The paper, analyses the role of measurable concepts in deductive explanation. It is shown that such concepts are, although imprecise in a defined sense, exact in that neutral candidates to them do not arise. An analysis is given of the way in which imprecision is related to generalisation, and it is shown how imprecise concepts are incorporated in testable deductive explanations.

An analysis of problematic dispositional predicates like ‘soluble’ is presented. The analysis attempts to combine cogent features of opposed previous analyses of Carnap and Bergmann, while avoiding problematic features of both. The suggestion that there is an ambiguity in negations of assertions of dispositional properties, and a consequent distinction between “not soluble” and “insoluble,” lies at the core of the solution.

The postulates of rational preference suggested by Von Neumann and Morgenstern have been defended as descriptive or empirical generalizations and as normative principles. It is argued that the postulates are inaccurate empirical generalizations and unacceptable normative principles.

Present-day interest in history among philosophers seems largely limited to a debate over the nature of historical explanation among those who for Humean reasons insist that all explanations must rest upon general laws and history cannot be an exception to this, and those who say the historians do explain and since they do not use general laws the Humean claim is obviously mistaken. Like the latter, the present paper takes the explanations of historians seriously, but unlike the latter it is not willing to limit the role of philosophy of history merely to the elucidation of the language in which historians give final expression of their work. Rather it recognizes that those explanations themselves set the stage for further inquiry in that they are required to be justified. It is here that the theories or general laws demanded by Humean analysis come in. After examining examples of general laws offered by way of example of what the “Humean” philosophers are supposed to have in mind, each of which is an immediate generalization of the explanation it is called upon to explain and is, hence, an instance of what has been called “the dogma of universality,” some examples of more promising prospects of theory in history are examined.

The paper has two main aims. The first is to reformulate Hempel's version of the thesis of the symmetry of explanation and prediction, as regards the deductive covering-law model, so as to generalise it and make it no longer subject to some of the criticisms which have been directed at it (Section II). The second aim is to consider, with special critical reference to Hempel's recent treatment in Aspects of Scientific Explanation (New York and London, 1965), some central criticisms of both the constituent parts of the above symmetry thesis, viz. that adequate explanations are potentially predictive (Section III), and that adequate predictive arguments are potentially explanatory (Section IV).

T. S. Kuhn's book, The Structure of Scientific Revolutions, [1], is a long and complex work, containing a large number of examples and arguments bearing on questions in the philosophy, history, and sociology of science. My treatment of it here will necessarily be limited, but I will try to state its main theses and discuss them insofar as this can be done without detailed examination of the examples cited from the history of science.

Reanimated for the contemporary literature in the writings of Quine ([15]), [16]) and Kuhn [7], the conventionalism of Duhem [2] and Poincaré [12] has emerged in the last few years as one of the genuinely interesting topics in the philosophy of science. The theory in question—let us follow Grünbaum [3] in calling it the D-thesis, after its founder, Pierre Duhem—claims three things: (1) a single scientific hypothesis H is never disconfirmable in isolation from its fellow; (2) every single hypothesis H of science presupposes, explicitly or implicitly, the support of a conjunction A = A, • A2 • … • Am of auxiliary assumptions or hypotheses; (3) the failure of an observational consequence of H in face of contradictory evidence disconfirms only the conjunction of H and A, not H alone—i.e. establishes only ∼ (H • A). The logical picture is as follows: