INTRODUCTION

In Chapter VI (“Time”) of Paul Weiss's first book, Reality, there are many incisive phenomenological reports concerning time, among them the following:

Weiss never revoked these early philosophical comments, but he did elaborate them. For instance, in First Considerations one finds the following:

The present paper is essentially an exploration of the ideas expressed in these three passages. I agree with them at the commencement of my analysis and continue to agree with them when the analysis is completed. However, my mode of analysis – which combines considerations from phenomenology, analytic philosophy, and natural science – is quite different from Weiss's, and I shall proceed without further reference to his texts.

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability condition implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates when factorisability is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed.

INTRODUCTION

In most of the discussions of Bell's Inequalities little notice is taken of the historical circumstances of their discovery. J. S. Bell was told by J. Jauch of the work of A. Gleason [1957] which showed that simultaneous values cannot be assigned to all observables of a quantum mechanical system in a way that respects their algebraic structure (except in the simple case in which the relevant Hilbert space has dimension less than three). Gleason's theorem thus precludes a type of hidden variables theory that has come to be called ‘noncontextual’. The question of agreement between the statistical predictions of quantum mechanics and those of a noncontextual hidden variables theory does not even arise, since such a theory cannot be consistently formulated.

CONTRIBUTION OF THE NATURAL SCIENCES TO A WORLDVIEW

In a sense every human being with rudimentary intelligence has a worldview, that is, a set of attitudes on a wide range of fundamental matters. A philosophical worldview must be more than this, however. It must be articulate, systematic, and coherent. A philosophical worldview may be naturally subdivided into at least the following parts: (1) a metaphysics, which identifies the types of entities constituting the universe (possibly organizing them into a hierarchy, with some fundamental and others derivative), and which in addition asserts fundamental principles, such as those of cause and chance, that govern these entities; (2) an epistemology, concerned with the assessment of human claims to knowledge or justified belief; (3) a theory of language; and (4) a theory of ethical and aesthetic values. For reasons of professional training and preoccupation, and also of relevance to this collection of essays, I shall confine my comments almost entirely to metaphysics and epistemology.

A necessary condition for the coherence of a philosophical worldview is the meshing of its metaphysics and its epistemology. The metaphysics should be capable of understanding the existence and the status of subjects like ourselves who are capable of deploying the normative procedures of epistemology. And the epistemology should suffice to account for the capability of human beings to achieve something like a good approximation to knowledge of metaphysical principles, in spite of the spatial and temporal limitations of our experience and the flaws and distortions of our sensory and cognitive apparatus.

In the world as we know it there is an immense variety of systems having identifiable parts. If one focuses only upon inorganic systems one can recognize a descending hierarchy of cosmos, metagalaxy, galaxy, star (possibly with attendant planets), macroscopic bodies, molecules, atoms, elementary particles; or, more accurately, one can recognize a number of alternative physical hierarchies. If one focuses upon organisms, one finds multi-cellular plants or animals, organs and suborgans, cells, and organelles; and there are molecules which are identifiable parts of cells. The taxonomy of systems can be extended further by considering entities which are less concrete than the foregoing. For example, space-time has regions of space-time as parts, and points as members.

In view of this variety, it is probably unwise to adopt a unitary position either of holism or of individualism concerning the ontological status of parts and wholes in systems generically. Furthermore, one should not characterize the philosophical position of a historical figure simplistically, without taking into account his treatment of different types of systems. Newton, for example, is often taken to be an arch-analyst, since he analyzes the behavior on any composite system in terms of the particles which compose it and the forces upon these particles (due either to each other or to external agents). Newton's ontological position, however, is holistic in at least two ways. First, his atoms are indivisible, even though they have geometrically discriminable parts.

INTRODUCTION

The orthodox logical empiricist treatment of the relation between scientific theories and observations (as exemplified in the work of Rudolf Carnap, Ernest Nagel, Carl Hempel, and R. B. Braithwaite) abstained as a matter of principle from considerations of empirical psychology. Since psychology is the least developed of the natural sciences, an appeal to it was supposed to subvert the epistemological program of establishing a firm foundation for all the sciences. Furthermore, epistemology was not considered to be in need of the answers to the questions typically investigated by empirical psychology. It is also likely that the abstention of the orthodox logical empiricists from empirical psychology in their treatment of the relation between theories and observations was in large part due to their acceptance of Gottlob Frege's polemic against psychologism in logic, for they regarded the central problem concerning this relation to be one of logic.

This essay is both an appreciation of the epistemological contributions of Donald Campbell and a statement of an epistemological program which is different from his in several respects.

In a lecture to the Boston Colloquium for the Philosophy of Science in 1977, he said:

Campbell's resolute restriction of his investigations to descriptive epistemology is both his great strength and his weakness. It is his strength because it frees him, at one stroke, from the slow-paced type of inquiry that dominates the literature of analytic epistemology: for example, “When I see a tomato there is much that I can doubt” (Price, 1932, p. 33).

BAYESIAN GENERALITIES ON INDUCTIVE INFERENCE

My most systematic discussion of inductive inference was “Scientific Inference,” published in 1970. The title indicates its primary concern with reasoning in the sciences, though many of its considerations also apply elsewhere. I aimed at articulating principles of inductive reasoning actually used by working scientists, sometimes explicitly and sometimes tacitly. And I proposed justifications of these principles, in spite of the powerful tradition from Hume onward that this exercise is futile. Of course, the proposals for justification had to be made in tandem with a dialectical examination of the criteria that “justification” should satisfy.

My proposals fell under the denomination of “Bayesian,” with some reservations. The central concept of inductive inference was taken to be epistemic probability: a quantitative measure of reasonable degree of belief in a hypothesis on specified evidence. The standard epistemic probability notation “P(h/e) = r” is to be read, “the reasonable degree of belief in h, given e as the total body of evidence, is (the real number) r.” This rough explication is vague, for the constraints on “reasonable” are not specified, and indeed the lines of cleavage of Bayesianism are largely determined by different specifications of these constraints. But all the Bayesians agree (in contrast with frequency theorists of probability and with statisticians of the schools of Fisher and Neyman-Pearson) that the domain of pairs of propositions over which the function P is well defined is very wide, permitting one inter alia to speak of the “prior probability” of a hypothesis h, the evidential proposition e being taken to be a tautology t or possibly the general background information b.

A RECONSTRUCTION OF ADAM'S REASONING

If Adam was a rational man even before he had garnered much experience of the world, and if the ability to reason probabilistically is an essential part of rationality (as Bishop Butler maintained when he wrote that “But, to us, probability is the very guide of life”), then Adam must at least tacitly have known the Principles of the Calculus of Probability. Specifically, Adam must have known that the epistemic concept of probability – probability in the sense of “reasonable degree of belief” – satisfies these Principles, for it is the epistemic concept, rather than the frequency concept or the propensity concept, which enters into rational assessments about uncertain outcomes. But what warrant did Adam have for either an explicit or a tacit assertion that epistemic probability satisfies the Principles of the Calculus of Probability?

Today, the best known and most widely accepted justification of this assertion is the “Dutch Book” Theorem, originally proved independently by F. P. Ramsey and F. DeFinetti for a subjectivist or personalist version of epistemic probability, but applicable also to non-subjectivist or not-entirely-subjectivist versions. It is most implausible, however, to attribute awareness of this theorem to Adam, partly because it requires some mathematics that is not completely trivial, partly because of the rarity of gambling in the Garden of Eden, and partly because in the one case in which Adam did indulge in a gamble he exhibited little skill at decision theory.