Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a (...) PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

“The Role of the Individual in Evolution” is a prescient yet neglected 1941 work by the 20th century’s most important paleontologist, George Gaylord Simpson. In a curious intermingling of explanation and critique, Simpson engages questions that would become increasingly fundamental in modern biological theory and philosophy. Did individuality, adaptation, and evolutionary causation reside at more than one level: the cell, the organism, the genetically coherent reproductive group, the social group, or some combination thereof? What was an individual, anyway? (...) In this introduction, we highlight two points in a wider historical context. First, recognizing the political context of Simpson’s writing profoundly deepens our understanding of the development of his science as the Modern Evolutionary Synthesis infused biology. Second, this story illuminates the emergence of debates around what would eventually come to be called multilevel selection theory. The organism-centered concept of biological individuality defended by Simpson is situated in relation to the then-emerging Synthesis, in which he was a renowned player, and also in relation to the views he opposed: the “metaphysical” ideas of paleontologists such as Henry Fairfield Osborn, who claimed that some evolutionary trends derived from potentialities already implanted in the germplasm; and the organicist ideas of Ralph W. Gerard and the Chicago School of ecologists, which he derided as all too congenial to totalitarianism. We find parallels between the ways that Simpson thought then about human individuality under totalitarianism and the way he thought about individuality in evolution; not that any causal relationship linked the two, but that commonalities of hierarchical structure exist between single entities and groups in both instances. We then trace the subsequent development of Simpson’s political and philosophical takes on the role of the individual in evolution through the 1960s and lightly sketch out the later fate of the organicist ideas of the Chicago School. Simpson’s paper, originally published in the Journal of the Washington Academy of Sciences, is available as supplementary material in the online version of this article, as part of the "Classics in Biological Theory" collection. (shrink)

The third volume of Professor Guthrie's great history of Greek thought, entitled The Fifth-Century Enlightenment, deals in two parts with the Sophists and Socrates, the key figures in the dramatic and fundamental shift of philosophical interest from the physical universe to man. Each of these parts is now available as a paperback with the text, bibliography and indexes amended where necessary so that each part is self-contained. The Sophists assesses the contribution of individuals like Protagoras, Gorgias and Hippias to the (...) extraordinary intellectual and moral fermant in fifth-century Athens. They questioned the bases of morality, religion and organized society itself and the nature of knowledge and language; they initiated a whole series of important and continuing debates, and they provoked Socrates and Plato to a major restatement and defence of traditional values. (shrink)

Working within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call RCA+ 0 and WKL+ 0, and show that RCA+ 0 suffices to prove B.C.T.II. Some model theory of WKL+ 0 and its importance in view of (...) Hilbert's program is discussed, as well as applications of our results to functional analysis. (shrink)

The third volume of Professor Guthrie's great history of Greek thought, entitled The Fifth-Century Enlightenment, deals in two parts with the Sophists and Socrates, the key figures in the dramatic and fundamental shift of philosophical interest from the physical universe to man. Each of the two parts is available as a paperback with the text, bibliography and indexes amended where necessary so that each part is self-contained. Socrates dominated the controversies of this period, as he has dominated the subsequent history (...) of western philosophy. He was the first to identify and grapple with some of the most intractable and persistent logical and philosophical problems; but he was also and has remained a highly controversial figure because of his extraordinary personal qualities and his remarkable career. Professor Guthrie offers a balanced and comprehensive picture of the man, his life, and his thought. (shrink)

The work of Professor Jaeger on the Aristotelian metaphysics, and its modification by the late Hans von Arnim, have raised many new points of the greatest interest, and may, I hope, be considered as having opened up a large and fascinating new field for discussion rather than as having closed the matter. It is a subject which must be considered as a whole. There would be little profit in writing short notes on isolated points in the arguments of the two (...) scholars. Anyone who, possessed of some previous acquaintance with the Aristotelian corpus, reads their work is inevitably stimulated to return to Aristotle with his mind full of fresh ideas. If after a re-examination of the texts he feels he has a different story to tell, he must tell it for himself. That is my excuse for an account which must include much which was always known and much which has arisen out of the work of Jaeger and von Arnim. My conclusions are not the same as theirs, and the argument must stand or fall as a consistent whole. (shrink)

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.