Confirmation theorists seek to define a function that will take into account the various factors relevant in determining the degree to which an hypothesis is confirmed by its evidence. Among confirmation theorists, only Rudolf Carnap has constructed a system which purports to consider factors in addition to the number of instances, viz. the variety manifested by the instances and the amount of analogy between the instances. It is the purpose of this paper to examine the problem which these additional factors raise for confirmation theory, and to prove that, despite Carnap's claim, no confirmation function satisfying the requirements he has specified can take account of variety and analogy. This result is first proved for a special case, and then, in a subsequent section, is generalized through the introduction of a theorem (the proof of which is given in Appendix I). In the final section of the paper it is shown that, contrary to a claim which Carnap has made, not even the concept of the “logical width” of a predicate will enable confirmation functions satisfying his requirements to take adequate account of analogies between instances.

Peter Achinstein gives in his papers [1] and [2] interesting analyses of some problems of inductive logic and of some approaches I have proposed. I shall discuss here some of these problems in order to clarify my present position. My comments will mainly concern the variety of instances, and only briefly the analogy influence, and the inductive methods for a coordinate language.

This paper is intended to explore Jeffrey's proposal for the measurement of the simplicity of scientific laws. The first part is a sketch of Jeffreys’ development of a view on simplicity, which will be followed by a discussion of what seem to be some rather crucial defects in the proposal as it stands. It will be suggested here that no plausible way of countering these defects seems available.

This article is concerned to argue that the social sciences and notably social anthropology, must necessarily be concerned with the physical environment of the societies investigated (which includes the biological nature of its members), and not only with the social reality which is at the centre of their concern. This is argued with special reference to fields such as kinship and politics, and to social relationships such as paternity or feuding. The article is concerned to refute arguments put forward in support of the logical autonomy of social studies, particularly in the sphere of kinship, in earlier articles by Barnes and Needham.

This paper deals with the problem of vindicating a particular type of inductive rule, a rule to govern inferences from observed frequencies to limits of relative frequencies. Reichenbach's rule of induction is defended. By application of two conditions, normalizing conditions and a criterion of linguistic invariance, it is argued that alternative rules lead to contradiction. It is then argued that the rule of induction does not lead to contradiction when suitable restrictions are placed upon the predicates admitted. Goodman's grue-bleen paradox is considered, and an attempt to resolve it is offered. Finally, Reichenbach's pragmatic argument, hinging on convergence properties, is applied.

Because Bertrand Russell adopted much of the logical symbolism of Peano, because Russell always had a high regard for the great Italian mathematician, and because Russell held the logicist thesis so strongly, many English-speaking mathematicians have been led to classify Peano as a logicist, or at least as a forerunner of the logicist school. An attempt is made here to deny this by showing that Peano's primary interest was in axiomatics, that he never used the mathematical logic developed by him for the reduction of mathematical concepts to logical concepts, and that, instead, he denied the validity of such a reduction.

If the currently available theories of semantic information and utility-expectation are to be applied in a satisfactory way, they must be combined with a message-processing procedure. This paper presents a model of communication within which such a procedure can be defined. In this model the sender's messages arrive over a period of time, the receiver can reject some messages and retain others, the receiver can change his mind in various ways, and the receiver can apply various evaluation functions to a “usable message total”. As one example of message-evaluation, a system for evaluating news-value is presented.

B. F. Skinner is perhaps even more widely known for his views on science than for his experimental work. His comments on the role of theory in science have been labeled “anti-theoretical,” “ultra-empirical”, “non-theoretical,” “radical,” and worse. His position appears to be both extreme and untenable. Scriven [1] has given us a critique of Skinner that goes beyond mere labeling; it is an examination of the assumptions and implications of such a position.

Hempel and Oppenheim have stated in Part III of their paper “Studies in the Logic of Explanation” [2] a set of conditions for deductive explanation. However, their analysis has come under damaging systematic criticisms in a recent paper by Eberle, Kaplan and Montague [1], The principal aim of the present paper is to review the Hempel-Oppenheim analysis and propose a strengthened version of it that avoids the recent criticisms.