundred who intentionally underwork-greatly underwork -every day of their lives, and who for this reason deliberately aid in establishing those conditions which in the end inevitably result in low wages. And yet hardly a single voice is being raised in an endeavor to correct this evil.

As engineers and managers, we are more intimately acquainted with these facts than any other class in the community, and are therefore best fitted to lead in a movement to combat this fallacious idea by educating not only the workmen but the whole of the country as to the true facts. And yet we are practically doing nothing in this direction, and are leaving this field entirely in the hands of the labor agitators (many of whom are misinformed and misguided), and of sentimentalists who are ignorant as to actual working conditions.

Second. As to the second cause for soldiering- the relations which exist between employers and employ,sunder almost all of the systems of management which are in common use-it is impossible in a few words to make it clear to one not familiar with this problem why it is that the ignorance of employers as to the proper time in which work of various kinds should be done makes it for the interest of the workman to "soldier."

The writer therefore quotes herewith from a paper read before The American Society of Mechanical Engineers,in June, 1903, entitled "Shop Management," which it is hoped will explain fully this cause for soldiering:

"This loafing or soldiering proceeds from two causes. First, from the natural instinct and tendency of men to take it easy, which may be called natural soldiering. Second, from more intricate second thought and reasoning caused by their relations with other men,which may be called systematic soldiering."

There is no question that the tendency of the average man (in all walks of life) is toward working at a slow,easy gait, and that it is only after a good deal of thought and observation on his part or as a result of example,conscience, or external pressure that he takes a more rapid pace.

"There are, of course, men of unusual energy, vitality,and ambition who naturally choose the fastest gait, whose up their own standards, and who work hard, even though it may be against their best interests. But these few uncommon men only serve by forming a contrast to emphasize the tendency of the average.

"This common tendency to 'take it easy' is greatly increased by bringing a number of men together on similar work and at a uniform standard rate of pay by the day.

"Under this plan the better men gradually but surely slow down their gait to that of the poorest and least efficient. When a naturally energetic man works for a few days beside a lazy one, the logic of the situation is unanswerable.'Why should I work hard when that lazy fellow gets the same pay that I do and does only half as much work?'

"A careful time study of men working under these conditions will disclose facts which are ludicrous as well as pitiable.

"To illustrate: The writer has timed a naturally energetic workman who, while going and coming from work, would walk at a speed of from three to four miles per hour, and not infrequently trot home after a day's work. On arriving at his work he would immediately slowdown to a speed of about one mile an hour. When, for example, wheeling a loaded wheelbarrow, he would go at a good fast pace even up hill in order to be as short a time as possible under load, and immediately on the return walk slow down to a mile an hour, improving every opportunity for delay short of actually sitting down. In order to be sure not to do more than his lazy neighbor, would actually tire himself in his effort to go slow.

"These men were working under a foreman of good reputation and highly thought of by his employer, who, when his attention was called to this state of things, answered: 'Well, I can keep them from sitting down, butthe devil can't make them get a move on while they are at work.' "The natural laziness of men is serious, but by far thegreatest evil from which both workmen and employers are suffering is the systematic soldiering which is almost universal under all of the ordinary schemes of management and which results from a careful study on the part of the workmen of what will promote their best interests.

"The writer was much interested recently in hearing one small but experienced golf caddy boy of twelve explaining to a green caddy, who had shown special energy and interest, the necessity of going slow and lagging behind his man when he came up to the ball,showing him that since they were paid by the hour, the faster they went the less money they got, and finally telling him that if he went too fast the other boys would give him a licking.

"This represents a type of systematic soldiering which is not, however, very serious, since it is done with the knowledge of the employer, who can quite easily break it up if he wishes.

"The greater part of the systematic soldiering, however,is done by the men with the deliberate object of keeping their employers ignorant of how fast work can be done.

"So universal is soldiering for this purpose that hardly a competent workman can be found in a large establishment, whether he works by the day or on piecework, contract work, or under any of the ordinary systems, who does not devote a considerable part of his time to studying just how slow he can work and still convince his employer that he is going at a good pace.

"The causes for this are, briefly, that practically all employers determine upon a maximum sum which they feel it is right for each of their classes of employees to earn per day, whether their men work by the day or piece.

"Each workman soon finds out about what this figure is for his particular case, and he also realizes that when his employer is convinced that a man is capable of doing more work than he has done, he will find sooner or later some way of compelling him to do it with little or no increase of pay.

"Employers derive their knowledge of how much of a given class of work can be done in a day from either their own experience, which has frequently grown hazy with age, from casual and unsystematic observation of their men, or at best from records which are kept, showing the quickest time in which each job has been done. In many cases the employer will feel almost certain that a given job can be done faster than it has been, but he rarely cares to take the drastic measures necessary to force men to do it in the quickest time, unless he has an actual record proving conclusively how fast the work can be done.

"It evidently becomes for each man's interest, then, to see that no job is done faster than it has been in the past.The younger and less experienced men are taught this by their elders, and all possible persuasion and social pressure is brought to bear upon the greedy and selfish men to keep them from making new records which result in temporarily increasing their wages, while all those who come after them are made to work harder for the same old pay.

"Under the best day work of the ordinary type,when accurate records are kept of the amount of work done by each man and of his efficiency, and then each man's wages are raised as he improves, and those who fail to rise to a certain standard are discharged and afresh supply of carefully selected men are given work in their places, both the natural loafing and systematic soldiering can be largely broken up. This can only be done, however, when the men are thoroughly convinced that there is no intention of establishing piece work even in the remote future, and it is next to impossible to make men believe this when the work is of such a nature that they believe piece work to be practicable. In most cases their fear of making a record which will be used as a basis for piece work will cause them to soldier as much as they dare.

"It is, however, under piece work that the art of systematic soldiering is thoroughly developed; after a workman has had the price per piece of the work he is doing lowered two or three times as a result of his having worked harder and increased his output, he is likely entirely to lose sight of his employer's side of the case and become imbued with a grim determination to have no more cuts if soldiering can prevent it. Unfortunately for the character of the workman, soldiering involves a deliberate attempt to mislead and deceive his employer,and thus upright and straightforward workmen are compelled to become more or less hypocritical. The employer is soon looked upon as an antagonist, if not ~an enemy and the mutual confidence which should exist between a leader and his men, the enthusiasm, the feeling that they are all working for the same end and will share in the results is entirely lacking.

"The feeling of antagonism under the ordinary piece-work system becomes in many cases so marked on the part of the men that any proposition made by their employers, however reasonable, is looked upon with suspicion, and soldiering becomes such a fixed habit that men will frequently take pains to restrict the product of machines which they X are running when even a large increase in output would involve no more work on their part."

Third. As to the third cause for slow work,considerable space will later in this paper be devoted to illustrating the great gain, both to employers and employs, which results from the substitution of scientific for rule-of-thumb methods in even the smallest details of the work of every trade. The enormous saving of time and therefore increase in the output which it is possible to effect through eliminating unnecessary motions and substituting fast for slow and inefficient motions for the men working in any of our trades can be fully realized only after one has personally seen the improvement which results from a thorough motion and time study, made by a competent man.

To explain briefly: owing to the fact that the workmen in all of our trades have been taught the details of their work by observation of those immediately around them,there are many different ways in common use for doing the same thing, perhaps forty, fifty,or a hundred ways of doing each act in each trade, and for the same reason there is a great variety in the implements used for each class of work. Now, among the various methods and implements used in each element of each trade there is always one method and one implement which is quicker and better than any of the rest.Aid this one best method and best implement can only be discovered or developed through a scientific study and analysis of all of the methods and implements in use,together with accurate, minute, motion and time study.This involves the gradual substitution of science for rule of thumb throughout the mechanic arts.

This paper will show that the underlying philosophy of all of the old systems of management in common use makes it imperative that each workman shall be left with the final responsibility for doing his job practically as he thinks best, with comparatively little help and advice from the management. And it will also show that because of this isolation of workmen, it is in most cases impossible for the men working under these systems to do their work in accordance with the rules and laws of a science or art, even where one exists.

The writer asserts as a general principle (and he proposes to give illustrations tending to prove the fact later in this paper) that in almost all of the mechanic arts the science which underlies each act of each workman is so great and amounts to so much that the workman who is best suited to actually doing the work is incapable of fully understanding this science,without the guidance and help of those who are working with him or over him, either through lack of education or through insufficient mental capacity. In order that the work may be done in accordance with scientific laws, it is necessary that there shall be a far more equal division of the responsibility between the management and the workmen than exists under any of the ordinary types of management. Those in the management whose duty it is to develop this science should also guide and help the workman in working under it, and should assume a much larger share of the responsibility for results than under usual conditions is assumed by the management.

The body of this paper will make it clear that, to work according to scientific laws, the management must takeover and perform much of the work which is now left to the men; almost every act of the workman should be preceded by one or more preparatory acts of the management which enable him to do his work better and quicker than he otherwise could. And each man should daily be taught by and receive the most friendly help from those who are over him, instead of being, at the one extreme, driven or coerced by his bosses, and at the other left to his own unaided devices.

This close, intimate, personal cooperation between the management and the men is of the essence of modern scientific or task management.

It will be shown by a series of practical illustrations that, through this friendly cooperation, namely, through sharing equally in every day's burden, all of the great obstacles (above described) to obtaining the maximum output for each man and each machine in the establishment are swept away. The 30 per cent. to 100 percent. increase in wages which the workmen are able to earn beyond what they receive under the old type of management, coupled with the daily intimate shoulder to shoulder contact with the management, entirely removes all cause for soldiering. And in a few years, under this system, the workmen have before them the object lesson of seeing that a great increase in the output per man-results in giving employment to more men, instead of throwing men out of work, thus completely eradicating the fallacy that a larger output for each man will throw other men out of work.

It is the writer's judgment, then, that while much can be done and should be done by writing and talking toward educating not only workmen, but all classes in the community, as to the importance of obtaining the maximum output of each man and each machine, it is only through the adoption of modern scientific management that this great problem can be finally solved. Probably most of the readers of this paper will say that all of this is mere theory. On the contrary, the theory, or philosophy, of scientific management is just beginning to be understood,whereas the management itself has been a gradual evolution, extending over a period of nearly thirty years. And during this time the employees of one company after another, including a large range and diversity of industries, have gradually changed from the ordinary to the scientific type of management. At least 50,000 workmen in the United States are now employed under this system; and they are receiving from 30 per cent.to 100 per cent. higher wages daily than are paid to men of similar caliber with whom they are surrounded, while the companies employing them are more prosperous than ever before. In these companies the output, per man and per machine, has on an average been doubled. During all these years there has never been a single strike among the men working under this system. In place of the suspicious watchfulness and the more or less open warfare which characterizes the ordinary types of management, there is universally friendly cooperation between the management and the men.

Several papers have been written, describing the expedients which have been adopted and the details which have been developed under scientific management and the steps to be taken in changing from the ordinary to the scientific type. But unfortunately most of the readers of these papers have mistaken the mechanism for the true essence. Scientific management fundamentally consists of certain broad general principles, a certain philosophy,which can be applied in many ways, and a description of what any one man or men may believe to be the best mechanism for applying these general principles should in no way be confused with the principles themselves.

It is not here claimed that any single panacea exists for all of the troubles of the working-people or of employers. As long as some people are born lazy or inefficient, and others are born greedy and brutal, as long as vice and crime are with us, just so long will a certain amount of poverty, misery, and unhappiness be with us also. No system of management, no single expedient within the control of any man or any set of men can insure continuous prosperity to either workmen or employers.Prosperity depends upon so many factors entirely beyond the control of any one set of men, any state, or even anyone country, that certain periods will inevitably come when both sides must suffer, more or less. It is claimed,however, that under scientific management the intermediate periods will be far more prosperous, far happier, and more free from discord and dissension. And also, that the periods will be fewer, shorter and the suffering less. And this will be particularly true in any one town, any one section of the country, or any one state which first substitutes the principles of scientific management for the rule of thumb.

That these principles are certain to come into general use practically throughout the civilized world, sooner or later, the writer is profoundly convinced, and the sooner they come the better for all the people.

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Modern History Sourcebook: Frederick W. Taylor: The Principles of Scientific Management, 1911

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Frederick W. Taylor was a mechanical engineer whose writings on efficiency and scientific management were widely read. The founder of "systems engineering," the selection below is from a collection of his essays published in 1911.

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The best example of Frederick Taylor's ideas at work in education today are high-stakes standardized tests -- tests which have a significant effect on funding for schools and the careers of individual students. Although these exams can create enormous tension for students and administrators, it is teachers whose lives are most affected by them.

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Welcome to Constructivism as a Paradigm for Teaching and Learning. Start with the Explanation section to gain a good understanding of the CONCEPT of constructivism. Then go on to Demonstration, where we move from CONCEPT TO CLASSROOM!

What is constructivism?
How does this theory differ from traditional ideas about teaching and learning?
What does constructivism have to do with my classroom?
Expert interview
What is the history of constructivism, and how has it changed over time?
What are some critical perspectives?
What are the benefits of constructivism?

What is constructivism?
Constructivism is basically a theory -- based on observation and scientific study -- about how people learn. It says that people construct their own understanding and knowledge of the world, through experiencing things and reflecting on those experiences. When we encounter something new, we have to reconcile it with our previous ideas and experience, maybe changing what we believe, or maybe discarding the new information as irrelevant. In any case, we are active creators of our own knowledge. To do this, we must ask questions, explore, and assess what we know.

In the classroom, the constructivist view of learning can point towards a number of different teaching practices. In the most general sense, it usually means encouraging students to use active techniques (experiments, real-world problem solving) to create more knowledge and then to reflect on and talk about what they are doing and how their understanding is changing. The teacher makes sure she understands the students' preexisting conceptions, and guides the activity to address them and then build on them.

Constructivist teachers encourage students to constantly assess how the activity is helping them gain understanding. By questioning themselves and their strategies, students in the constructivist classroom ideally become "expert learners." This gives them ever-broadening tools to keep learning. With a well-planned classroom environment, the students learn HOW TO LEARN.

You might look at it as a spiral. When they continuously reflect on their experiences, students find their ideas gaining in complexity and power, and they develop increasingly strong abilities to integrate new information. One of the teacher's main roles becomes to encourage this learning and reflection process.

For example: Groups of students in a science class are discussing a problem in physics. Though the teacher knows the "answer" to the problem, she focuses on helping students restate their questions in useful ways. She prompts each student to reflect on and examine his or her current knowledge. When one of the students comes up with the relevant concept, the teacher seizes upon it, and indicates to the group that this might be a fruitful avenue for them to explore. They design and perform relevant experiments. Afterward, the students and teacher talk about what they have learned, and how their observations and experiments helped (or did not help) them to better understand the concept.

Contrary to criticisms by some (conservative/traditional) educators, constructivism does not dismiss the active role of the teacher or the value of expert knowledge. Constructivism modifies that role, so that teachers help students to construct knowledge rather than to reproduce a series of facts. The constructivist teacher provides tools such as problem-solving and inquiry-based learning activities with which students formulate and test their ideas, draw conclusions and inferences, and pool and convey their knowledge in a collaborative learning environment. Constructivism transforms the student from a passive recipient of information to an active participant in the learning process. Always guided by the teacher, students construct their knowledge actively rather than just mechanically ingesting knowledge from the teacher or the textbook.

Constructivism is also often misconstrued as a learning theory that compels students to "reinvent the wheel." In fact, constructivism taps into and triggers the student's innate curiosity about the world and how things work. Students do not reinvent the wheel but, rather, attempt to understand how it turns, how it functions. They become engaged by applying their existing knowledge and real-world experience, learning to hypothesize, testing their theories, and ultimately drawing conclusions from their findings.

The best way for you to really understand what constructivism is and what it means in your classroom is by seeing examples of it at work, speaking with others about it, and trying it yourself. As you progress through each segment of this workshop, keep in mind questions or ideas to share with your colleagues.

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Thirteen | Thirteen Ed Online | thirteencelebration.org

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Constructivism as a Paradigm for Teaching and Learning

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Welcome to Constructivism as a Paradigm for Teaching and Learning. Start with the Explanation section to gain a good understanding of the CONCEPT of constructivism. Then go on to Demonstration, where we move from CONCEPT TO CLASSROOM! What is constructivism? How does this theory differ from traditional ideas about teaching and learning?

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Educational Research Paradigms: From Positivism to Multiparadigmatic Peter C. Taylor Science and Mathematics Education Centre (SMEC), Curtin University, Australia
Email: [email protected]
Milton Norman D. Medina Research and Development Center Office, Assumption College of Nabunturan, Philippines
Email: [email protected]
Abstract
In this paper we provide an overview of the characteristics of major educational research paradigms shaping contemporary educational research, ranging from the traditional positivist perspective to the latest multi-paradigmatic worldview. Our purpose is to orient students, faculty and beginning researchers to the newer paradigms that enable researchers to undertake uniquely powerful and insightful inquiries that contribute to transforming the landscape of education.

Keywords: postgraduate research, new paradigms, teacher education, transformation, metaphor
Introduction
For decades during the late 20 th century, 'paradigm wars' raged amongst supporters arguing fiercely for the superiority of their chosen paradigm. Over time, this gave way to a 'paradigm dialogue' in which supporters came to accept their differences and realised that every research paradigm is of equal importance. No research paradigm is superior, but each has a specific purpose in providing a distinct means of producing unique knowledge. Thanks to the newer paradigms, educational researchers (including teacher-researchers) are providing empirical and theoretical evidence of ways in which traditional curriculum and assessment policies unduly constrain teaching and learning, and research practices in schools, colleges and universities. And, importantly, these researchers are being empowered to envisage new policies and practices that better meet the emerging educational needs of their rapidly globalising societies.

The term paradigm needs clarification. Willis (2007) explains that: "A paradigm is thus a comprehensive belief system, world view, or framework that guides research and practice in a field" (p.8). From a philosophical perspective, a paradigm comprises a view of the nature of reality (i.e., ontology) - whether it is external or internal to the knower; a related view of the type of knowledge that can be generated and standards for justifying it (i.e., epistemology); and a disciplined approach to generating that knowledge (i.e., methodology). For educational researchers, there are several major paradigms that govern their inquiries into the policies and practices of education. Each paradigm carries related theories of teaching and learning (or pedagogy), curriculum and assessment, professional development, etc.
TRADITIONAL PARADIGMS
We will not spend much time on these tried and trusted paradigms, as there is a plethora of social science research methods textbooks that serve this purpose. The outlines provided here serve simply as a basis of comparison with the newer paradigms addressed later in the paper.
Positivist Paradigm
We start with positivism, a research paradigm that is very well known and well established in universities worldwide. This 'scientific' research paradigm strives to investigate, confirm and predict law-like patterns of behaviour, and is commonly used in graduate research to test theories or hypotheses. This is particularly useful in natural science, physical science and, to some extent, in the social sciences, especially where very large sample sizes are involved. Generally its focus is on the objectivity of the research process (Creswell, 2008). The positivist paradigm mostly involves quantitative methodology, utilizing experimental methods involving experimental (or treatment) and control groups and administration of pre- and post-tests to measure gain scores. Here, the researcher is external to the research site and is the controller of the research process.

An example of research in this paradigm is the second author's undergraduate biology research at Central Mindanao University, Philippines, entitled "Anti-diarrheal activity of M. Pudica leaf extract on white mice induced with E. coli pathogen". This experimental research utilized an experimental group and a control group. The experimental group was given a treatment (leaf extracts) while the control was left untreated. The ontology of this research was realism, the epistemology was objectivism, and a quantitative methodology governed the research process. The quality standards were validity and reliability, and the data were measured and analysed using statistics.
Post-Positivist Paradigm
Post-positivism, as Willis (2007) describes it is a "milder form of positivism "that follows the same principles but allows more interaction between the researcher and his/her research participants. It uses additional methods such as survey research and qualitative methods such as interviewing and participant-observation (Creswell, 2008). This paradigm is the modified scientific method for the social sciences. It aims to produce objective and generalizable knowledge about social patterns, seeking to affirm the presence of universal properties/laws in relationships amongst pre-defined variables. This epistemology is manifested by quasi-experimental research designs that utilize treatment, outcome measures and experimental units, but do not use random assignment to create comparison from which treatment caused change is inferred. It is very similar to the positivist approach of comparing mean scores but depends on non-equivalent groups that differ from each other in many ways other than the presence of the treatment whose effects are being tested (Depoy & Gitlin, 1998). The quality standards of this paradigm are objectivity, validity and reliability, which can be modified with the use of triangulation of data, methods and theories.

An exemplar is the second author's graduate research at the University of Southeastern Philippines, entitled ' The effectiveness of conceptual approach of teaching on the scores of students in a biotechnology achievement test '. Two groups were established, the experimental group was given a conceptual teaching approach and the control group was taught with the traditional board-talk method. To test the achievement of the students, a teacher-made test was designed and subjected to content and construct validity analysis. The two groups were tested and the data were analysed using statistics. Most often, graduate research in the Philippines is designed in this way.
RELATIVELY NEW PARADIGMS The Interpretive Paradigm
This humanistic paradigm arrived in educational research during the late 1970s, influenced strongly by anthropology which aims to understand other cultures, from the inside. That is, to understand the culturally different 'other' by learning to 'stand in their shoes', 'look through their eyes' and 'feel their pleasure or pain'. Thus the epistemology of this paradigm is inter-subjective knowledge construction. Interpretive knowledge of the other is produced through a prolonged process of interaction undertaken by ethnographers who immerse themselves within the culture they are studying. Using ethnographic methods of informal interviewing, participant observation and establishing ethically sound relationships, interpretive researchers construct trustworthy and authentic accounts of the cultural other. Applied to educational research, this paradigm enables researchers to build rich local understandings of the life-world experiences of teachers and students and of the cultures of classrooms, schools and the communities they serve.

The quality standards that regulate interpretive knowledge construction are varied, but arguably the most well-known and coherent are those of Guba and Lincoln (1989) who developed standards of trustworthiness and authenticity that are distinctly different but 'parallel to' the validity, reliability and objectivity standards of positivism. The trustworthiness criteria include: credibility (did the researcher undertake prolonged immersion in the field, check his/her interpretations with his/her informants, and display a process of learning?), dependability (did the researcher engage in open-ended or emergent inquiry?), transferability (is there sufficient rich description for the reader to compare his/her own social context with the social setting of the research?), and confirmability (can the research data be tracked to their source?).

The authenticity criteria focus on the ethics of the relationship established by the researcher with his/her participants and include: fairness (are the informants represented fairly?), educative (did the participants benefit by learning about their social world?), catalytic (did the participants benefit by identifying problems associated with their social world?), and tactical (did the research empower the participants to improve their social situation?) (Guba & Lincoln, 1989; Josselson, 2007). The authenticity criteria have a strong resonance with the standards of the critical paradigm outlined below.

Recent developments in the interpretive paradigm have highlighted the importance of the researcher's own subjectivity in the (hermeneutic) process of interpretation, and have emphasised its progressive development as a key part of the inquiry process, thereby adding to the emergent and reflective quality of interpretive research. Thus the interpretive researcher would constantly ask him/herself: What is the influence of my own (past and present) values and beliefs in interpreting the thoughts and feelings of the other? What hidden assumptions are constraining (distorting) the way I make sense of the other? Interpretive research methods include' narrative inquiry' and 'writing as inquiry', especially autobiographic and auto-ethnographic methods (Ellis & Bochner, 2000; Clandinin & Connolly, 1998; Richardson, 2000; Taylor & Settelmaier, 2003).

Applied to education, interpretive inquiry engages teachers as reflective practitioners in developing enhanced understanding of the life-worlds of their students by constantly asking questions such as: Who are these students who sit before me? Who is the self that teaches? (Palmer, 1998). A deeper understanding involves a broader focus on the social, political, historic and economic forces shaping the pedagogies, curriculum policies and schooling system in which teachers are immersed. Such an interpretive orientation is essential for teachers wishing to adopt more student-centred pedagogies such as constructivist approaches to teaching and learning. Rigorous standards have been developed for regulating the quality of reflective interpretive inquiry (or 'self-study') (e.g., Bullough & Pinnegar, 2001).
The Critical Paradigm
To resolve the global crises we are facing today we need to produce graduates capable not only of conducting scientific research reasoned out through objective quantitative strategies or engaging in interpretive research that deepens mutual understanding. The added challenge for educational research is to empower our students and colleagues to become imaginative and critical thinkers capable of addressing the question: 'Whose interests are not being (and should be) served by particular social policies and practices?'The critical research paradigm addresses this issue by enabling the researcher to practice 'deep democracy' (Kincheloe & McLaren, 2000) which involves identifying and transforming socially unjust social structures, policies, beliefs and practices. Its primary purpose is to identify, contest and help resolve 'gross power imbalances' in society which fuel ethically questionable profit-making activities that contribute to systemic inequalities and injustices such as social and economic exclusion of some sectors of society, loss of cultural capital and cultural identity amongst ethnic minorities, and anthropocentric climate change and loss of biodiversity.

In this type of research, the process of writing as inquiry (shared with the interpretive paradigm) has an added critical dimension and becomes a means of critical analysis and ideology critique of established policy and practice. The researcher raises his/her own critical consciousness (Brookfield, 2000) and constructs a moral vision of a better society. This can be done individually or, better still, in collaboration with less empowered others participating in 'critical action research' led by the researcher in the role of facilitator. The researcher's role is one of advocacy, a change agent who argues for and leads the way towards a more equitable, fair and sustainable society. The work of Jose Rizal (the national hero of the Philippines) and Patrick Awuah (founder of Ashesi University, Ghana) are good examples of this type of transformative leadership.

Applied to education, critical inquiry focuses first on raising the conscious awareness of teachers about established values and beliefs that underpin their seemingly natural teacher-centred classroom roles (Taylor, 2008). Once this process is underway, critical theory is introduced (e.g., critical pedagogy, cultural inclusiveness, social justice) that stimulates teachers' creative thinking about designing curricula and assessment that are more student-centred, inquiry oriented, culturally sensitive, community-oriented, socially responsible, etc.

The rigor of this type of research is evaluated in terms of quality standards that are very different from those of the positivist paradigm but which are congruent with the standards of the interpretive paradigm. It is important that the researcher demonstrates critical self-awareness and critical understanding of the complexity of social issues. But critique alone is not enough to nourish the soul, and so it is important for the critical researcher to develop a vision of a better way of teaching and learning, and research practices, a vision based explicitly on moral principles that support the 'shoulds/oughts' of a transformed professional practice.

And in order to avoid criticism of being an armchair academic or utopian, the critical researcher is well advised to take direct action, to 'make a difference', by enacting his/her ideals in a principled endeavour to transform the culture of his/her classroom community through, for example, critical action research. This involves evaluating the impact of one's transformative teaching on student learning and, ideally, leads to the teacher-researcher's evolving praxis. Critical researchers also choose to write in a way that is designed to elicit critical awareness and critical understanding in their readers, thereby writing for pedagogical thoughtfulness (Manen, 1990).

Various literary styles of writing are available to critical and interpretive writers to enable them to impact their readership, and this is taken up in the postmodern paradigm below.
The Postmodern Paradigm
This relatively new and challenging paradigm opens many new and exciting doors for educational researchers as it brings to our attention the very important concept of 'representation' (Denzin & Lincoln, 2005) which holds that what goes on in our minds and hearts is not directly accessible to the world outside us. There is no window in our heads that allows another person to look directly into our minds and see 'exactly what we mean'; the best we can do is 'represent' our thoughts and feelings through various means of communication (e.g., language, art, dance, gesture).

Equally for scientists, there is no window into nature that directly reveals nature's secrets; all scientific observations are 'theory laden' whether conducted using the human eye or technological extensions such as radio telescopes, electron microscopes, cloud chambers, x-ray crystallography, gamma spectroscopy, etc. Thus scientific knowledge is at best a model of the 'unseeable' and its viability (or usefulness) is tested against the human purposes that shape its production. Scientific knowledge remains forever contingent and open to challenge; and in that way it continues to evolve, sometimes making radical departures that overturn established models. Such is the case with our scientific knowledge of the cosmos and the sub-atomic universe (Dosch & Muller, 2010).

When educational research is under the governance of the positivist paradigm the scientific form of representation prevails: research reports are written objectively using the passive voice, past tense and third-person gender neutral pronoun ('it'). However, with the advent of newer paradigms, alternative means of representation are available to us. The interpretive paradigm requires that our personal perspectives, along with those of our research participants, are 'given voice'. Writing narratively (1 st person voice) about our unfolding experiences enables us to provide deep insight into the inquiry process and outcomes, demonstrating how we have constructed meaning (or interpreted) and providing rich detail of the context within which it occurred (thereby fulfilling important quality standards of the interpretive paradigm).

And for those who are drawn to the critical paradigm, a major goal of the 'researcher as activist' is to empower self and others by enabling 'critical voices' to be heard; voices of protest that point to personal experiences of oppression and the need for changes to policies and practices to ensure equity, fairness and social justice. Interpretive and critical researchers draw from the full range of pronouns (I, you, she, he, it, they), active and passive voice, and multiple tenses (past, present, future), depending on the (unfolding) purpose of their inquiries. The choice can be overwhelming for the novice researcher and quite confronting for 'elders of the tribe' still steeped in the positivist paradigm.

But more so, in celebrating pluralism and difference, the postmodern paradigm opens the door to other disciplines such as The Arts. In recent years Arts-based educational research has flourished, making available many new forms of representation such as: (i) literary genres of impressionist writing, autobiographical writing, storying, poetry, ethno-drama, screenplay and fiction, and (ii) visual imagery such as film, painting, sketching, dance and photography (Knowles, & Cole, 2008; Prendergast, Leggo, & Sameshima, 2009).

Another important contribution of the Arts to educational research is the availability of alternative modes of reasoning. The positivist paradigm privileges a particular form of reasoning - propositional, deductive and analytic logic - which serves well the purpose of reasoning objectively. However, interpretive and critical inquiries, with their emphasis on representing the progressive development of the researcher's professional practice, require alternative modes of reasoning such as metaphorical thinking, dialectical thinking, inductive thinking, mytho-poetic thinking and reflective thinking (e.g., Taylor, Taylor, & Luitel, 2011).

Arts-based educational research offers new quality standards for regulating our educational research inquiries. For example, if we write up our research using a literary genre (e.g., narrative, story or poetry) for the purpose of engaging our readers in critical reflective thinking about their own professional practice then the critical paradigm quality standard of pedagogical thoughtfulness is relevant (Manen, 1990). The literary quality of our writing that serves this purpose needs to have resonance with the experiences of the reader. In other words, we aim to write in a way that seems to the reader to be realistic, plausible or believable. The quality standard of verisimilitude is relevant to this purpose (Barone, 2001). Arts-based research provides many more quality standards for shaping the educative and literary quality of our research writing, thereby enriching the work of interpretive and critical researchers. They direct us to question our writing: Is the story engaging (dramatic, fun, odd)? Does the reader gain emotional appreciation such as empathic appreciation? Does the writing make the topic more complex (subtle, nuanced, deeper)?
Multi-Paradigmatic Research
Rather than standing alone as individual paradigms for framing the design of a researcher's inquiry, as does the positivist paradigm, the newer paradigms can serve as 'referents'. In other words, we can design our research by combining methods and quality standards drawn from two or more of the newer paradigms. It is not uncommon for a research study to combine methods and standards from the interpretive and critical paradigms to create a 'critical auto/ethnography'. And when new literary genres, modes of thinking and quality standards are added from Arts-based research such multi-paradigmatic studies become very powerful means of transformative professional development (Taylor, Taylor, & Luitel, 2011).

One of the second author's co-scholars at SMEC, Curtin University, Berhana Ignacio, conducted a multi-paradigmatic research for her Masters project. Drawing on the interpretive and critical paradigms and using literary genres (poetry, storying), she examined her real-life experiences as a learner, practising teacher and teacher educator. In particular, she excavated and reflected critically on her past experiences of and beliefs towards constructivist teaching. She narrated and storied aspects of her pre-service and in-service teaching experiences and her more recent experiences as a pre-service mentor and Masters student. Theorising about culturally inclusive teaching fuelled Berhana's vision of her future science curriculum, one that includes the indigenous knowledge of students from the local community.

As my writing evolved I came to understand that culture plays a vital role in promoting a constructivist informed curriculum and classroom practices. With this, I envisage a classroom where my students use their local knowledge (non-Western), such as their culture, beliefs, traditions, in concert with global (Western) knowledge in understanding the environment and in making sense of the world around them (Brickhouse & Kittleson, 2006). However, it will also be a classroom where students are made to realise though science and science education can bring prosperity, it can also bring annihilation depending on whose interest is being served (Beane, 1995). I believe that such type of classroom might help develop responsible decision makers and students who will see science as a means of understanding the inclusivity of both knowledge systems in attaining better lives on earth (Jardine, 1998).

(Ignacio, 2009, p. 74)

Multi-paradigmatic doctoral research studies have been supervised by the first author. These inquiries, which include compelling literary genres (semi-fictive stories, poems, ethno-dramas, screenplays), vivid visual imagery and alternatives modes of thinking, have been conducted by university-based science and mathematics teacher educators in Mozambique (Nhalivelo, 2008; Cupane, 2008) and Nepal (Luitel, 2009). Similar to Berhana's research, these intercultural researchers explored their culturally situated autobiographies as students, teachers and teacher educators. Having developed powerful critical theoretic perspectives, they deconstructed oppressive cultural myths governing the educational policies and practices of their (post-colonial) countries. As significant research outcomes, they developed philosophies of culture-sensitive curricula for preparing new science and mathematics teachers to take their respective countries forward into a culturally inclusive globalising world (Afonso & Taylor, 2009; Cupane, 2011; Luitel & Taylor, 2009; Taylor, 2010).
Closing
This has been a necessarily brief summary of the huge and rapidly evolving field of educational research, and much has been omitted, not the least of which is an account of the 'mixed methods' approaches employed by post-positivists who bring qualitative methods into their predominantly objectivist research. Also missing is an account of the new 'integral paradigm' that provides a rationale for drawing upon multiple paradigms to design new hybrid methodologies that involve multiple epistemologies and their accompanying quality standards. For more on this see Taylor, Taylor and Luitel (2011).

Returning to our purpose in writing this paper, we join Paul and Marfo (2001) in calling for graduate research programs to provide diverse philosophies of research and knowledge production. In making our education systems more ethically responsive to the urgent challenges of globalization - designing sustainable development, countering climate change, preventing ongoing loss of biocultural diversity - we cannot afford to simply look to the past for 'know-how'. Educators can learn from new developments in interdisciplinary collaboration (Linger, 2011) that bring together the Arts, Humanities, Social Sciences, Natural Sciences and Engineering in creative endeavours amongst discipline experts, policy makers and the public to engage in new forms of interdisciplinary knowledge production aimed at resolving real-world practical problems. For example, Robert Frodeman (2008) explains how philosophers and environmental scientists have joined forces to create the new interdisciplinary field of 'environmental philosophy' that is enabling local communities to resolve the complex problem of sustainable development, with its competing economic, environmental and socio-cultural interests. We need education systems that actively prepare young people with the social and cognitive skills to engage critically and imaginatively in ethical decision-making about complex issues facing their societies. By drawing on multiple paradigms educational researchers can make a major contribution to aligning curricula, teacher education, and classroom teaching and learning practices with the complex and challenging needs of the 21 st century. No country can afford not to take seriously the pressing need to produce educational researchers capable of using the powerful new interdisciplinary tools offered by the new research paradigms.
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About the Authors

Dr. Peter Charles Taylor is an Associate Professor of Transformative Education at the Science and Mathematics Education Centre (SMEC), Curtin University, Western Australia. His research focuses on the contextualization of science and mathematics education with/in postcolonial societies, especially culture-sensitive ways in harnessing global forces of modernisation. This research as/for professional development of teachers and teacher educators involves excavating personal education histories and alternative knowledge systems, examining critically the legacy of (neo) colonial education policies and practices, envisioning transformative curricular possibilities for creating Third Space Classrooms. Of particular research interest are auto/ethnography, literary genres of narrative, fictive and impressionistic writing, nondual logics such dialectics and poetics, and agentic standards of critical reflexivity and pedagogical thoughtfulness. Dr. Taylor draws on a wide range of theoretical referents, including critical constructivism, reconceptualist curriculum theory, research as reflective/imaginative praxis, the cultural/linguistic natures of science and mathematics and postcolonial theorising.

Milton Norman Dejadena Medina is an Assistant Professor and Research Coordinator of Assumption College of Nabunturan, Compostela Valley Province. He holds a bachelors degree in biology from Central Mindanao University, and a masters degree in science teaching major in biology from the University of Southeastern Philippines. He finished his masters degree in science education from the Science and Mathematics Education Centre (SMEC), Curtin University, Western Australia. His research interests are biodiversity research and conservation, and lately on transformative education research.

This article was accepted for publication after a double-blind peer review process. Receiving Editor: Dr. Elisa Garzitto-Michals, California State University, Sacramento, USA.

Suggested Citation

Taylor, P. C., & Medina, M. N. D. (2013). Educational Research Paradigms: From Positivism to Multiparadigmatic. The Journal of Meaning-Centered Education. Volume 1, Article 2, http://patrickblessinger.com/meaningcentered//journal/volume-01/educational-research-paradigms-from-positivism-to-multiparadigmatic

Copyright © [2013] Institute for Meaning-Centered Education (IMCE), Peter C. Taylor and Milton Norman D. Medina.

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Disclaimer

Opinions expressed in this article are those of the author, and as such do not necessarily represent the position(s) of other professionals or any institution.

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Educational Research Paradigms: From Positivism to Multiparadigmatic

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Educational Research Paradigms: From Positivism to Multiparadigmatic Peter C. Taylor Science and Mathematics Education Centre (SMEC), Curtin University, Australia Email: [email protected] Milton Norman D. Medina Research and Development Center Office, Assumption College of Nabunturan, Philippines Email: [email protected] Abstract In this paper we provide an overview of the characteristics of major educational research paradigms shaping contemporary educational research, ranging from the traditional positivist perspective to the latest multi-paradigmatic worldview.

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OK, I am exaggerating the positivist position (although you may be amazed at how close to this some of them actually came) in order to make a point. Things have changed in our views of science since the middle part of the 20th century.

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The term 'logical empiricism' has no very precise boundaries and still less that distinguishes it from 'logical positivism'. It is therefore hard to map. 'Logical empiricism' here includes three groups: (1) the Vienna Circle, here taken broadly to include those who were part of various private discussion groups, especially that around Moritz Schlick, and also the members of the more public Ernst Mach Society (Verein Ernst Mach), (2) the smaller, but perhaps more influential Berlin Society for Empirical Philosophy (later called the Berlin Society for Scientific Philosophy), and (3) those influenced by or who interacted with members of the first two groups and shared an intellectual kinship with them. Besides Vienna and Berlin, there were important centers of the movement in England, France, Scandinavia, at several universities in the U.S., and even China. This characterization includes thinkers who disagreed with doctrines espoused by members of the original groups and even some who defined themselves in opposition to the movement. This results in a vague boundary, but it suffices to identify a movement in which a large number of able philosophers self-consciously participated and to distinguish logical empiricism from other movements.

It does not, however, distinguish logical empiricism from logical positivism, and it is doubtful that any principled such boundary can be drawn along doctrinal or sociological lines (Uebel 2013). Usually when distinctions are drawn, 'logical empiricism' is the wider term. Members of the Berlin group never used the term 'positivism' about themselves, but did use it concerning some unnamed Viennese in stressing their differences from the latter. In any case, these differences, even if real, were smaller than the differences within the Vienna Circle on one hand or within the Berlin group on the other. 'Positivist' is a term usually applied by opponents of various doctrines. It was used by some of the Viennese logical empiricists about themselves but generally with caution and in stressing the differences between their own views and those of the 19 th century positivists. The one philosopher who would have unhesitatingly described himself as (having been) a logical positivist was A.J. Ayer.

Another way of mapping the boundaries of logical empiricism is to list the specific philosophers who were centrally or peripherally part of it. This included many of the most important philosophers of the mid-twentieth century. Hans Hahn, Moritz Schlick, Rudolf Carnap, and Otto Neurath were leaders of the Vienna Circle, and Kurt Gödel regularly attended its meetings. The list of its members, visitors, and interlocutors is staggering, including A.J. Ayer, Herbert Feigl, Philipp Frank, Hans Hahn, Carl Hempel, Karl Menger, Richard von Mises, Ernest Nagel, Karl Popper, W.V. Quine, Frank Ramsay, Hans Reichenbach, Alfred Tarski, Friedrich Waismann, and Ludwig Wittgenstein, among many others. Not all of these would admit to being part of the logical empiricist movement, of course, but a case can be made that all contributed to it. The Berlin Society for Empirical (or Scientific) Philosophy was, as stated, smaller but perhaps more influential. Led by Hans Reichenbach, it included Kurt Grelling, Walter Dubislav, Kurt Lewin, Richard von Mises, Paul Oppenheim, and others. Hempel took his doctorate in Berlin, working with Reichenbach until the latter was forced to leave in 1933. Hempel also spent time in Vienna and Prague. Of course, among the foremost associates of the Berlin Society was Albert Einstein, who was also in Berlin also until 1933.

There was also an important group of logicians in Warsaw of which Alfred Tarski is the best known. Tarski interacted significantly with the logical empiricists in Vienna, Berlin, and the U.S., but it is more reasonable to classify the Polish logicians as an allied group rather than include them within the logical empiricist movement.

Because of the catastrophic dislocations of Europe in the 1930s, the main focus of the logical empiricism moved from central Europe to America by the close of that decade. Erkenntnis, the main journal of the movement, which had been edited by Reichenbach and Carnap, ceased publication by 1940. In 1930 Feigl moved to the U.S., and Carnap moved to Chicago in 1936. Hempel came to Chicago and Menger to Notre Dame in 1937. The ensuing years witnessed a massive exodus to America from central Europe. Reichenbach arrived in the U.S. in 1938 after five years in Turkey. Also in 1938 Gustav Bergmann and Philipp Frank emigrated. Edgar Zilsel came in 1939. Alfred Tarski was on a visit to the U.S. when Poland was invaded in 1939, and so he stayed. And by 1940 Richard von Mises was also in America.

In the U.S., these exiles were joined by the Americans Nelson Goodman, Charles Morris, W.V. Quine, Ernest Nagel, and, after the war, by Reichenbach's UCLA students Hilary Putnam and Wesley Salmon. Adolf Grünbaum can also be considered as clearly in the Reichenbach lineage. And Wilfrid Sellars was, in his early years, a close associate of Feigl. The American incarnation of the logical empiricist movement enjoyed generally good relations with the American pragmatists, not only because many of the logical empiricists had a strong pragmatist component to their philosophy, but also because the pragmatists and logical empiricists shared a common concern for empirical methodology in the service of social reform. Institutionally, the movement was represented in most major American universities, and such journals as Philosophy of Science (with Carnap and Feigl on the Editorial Board and Reichenbach and Schlick on the Advisory Board) and Philosophical Studies (founded and edited for many years by Feigl and Sellars) provided ample outlet for their publications. In addition, the Inter-Scientific Discussion Group was founded by Philipp Frank at Harvard. That grew into the Institute for the Unity of Science, called by some the Vienna Circle in exile. Meanwhile in Chicago the Encyclopedia of Unified Science was established with Neurath, Carnap, and Morris as its editors.

But even from late 30s onward the movement was hardly limited to America. Ayer remained in England. Wittgenstein returned to Cambridge in 1929, but with regular visits to Vienna, including those on which he discussed issues surrounding a strong version of verificationism with Schlick and Waismann. Popper fled to New Zealand in 1937, and in 1946 moved to the London School of Economics. Neurath fled from Vienna to the Hague and then again in 1940 to England, where he remained till his death in 1945. Friedrich Waismann went to England in 1937. In 1939 Rose Rand, a less well-known member of the Vienna Circle, fled to England and then in 1954 emigrated once more to the U.S. There were like-minded thinkers in Scandinavia (such as Jørgen Jørgensen, Eino Kaila, and Arne Naess) and as far away as Argentina (H.A. Lindemann) and China (Tscha Hung).

It is impossible to say when logical empiricism ceased to be sufficiently cohesive to be identifiable as a continuing movement. Certainly by 1960 a great many philosophers, including many who had earlier clearly been part of the movement, were identifying themselves in opposition to what they took to be logical empiricism. And some members simply changed their minds or pursued different projects. Logical empiricism probably never commanded the assent of the majority of philosophers in either Europe or America, and by 1970 the movement was pretty clearly over-though with lasting influence whether recognized or not. In the 1980s there was a resurgence of historical interest in logical empiricism. That historical interest continues to clear away many of the caricatures and misconceptions about the logical empiricists. Among the major results of this work is the recognition of the tremendous variety and subtlety of views represented within the movement and the fact that many of the arguments later deployed by critics of logical empiricism had been pioneered by the logical empiricists themselves.

Given the emphasis on science and its technical apparatus, social renewal, clarity and rationality of belief, functionality, and above all the palpable sense of doing philosophy in an importantly new way, it is reasonable to associate logical empiricism with other forms of European modernism in the 1920s and 30s, such as Neue Sachlichkeit in art and the Bauhaus in architecture and design, and with mid-century modernism as well as with political liberalism, from the New Deal to the Great Society in the United States. There have been recognizably modernist developments in various fields including philosophy for centuries.

With a movement as large and complex as logical empiricism a great many factors went into raising the questions it would address, making them seem urgent, and making it seem as though the intellectual resources it would need to address these questions were either at hand or could be developed.

One long-term process with profound implications was the steady departure of the various sciences from philosophy to form autonomous disciplines. By early in the twentieth century mathematics, physics, chemistry, biology, and the social sciences were all pursued professionally and independently from philosophy. And psychology was just separating from philosophy. Yes, there were polymaths who could and did pursue a science and philosophy professionally. Those were increasingly rare, though single-discipline scientists did from time to time make philosophic-seeming pronouncements. But they did so from outside the field. This pattern of steady departures raised the pressing question: What sort of thing remained behind? Once mathematics and the empirical sciences all left, what was left for philosophy?

The nature of philosophy was always a vexed philosophic question, but now it was particularly insistent. Surely there was no domain of empirical facts that philosophy could call its own. All that real estate had been parceled out. One answer available at the time that logical empiricism flourished was that the genuinely philosophic remainder after the departure of the sciences is somehow deeper than the empirical sciences and gets at matters, perhaps cultural ones, that are more profound and important than anything that empirical science even can address. This is either because on this conception philosophy has a mode of access or "evidence" that the empirical sciences do not and cannot have, or because the very idea of fidelity to evidence and punctilious argument is somehow small-minded.

The logical empiricists found this answer unappealing. Indeed, this conception of philosophy is precisely what Carnap means by 'metaphysics'. (As a consequence, what Carnap meant by that word is different from what late twentieth and early twenty-first century philosophers generally mean in describing their own work as analytic metaphysics.) The logical empiricists were eager to conceive of their enterprise as scientific and to engage in philosophy only insofar as it was also scientific. This science need not be empirical and need not include all that was traditional in philosophy that had not been incorporated into the independent sciences. The decision to be scientific can hardly be the end of the story. It requires rather better and more detailed answers to questions about what scientific methods are, how the mathematical (and other apparently non-empirical sciences) fit together with the empirical ones, and what, more precisely, philosophy's role was.

A second series of developments that raised questions for logical empiricism to address were developments in the sciences themselves, especially the rise of non-Euclidean geometries in mathematics and the establishment of relativity theory in physics. These posed a serious challenge to what would otherwise be an attractive scientific philosophy, namely some version of Kantianism. Kant had recognized that the best of modern science was often mathematical in character and had labored to integrate both geometry and arithmetic into our empirical picture of the world. He had held that we could not represent the world except as a Euclidean structure and hence Euclidean geometry was, a priori, a permanent feature of any future physics. The demonstration that non-Euclidean pure geometrical structures were as consistent as Euclidean ones and that spaces can indeed be represented as a non-Euclidean manifolds was one half of the problem. The other half came when Einstein argued convincingly that physical space was best described as a non-Euclidean manifold of non-constant curvature. Plainly Euclidean geometry could not be guaranteed a future physics. Modern mathematical logic also posed a problem for other Kantian claims, but not in the same wrenching way.

Many logical empiricists started out as neo-Kantians: Reichenbach, Carnap, Schlick, and even Hempel (until he studied with Reichenbach, who by that time had revised his view). The difficulties with geometry and relativity certainly do not refute all forms of neo-Kantianism, but the difficulties are quite real nonetheless. The need is to understand how mathematics can be integrated into what is otherwise an empirical enterprise, i.e., physics, chemistry, biology, etc. Addressing this need was to be a major part of the logical empiricist program.

The background of logical empiricism described so far has been confined to the academic world, but events outside that domain shaped the movement as well. World War I was an unmitigated disaster for central Europe, followed by economic turmoil in the 20s and political upheavals of the 30s. It is hard to exaggerate these changes. Monarchies that had stood for centuries disappeared overnight and their empires disintegrated. This level of political convulsion had not been seen since the French Revolution, and that earlier upheaval was comparatively confined. Cultural changes were equally profound, and these were reflected by radical departures in the arts such as painting, music, and architecture, and even more importantly in new modes of living.

The logical empiricists were no mere bystanders. They, or at least the main leaders of the movement, were politically and culturally engaged. Even more important, this engagement was accompanied by the conviction that their cultures were incapable of the necessary reform and renewal because people were in effect enslaved by unscientific, metaphysical ways of thinking. Such ways of thinking might be exemplified in theology, in the racial hatreds of the day, in conceptions of property, and in traditional ideas about the "proper" roles of men and women in society. So to articulate a "scientific world conception" and to defend it against metaphysics was not just to express an academic position in the narrow sense. It was a political act as well; it was to strike a blow for the liberation of the mind. To articulate scientific methods and a scientific conception of philosophy was the essential first step in the reform of society and in the emancipation of humankind (Carnap 1958/2017, Creath 2009, Uebel 2012.

If all of this sounds like something out of the 18 th century Enlightenment, the analogy was not lost on the logical empiricists themselves. André Carus has argued that this is exactly what Carnap had in mind by "explication" (Carus 2007). Neurath frequently drew parallels between the logical empiricists' anti-metaphysical program and the earlier Enlightenment ambitions. Certainly Kant had inveighed against the metaphysics of his time, and the anti-metaphysical tradition remained strong within the scientific community through the 19 th century.

The point so far was not to ask whether the logical empiricists were right in any of this. That question will come up later. So far the issue has been only to see the motivations that the logical empiricists had-and from their point of view-for addressing certain questions and for thinking that answers to those questions were urgently needed. None of this, however, says why the logical empiricists thought they had or could have the means to answer these questions. To that we now turn.

Since Newton the most paradigmatic examples of empirical science were those claims, usually quantitative ones, that were properly inferred from or appropriately confirmed by experience. Speaking very informally, these are the ones that we have good reason to believe or at least better reason to believe than the available alternatives. The problem, of course, is to specify the form of proper inferences, the form of an appropriate confirmation relation, and/or the structure of good reasons. The task is daunting, but logic in a suitably broad sense seems to be the right tool. Still speaking informally, logic seems to give us the structure of (good) reasoning. There are other conceptions of logic, of course, but this is a standard one and pretty well describes what the movement needed.

If logic was the tool that was wanted, it was newly ready for service. The progress of modern mathematical logic from Bolzano through Russell and beyond was truly impressive. Arguably, it could now express all parts of classical mathematics. Besides the first order predicate calculus one would need either set theory or higher order logic, but these were recent developments as well. Logic, like the empirical sciences, was progressive and could be approached cooperatively by more than one investigator. In Our Knowledge of the External World (1914) Russell had even positioned logic as the locus of scientific method in philosophy. It is small wonder then that those who were looking for something scientific in what was left of philosophy turned to logic. Wittgenstein's no-content theory of logic in the Tractatus (1921/1922) was tantalizingly suggestive about how mathematics could be integrated into an overall empirical theory of the world. Wittgenstein also expressed a radical verificationism in the early 1930s in his conversations with Schlick, Waismann, and other members of the Vienna Circle. Many of the logical empiricists in turn could see in some version of that verificationism the ideal tool with which to carry out their anti-metaphysical program. There was, naturally, much left to accomplish, but even with Gödel's results one could expect that further impressive strides in logic could be made. Indeed, much was accomplished even if the perfect account of scientific reasoning proved elusive. Perfection is elusive in all the sciences, but that is no reason for despair.

The logical empiricist movement is the sum of the interwoven trajectories of its members, so one way of describing that movement is to trace those various trajectories. To do so in detail for all those involved would take rather longer than the movement lasted. That would be inappropriate for one entry in an encyclopedia, especially one in which entries for many of the members will appear independently. The thumbnail sketches of the work of some representative figures below show the breadth and international character of the movement. While the list is long, it covers only a small fraction of those involved and leaves out many important thinkers.

A.J. Ayer (1910-1989)

An English philosopher in the tradition of British empiricism, Ayer visited the Vienna Circle in 1932-33. His book Language, Truth, and Logic (1936) was a best seller after World War II and represents logical positivism to many English speakers

Rudolf Carnap (1891-1970)

German by birth, he taught in Vienna, Prague, Chicago, and Los Angeles. He was one of the leaders of the Vienna Circle and of logical empiricism, especially of those within the movement whose formulations were more liberal, e.g., with respect to the criterion of verification. He defended logical and methodological pluralism and worked to develop an epistemic approach to probability.

Walter Dubislav (1895-1937)

A German logician and philosopher of science, Dubislav was one of the founders, with Reichenbach and Grelling, of the Berlin Society of Empirical (later Scientific) Philosophy.

Herbert Feigl (1902-1988)

Born in what is now the Czech Republic, Feigl studied in Vienna with Schlick and Hahn. He emigrated to the U.S. before most other logical empiricists would do so. He taught at the Universities of Iowa and Minnesota and founded both Philosophical Studies, with Wilfrid Sellars, and the Minnesota Center for the Philosophy of Science. He is best known for his work on the mind-body problem.

Philipp Frank (1884-1966)

This Viennese physicist and philosopher of science taught at Vienna, Prague, and Harvard. He was part of a discussion group with Hahn, Neurath, and others that preceded the Vienna Circle. At Harvard he founded the Inter-Scientific Discussion Group that developed into the Institute for the Unity of Science. He was also one of the founders of the Boston Colloquium in the Philosophy of Science.

Kurt Gödel (1906-1978)

Born in what is now Slovakia, Gödel took his doctorate under Hahn in Vienna, studying with Carnap and Schlick as well. He also regularly attended Vienna Circle meetings and taught in Vienna. The bulk of his career was spent at the Institute for Advanced Study at Princeton. He is best known for his spectacular incompleteness theorems, and his Platonist orientation toward mathematics. Though a participant in the logical empiricist movement during the Vienna years, Gödel thought that Carnap's approach to mathematics could be refuted. The alleged proof (Gödel 1995) was not published in Gödel's lifetime and remains controversial.

Kurt Grelling (1886-1942)

Grelling was born in Berlin and took his doctorate in Göttingen under Hilbert. With Leonard Nelson he developed a famous semantic paradox that bears their names. He was one of the founders of the Berlin Society for Empirical (later Scientific) Philosophy. Grelling died in the Holocaust because for bureaucratic and political reasons news of an academic appointment in the U.S. reached him too late.

Adolf Grünbaum (1923-)

Grünbaum moved from his native Germany as a teenager, studied under Hempel at Yale, and spent the bulk of his career at the University of Pittsburgh, where he founded the Center for Philosophy of Science. The major themes of his work have been philosophy of space and time, rationality, and psychoanalysis.

Hans Hahn (1879-1934)

Hahn, a distinguished mathematician, took his doctorate in his native Vienna in 1902 and began teaching there in 1905. He was part of a group with Frank, Neurath and others that discussed logical and methodological issues prior to World War I. After teaching at Czernowitz (now in Ukraine) and Bonn he was given a chair in mathematics at Vienna in 1921. He was instrumental in bringing Schlick there in 1922 and so was called by Frank "the actual founder of the Vienna Circle" (Stadler 1997/2001, 642). His most famous student was Gödel.

Olaf Helmer (1910-2011)

Helmer took a doctorate in his native Berlin under Reichenbach and a second doctorate under Susan Stebbing in London. He collaborated with other logically minded philosophers. Indeed, the team of Hempel, Helmer, and Oppenheim became known as "H₂O". The bulk of his career was spent at the Rand Corporation.

Carl G. Hempel (1905-1997)

Born just north of Berlin, Hempel studied at both Göttingen and Berlin. Most of his doctoral work was completed under Reichenbach when the latter was forced to leave Germany. Hempel taught at a number of American universities, most famously at Princeton and the University of Pittsburgh. He was the doctor father of many prominent philosophers of science, and his work focused on confirmation, explanation, and concept formation.

Richard Jeffrey (1926-2002)

This American logician and philosopher of science earned an MA with Carnap (with whom he later collaborated) and a PhD with Hempel (with whom he was for many years a colleague and close friend at Princeton). He developed Jeffrey conditionalization (see below) and defended probabilism.

Kurt Lewin (1890-1947)

Born in what is now Poland, Lewin took his doctorate in Berlin in 1916. He lectured there in both philosophy and psychology until 1933 when he emigrated to the U.S. via England. Thereafter he taught at a number of American universities including Cornell, Iowa, MIT, and Duke. Credited with founding modern social psychology, he laid the foundations for what is now called sensitivity training as a way to combat religious and racial prejudices.

Richard von Mises (1883-1953)

Born in what is now Ukraine, Richard von Mises is the brother of the economic and political theorist Ludwig von Mises. Richard was a polymath who ranged over fields as diverse as mathematics, aerodynamics, philosophy, and Rilke's poetry. He finished his doctorate in Vienna. He was simultaneously active in Berlin, where he was one of the developers of the frequency theory of probability along with Reichenbach, and in Vienna, where he participated in various discussion groups that constituted the Vienna Circle. Eventually it was necessary to escape, first to Turkey, and eventually to MIT and Harvard.

Charles W. Morris (1901-1979)

Morris was an American pragmatist and philosopher of language at the University of Chicago when Carnap arrived there. These two, together with Neurath until the latter's death, were the chief editors of the Encyclopedia of Unified Science. After Carnap left Chicago, Morris moved to the University of Florida.

Otto Neurath (1882-1945)

This Austrian philosopher of science and sociologist took his doctorate in political science in Berlin. A member of the First Vienna Circle and a leader of the "left" wing of the Vienna Circle, he was also politically active. He was a significant museum director, and as part of this developed the ISOTYPE picture language. His main philosophic themes were physicalism, anti-metaphysics, and the unity of science. He was the Editor-in-Chief of the Encyclopedia of Unified Science until his death. Eventually he fled to the Netherlands and from there to England.

Paul Oppenheim (1885-1977)

A successful industrialist and heir to a substantial fortune, Oppenheim was trained in his native Germany in chemistry and philosophy. He was a close friend of Einstein, and helped to initiate the Berlin Society for Empirical Philosophy. Oppenheim collaborated with many important logicians and philosophers of science both in Europe and the U.S. He also helped many to escape Nazi oppression, and continued to help in a variety of ways even after he settled in Princeton in 1939.

Karl Popper (1902-1994)

Born in Vienna and with a doctorate there, Popper was intensely engaged in discussions with members of the Vienna Circle. His main philosophical work, The Logic of Scientific Discovery (1935/1959), appeared in a series edited by Schlick and P. Frank. He did not however, regularly attend meetings of the Vienna Circle and generally considered himself an outsider. Later he claimed to have "killed" logical positivism. From Austria Popper escaped to New Zealand and eventually to the London School of Economics, where he was knighted for his political writings.

Hilary Putnam (1926-2016)

This American philosopher of science, mathematics, mind and language earned his doctorate under Reichenbach at UCLA and subsequently taught at Princeton, MIT, and Harvard. He was originally a metaphysical realist, but then argued forcefully against it. He has continued the pragmatist tradition and been politically active, especially in the 1960s and 70s.

W.V.O. Quine (1908-2000)

Born in the U.S., Quine took his doctorate and spent his entire career at Harvard. In 1932-33 he visited the Vienna Circle and then Carnap and Warsaw. For the next six years, he said, he was a disciple of Carnap's and even after they began to disagree, Carnap set the agenda. Eventually they clashed over analyticity, modality, and intensional contexts generally. Many similarities of view with Neurath are apparent, especially on the issues of holism, underdetermination, and naturalism in epistemology.

Hans Reichenbach (1891-1953)

Reichenbach was born in Hamburg and, after immersing himself in mathematics, physics, and philosophy, took his doctorate in Erlangen, Germany. He was a founder and the leader for the Berlin Society for Empirical (later Scientific) Philosophy. In 1933 he was forced to leave Berlin. He went to Turkey and then in 1938 to UCLA. Among his many students were Hempel, Putnam, and W. Salmon, and so almost all philosophy of science in the U.S. can trace its academic lineage to Reichenbach. Though interested in social and educational reform, he worked primarily in philosophy of physics. He developed and defended a frequency theory of probability, and emphasized both scientific realism and the importance of causality and causal laws.

Wesley Salmon (1925-2001)

Salmon was born in Detroit and, after an initial interest in theology, earned his PhD under Reichenbach at UCLA. He taught at a number of universities including Brown, Indiana, Arizona, and Pittsburgh. His interests centered on causality and explanation, and his statistical relevance model of explanation can be thought of as addressing and in large measure resolving the problem of the single case in frequency theories of probability.

Moritz Schlick (1882-1936)

Schlick was born in Berlin and eventually took his doctorate there in mathematical physics under Max Planck. He taught at a number of German universities before he was, at the instigation of Hans Hahn, called to the Chair in the Philosophy of the Inductive Sciences at Vienna, a chair that was previously held by Boltzmann and Mach. Schlick was one of the first philosophers to write about Einstein's relativity theory. He was close to Wittgenstein and one of the conduits for the latter's strict verificationism. His work ranges from space and time to general epistemology and ethics. In 1936 he was assassinated on the steps of the university by a deranged student.

Wilfrid Sellars (1912-1989)

Wilfrid Sellars was the son of well-known philosopher, Roy Wood Sellars. Wilfrid studied at Buffalo, Oxford, and Harvard before teaching at Iowa, Minnesota, Yale, and Pittsburgh. He was a close associate and collaborator with Feigl at Minnesota. (He once said that he and Feigl were for years discrete parts of a single entity.) He defended scientific realism, pragmatism, and naturalism, and his philosophy of language drew heavily on Carnap's Logical Syntax (1934/1937)

Alfred Tarski (1901-1983)

Born and educated in Warsaw, Tarski earned his doctorate under Lesniewski. He happened to be visiting the U.S. when Poland was invaded and so avoided the fate of so many of his colleagues. He taught at the University of California at Berkeley for more than 30 years. While it is unclear whether he should be counted as a logical empiricist, he visited the Vienna Circle and hosted its members in Warsaw, and his "The Concept of Truth in Formalized Languages" (1936/1956) was very influential on Carnap and on the development of semantics among the logical empiricists generally.

Friedrich Waismann (1896-1959)

Waismann was born in Vienna and earned his doctorate there under the direction of Schlick in 1936. From 1926 to 1933 he held discussions with Wittgenstein, generally in the company of Schlick, but also sometimes Carnap or Feigl. Waismann kept detailed minutes of these conversations. At one point he and Wittgenstein contemplated a joint book, but Wittgenstein later changed his mind. Besides the printed text of the Tractatus these conversations were the main conduit of Wittgenstein's ideas into the Vienna Circle. In 1937 Waismann was able to emigrate to England. After a couple of years at Cambridge, where he was shunned by Wittgenstein, he moved to Oxford, where he taught until his death.

Ludwig Wittgenstein (1889-1951)

Born into an immensely wealthy Viennese family, Wittgenstein studied at Cambridge from 1911, where he formed friendships with Russell, Keynes, and Moore. His Tractatus Logico-Philosophicus (1921/1922), which among other things tries to show that logic has no content, was enormously influential on many logical empiricists. Wittgenstein continued to spend much of his time in Austria working variously as an elementary school teacher, a gardener, and as an architect of a house for his sister in Vienna. While there he held influential discussions with Schlick, Waismann, and others. From 1930 he held teaching posts at Cambridge and increasingly distanced himself from the logical empiricists. His later work focused on ordinary language and inspired many other philosophers as well.

It is not possible in an essay of this scope to trace all the issues that the logical empiricists addressed or even to treat any one of them with completeness. What is possible is to highlight some salient issues, clear away some misconceptions about them, and sketch a bit how those issues were developed over time. The first is a related set of concerns: empiricism, verificationism, and anti-metaphysics. The second is the logical empiricists' treatment of logic and mathematics as analytic. Third is the related issues of the unity of science and reduction. And finally, comes the issue of probability. Given what has already been said, the reader should be aware that none of the doctrines discussed below was shared by all members of the logical empiricist movement.

Since antiquity the idea that natural science rests importantly on experience has been non-controversial. The only real questions about the sources of scientific knowledge are: Are there parts of science that do not rest on experience or rest also on something other than experience? If so what account can we give of those parts? And to the extent that science does rest on experience how can we know that it does? There is another question about science related to these, though not strictly about the sources of science, and that is: Why, in making claims about the world, should we be scientific as opposed to say mystical? The difficulty is that any scientific answer to this last question would reasonably be thought to beg the very question it purports to address.

Long before the twentieth century the prevailing opinion was that Euclidean geometry, standard mathematics, and logic did not rest on experience in any obvious way. They were largely presupposed in our empirical work, and it was difficult to see what if anything might disconfirm them. Geometry was a special case and might be handled in different ways that we shall not discuss here. That leaves logic and mathematics.

If Frege and Russell were right, then mathematics could be thought of as expressing no more than logical truths and handled in whatever way logic was to be treated. For Frege both mathematics and logic were analytic, but that, even if true, does not provide the needed answers. Wittgenstein's no-content theory of logic suggested that all of the real claims, the ones that had genuine content, could be appropriately supported by experience, and the logical and hence mathematical claims had no content to support. This seemed to open the way for a thoroughgoing empiricism in which the logical and mathematical fit in with the ordinary claims of physics and biology in a harmonious way. The next subsection about analyticity discusses the question of whether the needed distinctions can be drawn.

In developing his theory of types Russell said in effect that some expressions that seem to be sentences in fact say nothing at all. This is because, despite appearances, they are not grammatically well formed. Wittgenstein found this suggestive. In the Tractatus he suggested that much else was nonsense as well including traditional metaphysics and supposed claims about the "higher". When in late 1929 Wittgenstein proposed (Waismann 1967/1979), in conversations with Schlick and Waismann, a strict verificationism as a basis for identifying the legitimate parts of discourse, this seemed to the logical empiricists to be a very attractive tool for setting aside the unscientific parts of philosophy.

This does not mean, however, that all logical empiricists or even all members of the Vienna Circle accepted the strict verificationist view that in order to be meaningful a claim must be implied by a finite number of observation sentences. Even though those observation sentences need not be true, this view had the drawback that so-called laws of nature would not be meaningful on this criterion. Schlick was prepared to bite the bullet and hold that laws were not statements at all but principles of inference. Others were not prepared to go so far and sought more liberal formulations. This more liberal or "left" wing of the Vienna Circle included Carnap, Philipp Frank, Hahn, and Neurath. Carnap does not seem to have been a strict verificationist even in the Aufbau (1928/1967).

Over the years a great many different formulations of verificationist principles ensued. Most of them came to a bad end rather quickly, and this is sometimes taken as a convincing argument that any form of verificationism is utterly misguided. Perhaps, but we should be cautious. There are undoubtedly many different features joined in any one of the proposals, and even a sequence of failures may not show where to place the blame. The central idea behind verificationism is linking some sort of meaningfulness with (in principle) confirmation, at least for synthetic sentences. The actual formulations embodied not only such a link but various particular accounts of confirmation as well. Now confirmation is a complex matter, and it is unlikely that we shall have the final satisfactory account any time soon. This should not persuade us, however, that there are no satisfactory accounts of confirmation any more than our current lack of the final physics should convince us that there are no physical facts of the matter. So even a string of failures in formulating verificationist principles may mean no more than that the embedded accounts of confirmation are too simple but the link between meaningfulness and confirmation is nevertheless sound.

Even if we set this caution aside, there may be parts of persistently employed strategy that lead to persistent failure. These parts and failures might be avoidable. To see how this may be so we will compare what is perhaps the most famous formulation of the verificationist principle, in Ayer 1936, with a later one, in Carnap 1956. A.J. Ayer had visited the Vienna Circle from late 1932 on into 1933, returning home for the summer term. While in Vienna he attended meetings of the Circle and overlapped for five weeks with Quine. Neither Carnap nor Neurath were there at the time, so the left wing of the Circle was not fully represented. When Ayer returned to England he published Language, Truth, and Logic in 1936. Even immediately it was widely discussed, and after the war sales were spectacular. For many in England this book was the epitome of logical positivism and remains so.

Ayer was careful to restrict his criterion of meaningfulness to synthetic sentences and to demand only in principle confirmation. And the formulation seems very natural: Confirmation is a feature that applies to sentences (or groups of them) and not to sub-sentential parts, and for an empiricist the content that a synthetic sentence has would be empirical content. So it would seem that to have empirical content a sentence, A, should either directly imply some observational sentence or add to the observational content of some other sentence, B. That is, the conjunction of A and B should imply some observational sentence not implied by B alone. This formulation may be natural, but it is also fatally flawed. It would declare any sentence whatsoever as meaningful: For any sentence A and any observation sentence O, A would be meaningful because it could be conjoined to A ⊃ O. The latter would not in general imply O, but the conjunction would.

Other more elaborate formulations followed along the same lines, and other more elaborate counterexamples appeared just as fast. Hempel reviewed the situation twice within about a year (Hempel 1950 and 1951). First he concluded that it was a lively and promising line of research and later concluded that it was not promising at all. In retrospect it may be that the problems arise because we were led by the fact that confirmation is a feature that applies to whole sentences into thinking that the level at which to apply the criterion was the level of whole sentences. Now a sentence with meaningless parts might well pass some test especially if the test involves its being combined with other sentences that can have meaningless parts. So one way to avoid this difficulty is to try to find a formulation that applies the test at the level of basic expressions, those that can be thought of as "not having parts" so to speak.

This is the strategy that Carnap employed in "The Methodological Character of Theoretical Concepts" (1956). Observational terms are assumed to have empirical content. Logical terms are assumed to have none. And all defined terms are assumed to be replaced by their definitions. If for some basic, non-logical term there is a sentence that contains that term as its only non-logical element and if that sentence implies some observation sentence, then that sentence has empirical content and so does its only non-logical term. If we have established that each term from some set, K, is empirically significant we might test still further terms by seeing whether those further terms can add to what is sayable with terms from K. Carnap's actual definition is quite complicated, but it does seem to avoid the difficulties of its predecessors. It also allows an account of why those predecessors ran into trouble, viz., that they applied at the level of whole sentences (naturally enough) rather than to elementary terms.

Not long after Carnap's definition was published David Kaplan devised what seemed to be counterexamples. They became fairly well known, but they were not published until 1975. Shortly thereafter it was shown (Creath 1976) that either Carnap's definition is not open to the counterexamples as presented or it can be patched in a very natural way so that it avoids them. This does not show that there are no counterexamples or that there are no other features of the definition to which one might object. But it does show that the situation is not as dire as Hempel supposed in 1951.

We need to address another issue in considering verificationism, the persistent criticism that it is self-undercutting. The argument for this claim goes like this: The principle claims that every meaningful sentence is either analytic or verifiable. Well, the principle itself is surely not analytic; we understand the meanings of the words in it perfectly well because we understand our own language. And we still do not think it true, so it cannot be true in virtue of meaning. And it is not verifiable either (whatever we choose 'verifiable' to mean).

This sounds more compelling than it is. Ayer understood the principle to be a definition, defining a technical term, 'meaning'. If so, then the sentence expressing the principle would indeed be analytic. So the self-undercutting charge strictly fails. But so construed and with nothing else said about it the principle would not have the same punch as before. Why should a metaphysician care whether his or her utterances lack some technical feature?

Carnap explicitly takes up the "self-undercutting" charge against verifiability in Philosophy and Logical Syntax (1935), and he is not interested in introducing a new technical term, 'meaning', so or in denying this new technical property to unverifiable sentences. Carnap is careful to distinguish the language for which the verifiability principle is given from the meta-language in which we talk about that language. This meta-language would be the language in which the principle would be expressed. This may seem to offer another strategy against the "self-undercutting" charge because the principle applies to a different language than that in which it is expressed. This is not Carnap's strategy. Carnap fully understands that if the general verificationist strategy is followed, there will also be a verificationist principle expressed in the meta-meta-language governing the meta-language.

Carnap's real defense of the principle was achieved by changing the nature of the discussion. By 1935 Carnap had introduced an important new element into his philosophy called the Principle of Tolerance. Tolerance is a radical idea. There is no uniquely correct logic (1934/1937 xiv-xv). Empiricism is a convention (Carnap, 1936/1937 33). Perhaps more precisely each of the various versions of empiricism (including some sort of verificationism) is best understood as a proposal for structuring the language of science. Before tolerance, both empiricism and verificationism are announced as if they are simply correct. Correspondingly, what Carnap called metaphysics is then treated as though it is, as a matter of brute fact, unintelligible. But what is announced thus dogmatically can be rejected equally dogmatically. Once tolerance is in place, alternative philosophic positions, including metaphysical ones, are construed as alternative proposals for structuring the language of science.

None of them is the uniquely correct one, and no theoretical argument or evidence can show that it is. Nor can theoretical arguments or evidence show that it is false. Neither proposals nor languages are the sort of thing to be true or false. Instead, proposals call for practical decisions and practical arguments rather than for theoretical reasons or evidence. Carnap believes that there are indeed very good practical reasons for adopting the proposal of verificationism, for choosing a language of science in which all substantive (synthetic) claims can, at least in principle, be brought before the court of public experience. The reason is that if we do not require this, the result is "wearisome controversies" that there is no hope of resolving. That, he thinks, is the sad history of attempts to get beyond science, and it is just too painful.

If the proposals constituting some version of verificationism are adopted, then in the language thus constituted it will be analytically true that there are no synthetic sentences that are both unverifiable and meaningful. The notion of meaning here is not some new technical invention. Rather, 'meaning' is used in something like the ordinary sense. No grammatically well-formed sentence of this new language violates the verifiability principle. And the principle itself is completely safe.

Thought of in this way the verifiability principle does not describe natural language, it is not intended to. It is intended to reform language to make it a more useful tool for the purposes of science. Carnap is under no illusion that natural languages are free from metaphysics. Nor is he under the illusion that defenders of the sort of metaphysics he targets will readily step up to the challenge of presenting precise rules of grammar and inference.

There is one other change that tolerance brings to Carnap's own vocabulary. Before tolerance, verificationism is stated in such a way that violations would count only as unintelligible gibberish. With tolerance in place, Carnap is prepared to imagine non-empiricist languages, though of course he thinks they are very unwise. So instead of saying that sentences in non-empiricist languages are meaningless, he says that they are empirically meaningless. And that has a very different flavor. There is no weakening of his defense of empiricism, but it is put on a somewhat different footing.

Logic, mathematics, and mathematical geometry had traditionally seemed to be confirmationally "different". Indeed it is hard to indicate any conditions under which any parts of them would be disconfirmed. Leibniz had called them truths of reason. Hume said that they represented relations of ideas. Kant had held that the truths in these areas were a priori. Mathematics and geometry were not analytic for Kant, but logic was. Kant had two criteria of analyticity, apparently thinking them equivalent. First, in subject-predicate sentences, an analytic sentence is one in which the concept of the predicate is contained in that of the subject. Second, an analytic sentence is one whose denial is self-contradictory. This seems to include not only the sentences whose surface logical form would be of the required sort but also those that can be got from such logical truths by making substitutions that were conceptually equivalent. The more modern rough analog of this is to say that the analytic sentences are those that are true in virtue of logic and definition.

Frege certainly developed logic beyond that which was available to Kant, but he did not think of himself as changing the analytic status of it. Logic is after all the only avenue we have for giving meaning to the notion of (logical) contradiction. Of course Frege also attempted to reduce mathematics to logic (including both first and second order logic), and insofar as that reduction was successful it would have implied that mathematics was analytic as well. Frege said little of geometry, but for him it was synthetic a priori.

Carnap had not only studied with Frege, but like many of the logical empiricists he had started out as a neo-Kantian as well. So especially in view of Russell's relatively more successful attempt at reducing mathematics to logic, it was perhaps natural that Carnap would consider both mathematics and logic as analytic. Geometry could be handled in several different ways that we will not discuss here. But from fairly early on there was widespread agreement among the logical empiricists that there was no synthetic a priori, and that logic and mathematics and perhaps much else that seemed impervious to empirical disconfirmation should be thought of as analytic. The point of drawing the analytic-synthetic distinction, then, is not to divide the body of scientific truths or to divide philosophy from science, but to show how to integrate them into a natural scientific whole. Along the way the distinction clarifies which inferences are to be taken as legitimate and which are not. If, as Carnap and Neurath were, you are impressed by Duhemian arguments to the effect that generally claims must be combined in order to test them, the analytic-synthetic distinction allows you to clarify which combinations of claims are testable.

If analytic, a sentence is true in virtue of the conventions of language. In saying that, however, we must pause to confront two widespread confusions. First, Quine alleges (1963, 385f) that the notion of analyticity was developed and purports to explain for both Kant and Carnap how certainty is possible. In fact certainty has little or nothing to do with analyticity for the leading logical empiricists. In saying that such claims are based on convention they were explicitly calling attention to the revisability of conventions and the sentences that owed their meanings to those conventions. Second, nowadays any talk of convention is likely to prompt the response: "But that cannot be! No proposition can be made true by our conventions or decisions." Unless it is a proposition about conventions, this second sentence of the response is true. But it is also completely irrelevant. Analyticity applies to sentences rather than propositions. Our conventions and decisions can and do affect what expressions mean and thus what sentences mean. Once the meaning is specified, it may well be that any sentence that has this meaning would be true even if, for example, the point masses of the universe were arranged quite otherwise than they in fact are. These are the analytic sentences. No claim is being made that meaning causes anything or that convention makes anything true. The "making" image here is out of place. It is just that in these cases the truth value of the sentence may well be functionally dependent on meaning alone. If it is, then in this special sense, truth value depends on meaning, and that depends on convention. Other sentences whose meanings are specified might well be true or false depending on how things in the external world, so to speak, are arranged. In this other category of sentence the truth value is not functionally dependent on meaning alone. They are the synthetic sentences. Now this puts matters extremely informally. But at least the nature of the confusions over certainty and convention should be clear.

In the Logical Syntax of Language (1934/1937) Carnap defined 'analytic' in a new way in order to circumvent Gödel's incompleteness results. The method used was to distinguish between a derivation relation (the relation that holds between some premises and what can be got from them in a finite number of steps) and a consequence relation. The latter is an essentially semantic relation that holds between some premises and some other claim such that on all valuations under which the premises are all true, so is that other claim. This definition bears a stronger resemblance to Tarski's account in (Tarski 1936b/1956). In any case, Carnap is able to show that for any sentence of pure mathematics either it or its negation is a consequence of the null set of premises. This leaves Gödel's results completely intact as they concerned what is provable, that is, derivable from the null set of premises or from any one consistent axiomatization of mathematical truths.

As noted above, another innovation of Logical Syntax is the Principle of Tolerance. While it reflects a long-standing attitude on Carnap's part, the principle itself is new. Later Carnap was to say that the Principle of Tolerance was "perhaps better called the principle of conventionality" (Carnap 1942, 247), that is, the conventionality of linguistic forms. Tolerance stabilizes the verification principle as well as Carnap's empiricism, and it reinforces the idea that the analytic-synthetic distinction is always relative to a particular language (Creath 2009).

In the late 1950s Carnap began exploring (1963a and 1966) how a notion of analyticity might be developed for novel theoretical terms where the theories in which those terms are embedded are presented by means of a system of postulates. It is not clear that the account he developed was intended to supersede his earlier account. In any case Carnap's suggestion is as follows (where for convenience terms are used autonymously): Let T be the totality of theoretical postulates, and C be the totality of mixed sentences (the sentences of the theory containing both antecedent and novel terms). Also let R( TC) be the Ramsey sentence for TC, that is, the result of replacing each of the non-observational terms in TC with predicate variables and closing that open sentence with corresponding existential quantifiers. R( TC) ⊃ TC can, Carnap says, be thought of as the analytic sentence for the theory, that is, a sentence that gives to the theoretical terms of TC their meaning. Over the last decade, this idea of Carnap's has provoked considerable discussion that has not yet been resolved. Whatever worries there may be concerning this part of Carnap's view, they are distinct from the more famous concerns raised by Quine.

Quine began having doubts about analyticity about 1940, though he seems not to have been firmly committed against it until later. In any case his doubts were not published until 1951 in his famous paper "Two Dogmas of Empiricism". Quine's readers have understood his arguments in many different ways. The most general form of his complaint is that 'analytic' so far lacks the appropriate tie to observational criteria that Carnap's own account of theoretical terms in empirical science would demand. More specifically, where there has been an attempt at such a general criterion it has resulted in either a "drastic failure as tended to admit all or no sentences as analytic, or there has been a circularity" (Quine 1963, 404) of a kind that defines 'analytic' in terms that themselves lack the appropriate empirical criteria and so can be accounted for only by appeal to analyticity itself.

This complaint falls far short, as Quine well understood, of a proof that Carnap's appeal to analyticity was doomed. First, it relies on the demand that theoretical terms must satisfy some empirical significance criterion. Many people at the time, including some who followed Quine in rejecting analyticity, also rejected any general empirical significance demand for theoretical terms. Second, one could accept the demand for theoretical terms in physics or chemistry and deny, as Carnap did, that the demand applied to his own work. This is because Carnap saw himself as working in an area within metamathematics rather than in empirical linguistics. Third, Quine did not pretend to have considered all of the possibilities for the explication of analyticity. And so it may be possible to meet Quine's demands to the extent that they are legitimate. Fourth and finally, Quine seems in Roots of Reference (1974) to have provided an explication for 'analytic' that meets his demand for empirical/behavioral criteria without inducing either the drastic failure or the circularity envisioned above.

There is another somewhat independent thrust to Quine's campaign against analyticity. In the last section of "Two Dogmas" (1951) Quine gives an extremely attractive sketch for an alternative epistemology that apparently makes no appeal to analyticity. Insofar as that sketch can be filled out successfully it would constitute a dispensability argument against analyticity. Whether it can be thus filled out, however, remains to be seen.

Quine's other provocative theses, including especially his claims about the indeterminacy of translation, while relevant to his assessment of analyticity, would carry us too far afield to consider their ramifications here. As with most topics in philosophy there is no uniform agreement in the literature as to whether the notion of analyticity is or can be made sufficiently clear for use in scientific philosophy. Nor is there such agreement that Quine's epistemological sketch can be satisfactorily filled out. Both approaches have their defenders and their detractors. But between them they seem to be the most promising avenues for integrating the logic-mathematical part of science with the more straightforwardly empirical parts. Since Carnap is and Quine can be argued to be within the logical empiricist tradition, this progress toward such unification can be counted as part of the legacy of the movement.

The commitment of some of the logical empiricists to the unity of science has been in recent years often discussed but less often understood. One hears in conversation that it was a sort of rearguard action designed to preserve as much as possible of a phenomenalist version of ontological reduction. One reads in print that it can be refuted by the obvious fact that the various sciences have quite distinct theoretical vocabularies (Suppes 1978). Both reactions are misplaced.

It was the left wing of the Vienna Circle, and above all Otto Neurath, that championed the unity of science. They also promoted physicalism, anti-foundationalism, and a generally naturalistic viewpoint. A main focus of their activities from the late 30s was The Encyclopedia of Unified Science edited by Neurath in Europe and Carnap and Charles Morris in Chicago. A great many philosophers of many different persuasions participated in that project. The project may have been unified science, but they did not have a completely unified view of what that project was. Here we will discuss the Neurath and Carnap versions of it to see what their central concerns were.

Neurath seems to have had two primary motivations to advance under the banner of the unity of science. First, he was concerned that there be no a priori methodological cleavage between the natural and the social sciences. On the social scientific side he was concerned that these sciences not condone some private, mysterious mode of insight (empathy) whose results could not be checked against more ordinary public observation. Such a methodology would be a harbor for metaphysics. On the natural scientific side, he was concerned to point out that, for Duhemian and other reasons, the situation is much messier than is sometimes supposed, and so invidious comparisons by natural scientists at the expense of social science were unwarranted.

Second, because Neurath was socially and politically engaged he was concerned that the various sciences be connected in such a way that they could be used together to solve complex human and social problems. For this, considerable overlap of vocabulary was needed, and this he called a "universal jargon".

In recent years it is sometimes claimed that Neurath meant by the unity of science what some contemporary philosophers have defended as the disunity of science. One cannot rule this claim out a priori. But the often substantial differences among the current defenses of disunity make evaluating this claim difficult. It is fair to say, however, that Neurath was suspicious of grand hypotheses, familiar since the 19 th century to derive all of chemistry, biology, psychology, and the social sciences (in that order) from a few basic principles of physics. It is unclear whether this stems from a general opposition to system building, since he was eager to develop inferential connections among the various sciences. Perhaps this is better expressed as an opposition to speculative system building and to the idea that there is only one way of systematizing our science than to systematicity as such.

Carnap's position on unity is different from Neurath's, but they overlap. Carnap distinguished the unity of the language of science from the unity of the laws of science. He wanted to defend the former and to say what would be required for the latter. As far as the unity of the language of science, Carnap did in the Aufbau try to initiate a program for defining all of scientific concepts on the basis of a very small number of basic concepts, perhaps only one basic concept. That does afford a certain conceptual economy, but it is now generally held by Carnap scholars (see especially Friedman 1987 and Richardson 1998) that ontological reduction and reduction to a phenomenalist basis was far from his motive. Carnap explicitly acknowledged that another system of definitions, one with a physicalist basis, might also be possible. Instead of ontological economy and a phenomenal basis, Carnap's project seems to have been the more Kantian one of indicating how semantic intersubjectivity is possible: How can it be that, even though I have only my own experiences and you have only yours, we can nevertheless share a common body of concepts? The answer is given in terms of shared inferential structure and identifying any given concept with a unique place within that shared overall structure. This is a highly holistic conception of concepts and it depends on thinking of the body of scientific commitments as a whole, as a unity.

The Aufbau was largely drafted before Carnap joined the Vienna Circle. Once there and under some influence from Neurath, Carnap campaigned more insistently for physicalism and for the unity of science. They seemed often to be two sides of the same coin. From 1933 onward there was a succession of monograph series with 'Unified Science' in the title. Until his death in 1945, Neurath was in each case the main editor and Carnap either the associate editor or one of the associate editors. The International Encyclopedia of Unified Science, begun in 1938 is undoubtedly the most famous of these. Carnap's own essay on this topic "Logical Foundations of the Unity of Science" (1938) was printed as part of the very first number in the encyclopedia.

The dates here are relevant because by the time of this essay Carnap had already decided (Carnap 1936-37) that theoretical terms could not in general be given explicit definitions in the observation language even though the observation reports were already in a physicalist vocabulary. The partially defined theoretical terms could not be eliminated. This seems to have caused Carnap no consternation at all, and it never seems to have occurred to him that there was any conflict whatever between this result and the unity of science. This is because by this point the elimination of concepts was not the point of the exercise; their inferential and evidential integration was.

In the 1936-37 article, "Testability and Meaning" Carnap called the partial definitions themselves "reduction sentences" and the system of definitions of theoretical terms, both partial and complete, as a reduction of the theoretical terms to the observational basis. Plainly he means by the word 'reduction' something other than what we currently mean, not that there is anything univocal about current uses of the word. By 'reduction' of vocabulary A to vocabulary B Carnap means the specification of the inferential relations that would allow us to say what sentences or combinations of sentences in A would count as evidence for sentences in B.

This is also the key to what Carnap means by the unity of the language of science. The language of science is unified, no matter how different and exotic its various technical vocabularies may be, when each of its terms is reduced to (can be tested in) a common public observation vocabulary. The call for the unity of the language of science, then, amounts to no more than the demand that the various claims of the separate sciences should be publicly testable in a common observation language. Controversies will of course arise as to what the observational vocabulary should be and what are the acceptable forms of linkage. Carnap's demand for unity in the language of science abstracts from those controversies to concentrate on the goal of public testability. That does not seem to be an unreasonable demand.

The unity of the language of science so far discussed is quite a different issue from the unity of the laws of science. And Carnap's attitudes toward them are quite different. The latter issue concerns the extent to which the laws of one special science can be inferred from those of another. Carnap tries to articulate what would be involved in such a unification, but he nowhere says that such a unity is either possible or mandatory. Finding any sort of inferential connections among sets of laws would be welcome of course. But the question of how much unity there is, if any, among the various sciences is an empirical question that philosophers are ill equipped to answer. Philosophers should not make pronouncements, especially in advance of having putative laws in hand, either that scientific laws are unified or that they are not. A certain modest deference to the empirical facts that philosophers generally do not have, again, does not seem unreasonable.

Taking unity as a working hypothesis, as some philosophers have done, amounts to looking for inferential and nomological connections among various sets of laws, but not to the assertion that such connection will be found. Even if we accept the idea that such connections would be welcome if found, the question of whether one should spend significant effort in looking for them is not thereby answered. That would be a difficult and delicate practical question of how to apportion one's research effort that for the purposes of this essay we must set aside.

There are two broad approaches to probability represented in logical empiricism. One of these, the so-called frequentist approach, has an extensive 19 th century history and was further developed from about 1920 onward by Richard von Mises and Hans Reichenbach. The other is the epistemic approach to probability. This goes back at least to Laplace at the end of the 18 th century. In the 20 th century Rudolf Carnap, who explored what he called logical probability, and Frank Ramsey and Richard Jeffrey whose accounts can be distinguished from Carnap's and are often called subjective probability, all defended the epistemic approach. While Ramsey visited the Vienna Circle he was not much influenced by its members on these matters. By contrast, Jeffrey studied and later collaborated with Carnap but also made significant contributions of his own.

It is natural to begin thinking about probabilities with a simple mathematical account that takes as its point of departure various games of chance involving cards, dice, or coins. Bettors have long noted that some outcomes are much more likely than others. In this context it is convenient to take the probability of a kind of outcome to be the ratio of such outcomes to all possible outcomes. Usually for reasons of symmetry in the physical set up, the possible outcomes are assumed to be equally likely. Where that assumption happens to be true or nearly so the empirical results of, say, a great many throws of a pair of dice tends to be close to what the simple mathematical account would suggest. Conversely, where the outcomes deviate from the expected ratios, bettors begin to suspect that the dice, coins, and cards (or the manipulations of them) are not all that they seem. The suspicion is that the outcomes are not equally likely and that the simple mathematical account does not apply.

These facts suggest both two limitations of the simple account and the beginnings of a way around them. The first limitation is that the account applies only where the outcomes can be partitioned into alternatives that are equally likely. This is not the case when dice are loaded or in such real world cases as radioactive decay or weather forecasting. A second limitation is that the account, in describing the possible outcomes as equally likely, implicitly appeals to the very probability notion for which clarification was sought. The realization that we can sometimes discover the falsehood of the assumption of equal likelihood and make a much more reasonable estimate of probability by making a large number of trials is very suggestive. And from his dissertation onward Reichenbach worked out a variety of imagined physical models that could guide ones thinking about probability in useful ways. The result is what is often called the frequency theory of probability (or sometimes the statistical frequency theory or the limit frequency theory).

Even a perfectly fair coin in an odd number of flips will never result in exactly the same number of heads and of tails. When the coin is fair and the number of flips is even, an outcome perfectly balanced between heads and tails is not guaranteed either. So, even on the assumption that the probability of the coin's coming up heads does not change over the course of the trials, we need to be cautious. A larger number of flips might make us more confident that the ratio we have seen is close to the "actual" value, but there is no finite number of flips after which we can say that the observed ratio is exactly right. We will never make an infinite number of flips either, and in actual cases a large finite number of flips might so erode the coin as to bias the coin and discredit the result. Notwithstanding these limitations on an actual series of trials one can imagine an infinite series of trials and define a notion of probability with respect to it. This raises its own difficulty, namely that ratios are not defined for infinite collections. They would be defined, however, for any finite initial segment of such an infinite series, thus giving a sequence of ratios. If this sequence of ratios settles down on a limit, the probability of the coin showing a head given that it has been flipped can be defined as the limit of the ratio of heads to total flips as the number of flips goes to infinity.

While probability thus defined has a somewhat counterfactual character, that is not an obvious defect. Moreover, this notion of probability applies perfectly well to biased coins and loaded dice, as well as to radioactive decay. On the surface at least it also seem to avoid using the notion of probability in its own definition, and in these respects it seems to be an important improvement over the simple mathematical model with which we began. The definition locates the probability objectively "out in nature" so to speak, and this comports well with Reichenbach's scientific realism.

A problem that remained troublesome concerns the fact that one often wants to assign probabilities to particular events, events that in the nature of things cannot be repeated in all their particularity. Thus it is unclear how a frequency theory of probability is to be applied to such individual cases. This is often called the problem of the single case. It is a little difficult to assess how serious this is, because in actual practice we often have no difficulty in making probability assignments to single cases. Suppose we are interested in the probability of rain tomorrow. Tomorrow will never be repeated, and we want to estimate the probability now. What we do is to look back through the records to find days relevantly like today and determine in what fraction of those cases those days were followed by rainy days and use that as our estimate. Even if we are comfortable with this practice, however, it is another matter to say why this should give us a reasonable estimate of the value of the limit involved in a logically impossible infinite sequence. This problem of the single case was much discussed, and Wesley Salmon made progress in dealing with it. Indeed, Salmon's account of statistical explanation can be viewed as a substantial mitigation of the problem of the single case (W. Salmon 1970).

There are residual difficulties in making estimates of the probabilities on the basis of finite evidence. The problem is that even when we are assured that the sequence of ratios has a limit, we have no a priori grounds for saying how close the current ratio is to that limit. We can boldly estimate the limit by means of the so-called "straight rule". This just takes the most recent ratio as the desired estimate. This is a good practical solution where the number of trials is already high, but this does not really say why the estimate should be good, how good it is supposed to be, or how many trials would be high enough. In addition, the straight rule can yield counterintuitive results where the number of trials is small.

Though there are these issues outstanding, frequency theories define a concept of probability indispensable for quantum theories and for a wide variety of other applications in the natural and social sciences. It was not the only concept of probability to be developed by the logical empiricist tradition. The primary other such concept was the epistemic conception of probability. We will begin with Carnap and then move to those who developed a subjectivist account.

Carnap is addressing a different issue than was addressed by von Mises and Reichenbach. Instead of focusing on physical phenomena and ratios within them, Carnap focuses on arguments and takes as his point of departure the widespread conviction that some arguments are stronger, in varying degrees, than others, even for the same conclusion. Similarly some bodies of evidence can give us more reason to believe a given conclusion than would another body of evidence. Carnap sets as his task the development of a quantitative concept of probability that will clarify and explicate these widespread convictions. Such a quantitative concept would be an extraordinarily useful tool, and it would be a useful successor to our ordinary, somewhat scattered notions of confirmation and induction.

Carnap approaches the problem by first considering extremely limited artificial languages and trying to find a confirmation function that will work for that. If he succeeds he would then try to develop an account that would work for a broader and richer range of languages. In this his approach is like that of a physicist developing a physical theory for the highly artificial situation of a billiard table or air track and then broadening the theory to deal with a wider range of cases. In Carnap's case, however, it is somewhat unclear what success would be in an artificial language very much unlike our own. In any case, Carnap is not trying to describe our linguistic habits but to clarify or even to replace them with something more useful.

As early as Logical Syntax (Carnap 1934/1937, 244/316-17) Carnap had suggested that Wittgenstein's remarks in the Tractatus about ranges ( Tractatus, 4.463) might be a starting point for thinking about probability. By 1945 Carnap also distinguished the two approaches described here, insisting that they were not competitors but were attempting to explicate two different concepts of probability. One need not choose one as the only concept; both concepts were useful. Reichenbach, by contrast, never conceded that both concepts were needed and insisted that his frequency notion could serve all epistemic purposes for which any notion of probability is needed.

Carnap's general strategy was first to identify a broad class of confirmation functions, as subjectivists Ramsay and de Finetti were also to do, and then find a natural way of limiting this class still further. The confirmation functions have to meet some basic mathematical conditions. The axioms that state these conditions partially define a function, and this function can be interpreted in a number of ways. Carnap himself lists three in Carnap 1950. In (1955), John Kemeny (one of Carnap's collaborators and later a co-inventor of BASIC programming language and still later president of Dartmouth College) gave an argument that persuaded Carnap that it was more fruitful to think of the function as indicating fair betting quotients rather than evidential support. This took Carnap even closer in conception to the work of such subjectivists as Ramsey and de Finetti. Indeed, the discussion of fair betting quotients, and related issues of Dutch book arguments had been initiated by de Finetti.

In Logical Foundations of Probability (1950) Carnap had discussed Bayes' theorem and promised to expand the discussion in a second volume. Carnap's interest in Baysianism grew, but that second volume never materialized, quite possibly because rapid development of the field was still under way at the time of Carnap's death. As his work proceeded Carnap tended to explain probabilities by reference to events and propositions rather than speak overtly about sentences. A similar change appears in the rest of Carnap's work as well. It is not clear, however, whether this amounts to a major change of view or a change in what he sees as the most felicitous mode of expression. As the years progressed Carnap tended to see the remaining differences between himself and his subjectivist co-workers as chiefly differences in emphasis. In any case the subjectivist tradition is now dominant in philosophical discussions of probability (Zabell 2007, 293). Richard Jeffrey whose own work arose out of logical empiricism carried on that tradition for 35 years after Carnap's death. Jeffrey himself made major contributions including a principle for updating ones beliefs when the evidence one learns is not certain. The world knows this principle as "Jeffrey conditionalization"; he called it simply "probability kinematics".

Popper's view of probability, his propensity theory, differs from either of the two approaches discussed above. Unlike the epistemic approach of Carnap and others, Popper was not trying to clarify inductive relations because he did not believe that there are inductive inferences. Theories can be corroborated by their passing severe tests, but they are not thereby inductively confirmed or made more probable. For a discussion of whether there are any significant similarities between Popper's idea of corroboration and the ideas of inductive confirmation that he rejects, see (Salmon 1967, 1968).

Propensities are thought of as tendencies of a physical event or state to produce another event or state. Because propensities are to be features of external events and not, to use Hume's phrase, relations of ideas, the propensity theory and the statistical-frequency theory are sometimes grouped together as accounts of chance. Popper has specifically applied propensities to single non-repeatable events (1957), and that suggests that the concept of propensity does not involve any essential reference to long sequences of events. Popper has also taken propensities as producing outcomes with a certain limit frequency (1959). This does suggest a rather closer tie to the statistical frequency approach. Later philosophers developed both sorts of propensity theories, single-case theories and long-run theories. (Gillies 2000) And like other approaches to probability and induction all these views remain controversial. While we will not discuss the relative merits of the various approaches further, those who are interested in Popper's views in this area should look at the many papers on probability, induction, confirmation, and corroboration, and Popper's replies, in The Philosophy of Karl Popper (Schilpp 1974).

In 1967 John Passmore reported that: "Logical positivism, then, is dead, or as dead as a philosophical movement ever becomes." (1967, 57) Earlier in the same article he had equated logical positivism with logical empiricism, so presumably that was dead too. At that time few would have disagreed with Passmore, even though Carnap was still alive and active. But in speaking of this movement Passmore was referring not to a movement but to specific doctrines, and his interpretation of them was much influenced by Ayer. Even so, Passmore conceded that the movement had left a legacy and that "the spirit which inspired the Vienna circle" persisted. It still does.

Part of the movement's legacy lies in contemporary philosophy of science. In the US nearly all philosophers of science can trace their academic lineages to Reichenbach. Most were either his students or students of his students and so on. His scientific realism inspired a generation of philosophers, even those clearly outside the movement. Even the reaction against various forms of realism that have appeared in recent decades have roots in the logical empiricist movement. Moreover, philosophers of science are expected to know a great deal of the science about which they philosophize and to be cautious in telling practicing scientists what concepts they may or may not use. In these respects and others contemporary philosophers promote a kind of naturalism, and by so doing they follow both the precept and the example of the logical empiricists.

There are other issues where the legacy of logical empiricism is still visible. Two different approaches to probability are still under discussion. One of them explores the objective chances of external events; this investigation follows in the tradition of the frequency theory of Reichenbach and von Mises. The second approach has an epistemic conception of probability as exemplified by Carnap. S.L. Zabell summarizes the current situation as follows:

But although the technical contributions of Carnap and his school remain of considerable interest today, Carnap's most lasting influence was more subtle but also more important: he largely shaped the way current philosophy views the nature and role of probability, in particular its widespread acceptance of the Bayesian paradigm (as, for example, in Earman, 1992; Howson and Urbach, 1993; and Jeffrey, 2004). (Zabell 2007, 294)

There is also a continuing concern for how the various sciences fit together. Some have scouted theoretical unification and others a more pluralistic model, just as the logical empiricists did. There was for a while a vogue for the disunity of science. Some even said that their conception of the disunity of science is just what Neurath meant by the unity of science. Parts of the discussion were intended as challenges to logical empiricism, but often the arguments used were pioneered by the logical empiricists themselves.

For the 30 years after Passmore's report metaphysics became ever more visible in philosophy. It was a diverse development, but in the self-conceptions of many of its most prominent practitioners there was no attempt to shun science or logic or to think that metaphysics had access to facts that were deeper than or beyond those that a proper science could reach. So the metaphysics that blossomed was not necessarily of the sort that Carnap and others combated. Most recently there are some in meta-ontology that want to reconsider and reconnect with Carnap's ontological caution.

Even in its heyday many philosophers who on either doctrinal or sociological grounds can be grouped with the logical empiricists did not see themselves that way. We should not expect philosophers today to identify with the movement either. Each generation finds its place by emphasizing its differences from what has gone before. But the spirit of the movement still has its adherents. There are many who value clarity and who want to understand the methodology of science, its structure, and its prospects. There are many who want to find a natural home within a broad conception of science for conceptual innovation, for logic and mathematics, and for their own study of methodology. And importantly there are those who see in science a prospect for intellectual and social reform and who see in their own study of science some hope for freeing us all from the merely habitual ways of thinking "by which we are now possessed" (Kuhn 1962, 1). These are the motives that define the movement called logical empiricism. As Twain might have said, the reports of its death are greatly exaggerated.

Cited Literature

Ayer, A.J., 1936, Language Truth, and Logic, London: Gollancz.

Carnap, R., 1928/1967, Der logische Aufbau der Welt, translated by R.A. George asThe Logical Structure of the World, Berkeley: University of California Press.

---, 1934/1937, Logische Syntax der Sprache, translated by A. Smeaton as The Logical Syntax of Language, London: Kegan Paul, Trench, Trubner & Co.

---, 1935, Philosophy and Logical Syntax, London: Kegan Paul, Trench, Trubner, & Co.

---, 1936-37, "Testability and Meaning", Philosophy of Science, 3: 419-71, 4: 1-40.

---, 1938, "Logical Foundations of the Unity of Science", International Encyclopedia of Unified Science (Volume 1, Number 1), Chicago: University of Chicago Press, 42-62.

---, 1942, Introduction to Semantics, Cambridge, MA: Harvard University Press.

---, 1950, Logical Foundations of Probability, Chicago: University of Chicago Press.

---, 1958 [2017], "Value Concepts", transcribed and translated by A. Carus, Synthese 194: 185-94. [Original manuscriptavailable online]

---, 1963a, "Carl G. Hempel on Scientific Theories", in The Philosophy of Rudolf Carnap, P.A. Schilpp (ed.), LaSalle, IL: Open Court, 958-66.

---, 1963b, "K.R. Popper on Probability and Induction", in The Philosophy of Rudolf Carnap, P.A. Schilpp (ed.), LaSalle, IL: Open Court, 995-998.

---, 1966, Philosophical Foundations of Physics, M. Gardner (ed.), New York: Basic Books.

Carus, A.W., 2007, Carnap and Twentieth-Century Thought, Cambridge: Cambridge University Press.

Creath, R., 1976, "On Kaplan on Carnap on Significance", Philosophical Studies, 30: 393-400.

---, 2009, "The Gentle Strength of Tolerance: The Logical Syntax of Language and Carnap's Philosophical Programme", inCarnap's Logical Syntax of Language, P. Wagner (ed.), Houndsmills, Basingstoke, UK: Palgrave Macmillan, 203-214.

Earman, J., 1992, Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory, Cambridge, MA: MIT Press.

Friedman, M., 1987, "Carnap's Aufbau Reconsidered",Noûs, 21: 521-45.

Gillies, D., 2000, "Varieties of Propensity", British Journal for the Philosophy of Science, 51: 807-835.

Gödel, K., 1995, "Is Mathematics Syntax of Language?" in K. Gödel, Collected Works (Volume 3), S. Fefferman, et al. (eds.), Oxford: Oxford University Press, 334-362.

Hempel, C.G., 1950, "Problems and Changes in the Empiricist Criterion of Meaning", Revue International de Philosophie, 11: 41-63.

---, 1951, "The Concept of Cognitive Significance: A Reconsideration", Proceedings of the American Academy of Arts and Sciences, 80: 61-77.

Howson, C. and Urbach, P., 1993, Scientific Reasoning: The Bayesian Approach, LaSalle, IL: Open Court.

---, 2004, Subjective Probability: The Real Thing, Cambridge: Cambridge University Press.

Kaplan, D., 1975, "Significance and Analyticity: A Comment on Some Recent Proposals of Carnap", in Rudolf Carnap, Logical Empiricist, J. Hintikka (ed.), Dordrecht, Boston: Reidel, 87-94.

Kemeny, J., 1955, "Fair Bets and Inductive Probabilities", Journal of Symbolic Logic, 20: 263-73.

Kuhn, T., 1962, The Structure of Scientific Revolutions,International Encyclopedia of Unified Science (Volume II, Number 2), Chicago: University of Chicago Press.

Passmore, J., 1967, "Logical Positivism", The Encyclopedia of Philosophy (Volume 5), P. Edwards (ed.), New York: Macmillan, 52-57.

Popper, K., 1935/1959, Logik der Forschung, translated by the author asThe Logic of Scientific Discovery, New York: Basic Books.

---, 1957, "The Propensity Interpretation of the Calculus of Probability", S. Körner (ed.), The Colston Papers, 9: 65-70.

---, 1959, "The Propensity Interpretation of Probability", British Journal for the Philosophy of Science, 10: 25-42.

Quine, W.V., 1951, "Two Dogmas of Empiricism", Philosophical Review, 60: 20-43.

---, 1963, "Carnap and Logical Truth", in The Philosophy of Rudolf Carnap, P. Schilpp (ed.), LaSalle, IL: Open Court, 385-406.

---, 1974, The Roots of Reference, LaSalle, IL: Open Court.

Reichenbach, H., 1916/2008, Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit, edited and translated by F. Eberhardt and C. Glymour asThe Concept of Probability in the Mathematical Representation of Reality, LaSalle, IL: Open Court.

---, 1938, Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge, Chicago: University of Chicago Press.

Richardson, A., 1998, Carnap's Construction of the World: The Aufbau and the Emergence of Logical Empiricism, Cambridge: Cambridge University Press.

Russell, B., 1914, Our Knowledge of the External World as a Field for Scientific Method in Philosophy, LaSalle, IL: Open Court.

Salmon, W., 1967, The Foundations of Scientific Inference, Pittsburgh: University of Pittsburgh Press.

---, 1968, "The Justification of Inductive Rules of Inference", in The Problem of Inductive Logic, I. Lakatos (ed.), Amsterdam: North-Holland, 24-43.

---, 1970, ""Statistical Explanation", in Nature and Function of Scientific Theories, R. Colodny (ed.), Pittsburgh: University of Pittsburgh Press, 173-231.

Schilpp, P. (ed.), 1974, The Philosophy of Karl Popper, LaSalle, IL: Open Court.

Suppes, P., 1978, "The Plurality of Science", in PSA 1978: Proceedings of the 1978 Biennial Meeting of the Philosophy of Science Association (Volume 2), P. Asquith and I. Hacking (eds.), East Lansing, MI: Philosophy of Science Association, 3-16.

Tarski, A., 1936a/1956, "Der Wahrheitsbegriff in den formalisierten Sprachen", translated by J.H. Woodger as "The Concept of Truth in Formalized Languages" in Logic, Semantics, Metamathematics, by A. Tarski, Oxford: Clarendon Press, 152-278.

---, 1936b/1956, "Über den Begriff den logischen Folgerung", translated by J.H. Woodger as "On the Concept of Logical Consequence", in Logic, Semantics, Metamathematics, by A. Tarski, Oxford: Clarendon Press, 409-20.

Uebel, T., 2012, "Carnap, Philosophy, and 'Politics in its Broadest Sense'", in Carnap and the Legacy of Logical Empiricism, R. Creath (ed.), Vienna: Springer, 133-145.

---, 2013, "Logical Positivism - Logical Empiricism: What's in a Name?", Prespectives of Science, 21: 58-99.

Waismann, F., 1967/1979, Wittgenstein und der Wiener Kreis, translated by J. Schulte and B. McGinnis asWittgenstein and the Vienna Circle, Oxford: Basil Blackwell.

Wittgenstein, L., 1921/1922, Logische-Philosophische Abhandlung, translated by C.K. Ogden as Tractatus Logico-Philosophicus, London: Routledge & Kegan Paul.

Zabell, S. L., 2007, "Carnap on Probability and Induction", in The Cambridge Companion to Carnap, M. Friedman and R. Creath (eds.), Cambridge: Cambridge University Press, 273-294.

Selected Secondary Literature

Awodey, S. and A. W. Carus, 2004, "How Carnap Could Have Replied to Gödel", in S. Awodey and C. Klein (eds.), Carnap Brought Home: The View From Jena, LaSalle, IL: Open Court, 203-223.

Blatti, S. and S. Lapointe (eds.), 2016, Ontology After Carnap, Oxford: Oxford University Press.

Cartwright, N. , J. Cat, L. Fleck, and T. Übel, 1996, Otto Neurath: Philosophy Between Science and Politics, Cambridge: Cambridge University Press.

Carus, A.W., 2007, Carnap and Twentieth-Century Thought, Cambridge: Cambridge University Press.

Friedman, M., 1987, "Carnap's Aufbau Reconsidered",Noûs, 21: 521-45.

---, 1999, Reconsidering Logical Positivism, Cambridge: Cambridge University Press.

---, 2000, A Parting of the Ways: Carnap, Cassirer, and Heidegger, LaSalle, IL: Open Court.

Friedman, M. and R. Creath (eds.), 2007, The Cambridge Companion to Carnap, Cambridge: Cambridge University Press.

Frost-Arnold, G., 2013, Carnap, Tarski, and Quine at Harvard: Conversations of Logic, Mathematics, and Science, Chicago: Open Court.

Hintikka, J. (ed.), 1962, Logic and Language: Studies Dedicated to Professor Rudolf Carnap on the Occasion of His Seventieth Birthday, Dordrecht: Reidel.

--- (ed.), 1975, Rudolf Carnap, Logical Empiricist: Materials and Perspectives, Dordrecht: Reidel.

Howson, C., 1973, "Must the Logical Probability of Laws be Zero?" British Journal for Philosophy of Science, 24: 153-163.

Jeffrey, R., 1975, "Probability and Falsification: Critique of the Popper Program", Synthese, 30: 95-117.

---, 2004, Subjective Probability: The Real Thing, Cambridge: Cambridge University Press.

Mancosu, P., "Harvard 1940-41: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science", History and Philosophy of Logic, 26: 327-57.

Miller, D., 1997, "Sir Karl Raimund Popper, CH, FBA", Biographical Memoirs of Fellows of the Royal Society of London", 43: 367-409.

Parrini, P., W. Salmon, and M. Salmon (eds.), 2003, Logical Empiricism: Historical and Contemporary Perspectives, Pittsburgh: University of Pittsburgh Press.

Rescher, N. (ed.), 1985, The Heritage of Logical Positivism, Lanham, MD: University Presses of America.

Rescher, N., 2006, "The Berlin School of Logical Empiricism and Its Legacy, Erkenntnis, 64: 281-304.

Richardson, A., 1998, Carnap's Construction of the World: The Aufbauand the Emergence of Logical Empiricism, Cambridge: Cambridge University Press.

Richardson, A. and Übel, T. (eds.), 2007, The Cambridge Companion to Logical Empiricism, New York: Cambridge University Press.

Salmon, W. and G. Wolters (eds.), 1994, Language, Logic, and the Structure of Scientific Theories: The Carnap-Reichenbach Centennial, Pittsburgh: University of Pittsburgh Press, and Konstanz, Germany: University of Konstanz Press.

Sarkar, S., (ed.), 1992, Synthese: Carnap: A Centenary Reappraisal, Volume 93, Numbers 1-2.

Schilpp, P. (ed.), 1963, The Philosophy of Rudolf Carnap, LaSalle, IL: Open Court.

Spohn, W. (ed.), 1991, Erkenntnis: Special Volume in Honor of Rudolf Carnap and Hans Reichenbach, Volume 35, Numbers 1-3.

Stadler, F., 1997/2001, Studien zum Wiener Kreis: Entwicklung und Wirkung des Logischen Empiricismus im Kontext, translated by C. Nielsen, et al. asThe Vienna Circle: Studies in the Origins, Development and Influence of Logical Empiricism, Vienna: Springer.

Übel, T., 2007, Empiricism at the Crossroads: The Vienna Circle's Protocol-Sentence Debate Revisited, LaSalle, IL: Open Court.

Zabell, S. L., 1996, "Confirming Universal Generalizations", Erkenntnis, 45: 267-283.

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The term 'logical empiricism' has no very precise boundaries and still less that distinguishes it from 'logical positivism'. It is therefore hard to map.