Although this note is prompted by the recent exchange between Gellner [2], [3] and Needham [4], I shall ignore the issues raised by Gellner's specification for an ideal language. I am concerned here only with Needham's statement that ‘biology is one matter and descent is quite another, of a different order’ which, it will be remembered, Gellner treats as Needham's first error. I write under a sense of obligation, for I discussed this matter with Gellner in 1955 while he was preparing his first article and my arguments then were phrased similarly to those advanced by Needham. It appears that I did not make myself clear to Gellner and I shall try again. I do not wish to attack or defend either protagonist; each is quite able to look after himself. Therefore I propose neither to examine where they have misunderstood each other, nor to discuss the difference between kinship (Gellner's starting-point) and descent (Needham's), but simply to state the connexion, as I see it, between physical and social kinship.

I am grateful to Professor Wheatley for his note, [3], on my analysis of interrogatives, [1]. His comments bring out very clearly a number of considerations that deserve our closest attention. For example, he shows that if we can classify interrogatives as true and false—as I proposed to do—then we can properly inquire about what sentences contradict them, and what sentences are contingently or logically equivalent to them. Furthermore, he shows that, on my analysis, no indirect question can contradict any other indirect question and he accordingly, and correctly, looks for such contradictories among declarative sentences. (Different considerations than any that Professor Wheatley brought out will equally well show that no direct question will contradict any other direct question: “Is Freeman Governor of Minnesota?” and “Is not Freeman Governor of Minnesota?” express different concerns with one and the same topic of concern, hence, are equivalent.) Finally, he notes, [3], p. 54, that in my article, I have treated only inquisitive questions and have said nothing about deliberative or practical questions. While practical questions (as well as their practical answers) demand a different kind of treatment than that which Wheatley speculatively, albeit very tentatively, extrapolates for me, still these questions do form a kind of interrogative that did not get any attention in my article. (But the problems are so complex that I shall not try to say anything about them in this Reply.)

Hempel and Oppenheim, in their paper ‘The Logic of Explanation’, have offered an analysis of the notion of scientific explanation. The present paper advances considerations in the light of which their analysis seems inadequate. In particular, several theorems are proved with roughly the following content: between almost any theory and almost any singular sentence, certain relations of explainability hold.

One does not only talk about the length in inches of this sheet of paper but also about the length of this sheet, about length in inches and about length. A clarification of these and related concepts results from a combination of the theory of the length in a definite unit as a fluent, developed by one of the authors, with the other's concept of 2-place fluents. The length ratio L is defined by pairing a number L (α, β) to any two objects of a certain kind, α, β (in a definite order). L thus may be described as the class of all pairs (α, β), L (α, β) for any objects α, β of the said kind. Length of this sheet and length in inches are specializations of this 2-place fluent.

Criticism of the deductive model of explanation continues. In a recent article, “Truisms as the Grounds for Historical Explanations,” Professor Michael Scriven hangs a great many critical points from the distinction between explanations and their justifications. I should like to examine his proposal with a view to showing that in so far as this distinction can be made, it cannot be used as a basis of criticisms of the deductive or covering law model, as it was originally outlined by Professor Carl G. Hempel.

One of the recurrent temptations in theory of knowledge is to try to provide an inductive justification for employing the principles of inductive inference. The purpose of the present paper is to suggest that this approach is misguided by exposing the deficiencies of what appears to be the most carefully constructed attempt of this kind which has thus far been made. I refer to the attempt made by R. B. Braithwaite in his Scientific Explanation.

The paper aims to put certain basic mathematical elements and operations into an empirical perspective, evaluate the empirical status of various analytic operations widely used within psychology and suggest alternatives to procedures criticized as inadequate.

Experimentation shows the “manyness” of items to be a perceptual quality for both young children and animals and that natural operations are performed by naive children analogous to those performed by persons tutored in arithmetic. Number, counting, arithmetic operations therefore can make distinctions that are not inevitably arbitrary, and conceptual operations can obviously have a status as natural events with psychology. If the elements and conceptual operations involved in mathematical systems were not inherent in physiological process, various primitive discriminations could not be possible. Also, since some calculi have a natural status in a given empirical circumstance, the axioms of others can not be satisfied. Therefore the psychologist when acting as an empirical scientist seeks a calculus having a structure whose elements are isomorphic with natural units of stimulus and response and whose operations are isomorphic with whatever natural processes are involved.

Measurement poses a special problem for the empirical scientist. It concerns but a single class of natural qualities and this only in a limited way. The concept of quantity has a natural counterpart but quantity and measurement are not wholly analogous. Measurement is defined, as H. S. Leonard suggests, as a theoretical activity. Measurement theory has a formal structure but empirical end. Measurement hypothesizes about the position of a particular quality within a definite range of qualities. It therefore is beholden to definite empirical restrictions.

Some hypotheses-making systems use terms and relations per se as the context and starting point for dealing with discriminable events. Such procedures are “transcendent.” In empirical science, questions are part of problem-solving activity and their reference is naturally restricted. In providing description and explanation, psychological researchers frequently use calculi in a transcendent way. This results in theories that are only quasi-empirical and “half” true.

The roles measurement plays in psychology are discussed. Of particular concern are those cases in which the results of measuring or a theory of measurement are used to define the “real” units, or the “real” relations involved in problematic psychological events, and thence to describe and explain behaviors of interest. Metaphysical or ontological usages of measurement sometimes occur. The implication of these arguments with regard to a view of empirical science is discussed.

In ‘Hempel and Oppenheim on Explanation’, (see preceding article) Eberle, Kaplan, and Montague criticize the analysis of explanation offered by Hempel and Oppenheim in their ‘Studies in the Logic of Explanation’. These criticisms are shown to be related to the fact that Hempel and Oppenheim's analysis fails to satisfy simultaneously three newly proposed criteria of adequacy for any analysis of explanation. A new analysis is proposed which satisfies these criteria and thus is immune to the criticisms brought against the earlier analysis.

The physics of the past half-century has thoroughly discredited the simple atomistic view that an ultimate explanation of all natural processes may be found in a mechanism of cause-and-effect relations among such clearly defined entities as point-like particles. And yet, physics and the other sciences continue to find nature to be orderly and lawful. How do we reconcile this breakdown of what once seemed to be the causal basis for the order of nature with the continued discovery of new manifestations of that order? The subject book [3] of this paper, written by the Professor of Theoretical Physics and Philosophy of Science at Buenos Aires University, may be considered to be a response to this question. There are many other things too in the book: it provides a much needed collecting, and sorting, of various questions that have been asked and answers that have been given with respect to causality. (The book could well serve as a textbook for a course on this topic.) There are statements in the book that may be justifiably criticised, as I hope later to show; but in all I believe that Professor Bunge has given us a work that makes a contribution of importance to philosophical discussions of causality.

This paper argues against the deductive reconstruction of scientific prediction, that is, against the view that in prediction the predicted event follows deductively from the laws and initial conditions that are the basis of the prediction. The major argument of the paper is intended to show that the deductive reconstruction is an inaccurate reconstruction of actual scientific procedure. Our reason for maintaining that it is inaccurate is that if the deductive reconstruction were an accurate reconstruction, then scientific prediction would be impossible.

The object of the present discussion is to show that the analysis of indirect discourse obtained when the concept of assertion is construed as a relationship that obtains between the asserting person and the asserted proposition—along the familiar lines proposed by Church [3, 4]—is entirely adequate of itself to circumvent the semantical paradoxes in which indirect discourse is involved.

In his review of our Gödel's Proof in the April 1960 issue of Philosophy of Science Professor Hilary Putnam severely criticizes the crucial chapter, in which we attempt to make intelligible to the non-specialist the general character of the argument for Gödel's main conclusions. Indeed, he asserts that “the chapter culminates in an extremely serious misstatement,” and that we “fail to give the proof that G [the Gödel sentence upon which the argument hinges] is not provable.” “The book,” he declares, “has thus a serious shortcoming (in a very literal sense of ‘shortcoming’: it comes right up to the heart of Gödel's argument and then stops short with a misstatement')” (p. 205). These assertions impugn the competence of our exposition of Gödel's achievements, and we therefore ask for the privilege of replying to Dr. Putnam's allegations.

A practical or pragmatic justification (“vindication”) applies to actions. The action concerned in the case of induction is the making of predictions, and—philosophically of prime importance—the adoption of such rules of procedure as will make the predictions maximally successful. Clearly all ordinary cases of the justification of actions utilize, and in this sense presuppose, inductions. (A prospector looking for gold presupposes that there is gold to be found somewhere in the area of his search. If he had no reason whatever for expecting gold there, we should call his belief irrational, a product of wishful thinking. Inductive evidence for the presence of gold is required.) When philosophers ask for a ground of induction in general the answer cannot be inductive evidence. This would be plainly circular or lead to an infinite regress. Hence we are here dealing with a limiting or degenerate case of justification. It is true that one important component of the meaning of such words as “reasonable” or “rational” is indeed the employment of inductive procedures. Many analytic philosophers rest their case right here and consider the quest for a justification of induction as a pseudo problem because, in their view, this quest comes down to asking “is it reasonable to be reasonable?” But—because of an ambiguity of the term “reasonable”—it is precisely here where the distinction between validation and vindication is helpful and points the way to one more step that can be taken in the overall justification of inductive inference.