The Foundations Of Scientific Inference

The Foundations Of Scientific Inference

Wesley C. Salmon
Copyright Date: 1967
Pages: 168
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  • Book Info
    The Foundations Of Scientific Inference
    Book Description:

    Not since Ernest Nagel's 1939 monograph on the theory of probability has there been a comprehensive elementary survey of the philosophical problems of probablity and induction. This is an authoritative and up-to-date treatment of the subject, and yet it is relatively brief and nontechnical.

    Hume's skeptical arguments regarding the justification of induction are taken as a point of departure, and a variety of traditional and contemporary ways of dealing with this problem are considered. The author then sets forth his own criteria of adequacy for interpretations of probability. Utilizing these criteria he analyzes contemporary theories of probability , as well as the older classical and subjective interpretations.

    eISBN: 978-0-8229-7125-2
    Subjects: Philosophy, General Science

Table of Contents

  1. Front Matter
    (pp. [i]-[vi])
  2. Table of Contents
    (pp. [vii]-[x])
  3. Introduction
    (pp. 1-5)

    Although perhaps born earlier, mathematical physics came of age in the seventeenth century through the work of such men as Descartes, Calileo, Kepler, and Newton. This development constituted one of the most far-reaching of all revolutions in human thought, and it did not go unnoticed by various philosophers, some of whom had made significant contributions to it. There were, consequently, serious philosophic efforts to understand the logic of the new science.

    Mathematical physics has an abstract and formal side as well as an observational and experimental side, and it has never been easy to understand the relations between them. Philosophies...

  4. I. The Problem of Induction
    (pp. 5-11)

    We all believe that we have knowledge of facts extending far beyond those we directly perceive. The scope of our senses is severely limited in space and time; our immediate perceptual knowledge does not reach to events that happened before we were born to events that are happening now in certain other places or to any future events. We believe, nevertheless, that we have some kind of indirect knowledge of such facts. We know that a glacier once covered a large part of North America, that

    the sun continues to exist at night, and that the tides will rise and...

  5. II. Attempted Solutions
    (pp. 11-54)

    It hardly needs remarking that philosophers have attempted to meet Hume’s intriguing challenge in a wide variety of ways. There have been direct attacks upon some of Hume’s arguments. Attempts to provide inductive arguments to support induction and attempts to supply a synthetic a priori principle of uniformity of nature belong in this category. Some authors have claimed that the whole problem arises out of linguistic confusion, and that careful analysis shows it to be a pseudoproblem. Some have even denied that inductive inference is needed, either in science or in everyday affairs. In this section I shall survey what...

  6. III. Significance of the Problem
    (pp. 54-56)

    Hume’s problem of induction evokes, understandably, a wide variety of reactions. It is not difficult to appreciate the response of the man engaged in active scientific research or practical affairs who says, in effect, “Don’t bother me with these silly puzzles; I’m too busy doing science, building bridges, or managing affairs of state.” No one, including Hume, seriously suggests any suspension of scientific investigation or practical decision pending a solution of the problem of induction. The problem concerns thefoundationsof science. As Hume eloquently remarks inEnquiry Concerning Human Understanding:

    Let the course of things be allowed hitherto ever...

  7. IV. The Philosophical Problem of Probability
    (pp. 56-65)

    The foregoing lengthy discussion of the problem of induction has been presented, not only for its own sake, but also for its crucial bearing upon the problem of explicating the concept of probability. Although I cannot claim to have provided an exhaustive discussion of the whole variety of ways in which philosophers have tried to solve or dissolve Hume’s problem, I do maintain that no such attempt has yet proved completely satisfactory. At the very least, there is nothing approaching universal agreement that any has succeeded. I have attempted to show, moreover, that the problem of induction does not immediately...

  8. V. Interpretations of Probability
    (pp. 65-96)

    This section will survey five leading interpretations of probability, confronting each of them with the three foregoing criteria.

    This interpretation is one of the oldest and best known; it defines probability as the ratio of favorable to equally possible cases.⁸⁶ With a perfectly symmetrical die, for instance, the probability of tossing an even number is three sixths. Three sides have even numbers—the favorable cases—and there are six equally possible sides. The immediate difficulty with this interpretation is that “equally possible” seems to mean “equally probable,” so the definition appears to be flagrantly circular. But the apparent circularity can...

  9. VI. Inferring Relative Frequencies
    (pp. 96-108)

    Theorists of various different persuasions agree that relative frequencies are basically germane to probability theory, whether or not they are willing todefine“probability” in terms of them. Carnap, who is the greatest proponent of the logical interpretation, insists that there are two concepts of probability—the logical concept and the frequency concept. He argues, moreover, for an intimate relation between relative frequency and degree of confirmation. The use of probability as a fair betting quotient rests upon its relation to the frequency with which various kinds of events occur. In addition, degree of confirmation can be interpreted in appropriate...

  10. VII. The Confirmation of Scientific Hypotheses
    (pp. 108-131)

    Quite early in this essay, I acknowledged the fact that induction by enumeration is a far cry from what we usually regard as scientific inference. When we think of scientific reasoning, we are likely to bring to mind the grand theories like those of Calileo, Newton, Darwin, or Einstein, and to contemplate the manner in which they were established. This is in obvious contrast to the attempt to infer the limit of a relative frequency from the observed frequency in an initial section of a sequence of events. Scientific inference is usually thought to be hypothetico-deductive in structure. Induction by...

  11. Conclusion
    (pp. 131-132)

    The analysis of the inference by which scientific hypotheses are confirmed by observational evidence shows, I believe, that its structure is given by Bayes’ theorem. This schema provides a place for the hypothetico-deductive method, showing that it is fallacious in its crude form, but that it can be made into a valid method when appropriately supplemented. Two kinds of probabilities are needed to supplement the hypothetico-deductive schema. We must assess the probability that our observational results would obtain even if the hypothesis under consideration were false. For strongest confirmation, this probability should be small. This seems a natural interpretation of...

  12. Notes
    (pp. 132-141)
  13. Addendum, April 1967
    (pp. 142-144)

    The Foundations of Scientific Inference, as here reprinted, is identical with the original version published inMind and Cosmos, except for the correction of typographical errors. In this brief supplement I should like to do two things. First, I want to bring the references up to date by taking note of a number of important publications that have direct bearing on the issues discussed here. Second, I shall try to clarify a couple of central points on which my formulations have led to misunderstanding or confusion.

    Since the writing of this study a number of significant developments have occurred, including...

  14. Index
    (pp. 145-157)