This paper tries to extend Hintikka's inductive logic so that we can confirm a causally necessary statement. For this purpose, a joint system of inductive logic and logic of causal modalities is constructed. This system can offer a plausible explication of the distinction between nomic and accidental universality, as well as a good formulation of a causal law. And the transition from actuality to causal necessity is construed, in this system, as essentially probabilistic; i.e. no statements about actuality can entail (...) a necessary statement, but certain statements about actuality can single out a most probable causal law. (shrink)

To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what?”, is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function (...) and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments. (shrink)

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.

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. (shrink)

This general type of view may be characterized more fully by using the notion of an inductive method. All scientists use approximately the same inductive method, which we will call the standard inductive method. This method is based on the rule of induction by simple enumeration, which may be roughly stated as follows: if it is known only that a certain property Ψ has accompanied another property Φ in a number of instances, then the larger this number of instances the (...) higher the probability that the next occurrence of Φ will be accompanied by Ψ. Though scientists actually reason inductively in accord with this rule, it is important that there are logically consistent inductive methods based on alternative rules. We will describe two of these briefly. The inverse inductive method assigns probabilities according to the rule that if it is known only that Ψ has accompanied Φ a number of times, then the larger the number of instances the lower the probability that the next occurrence of Φ will be accompanied by Ψ. The random predictive method assigns to the proposition that the next occurrence of Φ will be accompanied by Ψ a probability completely independent of the number of times that Ψ has accompanied Φ in the past.. (shrink)