In this paper a model is presented for the growth of knowledge in a dynamic scientific system. A system which is in some respects an idealization of a Lakatosian research program. The kinematics of the system is described in terms of two probabilistic variables, one of which is related to the evolution of its theoretical component and the other—to the growth of the empirical component. It is shown that when the empirical growth is faster than the theoretical growth the posterior probability of the theoretical component increases. Thus, empirical progressiveness of a research program, as explicated in this model, is accompanied by an increase in the degree of confirmation. In such a case the system grows in a Popperian-like spirit, while learning from experience in a Bayesian manner.

Olav Benjamin Vassend proposes two solutions to the “interpretive problem” of assigning nonzero probabilities to hypotheses that are known to be false. He argues that the verisimilitude interpretation (probability expresses the degree of belief that the hypothesis is closest to the truth) and the counterfactual interpretation (probability is conditional on a false supposition) are equivalent. While Vassend’s intuition about these two solutions is basically correct, the technical details of his treatment need elaboration and correction. Appropriate tools for combining verisimilitude and Bayesian probabilities can be found in my Truthlikeness.

In unseen and unacknowledged specter, an “X,” attends at every economic feast, and stands at the elbow of every modern wiseacre. It confounds the forecaster with seeming malice showing itself only in the event and even then with impish and uncertain effect. It laughs at pretensions to knowledge; it tantalizes all figurers, haunts all generalizers and keeps itself to itself, a shadow, an unknown. But phantom as it is, it is still a force, a potent, active, generative substance, mysterious in genesis, related to a dream, but able to accomplish miracles of reality. For the purpose here it will be called the creative experience.

It is commonly the case that a problem concerning a mathematical or physical system can be solved in two quite different ways—by an internal or an external approach. For example, the area of a triangle can be found by integration or by showing it to be half that of a certain rectangle. In general, the first approach is, to analyse the given system into component parts, and the second approach is to deal with the system as a whole.

It seems that even in cases where solutions to physical problems obtained according to these two approaches are equally valid, and are equally good as explanations, scientists prefer the solution obtained by the internal approach.

The reasons for this preference are examined. And it is suggested that whatever the reasons, this preference may have been partly responsible for the 19th century preference for the Kinetic Theory rather than Thermodynamics.

This rejoinder will be divided into two parts. The first part will be devoted to what appear to be serious disagreements between Professor Kyburg and me. I shall try to show that these disagreements are far more apparent than real. The second part will contain my criticism of Kyburg's constructive suggestion on the nature of explanation.

I. The present state of philosophy contrasted with that of the sciences. Both philosophy and science seek not mere opinion but knowledge. The sciences, however, have by now won a vast body of knowledge, and daily make positive additions to it notwithstanding their theoretical controversies. In philosophy, on the contrary, the same great problems are discussed by generation after generation with rather meager results other than a multiplication of theories and schools of opinion. One is therefore moved to wonder whether philosophy is forever doomed to inconclusiveness, or whether on the contrary knowledge and definite progress are possible in its field in the same sense as in the sciences.

Is metaphysics possible? From the beginning of our present sophisticated era we have continually been compelled to ask this question. For myself I confess to a growing impatience with this and like questions. I hold with Kant that metaphysics is a Naturanlage, that should all science pass away and should we revert to barbarism, there would still be metaphysics. I am also disposed to think that should mankind develop in the opposite direction, should we become the supermen or the angels which the perfectionists of all times have envisaged, metaphysics would not only remain, but metaphysical insight would be the very life of that perfection. As Dante said, “metaphysics is the bread of angels.”

In this paper Richard Jeffrey's ‘Logic of Decision’ is extended by examination of agents' attitudes to the sorts of possibilities identified by indicative conditional sentences. An expression for the desirability of conditionals is proposed and, along with Adams' thesis that the probability of a conditional equals the conditional probability of its antecedent given its consequent, is defended by informally deriving it from Jeffrey's notion of desirability and some weak constraints on rational preference for conditional possibilities. Finally a statement is given of a representation theorem establishing the conditions under which a rational agent's preferences for conditionals determines the existence of unique measures (up to choice of scale) of her degrees of belief and desire.

The supposed communication of one mind with another at a distance, without any means known to physical or psychological science, is a generally accepted definition of telepathy. Thus when persons sensorially isolated from each other experience congruence and coincidence of thoughts, emotions or actions they are considered as being in telepathic communication. Clairvoyance surmises the apprehension of particular objects and stimuli also without the employment of any of the agencies of the five senses. Although telepathy and clairvoyance have been thus recognized as distinct conjectures, either or both comprise features of Extra Sensory Perception (ESP). Both are conceived of as transcending the anatomical structures and physiological functionings that comprise the five senses. They therefore constitute a mysterious, additional sense which as yet cannot be ascribed to material bases or causes. However, the operations, if not the exact natures, of these recondite abilities have been, it is claimed, experimentally and precisely ascertained.