§1. The origins of recursion theory. In dedicating a book to Steve Kleene, I referred to him as the person who made recursion theory into a theory. Recursion theory was begun by Kleene's teacher at Princeton, Alonzo Church, who first defined the class of recursive functions; first maintained that this class was the class of computable functions ; and first used this fact to solve negatively some classical problems on the existence of algorithms. However, it was Kleene who, in his (...) thesis and in his subsequent attempts to convince himself of Church's Thesis, developed a general theory of the behavior of the recursive functions. He continued to develop this theory and extend it to new situations throughout his mathematical career. Indeed, all of the research which he did had a close relationship to recursive functions.Church's Thesis arose in an accidental way. In his investigations of a system of logic which he had invented, Church became interested in a class of functions which he called the λ-definable functions. Initially, Church knew that the successor function and the addition function were λ-definable, but not much else. During 1932, Kleene gradually showed1 that this class of functions was quite extensive; and these results became an important part of his thesis 1935a. (shrink)

Neuroscientists are searching for the engram within the conceptual framework established by John Locke's theory of mind. This framework was elaborated before the development of information theory, before the development of information processing machines and the science of computation, before the discovery that molecules carry hereditary information, before the discovery of the codon code and the molecular machinery for editing the messages written in this code and translating it into transcription factors that mark abstract features of organic structure such as (...) anterior and distal. The search for the engram needs to abandon Locke's conceptual framework and work within a framework informed by these developments. The engram is the medium by which information extracted from past experience is transmitted to the computations that inform future behavior. The information-conveying symbols in the engram are rapidly generated in the course of computations, which implies that they are molecules. (shrink)

This book charts new ground, specifically, in its negotiation of a definition of animal welfare, in its systematic discussion of the organizations actually ...

Owing to the illegibility of parts of the Fronto palimpsest and the carelessness of its first editor, Cardinal Mai, it was impossible, even after the critical labours of Niebuhr and his colleagues, to come to any satisfactory conclusion as to the chronology of the Letters. But the edition of S. A. Naber in 1867, which had the advantage of a fresh collation of the MS. by G. N. Du Rieu, further reinforced subsequently by a new examination of the Codex due (...) to W. Studemund, held out a better prospect of success. The labours of C. Brakman in the same direction, published in 1902, have also thrown fresh light upon the subject. Yet the critical world has long been awaiting the appearance of the authoritative recension by Professor E. Hauler of Vienna, who has spent infinite pains over a further, and what may well be a final, inspection of the Codex. A great desideratum, which it is much to be hoped that the new edition will supply, is an exact indication, as far as may be, of the extent of each lacuna in pages, lines, words, or letters. A knowledge of how much is lost in each case is essential for the true understanding of the sequence of thought and time in what remains. (shrink)

Recent research on the relations of personality to well-being shows that the people who are most healthy, happy and fulfilled are those who are high in all three of the character traits of self-directedness, cooperativeness, and self-transcendence as measured by the Temperament and Character Inventory. In the past, the healthy personality has often been considered to require only high self-directedness and high cooperativeness. However, now the self-centred behaviour of people who are low in self-transcendence is degrading the conditions needed for (...) sustainable life by all human beings. Consequently, human beings need to and can develop their capacity for self-transcendence in order to maintain their individual and collective well-being. (shrink)