Estimation of indifference points with an adjusting-delay procedure.

In a series of conditions, pigeons chose between 1.5 s and 3 s of access to grain, each preceded by some delay. The delay that preceded the small reinforcer was constant throughout a condition. The delay that preceded the large reinforcer was increased or decreased a number of times each session in order to estimate an "indifference point," a delay at which the subject chose each alternative about equally often. The experiment was designed to determine whether variations in any of four features of this adjusting-delay procedure would systematically alter the estimated indifference points. The four features were the total trial duration, the number of center-key responses necessary to begin a trial, the number of choice trials that preceded each change in the adjusting delay, and step size--the size of each increment and decrement in the delay. Manipulation of the first three features had no systematic effects on the indifference points. As step size was increased from 0.5 s to 6 s, within-session variability of the adjusting delay steadily increased, and the 6-s step size produced larger indifference-point estimates for some subjects. The results suggest that, within certain limits, these procedural features can be altered without affecting the indifference-point estimates, but that the use of a large step size can distort the estimates. Some theoretical implications of the relative constancy of indifference points across these procedural variations are discussed.     

Self-control in mentally retarded adolescents: choice as a function of amount and delay of reinforcement.

Three severely mentally retarded adolescents were studied under discrete-trial procedures in which a choice was arranged between edible reinforcers that differed in magnitude and, in some conditions, delay. In the absence of delays the larger reinforcer was consistently chosen. Under conditions in which the smaller reinforcer was not delayed, increasing the delay to delivery of the larger reinforcer decreased the percentage of trials in which that reinforcer was chosen. All subjects directed the majority of choice responses to the smaller reinforcer when the larger reinforcer was sufficiently delayed, although the value at which this occurred differed across subjects. Under conditions in which the larger reinforcer initially was sufficiently delayed to result in preference for the smaller one, progressively increasing in 5-s increments the delay to both reinforcers increased percentage of trials with the larger reinforcer chosen. At sufficiently long delays, 2 of the subjects consistently chose the larger, but more delayed, reinforcer, and the 3rd subject chose that reinforcer on half of the trials. These results are consistent with the findings of prior studies in which adult humans responded to terminate noise and pigeons responded to produce food.     

Changes in functional response units with briefly delayed reinforcement

In two experiments, key-peck responding of pigeons was compared under variable-interval schedules that arranged immediate reinforcement and ones that arranged unsignaled delays of reinforcement. Responses during the nominal unsignaled delay periods had no effect on the reinforcer presentations. In Experiment 1, the unsignaled delays were studied using variable-interval schedules as baselines. Relative to the immediate reinforcement condition, 0.5-s unsignaled delays decreased the duration of the reinforced interresponse times and increased the overall frequency of short (<0.5-s) interresponse times. Longer, 5.0-s unsignaled delays increased the duration of the reinforced interresponse times and decreased the overall frequency of the short interresponse times. In Experiment 2, similar effects to those of Experiment 1 were obtained when the 0.5-s unsignaled delays were imposed upon a baseline schedule that explicitly arranged reinforcement of short interresponse times and therefore already generated a large number of short interresponse times. The results support earlier suggestions that the unsignaled 0.5-s delays change the functional response unit from a single key peck to a multiple key-peck unit. These findings are discussed in terms of the mechanisms by which contingencies control response structure in the absence of specific structural requirements.     

A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

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.     

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     

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.     

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.