Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

A method of optimal scaling for multivariate ordinal data and its extensions

This paper develops a method of optimal scaling for multivariate ordinal data, in the framework of a generalized principal component analysis. This method yields a multidimensional configuration of items, a unidimensional scale of category weights for each item and, optionally, a multidimensional configuration of subjects. The computation is performed by alternately solving an eigenvalue problem and executing a quasi-Newton projection method. The algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items. Numerical examples and simulations are provided. The algorithm is discussed and compared with some related methods.Earlier results of this research appeared in Saito and Otsu (1983). The authors would like to acknowledge the helpful comments and encouragement of the editor.     

ON MARTIN EGER'S "A TALE OF TWO CONTROVERSIES"

Abstract. Criticisms are presented against Eger's challenge to the demarcation between the natural sciences and ethics. Arguments are given both against his endorsement of the "new" philosophy of science and against his rejection of the fact-value dichotomy. However, his educational recommendations are reinforced rather than weakened by these criticisms     

ON "HUXLEYS EVOLUTION AND ETHICS IN SOCIOBIOLOGICAL PERSPECTIVE" BY GEORGE C. WILLIAMS

Abstract. I concur with Williams that improving human ethics requires full consideration of the biogenetic facts; but I argue that the understanding of biogenetic facts, and of ethics also, can be improved by a fuller view of nature's mechanism for selecting what is fit, a view recently generated by physical scientists. For me ethics necessarily must fit the evolved genotype, but ethics does not emerge until the rise of cultural evolution, where nature selects a culturetype symbiotic with the genotype. I outline my integrated dynamics of the relation of culturetypes to genotypes and to the laws governing physical systems. The biologist's finding that a living organism is of transient significance compared with its lines of heritage and their consequences, I argue, is constructively important for ethical and theological understanding.     

The rhetorical foundation of philosophical argumentation

The rejection of rhetoric has been a constant theme in Western thought since Plato. The presupposition of such a debasement lies at the foundation of a certain view of Reason that I have called propositionalism, and which is analyzed in this article. The basic tenets of propositionalism are that truth is exclusive, i.e. it does not allow for any alternative, and that there is always only one proposition which must be true, the opposite one being false. Necessity and uniqueness are the ideals of propositionalism. But the question of the necessity of such a necessity is bound to arise. Foundationalism and propositionalism are intrinsically related. Since necessity excludes alternatives, rhetoric, which is based on the possibility of opposite standpoints, is unavoidably devalued as the crippled child of Reason, identical to sophistry or eristic. But propositionalism cannot justify itself and provide a justification for its own foundation without circle or contraditction. Since it responds to the problem of eradicating problems and alternatives through propositional entities, propositionalism is ultimately based on questioning to which it replies in the mode of denial. The unavowed foundation of Reason is therefore the question of questioning, even though this very question is suppressed as propositionalism. The trace of such a question is not only historical, but can also be seen, for instance, in the role played by the principle of contradiction in the constitution of propositional Reason (Artitotle): opposite propositions are not the expression of a problematic situation, they are either possible or successively unique propositions.We want to replace propositionalism by problematology which allows for the conceptualization of alternatives, thereby rendering a true rhetoric possible. Argumentation cannot then be equated with eristic any more, as propositionalism maintained.Rationality must be seen as having questioning as its true starting-point. Reason must be rhetorical if it is to survive the death of propositionalism which took place after the radical criticisms of Marx, Nietzsche and Freud. Even if it is still hard ffor philosophers and rhetoricians to think within another framework and even though they prefer endlessly to deconstauct the old one instead of changing it, problematology is bound to impose itself as the new voice for rationality, because Reason has always endeavored to solve problems. Propositionalism has been only one way of conceiving problems, based on the view that solutions could be but the suppression of questioning.     

Rhetoric and “doing philosophy”

By drawing new distinctions labelled appeal and response to replace traditional rhetorical modes of written discourse, the essay sketches a new perspective about what philosophers are doing rhetorically in doing philosophy. To think of philosophers as simply engaged in argument is an oversimplification and a distortion of what philosophers do. Crucial to doing philosophy are four activities: (1) definition and redefinition of problems and issues that form both the focus of the canonical historical literature of philosophy and what goes on in contemporary philosophy as a discipline, (2) the development and use of formal languages and technical vocabularies to abbreviate and label complexity and to disambiguate and precise distinctions necessary to deal with problems and issues, (3) the development and exploration of argumentative appeals for acceptance or refutation of answers to questions raised by the philosophical problematic, and (4) the development and exploration of explanatory responses to questions raised by the problematic. In so far as these four activities are driven and sanctioned by the current, self-defining philosophical problematic, contemporary philosophy as a body of knowledge is historical, cumulative, and marked by progress, and the doing of philosophy is fundamentally the making of written appeals and responses about its problematic.     

Effects of response requirement and alcohol on human aggressive responding.

Nine men participated in two experiments to determine the effects of increased response requirement and alcohol administration on free-operant aggressive responding. Two response buttons (A and B) were available. Pressing Button A was maintained by a fixed-ratio 100 schedule of point presentation. Subjects were instructed that completion of each fixed-ratio 10 on Button B resulted in the subtraction of a point from a fictitious second subject. Button B presses were defined as aggressive because they ostensibly resulted in the presentation of an aversive stimulus to another person. Aggressive responses were engendered by a random-time schedule of point loss and were maintained by initiation of intervals free of point loss. Instructions attributed these point losses to Button B presses of the fictitious other subject. In Experiment 1, increasing the ratio requirement on Button B decreased the number of ratios completed in 4 of 5 subjects. In Experiment 2, the effects of placebo and three alcohol doses (0.125, 0.25, and 0.375 g/kg) were determined when Button B presses were maintained at ratio values of 20, 40 and 80. Three subjects who reduced aggressive responding with increasing fixed-ratio values reduced aggressive responding further at higher alcohol doses. One subject who did not reduce aggressive responding with increasing fixed-ratio values increased aggressive responding at the highest alcohol dose. The results of this study support suggestions that alcohol alters aggressive behavior by reducing the control of competing contingencies.     

Choice with delayed and probabilistic reinforcers: effects of variability, time between trials, and conditioned reinforcers.

In a discrete-trials procedure with pigeons, a response on a green key led to a 4-s delay (during which green houselights were lit) and then a reinforcer might or might not be delivered. A response on a red key led to a delay of adjustable duration (during which red houselights were lit) and then a certain reinforcer. The delay was adjusted so as to estimate an indifference point--a duration for which the two alternatives were equally preferred. Once the green key was chosen, a subject had to continue to respond on the green key until a reinforcer was delivered. Each response on the green key, plus the 4-s delay that followed every response, was called one "link" of the green-key schedule. Subjects showed much greater preference for the green key when the number of links before reinforcement was variable (averaging four) than when it was fixed (always exactly four). These findings are consistent with the view that probabilistic reinforcers are analogous to reinforcers delivered after variable delays. When successive links were separated by 4-s or 8-s "interlink intervals" with white houselights, preference for the probabilistic alternative decreased somewhat for 2 subjects but was unaffected for the other 2 subjects. When the interlink intervals had the same green houselights that were present during the 4-s delays, preference for the green key decreased substantially for all subjects. These results provided mixed support for the view that preference for a probabilistic reinforcer is inversely related to the duration of conditioned reinforcers that precede the delivery of food.     

TEACHING SAFETY SKILLS TO HIGH SCHOOL STUDENTS WITH MODERATE DISABILITIES

Teaching students with disabilities to respond appropriately to potentially dangerous situations is a useful skill that has received little research attention. This investigation taught 3 students with moderate mental retardation to remove and discard broken materials (plates, glasses) safely from (a) a sink containing dishwater, (b) a countertop, and (c) a floor. A 4th student was instructed on the sink task only. A multicomponent treatment package was used to teach the skills. Simulated materials were used initially and were replaced with broken plates and glasses. A multiple probe design was used to evaluate the effectiveness of the treatment package. The results indicated that the treatment package was effective in teaching the skills. Data were collected 1 week and 1 month following the completion of training, and indicated mixed results. No student was injured during any phase of training. Issues pertinent to teaching safety skills to students with moderate disabilities are discussed.     

COVARIATION WITHIN FUNCTIONAL RESPONSE CLASSES: IMPLICATIONS FOR TREATMENT OF SEVERE PROBLEM BEHAVIOR

Two studies examined the effects of a reductive treatment versus instruction-based treatments on the generalized reduction of problem behaviors. Each study involved a detailed analysis of multiple problem behaviors performed by school-aged youth with severe intellectual disabilities. The analysis examined the contrasting effects of one of two different positive intervention procedures (teaching a positive alternative behavior or providing additional teacher assistance during instruction) versus blocking and/or verbally reprimanding a problem behavior. The focus of each analysis was on the covariation of multiple problem behaviors within functional response classes. Results of the investigation indicated that when only one member of the response class was blocked, a collateral increase was observed in one or more different problem behaviors from the same response class. Alternatively, when 1 participant was taught a functionally equivalent mand response, all problem behaviors in the response class were reduced. Problem behaviors also were reduced for the remaining participant by presenting antecedent teacher assistance. Implications of the research extend to analysis of covariation within response classes and to procedures that result in generalized reduction of problem behaviors within a response class.