The Problem of the Unity of Knowledge in Comte's Philosophy of Science*

Comte's philosophy of science is re-examined from the point of view of the rationalist problematic of the unity of knowledge. It is argued that Comte's attempt to answer this metaphysical problem is the single most important factor determining the final form of his system of positive philosophy, his hierarchy of the sciences, his conception of sociology, and ultimately his positive religion of Humanity. After rejecting the main solutions offered by modern rationalism, Comte provides a subjective unity for the sciences by establishing Humanity as the principle of organization for all knowledge. The article describes the various components of the positive synthesis, their background in the history of ideas, and the contemporary relevance of the problem of unity for logical empiricism and Husserl. Some have said that need for unity expresses the identity of the self; others, that it stands for economy of thought. Possibly, but this is interpretation, psychologically or sociologically tinged. The need for unity is a historical fact and, as such, unresolved. It is also a symbol of science, and its myth. Science is a finely defined and articulated system of symbols; but the ultimate symbol, that of unity, can have no referent. Rather one might say it stands for the totality of the knowable and the unknowable. A confusing situation for the scientific mind, but one it cannot escape. For the conflict at the heart of rationalism is the source of its strength, as long as it lasts. Once the faith is lost, something else has to be found. Under the relentless pressure of social change, with the growing operationalism of physical theory and the metaphysical devastations attendant on Darwinism, the myth of unity could no longer hold. It had to be replaced by unification. But with that the status of science is changed and also that of the scientist. The mirror of nature that reason had endeavored to build up through the ages is shattered, and we look for the first time straight out into an unknown world.     

Designing np control charts

This paper presents the results of a simulation approach to the design of economic attribute control charts. The approach taken differs from the classical studies reported in the literature in two respects. First, the often made assumption that the out-of-control state of a process will remain so until detection is relaxed. This in effect allows the average proportion of defectives to deteriorate further before the out-of-control state is detected. Second, there is no requirement for detailed information on the exact process behaviour in the out-of-control state. It is assumed that a multitude of out-of-control causes exist and that the proportion defective is equally likely to be within a specified range of values. The relaxation of these two assumptions makes the model realistic and gives it wide practical applications in the control of a manufacturing process. The simulation computer programs developed are sufficiently compact to run on the low cost microcomputers.     

Response and predictor folding to counter symmetric dependency in dimension reduction

In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualisation in a low‐dimensional framework. However, some popular dimension reduction methodologies fail to achieve this aim when faced with a problem often referred to as symmetric dependency. In this paper we show how vastly superior results can be achieved when carrying out response and predictor transformations for methods such as least squares and sliced inverse regression. These transformations are simple to implement and utilise estimates from other dimension reduction methods that are not faced with the symmetric dependency problem. We highlight the effectiveness of our approach via simulation and an example. Furthermore, we show that ordinary least squares can effectively detect multiple dimension reduction directions. Methods robust to extreme response values are also considered.     

DETECTING INFLUENTIAL OBSERVATIONS IN SLICED INVERSE REGRESSION ANALYSIS

The detection of influential observations on the estimation of the dimension reduction subspace returned by Sliced Inverse Regression (SIR) is considered. Although there are many measures to detect influential observations in related methods such as multiple linear regression, there has been little development in this area with respect to dimension reduction. One particular influence measure for a version of SIR is examined and it is shown, via simulation and example, how this may be used to detect influential observations in practice.     

Patterns of Crime and Drug Use Trajectories in Relation to Treatment Initiation and 5-Year Outcomes: An Application of Growth Mixture Modeling Across Three Datasets

Drug abusers vary considerably in their drug use and criminal behavior over time, and these trajectories are likely to influence drug treatment participation and treatment outcomes. Drawing on longitudinal natural history data from three samples of adult male drug users, we identify four groups with distinctive drug use and crime trajectories over the 5 years prior to their first treatment episode. The groups' characteristics of initial treatment are compared. The trajectory groups are then included in Poisson growth curve models to predict drug use, incarceration, and employment over the 5 years following first treatment. Findings indicate that posttreatment drug use decreased and posttreatment employment increased. There was little change in posttreatment incarceration. Posttreatment trajectories for drug use, incarceration, and employment were significantly different across the four trajectory groups.