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.     

New remarks on the cosmological argument

We present a formal analysis of the Cosmological Argument in its two main forms: that due to Aquinas, and the revised version of the Kalam Cosmological Argument more recently advocated by William Lane Craig. We formulate these two arguments in such a way that each conclusion follows in first-order logic from the corresponding assumptions. Our analysis shows that the conclusion which follows for Aquinas is considerably weaker than what his aims demand. With formalizations that are logically valid in hand, we reinterpret the natural language versions of the premises and conclusions in terms of concepts of causality consistent with (and used in) recent work in cosmology done by physicists. In brief: the Kalam argument commits the fallacy of equivocation in a way that seems beyond repair; two of the premises adopted by Aquinas seem dubious when the terms ??cause?? and ??causality?? are interpreted in the context of contemporary empirical science. Thus, while there are no problems with whether the conclusions follow logically from their assumptions, the Kalam argument is not viable, and the Aquinas argument does not imply a caused origination of the universe. The assumptions of the latter are at best less than obvious relative to recent work in the sciences. We conclude with mention of a new argument that makes some positive modifications to an alternative variation on Aquinas by Le Poidevin, which nonetheless seems rather weak.     

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 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 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.