This paper discusses the Einstein-Podolsky-Rosen paradox from a new point of view. In section II, the arguments by which Einstein, Podolsky and Rosen reach their paradoxical conclusions are presented. They are found to rest on two critical assumptions:

1. (a) that before a measurement is made on a system consisting of two non-interacting but correlated sub-systems, the state of the entire system is exactly represented by:

   

2. (b) that the exact measurement of an observable A in one of the sub-systems is possible.

In section III it is shown that assumption (b) is incorrect. Thus we conclude, as did Bohr, that the results of Einstein, Podolsky and Rosen are not valid.

The arguments of section III are quite distinct from Bohr's, and therefore in Section IV this work is related to that of Bohr.

The recent philosophy of physics is confronted with the new ontology, as it emerges after philosophy proper has fully articulated the linguistic turn. The classical ontologists asserted or denied, controversially, that certain entities “existed.” Rather than adding to these controversies, the new ontology uncovers their dialectics. The ontologically problematic entities of physics are of two kinds, represented by forces and particles, respectively. The dialectics has been dominated by eight patterns. Two of these, independence and realism, belong to philosophy proper. The latter is here considered in order to relieve the philosophy of physics of a burden only philosophy proper can bear. That leaves six patterns: concreteness (including the orbit feature), acquaintance, simplicity, significance, process, and model. The paper sketches how each of these may be used and probably has been used, either explicitly or implicitly, in the recent controversies.

It is widely agreed among philosophers of science today that no formal pattern can possibly be found in the origins of scientific theory. There is no such thing as a “logic of discovery,” insists this view—a scientific hypothesis is susceptible to methodological critique only in its relation to empirical consequences derived after the hypothesis itself has emerged through a spontaneous creative inspiration. Yet confronted with the tautly directed thrust of theory-building as actually practiced at the cutting edge of scientific research, this romantic denial of method in the genesis of ideas takes on the appearance of myth.

It is the contention of this article that as empirical data ramify in logical complexity, they deposit a hard sediment of theory according to a standard inductive pattern so primitively compelling that it must be recognized as one of the primary forms of inferential thought. This process, here called “ontological induction,” is a distillation out of unwieldly observed regularities of more conceptually tractable states hypothesized to underlie them, and is the wellspring of our beliefs in theoretical entities. Previous failure to recognize this pattern of induction has undoubtedly been in substantial measure a result of inadequate attention to the structural details of scientific propositions; for in order to exhibit the nature of ontological induction clearly, it is first necessary to make extended forays through sparsely explored methodological terrain—notably, the nature of scientific “variables,” the logical form of “laws,” and the type-hierarchy of scientific concepts.

One of the most difficult and interesting problems of rational decision is the choice among possible diverging paths in theory construction and among competing scientific theories—i.e., systems of accurate testable hypotheses. This task involves many beliefs—some warranted and others not as warranted—and marks decisive crossroads. Suffice to recall the current conflict between the general theory of relativity and alternative theories of gravitation (e.g., Whitehead's) that account for the same empirical evidence, the rivalry among different interpretations of quantum mechanics (e.g., Bohr-Heisenberg's, de Broglie-Bohm's, and Landé's), and the variety of cosmological theories (e.g., Tolman's cyclical model and the steady-state theory). They all account for the same observed facts although they may predict different kinds of as yet unknown facts; they are consequently, up to now, empirically equivalent theories even though they are conceptually different and may even involve different philosophical views—i.e., they are conceptually inequivalent.

The fundamental problem considered is that of the existence of a joint probability distribution for momentum and position at a given instant. The philosophical interest of this problem is that for the potential energy functions (or Hamiltonians) corresponding to many simple experimental situations, the joint “distribution” derived by the methods of Wigner and Moyal is not a genuine probability distribution at all. The implications of these results for the interpretation of the Heisenberg uncertainty principle are analyzed. The final section consists of some observations concerning the axiomatic foundations of quantum mechanics.

Mr. Sharp's resolution of the Einstein-Podolsky-Rosen paradox is, in my opinion, the right one. However, the resolution does not in my opinion show that “God's in his heaven; all's right with the world (quantum mechanics).” This is in no way a criticism of Sharp; rather, it is inevitable that any resolution of this paradox, dealing as it does with the quantum mechanical concept of “measurement”, must tangle with some of the real difficulties which are lurking in the notion. The purpose of these comments is to use Mr. Sharp's remarks as a basis for bringing out one of the serious conceptual difficulties connected with measurement.

Two solutions are offered to the problem of distinguishing “historical” from “functional” associations in cross-cultural surveys. The underlying logic of the mathematical model is discussed and three kinds of association distinguished: hyperdiffusional or purely “historical” association, undiffusional or purely “functional” association, and semidiffusional or mixed “historical-functional” association. Two overland diffusion arcs constitute the test sample; the relationship of social stratification to political complexity constitutes the test problem. A sifting test establishes a bimodal distribution of interval lengths between like types and sifts out repetitions with a lesser interval length than the second mode. A cluster test shows that for the test problem, the “hits” cluster more than the “misses”.

A logic of questions and answers exists within the logic of statements, if we make the following identifications (roughly): “Whether” questions are identified with true exclusive disjunctions, and “which” questions are identified with true existential quantifications. The question-and-answer process is interpreted as an information-matching game. The question mark is not needed except as a device of abbreviation. Complete and partial answers can be distinguished and various relations of relevance, independence, and resolution defined.

When the evidence leaves us with a choice among hypotheses of unequal strength, how is the choice to be made?

Caution would counsel us to choose the weakest, the hypothesis that asserts the least, since it is the least likely to fail us later. But the principle of maximum safety quickly reduces to absurdity; for it always dictates the choice of a hypothesis that does not go beyond the evidence at all.

While I do not accept any current analysis of theoretical terms I also reject certain criticisms of them. Specifically, I reject the criticism that the paradoxes of material implication and the counterfactual problem eliminate the explicit definition view; and I also reject the criticism that explicitly defined theoretical terms do not refer to anything which “really exists” or do not have “excess meaning.” I do argue, however, that the explicit definition view confuses and conflates the concepts of criterion and meaning analysis. I also defend reduction sentences against the counterfactual difficulty, but show, too, how this view is already logically committed to the network or postulational view of meaning. Finally, I show how the concept of reduction sentences confuses in several ways the concepts of criterion and meaning analysis—although not in quite the same way as explicit definitions do.

Science is a comparatively recent affair, but the alternatives at our command in philosophy are old ones. The range of Greek philosophy seems to have an astonishing stability. The philosophy of religion was used for centuries to bolster religion. It is some indication of the rapid growth of the prestige of science that now the philosophy of science is used to bolster philosophy.

In this note, we wish to remark on some of the relations between deciding one's own action and predicting one's own action. This topic is relevant both to current discussions of the nature of analysis and to the continuing controversy over the nature of scientific explanation.

An attempt is made in this paper to analyze the purely formal nature of information-theoretic concepts. The suggestion follows that such concepts, used to supplement the logical and mathematical structure of the language of science, represent an addition to this language of such a sort as to allow the use of a unitary language for the description of phenomena. (The alternative to this approach must be certain multi-linguistic and mutually untranslatable descriptions of related phenomena, as with the various versions of Complementarity).

This conception is tested for the specific case of Heisenberg's Uncertainty Principle, in order to show that, with the assumption of a suitable and intuitively satisfactory definition of the quantity of information contained in a measurement, the Heisenberg Principle becomes an informational restriction arising from the formal properties of the symbols of a given language rather than as a “law” of nature.

Factual statements that might qualify for the status of law statements are classed from various philosophically relevant standpoints (referents, precision, structure of predicates, extension, systemicity, inferential power, inception, ostensiveness, testability, levels, and determination categories). More than seven dozen of not mutually exclusive kinds of lawlike statements emerge. Strictly universal and counterfactually powerful statements are seen to constitute just one kind of lawlike statements; classificatory and some statistical laws, e.g., are shown not to comply with the requirements of universality and counterfactual force.

Conditions for lawlike statements to be called laws are then examined, and a liberal criterion of lawfulness is finally proposed, which reads thus: A proposition is a law statement if and only if it is a posteriori (not logically true), general in some respect (does not refer to unique objects), has been satisfactorily corroborated for the time being in some domain, and belongs to a theory (whether adult or embryonic). It is claimed that criteria of laws change alongside with the emergence of new usages of the term ‘law’, and that by adopting a liberal criterion of lawfulness we would conform to contemporary usage and would cease inhibiting the search for regularities in the sciences of man.

The fact that simplicity has been linked with induction by many philosophers of science, some of whom have proposed or supported criteria of “inductive simplicity,” means that the problem must be given some serious attention. I take “inductive simplicity” as a title, however, only by way of concession to these historical treatments, since it is precisely the burden of my paper to show that there is no such thing. So much for the conclusion. I shall spend the remainder of my time arguing for it.

Professor Leonard proposes that imperative and interrogative sentences be classified, together with declarative ones, as true and false. The interesting analysis he gives in connection with this proposal points out that these three types of utterance have something in common and has the merit of evincing the identity of this common element. Also it may seem to offer attractive possibilities of integrating various types of discourse in its promise of partial assimilation of interrogatives and imperatives to the model of truth-valuable language. Even so, Leonard's account is not altogether satisfactory. I shall not discuss his treatment of imperatives but shall argue that his conception of interrogatives has unacceptable consequences.

The author recently claimed that Pr(P, Q), where Pr is a probability function and P and Q are two sentences of a formalized language L, qualifies as an estimate—made in the light of Q—of the truth-value of P in L. To substantiate his claim, the author establishes here that the two strategies lying at the opposite extremes of the spectrum of truth-value estimating strategies meet the first five of the six requirements (R1-R6) currently placed upon probability functions and fail to meet the sixth one. He concludes from those two results that the value for P and Q of any function satisfying R1-R5 must rate “minimally satisfactory” and the value for P and Q of any function satisfying R1-R6 must rate “satisfactory” as an estimate—made in the light of Q—of the truth-value of P in L.

The title of this symposium, “Formal Simplicity as a Weight in the Acceptability of Scientific Theories,” to some people might seem to suggest that we are to be making positive proposals about how the concept of simplicity could be defined for formalized languages, defined so as to figure in a formalized theory of confirmation. I must confess at the start that I do not have any such ambitious object in view. I now feel, indeed, that premature formalizations have little power to illuminate the philosophically interesting questions which cluster round the problem of the role of simplicity in scientific thinking. So in this short paper I wish merely to present some elementary considerations, not very novel ones, concerning the role which simplicity seems to me to play in our non-demonstrative reasoning about matters of empirical fact. Although many writers have sought to analyze the logical character of such reasoning, little unanimity has been attained in their over-all views; thus it is that though the considerations which I wish to present are elementary, they are not wholly uncontroversial. But because these matters are elementary in nature, I do feel it appropriate in discussing them to use homely examples of uncomplicated kinds, rather than elaborate examples drawn from the more sophisticated reaches of scientific theory; in doing so, I am taking it for granted that scientific inference as regards its logical character is fundamentally a refinement of everyday thinking, rather than a procedure of some essentially different nature.

Prior to the advent of evolutionary theory the Natural System was generally conceived as based on “distinctions of kind, not consisting in a given number of definite properties” (J.S. Mill). It was considered final and unique, to be arrived at by more than one approach. Evolutionary theory has shifted emphasis to different characters, yet explicitly or implicitly the belief in a final natural system in biology persists in many textbooks and taints research. Allegedly natural systems are shown to be fundamentally arbitrary and artificial, dependent on numerous value judgments and intrinsically conflicting to varying degrees. Because of this and because it has turned into a bar to clear thinking, the adjective “natural” should be abolished.