I shall attempt in this paper to give a rounded, if schematic, account of the concept of probability. My central concern will be to clarify the sense in which law-like statements (including ‘statistical’ law-like statements) are made probable by observational data which, in a sense equally demanding analysis, ‘accord’ with them.

A loose analogy relates the work of Laplace and Hilbert. These thinkers had roughly similar objectives. At a time when so much of our analytic effort goes to distinguishing mathematics and logic from physical theory, such an analogy can still be instructive, even though differences will always divide endeavors such as those of Laplace and Hilbert.

In this paper I will argue that Professor Goodman was correct in thinking that there is a problem concerning counterfactual conditionals, but that it is somewhat different from the problem he thought it to be, and is one that is even more basic. I will also try to show that this problem is distinct from Hume's “problem” of induction, and that additional assumptions have to be made for counterfactual induction beyond those required for other kinds of induction.

The Gibbs’ Paradox is commonly explained by invoking some type of “principle of indistinguishability,” which asserts that the interchange of identical particles is not a real physical event, i.e., is operationally meaningless. However, if this principle is to provide a satisfactory resolution of the Paradox, it must be operationally possible to determine whether, in fact, two given systems are identical or not. That is, the assertion that the Gibbs’ Paradox is resolvable by an indistinguishability principle actually is an assertion that we can in principle possess a complete set of effective procedures for determining the identity or non-identity of arbitrary physical systems. We show that, in rather general situations, an assertion of this type is not well founded. It is further pointed out that a failure to recognize an incomplete set of “sameness criteria” can lead to serious blunders in physics and in biology.

Through an analysis of conditions under which the question of spatial anisotropy can be raised, the present paper brings out intimate conceptual relationships between the scientific concept of space and the concepts of entities, behavior, and explanation specified by scientific theories. Thus scientific departures from ordinary usage (or from usage in other scientific theories) of the term “space” entail corresponding shifts in the use of other terms not generally seen to be connected. As a case study of the relations between these terms, and of the refusal to allow the possibility of spatial anisotropy, Newtonian mechanics is examined.

The argument from analogy is examined from the point of view of Carnap's confirmation theory. It is argued that if inductive arguments are to be applicable to the real world, they must contain elementary analogical inferences. Carnap's system as originally developed (the λ-system) is not strong enough to take account of analogical arguments, but it is shown that the new system, which he has announced but not published in detail (the η-system), is capable of satisfying the conditions of inductive analogy. Finally it is shown that an elementary analysis of analogical inference yields postulates of the η-system with a minimum of arbitrary assumptions.

It is common knowledge that the notion of the unconscious is an essential part of psychoanalytic theory. In recent years, however, Arthur Pap and A. C. MacIntyre have argued that Freud's theory of the unconscious is not explanatory. But a close examination of Pap's and MacIntyre's arguments reveals that they are invalid. If one wishes to show that the theory of the unconscious is unexplanatory, different arguments will be necessary.

One style of conducting scientific research involves the application of theoretical propositions to an empirical domain under investigation. The investigator plans his research in terms of the theoretical propositions and states his findings in these terms as well. We wish to examine not the merits of this style of research but a difficulty inherent in it. The difficulty concerns what is to be done when disconfirmative results are produced by some discrete study or experiment in the course of such research.

Two types of philosophical arguments are employed by the defenders and critics of the Copenhagen Interpretation. One type of argument is a confrontation of an opponent's interpretation with criteria of demarcation and criteria of acceptability. The purpose of such arguments is either to exclude an opponent's interpretation from the range of permissible discourse in quantum physics, or to establish the inadequacy of an opponent's interpretation. A second type of argument is a justification of the value, or utility, of the criteria selected.

Recent accounts of scientific method suggest that a model, or analogy, for an axiomatized theory is another theory, or postulate set, with an identical calculus. The present paper examines five central theses underlying this position. In the light of examples from physical science it seems necessary to distinguish between models and analogies and to recognize the need for important revisions in the position under study, especially in claims involving an emphasis on logical structure and similarity in form between theory and analogy. While formal considerations are often relevant in the employment of an analogy they are neither as extensive as proponents of this viewpoint suggest, nor are they in most cases sufficient for allowing analogies to fulfill the roles imputed to them. Of major importance, and what these authors generally fail to consider, are physical similarities between analogue and theoretical object. Such similarities, which are characteristic in varying degrees of most analogies actually employed, play an important role in affording a better understanding of concepts in the theory and also in the development of the theoretical assumptions.

To illustrate one way in which philosophy may be helpful rather than merely critical in the present state of psychoanalytic theorizing, an attempt is made to disentangle issues in controversies about the unconscious. Eleven questions are distinguished and discussed. Logical, linguistic, methodological, metaphysical, empirical, and pragmatic components are set apart. It is found that there are no logical barriers to a construct of the unconscious, that it is linguistically feasible, need violate no methodological concepts, nor foreclose a metaphysical issue, nor have deleterious pragmatic effect. Feasibility and desirability of the construct in all these respects will depend on the character and extent of the scientific findings. Some issues are also raised concerning desirable types of models in the explanation of conduct, and concerning the relevance of recent studies of consciousness.

A certain dilemma is inherent in relational accounts of space and time. If any objects endure through change, then temporal elements other than relations are required to describe them. If, on the other hand, no objects endure through change, no permanent reference system is available in terms of which to define the “same place” at different times. An argument which, by exploiting this latter difficulty, attempts to show that “objects with some endurance through time” must be accepted as fundamental is examined and found inconclusive. A sketch is then given of an alternative scheme which does allow the relevant spatial comparisons, but which does not countenance the reidentification of particulars. The discussion is intended to show that the relationist can, as indeed he must, deny the second horn of this delemma.

Analogies have been traditionally recognized as a proper part of inductive procedures, akin to generalizations. Seldom, however, have they been presented as superior to generalizations, in the attainability of a higher degree of certitude for their conclusions or in other respects. Though Bacon definitely preferred analogy to generalization, the tradition seems to me to go the other way—until the recent publication of works by Mary B. Hesse (pp. 21-28 and passim) and, perhaps, R. Harré (pp. 23-28 and passim).

Newtonian theory has usually been accepted as a paradigm example of an explanation. There are two widely known analyses of what makes it so. According to one analysis, the deductive and predictive nature of the theory is what counts. The second analysis emphasizes the ability of the theory to connect widely different events and laws. The present paper proposes a third analysis stressing three characteristics. (1) The explanation includes a description which is in part of something unobserved. (2) The description is true in the sense of corresponding to the facts. (3) Through the description, the explanation confers “naturalness” upon the thing explained.

In this paper I shall argue that to a very significant extent mathematics is concept analysis, and that though the analysis of mathematical concepts is in a number of ways different from the analysis of philosophic concepts, the similarities between these two types of concept analyses are as important and far reaching as the differences. I shall argue that because mathematics and philosophy are each concerned with the analysis of concepts, they are much more like one another epistemologically than is often recognized. In insisting upon fundamental similarities between mathematics and philosophy, I shall be agreeing with the classical rationalists, but on a very different conception of both philosophy and mathematics from that held by the rationalists. The rationalists wished to assimilate philosophy to mathematics as understood in their time; viz. as a body of necessary propositions, which followed from self-evident axioms and postulates, revealed to the natural light of reason. As against this rationalistic position, I wish to make a comparison in the reverse direction, in which I shall presuppose a certain conception of philosophy as something given, and then insist that mathematics is in many important respects similar to philosophy as so understood. In particular, I wish to insist that there is a significant comparison between mathematics on the one hand, and philosophy as understood by probably a majority of philosophers today on the other—viz., philosophy understood as concept analysis—, where it is conceded that the analysis of philosophic concepts is inherently a tentative matter, wherein it is impossible—at least in the usual case—to offer any one analysis of a given philosophic concept as absolutely certain and beyond all revision. I shall argue that by virtue of the fact that mathematics, like philosophy, is concerned with the analysis of concepts, many at least of the propositions advanced within it are inherently revisable, and do not possess the kind of certainty the rationalists ascribed to them.

In the first part of this paper it is shown that unit names, whether simple or complex, whether of fundamental, associative or derivative measurement, may always be regarded as the names of scales. In the second it is shown that dimension names, whether simple, like “[M]”, “[L]” and “[T]”, or complex dimensional formulae, may always be regarded as the names of classes of similar scales. Thus, a new foundation for the theory of dimensional analysis is provided, and in the light of this, its nature and scope are examined. Dimensional analysis is shown to depend upon certain conventions for expressing numerical laws.

Conditions are stated under which the “argument by analogy” is consistent with the principle of inverse probability. It is contended that the argument by analogy, in conjunction with a crucial test, has a legitimate place in scientific logic. As an example the astrophysical problem of solar granulation is discussed in detail and other examples are mentioned more briefly.