There has been a good deal of discussion of the subject of reductionism in the literature of the history and philosophy of science. It would not be an understatement to claim that the standard or received account of the reduction of theories in science, characterized both by its close attention to the supposed connectability of terms between the theories involved in reduction, and, by the prominence assigned to derivation as the core of the reductionistic enterprise [27], has not fared well in recent critical evaluations ([7], [10], [11], [16], [17], [18], [19], [26], [29], [30], [38]). The derivational view of reduction, or at least the version put forth by Ernest Nagel in his book, The Structure of Science, has been criticized as impractical, inaccurate, idealized, distorting, sterile, and even incoherent [38]. Perhaps the most decimating of all the charges brought against the Nagelian account of derivational reduction is that there is not a single instance of derivational reduction to be found anywhere in the entire annals of scientific inquiry([3], [4], [38]).

The question of truth is central to current discussions in both of the major contemporary styles of philosophizing. In the Anglo-American linguistic and empiricist tradition there is a lively response (some might say backlash) to apparent difficulties caused by recent recognition of theory change and meaning variance in science. And within the Continental hermeneutio tradition there is raised the central question of the truth status of interpretations in the cultural sciences where these appear not to be subject to the criteria of empirical science. Let me say straight away that I believe that the almost universal dependence on versions of the correspondence theory of truth among analytical philosophers will prove seriously inadequate to both forms of the epistemological problem, and that we have to face here a deep challenge to many entrenched assumptions of empiricism — assumptions that are too infrequently brought to the light of day in these discussions.2

The relation of theory to practice has been a persistent concern of Marxist thought, so much so, in fact, that this type of acute self-consciousness might be regarded as one of its constitutive features. Thus in his introduction to the 1971 edition of Theory and Practice, Jürgen Habermas offers the following characterization of critical theory:

Habermas’ fundamental philosophical project is to reinstate, in a contemporary context, the classical idea that human lives can be guided by practical knowledge; i.e., that it is possible to know what are the ultimate human values and direct our lives in accord with this knowledge:2 This project has a central importance because of the ironic turn taken by the development of contemporary society. Previously, societies generally thought they had a clear and rationally founded notion of the ultimate values that should guide human lives; but they lacked the technical resources needed to implement (or remove obstacles to) these values. Today, we have the technical resources to at least make a significant effort toward the realization of our values. But the very scientific advances that have provided these technical resources have called into question the rational bases of traditional values and even led to the suggestion—urged by the positivists—that our ultimate values have no cognitive status but are merely irrational givens.

In a recent monograph, I advocated a new theory—the theory of belief functions—as an alternative to the Bayesian theory of epistemic probability. In this paper I compare the two theories in the context of a simple but authentic example of assessing evidence.

The Bayesian theory is ostensibly the theory that assessment of evidence should proceed by conditioning additive probability distributions; this theory dates from the work of Bayes and Laplace in the second half of the eighteenth century. It is indisputably the dominant theory of epistemic probability today.

The theory of belief functions differs from the Bayesian theory in that it uses certain non-additive set functions in the place of additive probability distributions and in that it generalizes the rule of conditioning to a general rule for combining evidence. As a mathematical theory its apparent origin is rather recent and abrupt; it first appears in work of A. P. Dempster, published in the 1960’s.

R.A.Fisher introduced the fiducial argument as a means for obtaining something from nothing. He thought that on some occasions it was legitimate to obtain a posterior probability distribution over a range of simple statistical hypotheses without commitment to a prior distribution [4].

H.Jeffreys thought he could tame Fisher by casting his argument in a Bayesian mold through a derivation of the fiducial posterior from a suitably constructed ignorance prior via Bayes’ theorem and conditionalization on the data of experimentation. According to Jeffreys, Fisher was using something to obtain something after all ([7],pp.381-383).

D.V.Lindley furthered the process of taming by specifying allegedly necessary and sufficient conditions for the consistency of fiducial reasoning in contexts of one parameter estimation with Bayesian requirements [14]. I. Hacking exploited Lindley’s result to supply his own ingenious method for taming Fisher([5],ch. 9).

T.Seidenfeld has recently demonstrated that Lindley’s conditions are insufficient for consistency and that reconstructions like Jeffreys’ or Hacking’s lead to contradiction ([15], PP. 721-727).

In his recent monograph [7], Professor Shafer has offered us an alternative to Bayesian inference with his novel theory of belief functions and, in his current paper [8], has characterized his position by pointing to two basic differences it shares with Bayesianism. First, belief functions are non-additive so that the degree of belief assigned to the disjunction ‘A1 or A2’ may be larger than the sum of the degrees of belief assigned to the separate disjuncts. Second, the theory of belief functions has its own rule for determining the commitments to changes in degrees of belief when evidence is compounded. So, instead of the Bayesian postulate of conditionalization, that is, in place of using Bayes’ theorem to identify the commitments to changes in probability when evidence accumulates, the theory advocated by Professor Shafer relies on a proposal he traces to A.P.Dempster, which he calls Dempster’s rule for combination of belief functions.

In setting forth a new theory of the growth of scientific knowledge, Larry Laudan shows that any account of scientific change has consequences for the relationship between the history, philosophy and sociology of science. It is a laudable feature of his work that he does not treat any of these disciplines as undifferentiated monoliths. In fact, one of his main goals is to show that his account of progress requires specific ways of doing and relating these three disciplines. As an historian invited to speak at the Philosophy of Science Association, it seemed appropriate for me to appraise the function of history of science in Laudan’s program. Without going into unnecessary detail, let me begin by examining some of his main claims.

The focus of Laudan’s argument is on science construed as a form of problem-solving activity and on progress and rationality as appraisals of problem-solving capabilities.

Like most philosophers, Laudan [7] believes that by and large science makes cognitive progress and that the development of science is more or less rational. His book deals with two major problems:

1. (a) In what sense does science progress? What is scientific progress?

2. (b) Wherein lies the rationality of the growth of science? What is scientific rationality?

In the main body of this paper, I first summarize and evaluate some of Laudan’s criticisms of his predecessors. Then I outline and criticize Laudan’s own theory of scientific progress and scientific rationality. In the Postscript I sketch my own views concerning the issue of changes in the canons of scientific rationality and the problem of using history to evaluate normative theories of scientific rationality.

The two other commentators, being, like Professor Laudan, scholars, have commented on the whole of his book. As a mere philosopher, I may perhaps be forgiven if I get little further than the first chapter of Progress and Its Problems.

We know that the practice of science increases our knowledge and understanding of things and events, and consequently our capacity to predict and control them. That is why the practice of science interests philosophers who are concerned to say how such knowledge and understanding, such capacity for prediction and control, can be acquired. It challenges them to show why scientific practice should deliver these cognitive goods. Some who decline the challenge, or fail to meet it, may deny that it does deliver the goods; but their conscious practice, of preferring aircraft to broomsticks for flight and telephones to telepathy for communication, belies the sincerity of their denials.

Philosophical dialogue is a curious activity. Arguments are expected to be rigorous, but no demand is made that there must be evidence for the premisses. Terminology is expected to be precise, but its appropriateness to the subject matter under discussion can be left unexplored. Officially, nothing is conceded; but, in fact, a great deal is taken for granted. Ad argumentum mingles indiscriminately with ad hominem; and, above all, the evidential warrant for one’s philosophical claims is, like the topics of sex and religion to the less enlightened, one of those delicate issues never to be discussed in mixed company.

Such conventions as these that are associated with contemporary philosophical exchange make it difficult to have a balanced discussion about Progress and Its Problems. That work is, in the first instance, a descriptive model of theory change in science. It purports to establish what sorts of factors have in fact influenced scientific decision-making.

By “Propensities” I mean the kind of probabilities that figure in laws of nature. Propensities might be (i) relative frequencies, finite or long run, de facto or modalized, or (ii) reflections of our epistemic probabilities or (iii) sui generus theoretical notions. I believe that the whole family of relative frequency proposals (i) are inadequate. As an alternative I wish to suggest (ii) an epistemic account of propensities and of nomic force in general, in the spirit of Hume, Mill, DeFinetti, Ayer, Suppes and Jeffrey. Whether accounts of the third kind differ in substance or in name only from the sort of account that I am proposing is a nice question, to which. I will devote some brief closing remarks.

In this paper I consider the question of the reality of chance. This is not what divides contemporary probabilists into the objective and subjective schools. That division is accomplished by the question whether there are objective grounds for the correctness of probability judgments. The subjectivists say that there need not be such grounds, and that probability judgments thus need not be empirically meaningful in the verificationist sense, or perhaps that they are not judgments at all, but rather expressions of attitude. (See [11], pp. 156-198). The objectivists say that the truth conditions for probability judgments are such as the frequencies of traits in populations or the existence of propensities. Objectivists and subjectivists are, however, agreed that there are no objective chances. (See [2], pp. 141, 142; and [12], §16).

There is a Humean argument against the reality of chance which depends mainly upon the premise that we have no experience of it.