I propose to fashion this paper after the pattern of a conventional sermon. That is, I shall begin by taking a text, and shall then elaborate on it. My text is a sentence of Whitehead, and it reads as follows: “It is more important that a proposition be interesting than that it be true; the importance of truth is that it adds to interest.” To my knowledge Whitehead makes this identical remark at least twice in his writings. It appears in (...) Process and Reality . And it appears again, word for word, several years later in Adventures of Ideas . The fact that he thus says it twice, in identical words, suggests to me that he is himself immensely pleased with it, and that he values highly the thought which it expresses. At this I am not at all surprised. For it seems to me that the remark enshrines one of those sudden flashes of insight for which Whitehead is famous, and which stamp him as, not merely the ordinary very clever or very learned man, but the man of genius. Speaking for myself, I can record that when I first read this remark it produced in me a sudden thrill, a sense of illumination, of the opening of new vistas, not wholly dissimilar to the thrill which, as a very young man, one felt when one first read certain stanzas of Shelley or Wordsworth. (shrink)

The results of two recent articles expanding the Gibbs variational principle to encompass all of statistical mechanics, in which the role of external sources is made explicit, are utilized to further explicate the theory. Representative applications to nonequilibrium thermodynamics and hydrodynamics are presented, describing several fundamental processes, including hydrodynamic fluctuations. A coherent description of macroscopic relaxation dynamics is provided, along with an exemplary demonstration of the approach to equilibrium in a simple fluid.

A selection of the writings of Wittgenstein in the philosophy of logic and mathematics written in the years 1937-1944. There is no concern with the foundations of mathematics in the sense of metamathematics nor in the sense of investigation of the possibility of providing secure axiomatic foundations for such notions as that of "set." Indeed, the original motives for these latter investigations are rejected; instead, a clarification of the grammar of mathematical propositions is sought. The author discusses the notions of (...) mathematical proof at length and attacks both the Russellian view that mathematics is an appendage of logic and Hilbert's program of proof-theory.--W. T. (shrink)

I emphasize four points: Socratic dialectic challenges the interlocutor not only to acquire the correct moral opinions, but to question and think for oneself and to develop one's own moral rationality; it involves anticipatory acts of several types of virtue: courage, moderation, and justice and concern for the common good as opposed to competition and jealousy; what is at stake is not only the topic of the particular exchange, but the opportunity for membership in a rational/educational community; and the fact (...) that Socrates' interlocutors typically reject the opportunity for moral insight and personal growth he makes available to them explains why he cannot be said to possess a techne of moral education, and why he insists that virtue cannot be taught. The process of education through the elenchus is not a matter of correct instruction, but of rational elicitation, which must be responded to by personal choice. Thus Socrates' principles may represent not only beliefs he has tested over many years of dialogue, but also values he has come to through participation in elenctic inquiry, the idealized extension of norms required by and created in the practice of dialectic. Socratic education involves the interlocutor in the confrontation with a self whose irrational attachments of appetite and ego are exposed and must be overcome for the interlocutor to experience catharsis. (shrink)

Brindley proposed that we initially generate movements , under higher cerebral control. As the movement is practiced, the cerebellum learns to link within itself the context in which the movement is made to the lower level movement generators. Marr and Albus proposed that the linkage is established by a special input from the inferior olive, which plays upon an input-output element within the cerebellum during the period of the learning. When the linkage is complete, the occurrence of the context (represented (...) by a certain input to the cerebellum) will trigger (through the cerebellum) the appropriate motor response. The movement is distinguished from the conscious movement by its now being automatic, rapid, and stereotyped. The idea is still controversial, but has been supported by a variety of animal studies and, as reviewed here, is consistent with the results of a number of human PET and ablation studies. I have added to the idea of context-response linkage what I think is another important variable: novel combinations of downstream elements. With regard to the motor system and the muscles, this could explain how varied combinations of muscles may become active in precise time-amplitude specifications so as to produce coordinated movements appropriate to specific contexts. In this target article, I have further extended this idea to the premotor parts of the brain and their role in cognition. These areas receive influences from the cerebellum; they are active both in planning movements that are to be executed and in thinking about movements that are not to be executed. From recent evidence, the cerebellar output extends even to what has been characterized as the ultimate frontal planning area, the cortex, area 46. The cerebellum thus may be involved in context-response linkage, and response combination even at these higher levels. The implication would be that, through practice, an experiential context would automatically evoke a certain mental action plan. The plan would be in the realm of thought, and could lead to execution. The specific cerebellar contribution would be one of the context linkage and the shaping of the response, through trial and error learning. The prefrontal and premotor areas could still plan without the help of the cerebellum, but not so automatically, rapidly, stereotypically, so precisely linked to context, or so free of error. Nor would their activities improve optimally with mental practice. (shrink)