Varieties of chemical and phase equilibria are controlled by the minimum Gibbs energy principle, according to which the Gibbs energy for a system will have the minimum value at any given temperature and pressure. It is understood that the minimum is with respect to all nonequilibrium states at the same temperature and pressure. The abstract relation between Gibbs energy and the equilibrium constant is deduced from fundamental laws of thermodynamics. However, actual use of this relation calls for the Gibbs energy as a function of concentrations of the chemicals. Since thermodynamics is formulated without any reference to materials, how does one get that relation? This article provides the answer, and in the process shows that application of theory to experiments requires several intermediate layers where theory and experiment commingle.

The purpose of this paper is to solve a serious problem for the projection postulate involving the time-energy uncertainty relation. The problem was recently raised by Teller, who believes that the problem is insoluble and, consequently, that the projection postulate should no longer be regarded as a serious focus for interpretive investigation.

The fundamental problem of what is explained in science should be considered and clarified since it determines the way of solving the problem of how something is explained as well as the entire view of explanation. In the first section after the introduction, Hempel's models of explanation are criticized for their narrow concern with logical reconstruction. In the next section a broader epistemological approach to explanation is presented, and in the last section an historical example of Newtonian explanation as epistemic activity is discussed.

This paper studies the extent to which probability functions are recursively definable. It proves, in particular, that the (absolute) probability of a statement A is recursively definable from a certain point on, to wit: from the (absolute) probabilities of certain atomic components and conjunctions of atomic components of A on, but to no further extent. And it proves that, generally, the probability of a statement A relative to a statement B is recursively definable from a certain point on, to wit: from the probabilities relative to that very B of certain atomic components and conjunctions of atomic components of A, but again to no further extent. These and other results are extended to the less studied case where A and B are compounded from atomic statements by means of “∀” as well as “~” and “&”. The absolute probability functions considered are those of Kolmogorov and Carnap, and the relative ones are those of Kolmogorov, Carnap, Rényi, and Popper.

The problem of synthesis in biology may have reference to the evolutionary origin of living organisms in past time, a process not directly observable but conceivably reconstructible in broad outline: thus to the biochemist this evolution may appear as the evolution of the special biological compounds, to the psychologist as the evolution of “mind”—or at least of types of behavior. Or the problem may refer to the synthesis of the individual animal or plant, a process of construction which typically starts from a detached portion of a parent organism, such as an egg or seed; this is the problem of individual development or ontogeny and is not essentially different from the general problem of growth. But it is clear that the processes of phyletic evolution and of ontogeny must be considered together, since evolutionary history is in reality the history of a succession of individual organisms, each developing from its germ, i.e. of ontogenies; and the ontogenetic process, so faithfully repeated in each individual as it comes into existence, is itself a product of evolution, having originated (apparently by slow and tentative efforts) in the remote past. The succession of individuals has undergone progressive diversification, culminating in the present condition. We may describe our problem, then, as the problem of the factors underlying the synthesis of a highly special process, that by which the diffusely distributed nonliving materials and energies of nature are brought together in a special kind of unification and transformed into a living organism.

This article presents and argues for modal structuralism, which is loosely derived from a position described by Wilfrid Sellars. Modal structuralism holds that a fundamental property is identified by the role it plays in the structure of possibilities. It implies necessitarianism about laws, which holds that at least some laws of nature are metaphysically necessary. The argument for these positions derives from the following assumptions: the principle of the identity of indiscernible properties and a modest antiquidditism. These assumptions are weaker than those of causal structuralism, which is a closely related view.

The Bohr-Heisenberg doctrine of wave-particle duality has been attacked in the past for its methodical defects, over-complication, internal contradictions, its positivistic phenomenalism, etc. The present investigation shows that duality, the doctrine of equivalence of the particle picture and the wave picture of matter, is untenable since its wave part leads to empirically wrong results in the relativistic domain, and violates the postulate of independence of the arbitrary choice of reference system in the non-relativistic realm. Therefore, when methodical objections were never quite conclusive, the physical failure of the duality idea seals its fate irrefutably, together with all its pseudo-philosophical implications.