General Propositions Research Articles

A Uniform Distribution Question Related to Numerical Analysis

Using the theory of uniform distribution modulo one, it is shown that under certain conditions on the real-valued functions $\alpha (x)$ and $g(x)$ on [0,1 ], \[ h\;\sum \limits _{\gamma = 1}^{[{h^{ - 1}}]} {{{\{ {h^{ - 1}}\alpha (\gamma h)\} }^m}g(\gamma h) = {{(m + 1)}^{ - 1}}\int _0^1 {g(x)\;dx + o\left ( {{h^{1/3}}\log \frac {1}{h}} \right )} \quad {\text {as}}\;h \to 0 + ,} \] where $m > 0$ and x denotes the fractional part of x. The conditions are as follows: $\alpha ”(x)$ exists for all but finitely many points in [0, 1], changes sign at most finitely often, and is bounded away in absolute value from both 0 and $\infty$, whereas $g(x)$ is of bounded variation on [0,1]. Also, under these conditions on $\alpha (x)$, \[ h\;\sum \limits _{\gamma = 1}^{[{h^{ - 1}}]} {{{\{ {h^{ - 1}}\alpha (\gamma h)\} }^m} = {{(m + 1)}^{ - 1}} + o({h^{1/3}})\quad {\text {as}}\;h \to 0 + .} \] These results, which are, in fact, deduced from somewhat more general propositions, answer questions of Feldstein connected with discretization methods for differential equations.

A uniform distribution question related to numerical analysis

Using the theory of uniform distribution modulo one, it is shown that under certain conditions on the real-valued functions α ( x ) \alpha (x) and g ( x ) g(x) on [0,1 ], \[ h ∑ γ = 1 [ h − 1 ] { h − 1 α ( γ h ) } m g ( γ h ) = ( m + 1 ) − 1 ∫ 0 1 g ( x ) d x + o ( h 1 / 3 log ⁡ 1 h ) as h → 0 + , h\;\sum \limits _{\gamma = 1}^{[{h^{ - 1}}]} {{{\{ {h^{ - 1}}\alpha (\gamma h)\} }^m}g(\gamma h) = {{(m + 1)}^{ - 1}}\int _0^1 {g(x)\;dx + o\left ( {{h^{1/3}}\log \frac {1}{h}} \right )} \quad {\text {as}}\;h \to 0 + ,} \] where m > 0 m > 0 and x denotes the fractional part of x. The conditions are as follows: α ( x ) \alpha (x) exists for all but finitely many points in [0, 1], changes sign at most finitely often, and is bounded away in absolute value from both 0 and ∞ \infty , whereas g ( x ) g(x) is of bounded variation on [0,1]. Also, under these conditions on α ( x ) \alpha (x) , \[ h ∑ γ = 1 [ h − 1 ] { h − 1 α ( γ h ) } m = ( m + 1 ) − 1 + o ( h 1 / 3 ) as h → 0 + . h\;\sum \limits _{\gamma = 1}^{[{h^{ - 1}}]} {{{\{ {h^{ - 1}}\alpha (\gamma h)\} }^m} = {{(m + 1)}^{ - 1}} + o({h^{1/3}})\quad {\text {as}}\;h \to 0 + .} \] These results, which are, in fact, deduced from somewhat more general propositions, answer questions of Feldstein connected with discretization methods for differential equations.

Space syntax

This paper addresses itself to the question of how and why different societies produce different spatial orders through building forms and settlement patterns. It consists of three parts. Firstly, at a metatheoretical level, it is suggested that spatial organization should be seen as a member of a family of ‘morphic languages’ which are unlike both natural and mathematical languages but which borrow properties from each. In general, morphic languages are used to constitute rather than represent the social through their syntax (that is the systematic production of pattern). Secondly, a general syntactic theory of space organization is proposed. It is argued that spatial patterns in both complex buildings and settlements fall into eight major types, which are interrelated in structural ways. Finally, the syntactic theory is used to integrate a number of recent general propositions made in anthropology regarding human space organization.

Problem-solving in science.

Problem-solving is a characteristic activity of scientists, Theoretical problems are formulated as a consequence of scientists' thirst for knowledge, and their solutions take the form of general propositions, termed hypotheses, which are consistent with, and provide provisionally satisfactory explanations of, empirical observations. Practical problems appear as the result of feedback from the extra-scientific world of everyday life, industry and professional practice. Their solutions provide an improved basis for decision-making in terms of existing options or increase the number of options from which a choice may be made. The categories theoretical and practical are not mutually exclusive: practical problems often generate interesting theoretical problems, and the solution of a theoretical problem may entrain the solution of a host of practical problems. All hypotheses are provisional because it is impossible to establish the truth of a generalization by rigorous deduction from any number of particular instances, though a single instance may suffice to refute it. This asymmetry forms the basis of Popper's analysis of scientific methodology. This analysis, though acceptable in the main, is open to criticism in the following respects; (1) it ignores the contribution to scientific progress made by unplanned perceptions; (2) it ignores the contribution of hypotheses which do not generate testable predictions; (3) it does not do justice to the extra-logical component in knowing (Polanyi's tacit dimension); and (4) its treatment of practical problems in inadequate.

Landscape Evaluation: The Theoretical Vacuum

The empirical methodology of landscape evaluation could be strengthened if it were underpinned by a more convincing theoretical base, but there is no general understanding of how this might be done. This introductory paper poses three main questions: first, what, in any context do we expect of a theory; second, how, in the present context, does the weakness of theory adversely affect our methodology; and third, what can we do about it. IN reviewing the attempts so far made to evaluate landscape aesthetically, most people would agree that techniques of evaluation are overwhelmingly dominated by an empirical methodology, that they could be greatly strengthened if they were underpinned by a more convincing theoretical base, but that it is not clear exactly how such an underpinning could effectively be made. When we are considering the practicalities of landscape evaluation it is this last problem which emerges as crucial, and it may help if we tackle it by posing three questions. First, 'What, in any context, do we expect of a theory ?'; second, 'How, in the present context, does the weakness, or even absence, of theory adversely affect our methodology ?', and third, 'What can we do about it?' First, then, what do we expect of a theory ? It might help if we were to examine briefly the relationship between empirical and theoretical techniques in an example drawn from a different field. A medical diagnosis commonly begins with an empirical phase, in which a questionnaire establishes the signs (that is those manifestations of disorder which can be directly observed by the enquirer) and the symptoms (that is those which are perceived, correctly or incorrectly, by the patient). On the basis of such a questionnaire we may observe that a patient has a blotchy rash on the face and chest, small spots in the mouth, a running nose and eyes, and a raised temperature. From his own perception of his condition we may also learn that he experiences the sensation of a sore throat and a headache. To make the further assertion that the patient is suffering from measles we need a measure of theory, if only at an elementary level, so that we can relate the observed phenomena of the individual case to the general principles by which we can attribute those phenomena to the disease we call measles and not to some other disorder. Let us, by comparison, look at our own methodology in the aesthetic evaluation of landscape. Do we use the information acquired from our questionnaire to lead us into a body of theoretical knowledge which enables us to identify a condition, to prescribe, if necessary, a procedural intervention for remedying or ameliorating that condition, and to predict the consequences of this or some other intervention, basing our diagnosis, prescription and prognosis on our understanding of the known principles which govern this field of human experience ? Do we not rather stick at the empirical stage without ever reaching the underlying principles ? I am not suggesting, of course, that those who evaluate landscape have no principles, but we must be careful not to confuse those principles which underlie the aesthetic pleasure we obtain from landscape with those principles by which we seek to regularize-perhaps even standardize-the procedures we apply to the investigation of particular cases. It may further help to clarify our problem if we recognize that geographers commonly employ two kinds of theory, which we may call 'spatial' and 'non-spatial'. 'Spatial theory' is the proper concern of their discipline. It consists of general propositions about the distribution, location and spatial relationships of phenomena, and it may extend not only to description, but also to explanation and prediction. Increasingly spatial theory has tended to find expression in mathematical terms, involving, for instance, models or formulae; but it need not be so expressed. It may take the form of a statement, quantitative

The helping process as developmental existentialism

The purpose of this article is to present a new orientation toward the helping process in order to suggest additional practical strategies for helpers. The position is labeled “developmental existentialism” because it places existential principles within a developmental framework. The author examines the general features, assumptions, defining dimensions, and propositions of the position. The perspective of this new approach enables clients to be assessed in terms of their degree of health, types of anxieties, motivational levels, means of coping, and developmental strengths and weaknesses.

Education and Politics in Brazil

THE BRAZILIAN coup d'etat of 1964 replaced one of Latin America's most important representative democracies with a military-controlled authoritarian regime that had a decidedly rightist political philosophy. Some years later, roughly from 1968 onward, a spectacular growth of Brazil's peripheral capitalistic economy began, and was soon termed the miracle. As a consequence of both its political alignment and its economic expansion, Brazil began to acquire an entirely new importance on the international scene, although mainly within the American hemisphere, also increasingly beyond. In seeking to explain this process, scholarly efforts have followed two distinct, though virtually complementary, directions: that of preparing or tentatively offering analyses in terms of more or less elaborated comparative theory; and that of understanding contemporary events as an outcome of Brazil's political, economic, and social history. Following the latter perspective, this paper tries to show that education is one of the mechanisms developed by the dominant segments of (or the segments competing for influence in) Brazilian society, through direct initiatives and/or use of the political system, to enforce their respective interests. By examining this mechanism it is hoped that important insights will be gained into the overall process of the transformation of the Brazilian society -particularly the relationship between changes in social stratification and the political system. Its contention, furthermore, is that in Brazil the societal role of education has overwhelmingly been that of reinforcing the social dynamics prevailing at any given moment. The two general propositions summarize a pattern that seems to emerge from a variety of studies-in history, sociology, political science, economics, and education-published over the last twenty years. Sketching out this pattern this paper suggests a line of interpretation that seems helpful for understanding the politics of education in Brazil.

Ergebnisse eines Modellversuchs zur quantitativen Erfassung von Umweltänderungen mit Hilfe von Ökosystemen: I. Versuchsobjekt, Methodik, univariate Analyse

Summary A simple ecosystem was disturbed by 2,2-dichlorpropionic acid-Na and afterwards the response of single elements (plants, ecofactors) was analysed in comparison with control and reference plots. Design of experiment and results are interpreted as quantitative bioindication of an ecosystem for disturbance of the environment resp. environmental changes. General propositions on the indication of environmental influences by means of ecosystem elements are derived and it is tried to describe the indicator elements, their interactions and the indication sphere within the ecosystems by means of graphs theory methods. References to problems of research, control and protection of environment are pointed out.

Employing the Disadvantaged: Lessons from the Past Decade

Based upon a cumulative assessment of research on employing the disadvantaged, this review concludes that success hinges upon several critical aspects of social learning and organizational adaption. Eight general propositions are developed to summarize empirical research and integrate findings for organizational decision-makers.

Die induktive Methode und das Induktionsproblem in der griechischen Philosophie

The definition of Induction in the „topic“ is but a description of the prearistotelian process of generalisation. — The genuine aristotelian theory of induction does not concern general propositions but the objectonstruction; it tries to give a logical solution to the theory of anamnesis. — The inductive syllogism is not a summative induction but a suggestion that the relation of extensions of classes is the only criterion for the projectibility of known cases on unknown. — The stoics accept contraposition as the only form of scientific inference while the epicureans introduce a pure empirical criterion for sound general propositions. Both theories however, suggest an identification of the problem of induction with the problem of possibility. — Philoponos is the first author to give a classification of sciences from a methodological point of view. He rejects pure induction and proposes the hypothetico — deductive Method as a solution of the problem of induction.

On the Relation Between Human Ecology and Behavioral Social Psychology

Human ecology and operant conditioning are compared in order to consider the feasibility and desirability of linking human ecology and behavioral social psychology. General similarities between human ecology and operant conditioning include a recognition of the interaction between behavior and environment, the necessity of longitudinal analyses, the view that change is externally determined, and quantitative analyses involving aggregated behaviors. Major differences include origins of general principles, methodology, and units of analysis. Many similarities also exist among general concepts and principles. Operant principles might be applied to provide complex psychological, social-psychological, sociological, and human-ecological analyses. The major barrier between human ecologists and behavioral social psychologists and sociologists now appears to be the discrepancy in the size of the social systems each studies. The relation between human ecology and social psychology has been discussed on several occasions (e.g., Duncan and Schnore, 1959; Hawley, unpublished manuscript), and in most cases the conclusion has been that the relationship is one of mutual independence. In most cases, however, human ecology has been discussed in relation to the cognitive branch of social psychology. The relation between human ecology and the behavioral branch of social psychology has apparently not been considered in spite of the fact that the two approaches employ similar orienting strategies and have produced numerous strikingly parallel general concepts and propositions. This article calls attention to such parallels and discusses the feasibility and desirability of a symbiotic relationship between human ecologists and behavioral social psychologists and other sociologists who have begun applying the concepts and principles of operant conditioning to the analysis of social process and social organization. ORIENTING DESCRIPTIONS OF HUMAN ECOLOGY AND OPERANT CONDITIONING1 Human ecology can be generally defined as the study of the relationship between a human population and its environment. The bulk of human ecology falls within the branch of general ecology called synecology, the study of the relationships among groups of organisms engaged with a given environment. A second branch, autecology, is the study of the individual organism's interaction with its environment. The human ecologist, however, studies primarily a population's collective interaction with its environment. Such interactions with the environment are viewed as collectively adaptive and produce a recognizable form of organization seen in the relationships among the activities emitted by different functional units. The adaptive notion gives human ecology its characteristic equilibrium position. Duncan (1959) has distinguished four major interdependent variables constituting an ecosystem. These are population, organization, environment, and technology-any of which may constitute the major dependent variable for certain purposes. Operant conditioning, strictly speaking, is the conditioning of operants. An operant is any behavior which can be strengthened or weakened by the contingent events which follow the behavior. The behavior may be referred to as a response, and its strength may be indicated by several dimensions including its frequency * This article is a revision of a paper presented at the annual meeting of the Southern Sociological Society, 1971. I wish to acknowledge the useful comments and suggestions of Amos Hawley and James Wiggins. 1 The present description of human ecology is based largely on Hawley's (1968) elaborated description. The reader is referred to Reese (1966) and Reynolds (1968) for efficient introductions to operant conditioning.

Conditions of Americari-Soviet Commerce: The Beginning of Direct Cotton Trade, 1923-1924

AbstractThe history of American-Soviet commerce contains numerous turning points, but none is perhaps so little appreciated as the commencement of direct cotton trade. This development occurred as a result of the visit of Viktor P. Nogin to America from November, 1923 to January, 1924.1 It is particularly informative to discuss the events of this period within a framework of general propositions concerning American-Soviet trade.

Understanding Beliefs: An Essay on the Methodology of the Statement and Analysis of Belief Systems

The essay sketches a comprehensive methodology for the study of beliefs and belief systems. It considers the situation of the anthropologist studying the beliefs of natives of whose language and society he is relatively ignorant, but its conclusions are thought to be applicable as well in understanding the beliefs of those speaking the same language and living in the same society. The essay elaborates and recommends a conception of beliefs as general propositions about the world (consciously) held to be true; it suggests that other concepts (e.g., of beliefs as unconscious as well as conscious) have never been adequately explicated. The remainder of the essay deals with the logic of the interpretation of beliefs and with the nature of anthropological formulations of foreign belief. Following Quine, it presents a referential theory of translation, arguing that one translates by correlating native utterances with one's own labels for the 'situations' to which both (utterances and labels) refer. It proceeds to discuss the implications of the dependence of the anthropologist's data on interaction with natives and the effect of his behavior on the native's sincerity. It then discusses the logic by which (1) a series of beliefs is stated as a system and (2) the beliefs and systems so stated are analyzed and compared with others. It concludes by enumerating the ways in which anthropologists' formulations of native beliefs and belief system are logically interactive products of the the beliefs of native and anthropologist. It relates the study of belief to other disciplines, and discusses some epistemological limits of the knowledge of foreign beliefs.

OPEN SYMMETRIC ORBITS OF REDUCTIVE GROUPS IN SYMMETRICR-SPACES

One considers symmetric spaces which are simultaneously R-spaces, i.e. factor spaces of semisimple Lie groups by parabolic subgroups. By a symmetric domain is meant a domain, each point of which is an isolated fixed point of an involutive transformation of the domain. In the work one finds an explicit list of all reductive groups in symmetric R-spaces which have open symmetric orbits. For spaces which are connected by means of the Kantor-Koecher construction with semisimple Jordan algebras, the problem is solved by means of the reduction obtained by A. A. Rivilis and some general propositions supplementing his results. Moreover, one applies other methods based on the theory of representations and using the theorem on decompositions of semisimple Lie groups. Bibliography: 10 items.

Professionalism and the erosion of rationality in the health care field.

This paper poses some fundamental, and therefore naive, questions about the purposes health care delivery systems should serve, and it analyzes the discrepant purposes our current systems do serve. After considering some general propositions from the sociology of organizations, and then some derived propositions bearing specifically on the roles of professionals today, it argues that professional dominance tends to produce results that are dysfunctional in terms of the purposes health care delivery systems should serve, and explores implications of these general dilemmas in the mental health field.

The Trial Judge: Pilot, Participant, or Umpire?

The recent decision in Phillips v. Ford Motor Co. of Canada Ltd. et al.t has reopened question which some might have considered to be somewhat settled: the role and function of the trial judge. Professor Silverman has taken the Phillips decision as cue for making comprehensive analysis of the English and Cana dian case law concerning the trial judge's function, in civil as well as criminal cases. Such issues as the rule requiring the presentation of evidence in open court, the limitations on the trial judge's right to call witnesses, his interference in the examination of witnesses and his intervention in the trial as whole are examined. Professor Silverman notes that although there may be dicta in some criminal and civil cases which apply to both, the better approach for the trial judge is to restrict himself "as much as possible" to the principles set out in cases of the same nature (criminal or civil) as the one before him. However, the author does lay down several general propositions delineating the boundaries of the trial and the role of the trial judge, which are applicable to both criminal and civil cases. Professor Silverman concludes, that although a trial judge may be pilot he "is certainly more than an umpire, watching the sporting-theory of litigation in action; and he is less than participant in that he should not enter into the fray of combat nor take on the mantle of counsel".

Art and Society in England and France in the Mid-Nineteenth Century: Two Paintings before the Public

The primary source material for the art historian is of course the work of art, and this in itself places him in a fortunate position because the permanent relevance of the work of art is, I take it, self-evident. For the art historian, the work of art is an historical fact, pre-selected for generally accepted aesthetic reasons. But the work of art has no absolute meaning: it does not exist in a vacuum. It has both what we might call a history and a geography—the history being that record of interpretation and evaluation which accrues to the work of art from the moment of its creation down to the present day; and the geography being the particular artistic and social context of its original creation. The history can at times be very misleading: it is obvious that each generation is going to interpret the past as it wishes, and no judgment can be objective. So it is the geography that is more important, and this is extremely difficult to define. But if we are to understand the work of art, we need to enquire into the circumstances of its creation: we must ask, what did this painting or sculpture or building signify when it first appeared? Only from such specific investigations can one proceed to general propositions about the state of art at any particular moment, and perhaps also about the state of society which produced the art.

The Anthropologist as Broker in Community Education: A Case Study and Some General Propositions

The Anthropologist as Broker in Community Education: A Case Study and Some General Propositions

Reference-Other Support and Ethnic Attitudes as Predictors of Intergroup Behavior

A number of general propositions are proposed concerning the manner in which reference-others and ethnic attitudes influence intergroup behavior. In a laboratory setting, it is shown that the influ...

Law and Development: A General Model

As Mark Twain once remarked about the weather, everyone talks about law and development, but nobody does much about it. How does law “set off, monitor, or otherwise regulate the fact or pace of social change?” (Friedman, 1969). Atomistic studies relating specific norms of law to specific sorts of social change are plentiful. Holistic studies purporting to explicate general propositions relating rules and behavior can hardly be found. The few that do exist do hardly more than assure us, most sincerely, that yes, there really is a relationship between law and social change.What is needed is a general model relating law and social change. Here, we discuss (1) the definition of the problem; (2) its parameters; (3) an heuristic model; and (4) a variety of “middle-level” hypotheses that can be suggested. The specific focus of this discussion is on Africa.