We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.

– The paper explores first the postulational basis and significance of‘measures of information’in current information theory and their possible relations to physical entropy and Brillouin's‘negentropy’regarded as the negative of entropy. For some purposes, the same pattern or formal structure may be abstracted from both‘entropy’and‘information’. The paper analyzes, in the second place, the mathematical analogies which have been traced between information theory and quantum mechanics and argues that the analogies have but a limited value when we come to grips with the (...) deeper, and yet unsolved, problems of quantum theory. Lastly it is urged that the indiscriminate extensions of statistical and information‐theoretic methods, and of quantum‐mechanical analogies, e.g.‘linguistic duality’, to psycholinguistics, literary and aesthetic Gestalten, can result only in crude exaggerations. Dialectical methodology requires the continual reformulation of all scientific descriptions which have to reckon perpetually with the richness of human materials. (shrink)

We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models. and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey's Theorem for Pairs.

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

Starting from the importance of the figure of the parrhesiastes — the political and therapeutic truth- teller— for Foucault’s understanding of the care of the self, this paper traces the political figuration of the analogy between philosophers and physicians on the one hand, and rhetors and disease on the other in Plato’s Gorgias. I show how rhetoric, in the form of ventriloquism, infects the text itself, and then ask how we account for the effect of the “ contaminated ” philosophical (...) dialogue on our readerly health. Is the text placebo, vaccine, or virus? All of these options, I argue, complicate Foucault’s prescription for parrhesia, requiring us to think anew the continuing political ramifications of the metaphor of care. (shrink)

Starting from the importance of the figure of the parrhesiastes—the political and therapeutic truth-teller—for Foucault’s understanding of the care of the self, this paper traces the political figuration of the analogy between philosophers and physicians on the one hand, and rhetors and disease on the other in Plato’s Gorgias. I show how rhetoric, in the form of ventriloquism, infects the text itself, and then ask how we account for the effect of the “contaminated” philosophical dialogue on our readerly health. Is (...) the text placebo, vaccine, or virus? All of these options, I argue, complicate Foucault’s prescription for parrhesia, requiring us to think anew the continuing political ramifications of the metaphor of care. (shrink)