In their logical analysis of theorems about disjoint rays in graphs, Barnes, Shore, and the author (hereafter BGS) introduced a weak choice scheme in second-order arithmetic, called the $\Sigma ^1_1$ axiom of finite choice (hereafter finite choice). This is a special case of the $\Sigma ^1_1$ axiom of choice ( $\Sigma ^1_1\text {-}\mathsf {AC}_0$ ) introduced by Kreisel. BGS showed that $\Sigma ^1_1\text {-}\mathsf {AC}_0$ suffices for proving many of the aforementioned theorems in graph theory. While it is not known (...) if these implications reverse, BGS also showed that those theorems imply finite choice (in some cases, with additional induction assumptions). This motivated us to study the proof-theoretic strength of finite choice. Using a variant of Steel forcing with tagged trees, we show that finite choice is not provable from the $\Delta ^1_1$ -comprehension scheme (even over $\omega $ -models). We also show that finite choice is a consequence of the arithmetic Bolzano–Weierstrass theorem (introduced by Friedman and studied by Conidis), assuming $\Sigma ^1_1$ -induction. Our results were used by BGS to show that several theorems in graph theory cannot be proved using $\Delta ^1_1$ -comprehension. Our results also strengthen results of Conidis. (shrink)

Recall that B is PA relative to A if B computes a member of every nonempty $\Pi ^0_1(A)$ class. This two-place relation is invariant under Turing equivalence and so can be thought of as a binary relation on Turing degrees. Miller and Soskova [23] introduced the notion of a $\Pi ^0_1$ class relative to an enumeration oracle A, which they called a $\Pi ^0_1{\left \langle {A}\right \rangle }$ class. We study the induced extension of the relation B is PA relative (...) to A to enumeration oracles and hence enumeration degrees. We isolate several classes of enumeration degrees based on their behavior with respect to this relation: the PA bounded degrees, the degrees that have a universal class, the low for PA degrees, and the ${\left \langle {\text {self}\kern1pt}\right \rangle }$ -PA degrees. We study the relationship between these classes and other known classes of enumeration degrees. We also investigate a group of classes of enumeration degrees that were introduced by Kalimullin and Puzarenko [14] based on properties that are commonly studied in descriptive set theory. As part of this investigation, we give characterizations of three of their classes in terms of a special sub-collection of relativized $\Pi ^0_1$ classes—the separating classes. These three can then be seen to be direct analogues of three of our classes. We completely determine the relative position of all classes in question. (shrink)

Parker obviously has a warm fondness and a deep empathetic understanding of this period of history, and they are offered to the reader in every carefully worked sentence. In a narrative style that presents the human dimension as well as the central ideas of the Presocratics, Socrates, Plato, and Aristotle, Parker imaginatively reconstructs the phenomenological, empirical, and the homely rationale for their theories. He depicts the Presocratics as organized around the question "What is the universe made of?" and Socrates around (...) "What is Truth, Justice, Goodness?" There is a chapter giving a profile of Athens and Sparta. The three chapters on Plato cover the theory of forms, the Republic, and the Laws. The four chapters on Aristotle, besides the biographical inclusions, cover a scheme of his works, his view of nature, The Ethics, The Politics, and his lasting impact on the rest of intellectual history. The book ends with a brief treatment of Hellenism and a conclusion that takes its cue from the awe and excitement of Keats in On First Looking into Chapman's Homer. Altogether it is a simplified yet sympathetic, thoughtful, and sensitive introduction.--S. O. H. (shrink)

Pranger directs his attention to the everyday experience of citizens, including their Angst, their estrangement, and other existential phenomena, and extrapolates from them a political theory which will integrate the private and public dimensions of individual lives, and which will take into account the multiple political settings and allegiances within the overall national community. First, he explores the institutional setting of the citizen in which the citizen is seen as the player of a particular status role. Next he looks at (...) the category of action where citizen action is seen as basically anonymous, with its outcome ever unpredictable, a fact which Pranger feels any philosophy of government must take into account. By far the strongest chapter is the one on Symbolism and Attitude in which Pranger forges a theory of the relation between public and private and of the citizens' individual and collective symbolic construction of reality. The final chapter explores modern man's anomie, his Wendung, and his uprootedness, as a dimension of political reality. Pranger insists that modern striving for order must take seriously the disorder, confusion, and ambiguity in the daily lives of each individual citizen. Unfortunately Pranger's erudition and insistence on alluding to the work of others renders the book diffuse, his thesis elusive. This is especially unfortunate in light of the fact that he is at his best when he puts his note cards aside and speculates on his own.--S. O. H. (shrink)

This collection of essays, sketches, talks, and poems is hardly a must, even for Buber fans. It is not his best writing or his deepest thinking. However, each selection is short enough not to waste the reader's time and suggestive enough to lure him on to the next one in the hope that the real gems will be there. Buber seldom published his poems, and the reason is clear. With a few memorable exceptions the poems collected here are not strong--at (...) least not in the translations given; fortunately the German is printed alongside. Buber made these selections himself from writings between 1902 and 1964. The criterion of selection was to collect a valid and "survival-worthy expression of an experience, a feeling, a decision, yes even a dream." The ten sections of the book are not titled but some of the topics covered are: words and language, discussions of various thinkers, the idea of community, education, religion, psychology, and politics. Many of the pieces were prepared for particular occasions. Friedman explains those occasions in the back of the book and gives other bits of information that aid the translation and clear up some obscure references. Some of the themes that pervade the selections are: the togetherness of body and spirit, dialogue, the importance of existential trust, and the sacredness of the concrete world and of everyday encounters. Ruth Anshen's inspired introduction to the Credo Perspectives Series is worthy of its repetition in all the volumes.--S. O. H. (shrink)

This series of character sketches is disappointing to the reader expecting an interpretive historical document. The bulk of the book is taken up with reflections about the author's mother, who died when Svetlana was only six, her mother's family, her brothers, and her sweethearts. Many readers are naturally interested in the figure of Stalin, but he is treated directly only in small and scattered portions of the book with much of the information repeated. It becomes evident that the author knew (...) her father primarily through his impact on the people she loved. Consequently, the figure of Stalin emerges as somewhat enigmatic and mysterious, a combination god and devil. It is apparent that she did not really know him very well, see him very often, or think about him very much. The book is not really about Stalin at all. It is an enjoyable combination of behind-the-scenes gossip, and engrossing narrative fragments.—S. O. H. (shrink)

These essays were delivered at the Fourth East-West Philosophers conference at the University of Hawaii in 1964. Because the audience was of various traditions, most of the papers contain instruction in rudiments as well as points of more technical interest. The oriental speakers especially take pains not to spring their special terminology on the western listener. The book systematically and thoroughly works through the themes of the individual in Chinese, Indian, Japanese, and western metaphysics, methodology, religion, and ethics. Social, political, (...) and legal thought and practice are also covered. Some of the papers are followed by transcripts of questions and answers. These are often very helpful and revealing as they focus the issues and require the speaker to be specific in summarizing his points. Altogether there are thirty-three contributors, only a minority of whom are westerners. These include: Charles Moore, Wm. E. Hocking, H. E. McCarthy, John Smith, W. H. Werkmeister, E. W. Strong, R. Polin, and R. McKeon. Again and again both East and West stressed the interconnection and interdependence of the individual and the universal, the individual and the community. There is an appendix containing the conference's public lectures, which were given by S. M. McMurrin, C. Regamey, and D. T. Suzuki. The book and the conference end with Moore citing highlights and provocative points from virtually all the lectures. This provides a useful summary and synthesis of what would otherwise be an overwhelming deluge of intellection. There are notes on contributors and an index.--S. O. H. (shrink)

A large and fully representative edition of Emerson's most important and most penetrating prose. "The American Scholar" and the "Divinity School Address" plus essays on History, Self-Reliance, Love, Heroism, Art, The Over-Soul, The Poet, Character, Manners, Nature, Politics to name only a few. Parts from "The Conduct of Life," and from English Traits. The longer essays on Domestic Life, Plato, Thoreau, and Lincoln. The fifty pages of excerpts from Emerson's Journals are one of the most interesting features of this edition. (...) There is none of Emerson's poetry except what he placed at the beginning of some of the essays. There is a concise, informative, biographical introduction by Mumford who paints an unhealthy and shy, "cold but fiery" Emerson who nonetheless, through his writings, was a giant on the forefront of the new thinking and changing attitudes of his time. There is no critical apparatus or bibliographical information, but with the introduction the book is an effective and ample reader.--S. O. E. (shrink)

We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with similar results in computable topology.

This is a very useful collection of important, standard, primary sources. Two-thirds of volume one is taken up with Plato and Aristotle with the rest of the volume evenly divided among the Presocratics, Hellenistic philosophers and Medieval philosophers. Four of the Platonic dialogues are complete. Second edition changes in the first volume include: changes in translators and new entries. In both volumes Kaufmann's prefaces are very brief and mainly biographical. He consistently ties in information about each thinker's contemporaries. The second (...) volume has readings from Bacon, Descartes, Hobbes, Spinoza, Locke, Leibniz, Berkeley, Hume, and Kant. Almost half the second volume is taken up with Hume and Kant. The second edition changes in volume II are: expansion of Spinoza's Ethics, Locke's Essay, Berkeley's Principles; and additions of Descartes' correspondence with Princess Elizabeth, and a short Leibniz essay translated especially for this volume by M. Furth. The selections are adequately long and representational. The volumes contain double columns, no index, no bibliographies, no "Study Guides," just solid and important reading.--S. O. H. (shrink)