It might be thought that the basic concept in medical science is that of health. However, as it turns out, medicine has little or nothing to say about health. (This is less true of some of the other health sciences and health professions, notably nursing and public health.) Instead it is diseases, injuries, impairments, and, to a lesser extent, symptoms which are the focus of concern in medicine. It is a generally recognized and frequently bemoaned fact that in this country, contemporary medicine and medical education largely ignore, not only the promotion of health, but even the prevention of disease and injury. (Medical educators are among those most acutely aware of this situation.) Instead, medicine is principally concerned with the diagnosis and treatment of medical crisis.

It is small wonder that in explicating the concept of health as it is found in the theories which inform the practice of medicine, Boorse arrives at a negative notion, viz., health as the absence of disease and injury.

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]).

Most philosophers and historians of science agree that astrology is a pseudoscience, but there is little agreement on why it is a pseudoscience. Answers range from matters of verifiability and falsifiability, to questions of progress and Kuhnian normal science, to the different sorts of objections raised by a large panel of scientists recently organized by The Humanist magazine. Of course there are also Feyerabendian anarchists and others who say that no demarcation of science from pseudoscience is possible. However, I shall propose a complex criterion for distinguishing disciplines as pseudoscientific; this criterion is unlike verificationist and falsificationist attempts in that it introduces social and historical features as well as logical ones.

I begin with a brief description of astrology. It would be most unfair to evaluate astrology by reference to the daily horoscopes found in newspapers and popular magazines.

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:

The problem of scientific rationality and Feyerabend's views on the subject need no special introduction in this context. What does need emphasis is the desirability of resisting the widespread tendency either to dismiss him as a Dadaist or to take his rhetoric seriously and despair about the rationality of science. Both tendencies betray a failure to appreciate his peculiar contributions, which are a (relatively) novel theory of rationality, and a (relatively) novel problem. The theory is that scientific rationality is essentially rhetorical, in the sense that scientific method ultimately reduces to a matter of techniques of persuasion (as distinct from, say, a matter of “method”); and the problem, which remains even for those who may reject the theory, is that of the role of rhetoric in science.

Since Feyerabend's latest book is full of the rhetoric of irrationalism, it is best to begin by purifying the air surrounding such rhetoric.

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 order to establish the object language of quantum physics, we begin with a quantum mechanical system S (atom, nucleus, elementary particle) and consider propositions A,B,… about this system S which can be proved or disproved by measuring processes. These propositions will be called elementary propositions. We will assume here that elementary propositions are value definite, i.e.,there always exists an experimental testing procedure which decides between truth and falsity of the respective proposition.

The logical connectives A ∧ B (A and B), A ∨ B (A or B), A → B (A then B) and ┐ A (not A) will be defined by means of dialogs. A dialog is a formalized kind of discussion between two participants, the proponent P who asserts a certain proposition and the opponent 0 who attempts to refute it.

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.

In this paper I shall outline a possibility for incorporating category theory in an essential way into the foundations of quantum theory. The role for category theory which I shall sketch here is strictly foundational in the sense that it offers no new perspectives for a physicist working within the quantum formalism, but rather provides a way of interpreting the algebraic structure by giving an alternative axiomatization of the underlying logic of the theory. The axiomatization is given without recourse to any classical set theory by invoking methods closely connected with the work of F. W. Lawvere. More precisely, then, a possible approach to the foundations of physics which axiomatizes its algebraic structure in a way which is independent of set theory and hence points, as it were, to a structuralist foundation of physical theories, will be proposed.

Perhaps no claim in the philosophy of logic has attracted as much attention in the last decade as one defended by Hilary Putnam: some of the so-called ‘necessary truths’ of logic may turn out to be false for empirical reasons and consequently “logic is, in a certain sense, a natural science.” (p. 216). Putnam and others have attempted to reinforce this position by citing findings from quantum mechanics, findings which are intended to provide empirical reasons leading to the conclusion that particular aspects of classical logic have in fact turned out to be false. In this paper I will challenge one of the major procedures leading to the conclusion that quantum mechanics provides ample reason to revise logic. Quantum mechanics, I will argue, has shown neither that logic is empirical nor that some aspect of classical logic is false.

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.

It is natural to regard a given datum, x, as favoring that one of two rival hypotheses, H or K, which affords x higher probability, so that H is favored iff the likelihood ratio; P(x|H):P(x|K) exceeds one. More generally, the relative support x accords the different members of a partition of hypotheses, H1,…,Hn, is assessed by comparing their likelihoods, P(x|Hi). Considered as a function of the Hi, L(Hi) = P(x|Hi) is called the likelihood function. If we view the likelihood function associated with an observed experimental outcome, x, as conveying the entire evidential import of the experiment, then it follows that the two outcomes, x and y, whether of the same or different experiments, are evidentially equivalent just in case they give rise to the same relative likelihoods, P(x|Hi):P(x|Hi) = P(y|Hi):P(y|Hj) for all i,j, or , in other words, iff P(x|Hi) α P(y|Hi) for all i.

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.

I will present a theory of confirmation (support or corroboration) which can be considered both an extension of the work of Ian Hacking on support and of Karl Popper on corroboration. However, it will be clear that my theory is not a “mere conjunction of these two theories” (p. 202) but a formally simple and intuitive synthesis that explains their strengths and corrects their weaknesses.

Popper's explication of corroboration relies on the expression P(e,h) - P(e)2 normalized in different ways (p. 410). He goes on to state the following additional criteria for the corroboration of h by e: (a) we can only “rationally justify a preference for one theory out of a set of competing theories…. so far proposed” (p. 82); (b) e must be the result of a severe test (pp. 414, 418); (c) more-falsifiable hypotheses must be preferred (p. 41); (d) if h is a probabilistic hypothesis then e can only be a statistically interpreted finding, and thus e is often not allowed to be the total available evidence (p. 413).

Smokers are more likely to develop lung cancer than non-smokers. This statistical association gives us reason to suppose that smoking can cause lung cancer. But we would come to reject this supposition if we discovered that when family histories of lung cancer are taken into account smoking makes no further difference to the probability of lung cancer: that amongst those with a family history of lung cancer (and amongst those without) non-smokers are just as likely to develop lung cancer as smokers. Such a discovery would lead us to conclude that, despite initial appearances, smoking actually makes no causal contribution to lung cancer, but is statistically associated with it only because a genetic predisposition to lung cancer also somehow predisposes people to smoke.

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.