Because statements like ‘This object is soluble in aqua regia’ involve the causal modalities, we call them causal dispositional statements. Now while this involvement has long been recognized, no thorough examination of its exact nature has ever been made. One purpose of this paper is to begin such an examination. In Sec. 2 we will suggest an analysis of causal dispositional statements, and in Sec. 3 we will discuss some philosophic issues to which this analysis is relevant.

In order to determine what are the metaphysical presuppositions of science (if any), we have to first define the terms ‘presupposition’ and ‘metaphysics’ or ‘metaphysical’. We shall begin with the former.

Arthur Pap in his article Does Science Have Metaphysical Presuppositions? discusses two senses of the term. A presupposition may be (a) a necessary condition: p presupposes q, dt = p implies q, i.e. not-g implies not-p. (b) a premise or a rule (or a set of rules) of inference used in deriving a belief. Thus in this sense, p presupposes q means that if q were false, then the belief in p would cease to be grounded.

Dialectic, like love, has a good and a bad reputation. This ambivalence may be illustrated in different ways in almost every period of philosophical history. One may even suspect that this richness borders upon confusion. And yet, the attempt to orientate oneself in this jungle of meanings can be expected to be profitable, for the term “dialectic” has always referred, although often obscurely, to notions and processes of the first importance. The definition, illustration, and evaluation of the uses of this term should, accordingly, be a task promising some value.

1. The Problem. In spite of the vast discussion which has been devoted to the theory of probability, the problem of the short run has received surprisingly little attention. Yet, the whole significance of the theory depends upon a solution of this problem, for without an answer to it we cannot say why it is useful to have knowledge of probabilities or why we should take account of this knowledge in making practical decisions. As far as I know, Charles Peirce was the first to appreciate the importance and difficulty of the question, and his characteristically vivid formulation serves as an excellent starting point for its consideration. He says:

According to what has been said, the idea of probability essentially belongs to a kind of inference which is repeated indefinitely. An individual inference must be either true or false and can show no effect of probability; and therefore, in reference to a single case considered in itself, probability can have no meaning. Yet if a man had to choose between drawing a card from a pack containing twenty-five red cards and a black one, or from a pack containing twenty-five black cards and a red one, and that of a red one were destined to transport him to eternal felicity, and that of a black one to consign him to everlasting woe, it would be folly to deny that he ought to prefer the pack containing the larger proportion of red cards, although from the nature of the risk, it cannot be repeated. [Collected Papers, 2.652]

When Whitehead's views of relativity are mentioned, everyone thinks of the views Whitehead published between 1919 and 1924. Concerning these views, C. D. Broad is “depressed”1 (1: pp. 143–4) that physicists paid so little attention. And Victor Lowe has written:

There is a bare possibility that Whitehead's theory of relativity may yet affect the history of science. (4: p. 69)

The central concept of Carnap's probabilistic theory of induction is a triadic relation, c(h, e), the probability or degree of confirmation of the hypothesis, h, on evidence, e. The relation is a purely logical one. The value of c can be computed from a knowledge of h, of e, of the structure of the language, and of the inductive rule to be employed.