Some remarks on the kuder-richardson reliability coefficient

The Kuder-Richardson reliability coefficient is derived in a manner independent of that originally given. Various alternative forms applicable to special situations are exhibited with the purpose of making them available to others interested in using this formula. A simplification in computation is suggested for use with a calculating machine.     

Some remarks on restricting the knowability principle

The Fitch paradox poses a serious challenge for anti-realism. This paper investigates the option for an anti-realist to answer the challenge by restricting the knowability principle. Based on a critical discussion of Dummett??s and Tennant??s suggestions for a restriction desiderata for a principled solution are developed. In the second part of the paper a different restriction is proposed. The proposal uses the notion of uniform formulas and diagnoses the problem arising in the case of Moore sentences in the different status propositional letters receive. The new proposal is able to avoid some of the criticism on its predecessors.     

Some remarks on the Rationality of Induction

This paper begins with a rigorous critique of David Stove's recent bookThe Rationality of Induction. In it, Stove produced four different proofs to refute Hume's sceptical thesis about induction. I show that Stove's attempts to vindicate induction are unsuccessful. Three of his proofs refute theses that are not the sceptical thesis about induction at all. Stove's fourth proof, which uses the sampling principle to justify one particular inductive inference, makes crucial use of an unstated assumption regarding randomness. Once this assumption is made explicit, Hume's thesis once more survives.The refutation of Stove's fourth proof leads to some observations which relate Goodman's grue paradox with randomness of a sample. I formulate a generalized version of Goodman's grue paradox, and argue that whenever a sample, no matter how large, is drawn from a predetermined smaller interval of a population that is distributed over a larger interval, any conclusion drawn about the characteristics of the population based on the observed characteristics of the sample is fatally vulnerable to the generalized grue paradox.Finally, I argue that the problem of justification of induction can be addressed successfully only from a cognitive point of view, but not from a metaphysical one. That is, we may ask whether an inductive inference is justified or not within the theories or cognitive structures of a subject, but not outside them. With this realization, induction is seen as a cognitive process, not unlike vision, that is useful at times, and yet has its own illusions that may make it a serious obstacle to cognition at other times.     

Some remarks on the quantitative analysis of behavior

This paper discusses similarities between the mathematization of operant behavior and the early history of the most mathematical of sciences-physics. Galileo explored the properties of motion without dealing with the causes of motion, focusing on changes in motion. Newton's dynamics were concerned with the action of forces as causes of change. Skinner's rationale for using rate to describe behavior derived from an interest in changes in rate. Reinforcement has played the role of force in the dynamics of behavior. Behavioral momentum and maximization have received mathematical formulations in behavior analysis. Yet to be worked out are the relations between molar and molecular formulations of behavioral theory.     

Some remarks on Scheiblechner's treatment of isop models

Scheiblechner (1995) proposes a probabilistic axiomatization of measurement called ISOP (isotonic ordinal probabilistic models) that replaces Rasch's (1980) specific objectivity assumptions with two interesting ordinal assumptions. Special cases of Scheiblechner's model include standard unidimensional factor analysis models in which the loadings are held constant, and the Rasch model for binary item responses. Closely related are the doubly-monotone item response models of Mokken (1971; see also Mokken & Lewis, 1982; Sijtsma, 1988; Molenaar, 1991; Sijtsma & Junker, 1996; and Sijtsma & Hemker, in press). More generally, strictly unidimensional latent variable models have been considered in some detail by Holland and Rosenbaum (1986), Ellis and van den Wollenberg (1993), and Junker (1990, 1993). The purpose of this note is to provide connections with current research in foundations and nonparametric latent variable and item response modeling that are missing from Scheiblechner's (1995) paper, and to point out important related work by Hemker, Sijtsma, Molenaar, & Junker (1996, 1997), Ellis and Junker (in press) and Junker and Ellis (1997). We also discuss counterexamples to three major theorems in the paper. By carrying out these three tasks, we hope to provide researchers interested in the foundations of measurement and item response modeling the opportunity to give the ISOP approach the careful attention it deserves. This research was supported by the National Science Foundation, Grant DMS-94.04438. I thank the Editor and three anonymous referees for careful readings that improved the completeness of this note.