We statisticians, with our specific concern for uncertainty, are even more liable than other practical men to encounter philosophy, whether we like it or not. For my part, I like it comparatively well. That is why the honor of opening this session of discussion has come to me, though my background makes my knowledge and idiom somewhat different from your own.

This paper presents a critical examination of claims advanced by several philosophers to the effect that ‘time travel’ represents a physical possibility and that the interpretation of certain actually observed phenomena in terms of ‘time travel’ is both legitimate and advantageous. It is argued that (a) no convincing motivation for the introduction of the time travel hypothesis has been presented; (b) no coherent and interesting sense of ‘going backward in time’ has been supplied which makes ‘time travel’ compatible with Special Relativity; (c) even the conceptual possibility of ‘time travel’ is an unsettled and somewhat nebulous question.

Because physical theories typically predict numerical values, an improvement in experimental precision reduces the tolerance range and hence increases corroborability. In most psychological research, improved power of a statistical design leads to a prior probability approaching ½ of finding a significant difference in the theoretically predicted direction. Hence the corroboration yielded by “success” is very weak, and becomes weaker with increased precision. “Statistical significance” plays a logical role in psychology precisely the reverse of its role in physics. This problem is worsened by certain unhealthy tendencies prevalent among psychologists, such as a premium placed on experimental “cuteness” and a free reliance upon ad hoc explanations to avoid refutation.

The following intellectual as opposed to practical reasons for all anthropologists doing fieldwork are examined: fieldwork: (1) records dying societies, (2) corrects ethnocentric bias, (3) helps put customs in their true context, (4) helps get the “feel” of a place, (5) helps to get to understand a society from the inside, (6) enables appreciation of what translating one culture into terms of another involves, (7) makes one a changed man, (8) provides the observational, factual basis for generalizations. None of these is found sufficient to make fieldwork imperative for all anthropologists, although they are quite sufficient to allow that it is imperative for anthropology as a whole that fieldwork in some form by some people continue. In place of the view of fieldwork as an essential preparation for doing anthropology, an alternative role for it is explored: namely as a testing procedure. The implications of this—that the study of problems and the articulation of theories can usefully proceed prior to or even independently of fieldwork—are drawn out, and a new institution of selective fieldwork is proposed.

In his original paper of 1905, “On the Electrodynamics of Moving Bodies”, Einstein described a procedure for synchronizing distant clocks at rest in any inertial system K. Clocks thus synchronized may be said to be in standard signal synchrony in K. It has often been claimed that there are no logical or physical reasons for preferring standard signal synchronizations to any of a range of possible non-standard ones. In this paper, the range of consistent non-standard signal synchronizations, first for any one inertial system, and second for any set of such systems, is investigated, and it is shown that the requirement of consistency leaves much less room for choice than is commonly supposed. Nevertheless consistent non-standard signal synchronizations appear to be possible. However, it is also shown that good physical reasons for preferring standard signal synchronizations exist, if the Special Theory of Relativity yields correct predictions.

The thesis of the conventionality of distant simultaneity espoused particularly by Reichenbach and Grünbaum is thus either trivialized or refuted.

The paper, analyses the role of measurable concepts in deductive explanation. It is shown that such concepts are, although imprecise in a defined sense, exact in that neutral candidates to them do not arise. An analysis is given of the way in which imprecision is related to generalisation, and it is shown how imprecise concepts are incorporated in testable deductive explanations.

A person required to risk money on a remote digit of π would, in order to comply fully with the theory [of personal probability] have to compute that digit, though this would really be wasteful if the cost of computation were more than the prize involved. For the postulates of the theory imply that you should behave in accordance with the logical implications of all that you know. Is it possible to improve the theory in this respect, making allowance within it for the cost of thinking, or would that entail paradox?

Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an “isomorphic model” schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessitated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scientific practice, and (3) clarifies the problems of meaning variance and ontological reduction.

Professor Savage has been candid and generous in stating his interest in philosophy, and the philosophers who have heard him are surely grateful for this. His attitude is very far from that of some competent scientists and mathematicans who purport to clear up the questions which philosophers raise concerning their disciplines by means of a battery of technical results of varying relevance—a procedure which can often be appropriately described as “an abominable snow-job.” However, Professor Savage's generosity places a responsibility on philosophers, since the questions he raises are difficult.

An analysis of problematic dispositional predicates like ‘soluble’ is presented. The analysis attempts to combine cogent features of opposed previous analyses of Carnap and Bergmann, while avoiding problematic features of both. The suggestion that there is an ambiguity in negations of assertions of dispositional properties, and a consequent distinction between “not soluble” and “insoluble,” lies at the core of the solution.

The axiom of comparability has been a fundamental part of mathematical choice theory from its beginnings. This axiom was a natural first assumption for a theory of choice originally constructed to explain decision making where other assumptions such as continuous divisibility of choice spaces could legitimately also be made. Once the generality of application of formal choice theory becomes apparent, it also becomes apparent that both continuity assumptions and the axiom of comparability may be unduly restrictive and lead to the neglect of decision situations which are important and which can be handled on a modified axiom set. These considerations bear on the philosophical analysis of the concept of rational decision.

By means of a critical examination of a number of theses as to the nature of game-playing, the following definition is advanced: To play a game is to engage in activity directed toward bringing about a specific state of affairs, using only means permitted by specific rules, where the means permitted by the rules are more limited in scope than they would be in the absence of the rules, and where the sole reason for accepting such limitation is to make possible such activity.

This paper contributes to the mathematical foundations of the model for utility theory developed by Richard Jeffrey in The Logic of Decision [5]. In it I discuss the relationship of Jeffrey's to classical models, state and interpret an existence theorem for numerical utilities and subjective probabilities and restate a theorem on their uniqueness.

Philosophers who hold that the correct ontological analysis of things includes both properties and particulars have often been pressed to “show” the particular. If we are not acquainted with them, it is argued, then we should not suppose that they exist. I argue that, while we do have good and sufficient reasons for supposing there to be particulars, we are not acquainted with them. To suppose that we are acquainted with them is to treat particulars as if they were properties and to fail to realize how radically different particulars are from properties. The relevance of these matters to some considerations of “simplicity” and the principles of empiricism is explored.

The postulates of rational preference suggested by Von Neumann and Morgenstern have been defended as descriptive or empirical generalizations and as normative principles. It is argued that the postulates are inaccurate empirical generalizations and unacceptable normative principles.

F. P. Ramsey pointed out in Theories that the observational content of a theory expressed partly in non-observational terms is retained in the sentence resulting from existentially generalizing the conjunction of all sentences of the theory with respect to all nonobservational terms. Such terms are thus avoidable in principle, but only at the cost of forming a single “monolithic” sentence. This paper suggests that communication may be thought of as occurring not only by sentence but by clause, a sentential formula closed except for a special kind of variable. Understanding such clauses requires incorporating them within the scope of one's own Ramsey sentence. Many concepts of deductive and inductive logic carry over without great change. But the concepts of truth and designation are extendible to clauses only in the sense that assertions involving them must, to be understood, in turn be construed as clauses and incorporated into the Ramsey sentence. The behavior of these extended concepts of truth and designation suggests an explication of coherence truth within a correspondence-truth framework.

Difficulties with the typological concept of species led biologists to reject the “typological” presupposition of an archetype which is manifest in each member of a species. The resulting concept of species, which is here called the phenotypic species concept, is considered as implying that biological species are not real. Modern population thinking has given rise to the concept of a species as a gene-pool. This modern concept is contrasted here with the phenotypic concept in light of some general criteria for evaluating species concepts and is shown to be more satisfactory. Finally, it is held that to ask if a species is real is to ask whether the species grouping arrived at by applying the principles involved in the species concept corresponds with groups of organisms amongst which important biological relationships exist. It is argued that in this sense species, as defined by the gene-pool concept, are certainly real.

Present-day interest in history among philosophers seems largely limited to a debate over the nature of historical explanation among those who for Humean reasons insist that all explanations must rest upon general laws and history cannot be an exception to this, and those who say the historians do explain and since they do not use general laws the Humean claim is obviously mistaken. Like the latter, the present paper takes the explanations of historians seriously, but unlike the latter it is not willing to limit the role of philosophy of history merely to the elucidation of the language in which historians give final expression of their work. Rather it recognizes that those explanations themselves set the stage for further inquiry in that they are required to be justified. It is here that the theories or general laws demanded by Humean analysis come in. After examining examples of general laws offered by way of example of what the “Humean” philosophers are supposed to have in mind, each of which is an immediate generalization of the explanation it is called upon to explain and is, hence, an instance of what has been called “the dogma of universality,” some examples of more promising prospects of theory in history are examined.

Philosophers have long believed that if the Principle of the Identity of Indiscernibles were logically true, there would be no problem of individuation. I show (a) that if spatial relations are, as seems plausible, of such a nature that it makes no sense to say of one thing that it is related to itself, then the Principle is a logical truth, asserting that a certain kind of state of affairs is impossible because the kind of sentence purporting to express it is ill-formed and (b) that even if the Principle were such a truth the problem of individuation would remain. I then examine some of what Leibniz and Wittgenstein have said about the notions of individuation, difference and non-identity.