The old quarrel between the logical empiricists or pragmatists and the defenders of metaphysics is still far from being settled. This situation is at least partly due to the fact that neither of the two antagonists has a clear insight in the historical background, the systematical validity, and the practical purposes of the concepts and methods used in traditional philosophy. Therefore further clarification is needed.

The following paper does not claim to give final definitions and decisions. It will rather try to draw the attention to certain ways of reasoning still very widespread in metaphysics and moral theory. Their careful analysis may throw light on some of the so-called eternal philosophical problems.

4. The Mind's Lawmaking: Critical Idealism. Pleased with something dramatic in the phrase, we often characterize experiment as “a question put to Nature.” But if there be anything flattering to our state in Nature's submission to our questioning, there can be nothing grateful to our heart in her manner of answering. “Are we all to die?” Nature answers, “Yes.” “Will the sun that warmed our fathers last out our children?” Nature answers, “No.” Thus Nature giveth and Nature taketh away; her complaisance ends with letting us know her way with us.

In a number of essays published over the last decade or so, W. V. Quine has made some interesting suggestions concerning the ontology of theories. (3; 4; 5; 6; 7; 9; 10) If I understand him correctly, one of his principal objects has been to formulate a criterion by means of which one can correctly decide what are the ontological commitments of any given theory. My aim in this paper is to reveal what I think are inadequacies in Quine's criterion and to indicate the direction in which a proper formulation lies.

This paper attempts to present a formal model for the science of decision where “science of decision” is restricted to the work that has been done in formal models and not those aspects connected with the gathering of empirical data and development of measures for the data. One of the difficulties in treating such a phenomenon as decision-making has been to give a precise statement of the problem. The literature of numerous fields is filled with models and talk about models where various restrictions are imposed. Among all of these it seems that the formalistic or logical, game-theoretic, and statistical decision function conceptual schemas have solved some decision problems largely due to the fact that they could give a mathematical formulation of the problem and its solution. The result is that in these three fields the decision problem can be fed into a computer which grinds out an answer for each particular set of parameters.

The purpose of this note is to examine a recent axiomatization of classical particle mechanics, and its relation to an alternative axiomatization I had earlier proposed. A comparison of the two proposals casts some interesting light on the problems of operationalism in classical celestial mechanics.

1. Comparison of the Two Axiomatizations. The basic differences between the two proposals arise from the nature of the undefined terms. Both systems take the set of particles, time, and position as primitive notions. Both systems assume that there exists a set of particles having continuous, twice-differentiable paths over some time interval. In addition, CPM takes mass and force as primitive notions, and assumes that with each particle there is associated a mass and a set of forces such that Newton's Second Law is satisfied (Axiom P6). A system with these properties is called in CPM “a system of particle mechanics.” If, in addition, the set of forces in the system satisfies Newton's Third Law, the system is called in CPM “Newtonian.”

Current preoccupation with learning-theory has led psychologists, and other social scientists, to expect more from it than can presently be delivered. The subsequent reflections are submitted in order to suggest that at least some formulations of the relation between learning-theory and the “culture-concept” are somewhat defective. More specifically, I shall examine two recent contributions by O. K. Moore (one of which appeared in this journal (1)), whose attempts at definition are distiguished by the employment of the formidable weapons of symbolic logic. Without denying the advantages to be gained, by the sciences in general and the social sciences in particular, from the introduction of this new logic, I would justify my critical concern with Moore's definition of “culture” in terms of “learning-theory,” because it may become representative of other contributions whose partial inadequacies are easily obscured by the technicality of a symbolic language into which the actual empirical complexity of an issue could be falsely thought to have been properly translated.

The purpose of this note is to present a set of rules for the syllogism which not only is equivalent with the set ordinarily used, but also is the dual of the latter. It must be emphasized, however, that the discussion of both of these sets presupposes the hypothetical interpretation of universal propositions, and would not hold true of the existential interpretation of such propositions. A universal proposition is interpreted hypothetically, rather than existentially, when it is not assumed that the class denoted by its subject must have members. Thus the hypothetical interpretation of “All unicorns are mammals” would be just “If anything is a unicorn, then it is a mammal—but it is not necessarily true that unicorns exist.” One important consequence of the distinction between these two modes of interpretation is that rule 3, below, is true for the hypothetical interpretation, but not for the existential.