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.

Related Works: Part II: C. T. Chong, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part II: Tame $\Sigma_2$ Coding and the Jump Operator. Ann. Pure Appl. Logic, vol. 87, no. 2, 103--116. Mathematical Reviews : MR1490049 Part III: C. T. Chong, Lei Qian, Theodore A. Slaman, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part III: Prompt Sets, Minimal Paries and Shoenfield's Conjecture. Mathematical Reviews : MR1818378.

The kleptocratic supremacy of the praetorian prefect C. Fulvius Plautianus was felt throughout the city of Rome, the Empire and even beyond the imperial frontiers. Indeed, for the senatorial historian Dio Cassius, there was no more picturesque demonstration of Plautianus' acquisitiveness than his seizure of strange striped horse-like creatures from ‘islands in the Erythraean Sea’. The passage, as preserved in the text of Xiphilinus' Epitome, reads as follows : καὶ τέλος ἵππους Ἡλίῳ τιγροειδεῖς ἐκ τῶν ἐν τῇ Ἐρυθρᾷ θαλάσσῃ νήσων, (...) πέμψας ἑκατοντάρχους, ἐξέκλεψεν·In the end he even stole tiger-like horses to Helios from the islands in the Erythraean Sea, having sent some centurions to carry out the task. (shrink)

We are told that when news of Caracalla's death reached Rome a group of senators denounced their former emperor, likening him to all the tyrants of the past who had ruled over them. The senator who recorded these actions, the historian Cassius Dio, does not say which tyrants were listed, but it is likely that such a comprehensive list included the last king of Rome, Tarquinius Superbus, and his son Sextus. The senators' actions were doubtless more an act of group (...) catharsis than a private show of loyalty to their new emperor, Marcus Opellius Macrinus. Yet what the scene reveals perhaps most clearly is the Romanexemplatradition in practice. (shrink)

At some point before the late fifth centurya.d.an unidentified writer compiled and affixed to each book of Dio'sRoman Historyan index, most notably comprising a table of contents and an excerpt of the consularfasti. Of dubious provenance these paratexts have played a peripheral role in the editorial history of the work. Bekker and Dindorf, with somewhat puritanical zeal, removed them from the main text of their editions of theRoman Historyin the belief that they were not by Dio's hand. Conversely, the stereotyped (...) edition of Dio's history produced under the auspices of Karl Tauchnitz at Leipzig in 1818 provided Latin translations of the indices, but omitted the Greek. Dio's more recent editors have restored them to their editions of theRoman History, despite questions over their origins. (shrink)

In spite of its title, this volume sheds no new light on the debated problem of whether Peirce's ideas form, or can be reconstructed to form, an integrated and internally consistent system. The book, instead, avoids the problem entirely, the pith of its thesis about the unity of Peirce's philosophy being that, in various guises, the notion of Thirdness permeates his thought. Apparently, Haas thinks it evident that to point up the central role of this notion in each of Peirce's (...) subdivisions of philosophy—Phenomenology, Logic, and Metaphysics—is to show the unity of the philosophy as a whole. But he does not counter any specific charges brought against this claim of unity—though he mentions some of them—or even outline how the conception of law is to vindicate this claim. What he does do, following Peirce's three-fold division of philosophy, is to conduct a survey built around the Firstness-Secondness-Thirdness theme; and this exposition, though uncritical, is not lacking in care and subtlety, so that those looking for an overview of Peirce's thought can profit from the book.—C. T. W. (shrink)

A scholium in codex Vaticanus graecus 156 provides evidence that Cassius Dio'sRoman Historyonce contained an explicit reference to theludi saecularesofa.d. 204, something that has been denied in recent scholarship.

This is a book about the philosophy of Henri Bergson which shows how relevant Bergson is to much contemporary philosophy. The book takes as its point of departure Bergson's insistence on precision in philosophy. It then discusses a variety of topics including laughter, the nature of time as experienced, how intelligence and language should be construed as a pragmatic product of evolution, and the antinomies of reason represented by magic and religion. This is not just another exposition of Bergson's work. (...) It offers an account of why Bergson commanded such a massive reading public in his own day and why he deserves to be read now. Written in a terse and clear style, this book will prove appealing to teachers and students of philosophy, cognitive science, psychology, religious studies and literature. (shrink)

An elaborate epitomization of the thought of all the main philosophers, grouped according to the conventional "schools of thought." The scope of the undertaking in this introductory text is ambitious, though some may feel that its manner of categorizing philosophers tends to blur the line between epitome and caricature.—C. T. W.

Although extremely comprehensive in its subject-matter, catholic in its treatment of diverse points of view, and lucid, this book is not simply a survey. Rather, it is, in its own way, original—not because any information or thesis it contains is new, but because it offers a clear, synoptic, and sophisticated look at what has been a relatively ill-defined and fragmented sector of philosophy, that of determining the nature of the "behavioral sciences." Kaplan's way of accomplishing this is to consider the (...) concepts and activities of science "functionally"; and he generally finds that "no one function can suffice" to show us what, e.g., a law of nature is, or what an experiment is, or what a model is, etc. Thus he typically finds other, mutually competing theories both partially true and too narrow. He also has much that is illuminating to say about the Deweyan ideas that the logic of science is fundamentally a "logic-in-use" ; and that scientific concepts are "open" and properly depend on the context of inquiry, rather than on the logician, for their "closure." Consonant with these themes is his stress on the openness of the concept of methodology itself: behavioral scientists, he contends, will gain no salvation merely by finding better procedures. Of greater importance are the values, choices, and invention of the inquirer himself; and Kaplan, accordingly, treats these matters in detail.—C. T. W. (shrink)