John Wheeler is the effective owner of the trade mark ‘geometrodynamics’, since he coined the word, so we look to him for the definition. In his introduction, Professor Grünbaum has quoted a number of things from Wheeler. I would like to point out that in recent papers Wheeler refers to “Einstein's standard battle-tested 1915 geometrodynamics.” Wheeler therefore takes geometrodynamics as simply another name for standard general relativity. I think there is no doubt that he intends to exclude aberrations, such as the cosmological constant or the scalar-tensor (Brans-Dicke) theory of gravity. The central feature, in this view, is that geometry is part of physics. Geometry may even be such a blindingly beautiful part of physics as to nearly eclipse everything else. But there is no assertion (although also no denial) that all of physics is geometry. The coupled Einstein-Maxwell equations are a standard basis for current discussions of geometrodynamics.

One thing that everyone can agree on is that the subject of geometrodynamics, whatever we interpret it as covering, is inseparably associated with the name of John Wheeler. To discuss the history and current status of geometrodynamics thus necessitates the discussion of the evolution of Wheeler's ideas on the subject. This is not meant to detract, in any way, from the fact that he has been ably assisted in his intellectual Odyssey by a distinguished group of co-workers; most prominently by Charles Misner, whom we have been fortunate to hear today on the subject. Since Professor Wheeler has recently indicated his abandonment of major features of the original geometrodynamic program, as I shall discuss later, I hope he will forgive me the rather dramatic title I have chosen for my talk.

Serious students of cellular and developmental biology confront what may well be the gravest epistemological problems ever faced by scientists. These are direct consequences of the immense, ordered biochemical complexity of organisms.

One of the most extensive discussions of the epistemological problems confronting cell biologists has been supplied by Elsasser, whose views have had a rather wide audience [1, 2]. Elsasser is greatly to be admired for his insistence that biologists confront the epistemological problems of their science, and for his efforts to analyze those problems, which he feels center in our incapacity to know the quantum microstate of an organism. While I am sympathetic with his effort, I feel he misconstrues the epistemological consequences of our failure to know completely the organism's quantum microstates.

In his now classic paper, ‘The Architecture of Complexity’, Herbert Simon observed that “… In the face of complexity, an in-principle reductionist may be at the same time a pragmatic holist.” (Simon, 1962, p. 86.) Writers in philosophy and in the sciences then and now could agree on this statement but draw quite different lessons from it. Ten years ago pragmatic difficulties usually were things to be admitted and then shrugged off as inessential distractions from the way to the in principle conclusions. Now, even among those who would have agreed with the in principle conclusions of the last decade's reductionists, more and more people are beginning to feel that perhaps the ready assumption of ten years ago that the pragmatic issues were not interesting or important must be reinspected.

Once upon a time in the land of Psi there lived a very famous baker named Fred. Fred the baker was known from far and wide as the very best baker in the land. His skill at baking was unmatched for he could produce loaves of any size or shape - long and thin bread sticks, round Kaiser rolls, crescent-shaped croissants, twisted oval loaves, and so on. His famous motto was: “Give me the unkneaded dough and in time I can produce any kind of loaf of bread desired.” Fred called this process ‘shaping’.

There was a limit, of course, to what even Fred could do: he could not, for example, create whole-wheat bread from white flour. But this was a small flaw in an otherwise unblemished character, and although Fred frequently admitted the importance of the kind of flour one began with, rumor had it that he was even working on the possibility of overcoming this limitation.

Until recently, the debate concerning whether chance, randomness and disorder are ever instantiated in Nature has been considerably one-sided. Since Aristotle, the mainstream of philosophical thought seems to have been nearly unanimous in agreeing that these characters exist only ‘in the mind’. The shared conviction that every event has a cause or a determining condition led most philosophers who addressed themselves to the topic to the conclusion that there is no randomness in things.

The disquieting suggestion of twentieth century physics that the appeal to probabilities in our attempt to describe the world was not merely a convenient device, dispensable in principle, but maybe the best that can be done, brought the classical problem of chance back to the attention of philosophers of science. Those committed to a realistic interpretation of science felt it was incumbent upon them to provide a realistic interpretation of chance.

In this paper I shall bring together some philosophical and logical ideas about randomness many of which have been said before in scattered places. For less philosophical aspects see, for example [27].

When philosophers define terms, they try to go beyond the dictionary, but the dictionary is a good place to start and one dictionary definition of ‘random’ is ‘having no pattern or regularity’. This definition could be analyzed in various contexts but, at least for the time being, I shall restrict my attention to sequences of letters or digits, generically called ‘digits’. These digits are supposed to belong to a generalized alphabet; perhaps a new word should be used, such as ‘alphagam’, but I shall use the word ‘alphabet’ in the generalized sense so as to avoid a neologism. For simplicity I shall assume that the alphabet is finite and consists of the t digits 0, 1, 2,…, t — 1.

Mr. Coffa's admirable and lucid exposition of the history of mathematical randomness, leaves, to my mind, nothing to be desired. I am not sure whether, or how, its end result is of use to the theoretically minded statistician, but it is certainly interesting enough in its own right to need no excuse.

I tend also to agree wholeheartedly with Mr. Coffa's treatment of physical randomness, or at least with his conclusion. I can easily imagine that he will not have succeeded in convincing those who are sure that epistemology is built into physics - say in quantum mechanics - but he has certainly given even these people some food for thought. I can even swallow the peroration of his last paragraph whole, and agree that one might hope and expect that physics can make its claims without a reference to knowledge or to randomness.

Both the history of science and the history of philosophy demonstrate that different explanations of nature are motivated by different assumptions about what types of things need to be explained and what types of things are capable of explaining them. The view that diversity must be explained, for example, decrees that what is most fundamental is the immutable, and that diverse features of nature arise from essentially unchanging elements. This sort of view is best illustrated in atomistic theories where the characteristics of objects of our experience are ultimately accounted for in terms of the varying configurations and motions of indestructible atoms.

When we examine physical theories in order to determine what assumptions lead philosophers to value some aspects of nature as more fundamental than others, we will find that the focal point for these underlying assumptions is the concept of matter expounded in the theory.

One of the more constant elements in the ‘legacy of logical positivism’ has been a rather low estimate of the importance of the concept of Verstehen for a logic of the social sciences. To be sure, it has been the accepted practice among philosophers under the influence of this movement that any extended treatment of the logic of the social sciences include an analysis of the role of Verstehen. But these analyses have almost invariably taken the form of a whittling down to size of an outsized concept with, it is often noted, rather suspicious origins in German metaphysical thought.

Apart from the philosophical arguments advanced, there are a number of historical considerations which throw some light on the sceptical attitude of the logical positivists and of their descendants towards the idea of a procedure peculiar to the social sciences.

Partly through reading the works of Paul Feyerabend I have become intrigued with the following questions:

1. (1) Is it possible to have a non-trivial theory of scientific method - that is, a fairly detailed and comprehensive theory of the best way(s) to try to increase and improve our knowledge? Is it possible to have a unified theory which would apply both to physical science and social science, and perhaps even to technological innovation as well?

2. (2) If we could find such a theory of the scientific process, how would it have to be modified if we were to decide that our aim were not just ultimately to understand the world (i.e., to find well-tested explanatory theories of high empirical content) but also continually to change the world - to improve the human condition?

Given their importance in the history of ideas, monistic theories of society have received little serious attention in the literature. By a monistic theory, I mean one which holds that in a given area, one factor (or variable, as I shall usually call it) determines everything that happens; or, less strictly, that the one variable is the most important or crucial one in determining what happens in the given domain. There are social theories which hold, for example, that ideas are the only or crucially determining factor in history and theories which hold that certain ones among our ideas - religious or philosophical or scientific - constitute that factor. Other theories have maintained that a certain biological factor such as race or size is the major factor in the social process.

If there is one set of arguments worse than those put forward for ‘value-free science’, it is those put forward against it. Both sets have one common characteristic, besides a high frequency of invalidity, and that is the failure to make any serious effort at a plausible analysis of the concept of ‘value judgment’, one that will apply to some of the difficult cases, and not just to one paradigm. Although the problem of definition is in this case extremely difficult, one can attain quite useful results even from a first step. The analysis proposed here, which goes somewhat beyond that first step, is still some distance from being satisfactory. Nevertheless, we must begin with such an attempt since any other way to start would be laying foundations on sand. And we'll use plenty of prescientific examples, too, to avoid any difficulties with irrelevant technicalities.

This paper argues that the ignorance interpretation of mixtures is physically unrealistic. The ignorance interpretation is the orthodox interpretation for mixtures, and should not be confused with the ignorance interpretation for superpositions, which has been largely abandoned. Mixtures, unlike superpositions, do not interfere. They are represented by mixed (or non-idempotent, i.e. W2 ≠ W) operators; superpositions, by pure (or idempotent) operators or by vectors. In the minimal interpretation both pure and mixed operators may be taken to describe collections. Any pure state, ψ, may be expressed as a sum of other pure states, ϕ 1, ϕ2, …, ϕn. Yet we cannot postulate that the members of the collection described by ψ are each in one of the pure states ϕ1, ϕ2, …, ϕn. This is because of the interference between the pure ϕ1, …, ϕn. On the other hand, if we have a mixture of ϕ1, …, ϕn, we can consistently postulate that the members of the collections are each in one of the pure states ϕ1, …, ϕn.

The phrases ‘Absolute Becoming’, ‘Pure Becoming’, ‘Temporal Becoming’, and ‘Temporal Passage’ which figure so prominently in discussions about time seem to have the same halo of meanings associated with them. Those who say that they believe in the objective reality of Absolute Becoming (or Pure Becoming, etc.) maintain that it is a feature peculiar to time, which distinguishes it from any spatial dimension. They sometimes claim in addition that Absolute Becoming explains some of the facts or alleged facts about time which lack spatial analogue. One such fact is the curious tendency of causes to bring about effects later rather than earlier than themselves. Another is the ‘passage’ of time in contrast to the static character of space, which dynamism may or may not be the same as its supposed ‘arrow’ or ‘irreversibility’ or ‘anisotropy’.

Natural sciences such as geology, geography, and astronomy are mainly interested in describing features of the real world. Other sciences such as physics and chemistry deal with certain classes of possible phenomena, no matter whether they really taken place or not. The former sciences are based on the latter, so that all are interested in possible phenomena or worlds.

Roughly speaking, on the one hand there are some axiomatic theories - e.g. theories of classical mechanics similar to Newton's presentation of mechanics - that speak of phenomena occurring in the typical possible world, without considering basic relations involving several of these worlds. These theories do not aim very much at reducing primitive concepts. On the other hand, to make assertions involving possible worlds is practically compulsory in theories that include the definition of some constitutive magnitudes, i.e. magnitudes that characterize the reaction of a system S to a situation Σ possibly depending on parameters.

When J. C. C. McKinsey and I were working on the foundations of mechanics many years ago, we thought it important to give a rigorous axiomatization within standard set theory, and we therefore resisted any use of modal concepts or counterfactual conditionals in the formulation of the axioms of mechanics. I continue to think that the use of an extensional set-theoretical framework is appropriate and adequate for most, if not all, scientific discourse. As my interests have shifted more to the foundations of probability and the applications of probability concepts in the behavioral sciences, however, I have gradually come to the position that modal concepts, especially as expressed in the use of probability concepts, are essential to standard scientific talk. Yet, in a majority of cases the modal concepts remain implicit in that talk, and their logic is scarcely used in either theoretical or experimental analyses of empirical phenomena.