Discovery as the context of any scientific justification

Summary The analysis of philosophically important themes can depart from two different angles. The first one investigates the various answers that have been given to a certain issue, like that of the problem of knowledge, the justification of theories, the notion of culture, etcetera. These answers are often mutually contradictory which, by the way, facilitates their overview (like the schemes of rationalism-empiricism, justification-discovery, universalism-relativism). A second approach starts from the problems (or: problematique) behind the divergent answers (e.g., foundationalism behind both, empiricism and rationalism).In the following sections the issue of discovery is discussed. Here the second line of approach has been followed, not only by making visible a same problematique, but more by trying to set out the common context of the discussion about context of discovery and context of justification. The idea is that this discussion, or better the shift taking place in that discussion, finds its reason in a context in which the distance between traditional methodology and contemporary scientific practice, also between scientific knowledge and the experience of reality has become greater. This is related to the deepening awareness of the cultural context of scientific method. Man and world, scientific method and cultural context are always interacting.From this point of view quite different philosophical approaches show nevertheless similar features pointing to new solutions. A more psychological approach to scientific method (like: Gordon's and Grmek's, even perhaps Gutting's reinterpretation of Popper) and a sociological one (e.g., Barnes, Bloor, and already Durkheim) are opposed to a more logically structured analysis of Nagel, Hempel, and also Popper. Nevertheless the view on the flexibility of scientific method defended along different lines by for instance Achinstein, Bachelard, Hesse, Piaget, Polanyi, Toulmin manifests a certain convergence in those divergent standpoints, the more so since often the cultural context of science is being stressed (e.g., Ladriére, Prigogine, Needham).The miscellany of philosophical orientations, presented in the following sections, can in this way perhaps give profile to deeper tendencies: to relate again scientific method to the context of culture and of human strategy in general. This does not blend, however, the distinction between context of justification and context of discovery. By changing their roles a new overview of this dilemma becomes possible. There is no juxtaposition of both, nor has the one to be absorbed by the other. The conclusion will be that there are still two contexts, but that one is wider, less defined and demarcated from the wider field of daily culture, and that the other is more restricted, functioning as a kind of safetydevice on behalf of the wider strategy of discovery. In such a way discovery is regarded as the wider context of the more restricted context of justification.     

The logical study of science

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4).I would like to thank David Pearce and Veikko Rantala for their helpful comments.     

A SELF-INSTRUCTIONAL PACKAGE FOR INCREASING ATTENDING BEHAVIOR IN EDUCABLE MENTALLY RETARDED CHILDREN

The purpose of this study was to develop a self-instructional package that would aid highly distractible retarded children in increasing their attending behavior in a training and two generalization (a one-to-one and a classroom) situations. Three untrained subjects were monitored for general comparison and social validation purposes. One of these control subjects was distractible and the other two (criterion comparison) were evaluated as not having attentional problems. A multiple baseline design was employed in which training was sequentially introduced across subjects. During training, the experimental subjects were taught through self-instruction to focus their attention and to cope with two tasks, math and printing. After learning the self-instructions the subjects were systematically and sequentially exposed to photo-slides of distracting situations, to audio-distractors composed of noisy lunchroom verbal peer interactions, and to in vivo distractors provided by kindergarten children playing with wooden blocks in the training setting. The entire training procedure was handled in a game-like context to maintain subject interest and to facilitate generalization. The results suggested that the training package produced direct and generalized changes in self-instructional behavior. In addition, a decrease in off-task behavior occurred during math, printing, and also during a phonics program in the one-to-one and classroom situations. However, reliable changes in academic task performance were not observed. Finally, no systematic changes on any of the dependent measures occurred for the three untrained subjects.     

The level of organization of the motor schema

The interpretations of Piaget and Schmidt on the level on which the motor schema is supposedly effective were evaluated in pre-school children of different ages in a throwing task. In an analysis of variance on the accuracy scores, significant main effects for age, sex, and throwing arm were found. Further, the results showed no relationship between accuracy scores with the preferred and non-preferred arm in the younger group, while in the older group a moderate relationship was found. This result was interpreted in terms of structural development and as a warning for studies where Schmidt's variability-of-practice hypothesis is tested.     

Some kinds of modal completeness

In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability and preservation under ultrafilter extensions are introduced and studied as well.     

Perceptual interpretation of complex line patterns

Leeuwenberg's coding system for the representation of line pattern interpretations is tentatively applied to the interpretation of complex line patterns, that is, line patterns with intersecting lines. Perceptually preferred interpretations of complex line patterns can only be predicted correctly if two requirements are met: (a) The codes of line patterns should contain information about the objects represented by the line patterns, not about the line patterns as drawings; and (b) effects of the gestalt law of good continuation have to be taken into account.     

A general nonmetric technique for finding the smallest coordinate space for a configuration of points

LetA ₁,A ₂, ...,A _n be anyn objects, such as variables, categories, people, social groups, ideas, physical objects, or any other. The empirical data to be analyzed are coefficients of similarity or distance within pairs (A _i,A _i ), such as correlation coefficients, conditional probabilities or likelihoods, psychological choice or confusion, etc. It is desired to represent these data parsimoniously in a coordinate space, by calculatingm coordinates {x _ia } for eachA _i for a semi-metricd of preassigned formd _ij =d(|x _i1 -x _j1 |, |x _i2 -x _j2|, ..., |x _im -x _jm |). The dimensionalitym is sought to be as small as possible, yet satisfy the monotonicity condition thatd _ij <d _kl whenever the observed data indicate thatA _i is closer toA _j thanA _k is toA _l . Minkowski and Euclidean spaces are special metric examples ofd. A general coefficient of monotonicity is defined, whose maximization is equivalent to optimal satisfaction of the monotonicity condition, and which allows various options both for treatment of ties and for weighting error-of-fit. A general rationale for algorithm construction is derived for maximizing by gradient-guided iterations; this provides a unified mathematical solution to the basic operational problems of norming the gradient to assure proper convergence, of trading between speed and robustness against undesired stationary values, and of a rational first approximation. Distinction is made between single-phase (quadratic) and two-phase (bilinear) strategies for algorithm construction, and between hard-squeeze and soft-squeeze tactics within these strategies. Special reference is made to the rank-image and related transformational principles, as executed by current Guttman-Lingoes families of computer programs.This research was supported in part by the National Science Foundation of the United States Government, through Grant No. GS 929 to the University of Michigan.I am deeply indebted for many helpful comments on earlier drafts of this paper received from Joseph Kruskal, James Lingoes, and the managing editor.