Theoretical physics is a deductive discipline which presupposes the validity and applicability of certain other disciplines. Among these are logic, algebra, analysis, and geometry. Before relativity, Euclidean geometry was the only one thought to be important for physical space. These disciplines correlate well with experience, and, in the course of time, a priori validity came to be ascribed to them. To Kant, for example, the universe could not possibly be based on any geometry other than Euclid's. The discovery of non-Euclidean geometries by Bolyai and Lobatchevsky, its systematic extension by Riemann, and the critical scrutiny of foundations by Mach and Poincaré shook the “self-evident truth” of Euclidean geometry as applied to the world of physics. The death knell of the a priori truth of any geometry was supplied by Einstein. He showed that a wider body of experience was coordinated by a Riemannian geometry than by Euclidean. He traced the success of Euclidian geometry back to the existence of so-called rigid bodies, in terms of which operations can be associated with numbers which correlate well with numbers associated in a purely mathematical way with mathematical constructs put in correspondence with these bodies. For the physicist, then, the geometry of the real world is now a physical theory whose “truth” like that of all physical theory, is measured by its degree of success in coordinating experience.

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.

This paper presents a theory of conclusions based upon the suggestions of Tukey [21]. The logic offered here is based upon two rules of detachment that occur naturally in probabilistic inference, a traditional rule of acceptance, and a rule of rejection. The rules of detachment provide flexibility: the theory of conclusions can account for both statistical and deductive arguments. The rule of acceptance governs the acceptance of new conclusions, is a variant of the rule of high probability, and is a limiting case of a decision-theoretic rule of acceptance. The rule of rejection governs the removal of previously accepted conclusions on the basis of new evidence. The resulting theory of conclusions is not a decision-theoretic logic but does, through the aforementioned limiting property, provide a line of demarcation between decision and conclusion (i.e., nondecision) logics of acceptance. The theory of conclusions therefore complements decision-theoretic inference.

The theory of conclusions presented here satisfies Tukey's desiderata, specifically:

1. (1) conclusions are statements which are accepted on the basis of unusually strong evidence;

2. (2) conclusions are to remain accepted unless and until unusually strong evidence to the contrary arises;

3. (3) conclusions are subject to future rejection, when and if the evidence against them becomes strong enough.

Finally, the preferred theory of conclusions has a strong conservative bias, reflecting Tukey's aims.

In this article we will explain and defend the proposition: “A statement which prescribes (entails) the conditions for its verification is a scientific statement.” We will confine our consideration to factual (synthetic) statements alone, although it may be true that our proposed proposition refers to formal, analytic statements also.

If prescribing the conditions for its verification is the only necessary qualification for a statement to be scientific then obviously the means of arriving at such a statement is irrelevant. It does not matter whether we have performed many experiments or none before making a scientific statement. There are, of course, reasons for having a systematic method of arriving at the formulation of scientific statements, but this does not make them more, or less, scientific.

John Worrall and Nancy Cartwright have both argued that randomized controlled trials (RCTs) are “testing the wrong theory.” They claim that RCTs are designed to test inferences about the causal relationships in the study population, but this does not guarantee a justified inference about the causal relationships in the more diverse population in clinical practice. In this article I argue that the epistemology of theory testing in trials is more complicated than either Worrall’s or Cartwright’s accounts suggest. I illustrate this more complex theoretical structure with case studies in medical theory testing from Alzheimer’s research and anticancer drugs in personalized medicine.

Philosophizing about the social sciences involves an initial problem of denotation. Although the natural sciences are the scene of intramural disputes like those between proponents of quantum mechanics and relativity theory, no one doubts either what the natural sciences are or that they are sciences; and all of them may be said to use, broadly speaking, the same scientific method. But the case of the social sciences is different. It resembles somewhat the situation in mathematics where the intuitionists deny that non-constructible concepts or problems belong to mathematics; and even more the situation in philosophy where groups like the analysts and the existentialists not only do not speak the same language but do not even recognize one another's right to be called “philosophy.” Similarly, the disciplines which comprise the social sciences today differ from one another in basic ways, involving long-standing disputes over which ones have a right to the names of the several social sciences and what their proper methods are. Familiar examples of these disputes are the controversies between the classicists and institutionalists in economics, and between the analytical and sociological schools in jurispurdence. Consequently, it is impossible for philosophers, or social scientists philosophizing about their general field, to proceed to discuss “the” subject-matter or “the” method of “the” social sciences as if the phrases containing these definite articles were definite descriptions on whose objects there was general agreement.

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.

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: (i) the “classical” Boltzmann entropy (SB1); (ii) the modified Boltzmann entropy that is usually proposed in response to the paradox (SB2); and (iii) a generalized version of the latter (SB2G). It is argued that (i) notwithstanding a recent suggestion to the contrary, the paradox does imply that SB1 is not a satisfactory definition of entropy; (ii) SB2 is undermined by “second-order” versions of the paradox; and (iii) SB2G solves the paradox but is not a satisfactory definition of entropy.

Reanimated for the contemporary literature in the writings of Quine ([15]), [16]) and Kuhn [7], the conventionalism of Duhem [2] and Poincaré [12] has emerged in the last few years as one of the genuinely interesting topics in the philosophy of science. The theory in question—let us follow Grünbaum [3] in calling it the D-thesis, after its founder, Pierre Duhem—claims three things: (1) a single scientific hypothesis H is never disconfirmable in isolation from its fellow; (2) every single hypothesis H of science presupposes, explicitly or implicitly, the support of a conjunction A = A, • A2 • … • Am of auxiliary assumptions or hypotheses; (3) the failure of an observational consequence of H in face of contradictory evidence disconfirms only the conjunction of H and A, not H alone—i.e. establishes only ∼ (H • A). The logical picture is as follows:

This paper presents two interpretations of the fiber bundle fonnalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical fonnalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure fonnal arguments.

In recent years there has been a rebirth of interest in the philosophy of Pierre Duhem. Although I applaud the spirit of this movement, one finds the critics of Duhem frequently lacking in a basic understanding of Duhem's tenets, sometimes to the extent that one doubts a familiarity with the Duhemian text. One of the few papers which is designed to remedy this state of affairs is that of Philip Quinn entitled “What Duhem Really Meant.” Quinn is to be applauded for his meticulous and rigorous exegetical work on the Duhemian text. Unfortunately, Quinn's characterization of the logical relations of two of the central Duhemian theses is erroneous. I shall endeavor to correct these errors in this paper.

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in the language of science is presented here. This approach preserves compositionality to a large extent.

We consider the mind-dependence or independence of the “now,” of “becoming,” and of “time's arrow,” by considering the various senses in which these notions might be mind-dependent or not. These matters cannot be sensibly discussed without taking a stand regarding criteria of “reality.” Proceeding from a basically phenomenalist position we conclude that merely to differentiate between appearance and reality is implicitly to assume a directed flow of time. We discuss the relationship between phenomenological and physical time and their possible asymmetries. We find that physical time acquires meaning only through phenomenological time, and that phenomenological time is fundamentally asymmetric. This still leaves room for the question: Is there anything in physical time which reflects the fact that it, to be meaningful, must be applied asymmetrically? The relevance of relativity theory to this question is discussed.

Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.

“Reason,” said Lao Tze some twenty five hundred years ago, “is of all things the emptiest. Yet its use is inexhaustible.” With equal justice, he might have said the same of language. But Lao Tze, whose profound metaphysical probing appeared to carry him beyond the reach of linguistic aid, was led to insist that “Those who know do not speak; those who speak do not know.” Yet the “Old Philosopher,” as he is known to the Chinese, might be said to admit, by the very implications of his insistence, that language can exercise the greatest influence on thought, if only, in his viewpoint, to nullify it. Today we acknowledge this influence by reversing the great metaphysician's statement, those without speech (i.e. language) in some form or other cannot know.

In the fourteenth century William of Occam in the course of his attack on the medieval scholastic philosophy enunciated his famous “razor”: Entia non sunt multiplicanda praeter necessitatem (hypotheses should not be multiplied unnecessarily). This is the classic claim for the description of nature in terms of the minimum possible number of fundamental concepts. It was presumably so recognized by Newton in the third book of his “Principia” in 1687 when he wrote: “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes.”

In “Laws of Nature” [1] I argued that natural laws are not universal truths. Laws have properties that enable them to function in a special way. Since universal truths do not have these properties, they cannot be promoted to the status of laws by assigning them this function, by using them in the way laws are typically used. To suppose that we could effect this transformation by the way we used a generalization is like supposing that we could make thumb tacks into garden hoses by using them to water flowers. It will not work. Thumb tacks lack the requisite structure. Hence, they cannot be used in the way garden hoses are normally used. And universal truths lack the properties that would enable them to function, and thereby qualify, as laws of nature.

Russell's introduction of negative facts to account for the truth of “negative” sentences or beliefs rests on his collaboration with Wittgenstein in such efforts as the characterization of formal necessity, the theory of logical atomism, and the use of the Ideal Language. In examining their views we arrive at two conclusions. First, that the issue of negative facts is distinct from questions of meaning or intentionality; what a sentence or belief means or is about rather than what makes it true or false. Second, that the ontological use of the Ideal Language is incompatible with the requirements of its employment in the logical study of inferences. On this basis we conclude that despite elaborations by recent proponents, the doctrine of negative facts lacks adequate support, and perhaps more importantly, it is proper ontological method to free the Ideal Language from the exigencies of a symbolism constructed for logical investigation.

This paper argues that if a person's beliefs are idealized as a set of sentences (theoretical, observational, and mixed) then the device of Ramsey sentences provides a treatment, of the mind-brain problem, that has at least four noteworthy characteristics. First, sentences asserting correlations between one's own brain state and one's own “private” experiences are, on such treatment, reconstrued as neither causal, coreferential, nor as meaning postulates, but as clauses in an overall hypothesis (Ramsey sentence) whose only nonlogical constants have “private” meanings. Second, sentences asserting psycho-physical correlations in general, or in other individuals, remain theoretical and susceptible to scientific reduction, though not prejudged to be so. Third, communication between persons having mutually exclusive, “private,” observational vocabularies can be made intelligible. Fourth, it becomes possible in principle (though not necessary) that the world could ultimately be given a total description in a scientific language, Lφ, without mental primitives. However, such a language would be susceptible to interpretation by a given individual using a metalanguage whose primitives (not among those of Lφ) were privately observational to that individual. His procedure in accomplishing such an interpretation would be to construct a Tarskian truth definition in a metalanguage MLφ and then to incorporate it, by Ramsifying its descriptive terms, in his own overall Ramsey sentence. The physical language, Lφ, while not containing a person's primitives, would, of course, be able to define their physical correlates, thus providing a certain sort of mutual mirroring, and a certain sort of relativity.