Using H. Whitney's algebra of physical quantities and his definition of a similarity transformation, a family of similar systems (R. L. Causey [3] and [4]) is any maximal collection of subsets of a Cartesian product of dimensions for which every pair of subsets is related by a similarity transformation. We show that such families are characterized by dimensionally invariant laws (in Whitney's sense, [10], not Causey's). Dimensional constants play a crucial role in the formulation of such laws. They are represented as a function g, known as a system measure, from the family into a certain Cartesian product of dimensions and having the property gφ = φg for every similarity φ. The dimensions involved in g are related to the family by means of certain stability groups of similarities. A one-to-one system measure is a proportional representing function, which plays an analogous role in Causey's theory, but not conversely. The present results simplify and clarify those of Causey.

The nature of the connection between theory and observation has been a major source of difficulty for philosophers of science. It is most vexing for those who would reduce the terms of a theory to those of an observation language, e.g. Carnap, Braithwaite, and Nagel. Carnap's work, particularly his treatment of physical theories as partially interpreted formalisms, forms the point of focus of this paper. Carnap attempted to make the connection between theory and observation through correspondence postulates. It is pointed out that such postulates depend in critical ways upon theoretical truths. This particular type of theoretical dependence produces serious trouble for Carnap's approach. For reasons given it may make it untenable. Furthermore, this problem when generalized creates difficulty for any similar reductionist program. Not only is this kind of theoretical dependence pointed out, but more important, the logical conditions which produce it are revealed. In this way light is shed upon the formal characteristics of the notion of theory dependence, especially upon the way in which observation terms depend upon theories for their meaning.

Philosophers of science have used various formulations of the “random mutation—natural selection” scheme to explain the development of scientific knowledge. But the uncritical acceptance of this evolutionary model has led to substantive problems concerning the relation between fact and theory. The primary difficulty lies in the fact that those who adopt this model (Popper and Kuhn, for example) are led to claim that theories arise chiefly through the processes of relatively random change. Systems theory constitutes a general criticism of this model insofar as it demonstrates the necessity of supplementing this mechanism with the non-random influences exercised by the internal organization of a system on its own development.

In this paper I attempt to show that adaptational sentences (i.e. sentences containing the terms “adaptive”, “adapted”, etc.) in evolutionary biology are best interpreted as equivalent to sentences about Darwinian or genetical selection. Thus, the use of adaptational languages does not introduce final purposes or other nonempirical notions into biology. I also try to demonstrate that adaptational sentences and functional sentences are not equivalent in an evolutionary context so that an analysis of function does not dispense with the need for an analysis of adaptation. Finally, it is argued that, although some adaptational sentences might be construed as teleological explanations, given an empirical content, they do not serve as explanations. Rather, they express the outcome of selection, regarded in one way, and regarded in another, they express data for which a theory of evolution must account.

Though one believes that P is true, one can have reasons for thinking it false. Yet, it seems that one cannot know that P is true and (still) have reasons for thinking it false. Why is this so ? What feature of knowledge (or of reasons) precludes having reasons or evidence to believe (true) what you know to be false? If the connection between reasons (evidence) and what one believes is expressible as a probability relation, it would seem that the only satisfactory explanation of this fact is that when one knows that P is true, the reasons or evidence one has in support of P are such as to confer upon P the probability of 1. It is shown by an application of Bayes' Theorem that any value smaller than 1 would permit having reasons to believe what one knows to be false. Hence, it would seem that knowledge requires conclusive reasons to believe (if reasons or evidence is required at all).

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.

D. H. Sharp has recently argued that Einstein, Podolsky, and Rosen failed to make good their claim that elementary quantum theory provides only an incomplete description of physical reality. Sharp expounds in detail three criticisms (a fourth is mentioned) which focus largely on formal features of the quantum theory. I argue, on grounds centered largely in our search for an adequate physical understanding of the micro domain, that each of these criticisms must be rejected. The original criticism of quantum theory reemerges as a still-important baseline in our search for an adequate understanding of quantum theory.

Thesis : Art like science radically affects our perceiving and thinking, and the two are substantially alike in that together—along with an inherited “natural” language system with which they overlap—they enable us to articulate the world.

Science has been advanced as the measure of all things: scientific realism. By implication, art pertains to beauty, science truth. Science effects conceptual breakthroughs, changes our models of natural order. On the contrary (I argue), as a nonverbal symbol system art similarly affects paradigm-induced expectations. Substantively there is no difference in the way each enables us to articulate or measure the world : symbolic realism.

The myth of resemblance as a criterion of representation—imitation as a one-one relation—has, at least since the time of Plato, obscured this truth. Once the distinction between representational and nonrepresentational art falls, the true nature of artist (like scientist) as maker is illumined. The artist, the scientist (disciplinarian), the cosmologist (those responsible for the formulation of so-called natural languages—in time all of us) make the world or, what practically amounts to the same thing, the known, perceived world. This is the claim of the symbolic realist. Is symbolic realism itself only a watershed ? What implication does this critique have for assessing the role of the philosopher today?

The claim that there are nonpurposive functional statements is critically examined by looking at nine translation schemata, several of which are drawn from recent literature. All but one or two fail, suggesting that all functional statements (a) are causal (and not about probabilities or necessary conditions), and (b) have implicit reference to goals. If so, then the possibility of nonpurposive functional statements rests squarely on the possibility of nonpurposive goals.

Various laws and theories in the natural and social sciences are presented with a view to discerning the syntactic and semantic characteristics of many idealizations in science. Three different kinds of idealizations are discussed: ideal conditions, ideal cases, and idealized theories. An ideal condition is a formula in which state variables occur, whose existential closure is false, and for which there is another formula that can be constructed out of the original formula such that the existential closure of the new formula is true. An ideal case is a statement which is logically equivalent to a universal conditional which has an ideal condition as its antecedent. And an idealized theory is a set of false universal conditional statements. Alternative syntactic and semantic analyses are viewed and criticized.