Item: One of the earliest surprises to emerge from Carnap’s precise and systematic study of confirmation was the untenability of the initially plausible Wittgenstein confirmation function ct. Carnap’s objection rested on the fact that ct precludes “learning from experience” because it fails to incorporate suitable relevance relations. Carnap’s alternative confirmation function c* was offered as a distinct improvement because it does sustain the desired relevance relations.¹

Item: On somewhat similar grounds, it has been argued that the heuristic appeal of the concept of partial entailment, which is often used to explain the basic idea behind inductive logic, rests upon a...

“Our knowledge is of matters of fact and of relations of ideas. Logic — inductive and deductive — concerns relations of ideas. As to our factual knowledge, some of it we have direct, through the senses, and the rest we have from the direct part, through logic.” This is a rough sketch of Carnap’s empiricism. Let me now try to fill it in, to get a fair likeness.

For at least his last thirty years, this much of Carnap’s view was constant: Inductive logic ought to be representable by a network, the nodes of which are the sentences (or, indifferently, the propositions...

In the past, objections have been raised to the notion of a probabilistic confirmation theory on the grounds that it required assignment of initial probabilities to expressions of hypotheses and evidence and that these probability values are not directly verifiable as are probabilities in the classic theories of equipossible alternatives or in the statistical frequency theory. Such objections have often come from philosophers and statisticians of positivist bent¹ and are closely parallel to objections within science itself to introduction of theoretical concepts that are not directly verifiable. The deductivist analysis of science has, however, released us from the tyranny of...

The theory of confirmation sketched herein is subjectivist in a manner that will be explained. According to it, however, the degree of confirmation of a hypothesis is an objectively existing relative frequency (or a propensity, if one prefers). The resolution of this apparent paradox is simple, but its implications are, I believe, profound. I am convinced that they provide the means for resolving all of the current “paradoxes,” “riddles,” and “puzzles” of confirmation and induction. This is an overstatement only if one assumes, contra hypothesis, that all is pretty much all right with contemporary theories of confirmation and that resolution...

In his essay, “Scientific Inference,” Abner Shimony presents an analysis of scientific confirmation which ties together two twentieth-century proposals for treating the justification of our scientific methodology. To characterize the first of these proposals, to be referred to as the method of pragmatic justification, scientific inference is analyzed as an activity which we undertake in order to achieve certain more or less specifically described ends. It is admitted that we cannot be sure of achieving those ends. But, on this view, if we desire the ends and if we have no reason to suppose them unattainable, we are justified in...

1. One of the few things about which I am optimistic is that we are close to a clear understanding of scientific inference. I think that, as a result of the work of many contributors, all the elements for a complete theory of scientific inference are at hand — although it is risky to say so, especially in view of the dramatic history of deductive logic after it was commonly supposed to have been a complete science. However, even if the requisite elements have all been discovered, there is still hard work to do in properly combining them, for what is...

The objective of this paper is to complete one part of a broad program for resolving all important issues involving probability, inductive logic, and scientific inference generally. I shall begin by sketching the general program and locating the specific problem of interest in the general scheme. After the specific problem has been resolved I will conclude with some further discussion of the general program.

Though metaphilosophy belongs last in the order of discovery, there are good reasons for putting it first in the order of exposition. Let us begin, therefore, with the meta-question: What is the ultimate goal of inquiry...

Many people suppose that there isn’t any real problem in arguing from known relative frequencies or measures to epistemological probabilities. I shall argue the contrary — that there is a very serious and real problem in attempting to base probabilities on our knowledge of frequencies — and, what is perhaps more surprising, I shall also argue that this is the only serious problem in the epistemological applications of probability. That is, I shall argue that if we can become clear about the way in which epistemological probabilities can be based on measures or relative frequencies, then we shall see, in broad outlines,...

1. Introduction. The purpose of this paper is to present a theory of inductive inference and rational acceptance in scientific inquiry. A concept ofrelevantdeduction is defined in which the truth of each and every premise of a deductive argument is essential to establishing the truth of the conclusion by deduction from the premises. This definition is based on the completely abstract notion of a minimally inconsistent set of statements. In terms of this same abstract logical concept and the relation of probability, we shall define a concept of inductive inference that is a principle of rationality. This concept...

I shall attempt to deal with the most basic issues of confirmation, inquire what precisely the term ‘induction’ stands for, what the problem of induction amounts to and what, if anything, can be suggested in a way of solution.

Let us begin by picturing to ourselves Galileo rolling down round objects along an inclined plane in an effort to discover experimentally the law governing the relationship between the distance traveled by the rolling body, subject to the earth’s gravity and the time taken to cover that distance. We shall imagine that at the end of seven experiments he has collected...

Professor Schlesinger presents us with an argument which he hopes will justify use of his methodological principle, that of picking among competing hypotheses the simplest one which is not contradicted by the evidence. The argument seems to take several different forms none of which I find convincing. Let me try to explain briefly what seems to go wrong.

Professor Schlesinger remarks (p. 331) that, at least when our behavior is concerned, we cannot remain agnostic with respect to many propositions about the unobserved. And (though this is not explicitly said) if we are not to form our beliefs about the...

At the outset of his comments Professor Teller expresses disquiet at what seems to him my claiming to have a rule which is capable of automatically generating the hypothesis to be adopted when given nothing but the experimental data. Such a claim would indeed be quite preposterous since everybody knows that there are no clear-cut principles for the production of hypotheses, but that these are suggested by the imaginative insights of a high talent which conjectures without the aid of any rules of scientific discovery. Subsequently, he expresses the hope that I may not have had such a claim in...

In this paper¹ I present no results, only questions; and, I hope, difficulties.

1. Central to all theories of induction is an insistence on instances. Instances of a universal theory are needed to confirm it. The problem is: how many?

Hume of course showed that no quantity of instances could verify a universal generalization. In his Abstract (1740, p. 15) he argued further that no number of instances could make a universal generalization even probable. The former result is not seriously contested these days; if we can judge by the continued interest in probabilistic inductive logic, the latter is. Since...

An important feature of Carnap’s approach to the problems of probability and induction is his sharp distinction between inductive logic proper and the methodology of induction.¹ His formula for the singular predictive inference, for example, belongs to the former, and his requirement of total evidence to the latter. Under the methodology of induction he subsumes, among other things, all matters concerning random samples. His view seems to be that a methodological rule requires samples to be chosen by random methods, and hence the theorems of inductive logic itself need not concern themselves with considerations of randomness.²

A less-noticed and seemingly...

A fully satisfactory account of a propensity theory has yet to be given even by proponents. Much less satisfactory have been the accounts given of propensity theory by its opponents. This paper is aimed to contribute to the debate over propensity theory by drawing attention to its metaphysical presuppositions. Although I do endorse a propensity theory of probability, this paper aims only secondarily to defend propensity theory against attack. Nonetheless a good starting point in my exposition might be an initial appraisal of a number of recent writings, in the hope that creative criticism may aid a more satisfactory characterization...

This paper is a critique of Popper’s interpretation of quantum mechanics and the claim that the propensity interpretation of probability resolves the foundational problems of the theory. The first two sections are purely expository. In section 1, I sketch Popper’s conception of a formal theory of probability and outline the propensity interpretation. Section 2 is a brief description of the gist of Popper’s critique of the Copenhagen interpretation of quantum mechanics and his proposed solution to the measurement problem (the problem of the “reduction of the wave packet”). In section 3, I show that the propensity interpretation of probability cannot...

The problems of inference are manifold: the first task facing the theorist concerned with them is to attempt an ordering of priorities, to decide which of them to tackle. One must assay not only the relative importance of the various problems but also the possibilities of achieving their successful solution; only then may the individual problems profitably be addressed. Historically, the majority of philosophers have concluded that the problem of inference is that of induction, and more specifically the problem of thejustificationof induction. According to the point of view from which they operate, the prime task of the...

In this paper I wish to raise a philosophical question about logic, namely, the question whether its laws can consistently be thought of as analogous to those of the empirical sciences, i.e., as subject in some sense or other to test and confirmation, or whether, as is more often maintained, they must be thought of as analytic and a priori if not as coventional. In order to float the question, some general idea of what kind of activity logic is must be presupposed. The problem of logic I take to be as follows: Given the truth (or probability) of sentences...

This paper is addressed to a philosophical problem posed by physical laws. The problem is one of meaning and metaphysics. How are the meanings of physical laws to be distinguished from the meanings of accidental generalizations? Two prima facie alternatives are as follows:

(1) Physical necessity and possibility and causal relationships arereal relationsin the world. The claim made by a physical law is the claim made by the corresponding accidental generalizationplusthe claim that such relations obtain.

(2) The apparent difference in meaning between physical laws and accidental generalizations is an illusion. The meaning of the law...

When I first considered writing this paper, I thought that perhaps one way to do it would be to have one page contain the title and then devote a few blank pages to what I want to say. Instead I have decided to put some marks on the pages. I will relate some parables and poems of science, some tales of science fiction-fact, which will (like the koans of the Zen master) lead you into paradoxes. In this way I will show you the paradoxes rather than tell them to you. Sometimes I will try to tell you them. But...