In lieu of an abstract, here is a brief excerpt of the content:98 HISTORY OF PHILOSOPHY quoted in great numbers. The other is Kern's philosophical competence and his skill in handling complex problems. The book is divided into two parts. Part I gives the reader a brief historical survey of Husserl's changing attitudes toward Kant and the neo-Kantians (especially Natorp and ttickert). Indicating the influences which shaped Husserl's thinking during the years of his studies at the universities of Berlin and (...) Vienna, Kern traces Husserl's development throughout his career as a thinker and a writer. But this survey (pp. 1-50) provides merely the general framework within which the intensive and detailed analyses of Part II (pp. 51-424) must be viewed. Two appendices, an extensive bibliography, and a name index complete the work. The detailed discussions of Part II are, of course, the really important contributions to our understanding of Husserl's relation to Kant and the Kantians. As was to be expected, Husserl found in Kant's works formulations of problems and profound insights that he regarded as crucial to any philosophy. At times, however, Husserl was sure that because of mistaken assumptions, insufficiently clarified presuppositions, and methodological deficiencies Kant himself had not fully realized his intentions. Still, it is evident that, in time, Husserl found himself increasingly in sympathy with Kant's postion. In fact, in the end he used Kant's term "transcendental idealism" to designate his own philosophy. In the course of this development, however, Husserl's thinking underwent various changes and reversals. The detailed analyses of them make fascinating reading and are most revelatory of Husserl's own struggles with obtrnsive problems. In Chapter z of Part II (pp. 55-134), the author discusses Husserl's criticism of Kant's positionwKant's conception of the apriori, his strict separation of "sensibility" and "understanding," his presupposition of a "natural world view," his failure to ask sufficiently radical questions concerning the foundations of knowledge, his lack of a proper method of analysis, and his "psychologism." In the course of his own development, however, Husserl modified and, in some respects, even reversed his criticisms of Kant. Chapters ~, m, re and v of Part II, dealing with problems of formal and transcendental logic, with the possibihty of metaphysics on Kantian principles, and with the complex problems of subjectivity, bear witness to the fact that Huseerl often changed his opinion of Kant's work. Of special interest, however, is Chapter vz. It is devoted to a comparison of Husserl's and Kant's "transcendental idealism" and reveals most strikingly the similarities of the two positions. The chapter dealing with Husserl's relation to l~atorp and Rickert, interesting in its own way, is essentially only a footnote, as it were, to the rest of the hook; but it completes the survey. As I said before, this book gives us not only a remarkable insight into the various phases of development in Husserl's thinking and is therefore indispensable to a real understanding of Husserl's intentions and achievements; it also lets us see Kant's philosophy in a new and revealing perspective--both as to its value and it deficiencies. Only a detailed study can do justice to this book. W. H. WF~mMF~STZR Florida State University Ludwig Wittgenstein. Zettel. Edited by G. E. M. Anscombe and G. H. von Wright. Translated by G. E. M. Anscombe. (University of California Press and Basil Blackwell, 1967. Pp. v + 124 [German and English on facing pages]. $6.95.) The paragraphs in this volume, the editors tell us, were collected in a box-file by Wittgenstein from a period beginning in 1929,though the bulk of them come from typescripts dictated between 1945 and 1948. The editors credit Peter Geach with the major work of arrangement. Whoever is responsible did a superlative job, a remark that holds as well for Miss Anscombe's translation. The editors and Mr. Geach have performed an invaluable service to those interested BOOK REVIEWS 99 in Wittgenstein and--quite apart from Wittgensteinian exegesis--in the problems treated in these pages. The philosophical topics are those of the Investigations (PI) and The Remarks on the Foundations o] Mathematir~ (RFM)---e.g., the attack on... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:98 HISTORY OF PHILOSOPHY quoted in great numbers. The other is Kern's philosophical competence and his skill in handling complex problems. The book is divided into two parts. Part I gives the reader a brief historical survey of Husserl's changing attitudes toward Kant and the neo-Kantians (especially Natorp and ttickert). Indicating the influences which shaped Husserl's thinking during the years of his studies at the universities of Berlin and (...) Vienna, Kern traces Husserl's development throughout his career as a thinker and a writer. But this survey (pp. 1-50) provides merely the general framework within which the intensive and detailed analyses of Part II (pp. 51-424) must be viewed. Two appendices, an extensive bibliography, and a name index complete the work. The detailed discussions of Part II are, of course, the really important contributions to our understanding of Husserl's relation to Kant and the Kantians. As was to be expected, Husserl found in Kant's works formulations of problems and profound insights that he regarded as crucial to any philosophy. At times, however, Husserl was sure that because of mistaken assumptions, insufficiently clarified presuppositions, and methodological deficiencies Kant himself had not fully realized his intentions. Still, it is evident that, in time, Husserl found himself increasingly in sympathy with Kant's postion. In fact, in the end he used Kant's term "transcendental idealism" to designate his own philosophy. In the course of this development, however, Husserl's thinking underwent various changes and reversals. The detailed analyses of them make fascinating reading and are most revelatory of Husserl's own struggles with obtrnsive problems. In Chapter z of Part II (pp. 55-134), the author discusses Husserl's criticism of Kant's positionwKant's conception of the apriori, his strict separation of "sensibility" and "understanding," his presupposition of a "natural world view," his failure to ask sufficiently radical questions concerning the foundations of knowledge, his lack of a proper method of analysis, and his "psychologism." In the course of his own development, however, Husserl modified and, in some respects, even reversed his criticisms of Kant. Chapters ~, m, re and v of Part II, dealing with problems of formal and transcendental logic, with the possibihty of metaphysics on Kantian principles, and with the complex problems of subjectivity, bear witness to the fact that Huseerl often changed his opinion of Kant's work. Of special interest, however, is Chapter vz. It is devoted to a comparison of Husserl's and Kant's "transcendental idealism" and reveals most strikingly the similarities of the two positions. The chapter dealing with Husserl's relation to l~atorp and Rickert, interesting in its own way, is essentially only a footnote, as it were, to the rest of the hook; but it completes the survey. As I said before, this book gives us not only a remarkable insight into the various phases of development in Husserl's thinking and is therefore indispensable to a real understanding of Husserl's intentions and achievements; it also lets us see Kant's philosophy in a new and revealing perspective--both as to its value and it deficiencies. Only a detailed study can do justice to this book. W. H. WF~mMF~STZR Florida State University Ludwig Wittgenstein. Zettel. Edited by G. E. M. Anscombe and G. H. von Wright. Translated by G. E. M. Anscombe. (University of California Press and Basil Blackwell, 1967. Pp. v + 124 [German and English on facing pages]. $6.95.) The paragraphs in this volume, the editors tell us, were collected in a box-file by Wittgenstein from a period beginning in 1929,though the bulk of them come from typescripts dictated between 1945 and 1948. The editors credit Peter Geach with the major work of arrangement. Whoever is responsible did a superlative job, a remark that holds as well for Miss Anscombe's translation. The editors and Mr. Geach have performed an invaluable service to those interested BOOK REVIEWS 99 in Wittgenstein and--quite apart from Wittgensteinian exegesis--in the problems treated in these pages. The philosophical topics are those of the Investigations (PI) and The Remarks on the Foundations o] Mathematir~ (RFM)---e.g., the attack on... (shrink)

Provability, Computability and Reflection.

This book examines the historical development of studies of the brain and behavior from the early work of Aristotle and Galen up to the late twentieth century. Modern neuroscience, a multidisciplinary endeavor, emerged only recently as a unified field . This book does not treat the disciplinary history of neuroscience per se but, rather, the history of attempts to understand the nervous system and its relationship to behavior from a constellation of disciplines all related to what we now call “neuroscience”: (...) anatomy, physiology, psychology, psychiatry, evolutionary theory, and anthropology.Louise H. Marshall is a neuroscientist and director of the UCLA Brain Research Institute's Neuroscience History Archives. Her coauthor, the late neuroscientist Horace W. Magoun, founded the Department of Anatomy at UCLA's Medical School in 1953. Their book grew out of a series of poster presentations put together by Magoun for several national and international neuroscience meetings during the early 1980s. Magoun wrote a twenty‐seven‐page brochure after receiving much enthusiasm from neuroscientists at these meetings—both students and those more established in the field—and many wanted a publication.Not surprisingly, given its early beginnings in poster presentations, the book is richly illustrated. The chapters are arranged only loosely chronologically; their sequence is directed more explicitly by investigative themes. The first chapter outlines three basic “postulates” that direct the organization of the rest of the book and act as conceptual threads: phylogeny , the idea of a structural and functional hierarchy in the nervous system, and the notion that function determines structure. The last chapter, by way of discussion, moves into twentieth‐century developments in the understanding of certain “integrative” systems in the brain and the recognition by neuroscientists of the need for multidisciplinary approaches that integrate anatomical, physiological, and behavioral perspectives.The third postulate, the idea that “form follows function,” receives the most emphasis in the book, and most chapters touch on the oscillating relationship between studies of form and studies of function . The book also illustrates certain historical trends: the anatomical studies of the ancient and Renaissance periods, the more physiological and clinical studies of the nineteenth century, and the instrument‐centered approaches of early twentieth‐century neurophysiology.The book has certain strengths and weaknesses related to the authors' perspective as neuroscientists. As one might expect, elements of presentism arise, as the work of some investigators is described as “anticipating” that of later scientists, and other research—for example, J. L. W. Thudichum's work on brain chemistry—is deemed “surprisingly modern” . However, the book gives wonderfully detailed, precise accounts of scientific developments related to brain and behavior. The authors demonstrate a critical mastery of both primary and secondary sources, with thorough citations, and the book comes with a comprehensive bibliography.Discoveries in the Human Brain does not place neuroscientific developments within a wider cultural or social context, but the authors had no ambitions to do so. They even point to drawbacks of such historical approaches, arguing that they “create issues where none exist and … couch ideas in such convoluted language that the events and concepts become unfamiliar and difficult to fathom” . This position reflects their intended audience: neuroscientists interested in the history of their field. While there is certainly room for professional historians of science to tackle the history of neuroscience, this book will be valuable for historians because literature in the history of neuroscience is sparse. However, it is likely to be of greater value to neuroscientists—in the authors' words, “those workers at the bench who are curious to learn how it all happened.”. (shrink)

In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure, the ultrapower ofmoduloDis denoted byD-prod. The ultrapower is important because it is a method of constructing structures which are elementarily equivalent to a given structure. Our ultimate aim is to find out what kinds of structure are ultrapowers of. We made a beginning in [5] by proving that, assuming the generalized continuum hypothesis, for (...) each cardinalαthere is an ultrafilterDover a set of powerαsuch that for all structures,D-prodisα+-saturated. (shrink)

We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.

Shelah's theory of forking is generalized in a way which deals with measures instead of complete types. This allows us to extend the method of forking from the class of stable theories to the larger class of theories which do not have the independence property. When restricted to the special case of stable theories, this paper reduces to a reformulation of the classical approach. However, it goes beyond the classical approach in the case of unstable theories. Methods from ordinary forking (...) theory and the Loeb measure construction from nonstandard analysis are used. (shrink)

Introduction. This paper is a sequel to our paper [3]. In that paper we introduced the notion of a finite approximation to an infinitely long formula, in a language L with infinitely long expressions of the type considered by Henkin in [2]. The results of the paper [3] show relationships between the models of an infinitely long sentence and the models of its finite approximations. In the present paper we shall apply the main result of [3] to prove a number (...) of theorems about ordinary finitely long sentences; these theorems are of a type which one might call “preservation theorems”. The following two known results are typical preservation theorems: A sentence φ is preserved under substructures if and only if φ is equivalent to some universal sentence ; φ is preserved under homomorphic images if and only if φ is equivalent to some positive sentence. An expository account of preservation theorems may be found in Lyndon [9].We shall use freely all of the notation introduced in [3], and shall not attempt to make this paper selfcontained. However, the reader should have no difficulty following this paper after he has read [3]. In § 1 we cover some preliminary topics. In § 2 and § 3 we shall illustrate our method in familiar situations by proving anew the two preservation theorems mentioned above. We shall then obtain four new preservation theorems in §§ 4, 5, and 6, involving respectively direct powers and roots, strong homomorphisms and retracts, and direct factors. The result in § 6 was stated in the abstract [4], while the results in § 5 were stated in the abstract [5]. (shrink)

When Newton articulated the concept of absolute time in his treatise, Philosophae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), along with its correlate, absolute space, he did not present it as anything controversial. Whereas his references to attraction are accompanied by the self- protective caveats that typically signal an expectation of censure, the Scholium following Principia’s definitions is free of such remarks, instead elaborating his ideas as clarifications of concepts that, in some manner, we already possess. This is not (...) surprising. The germ of the concept emerged naturally from astronomers’ findings, and variants of it had already been formulated by other seventeenth century thinkers. Thus the novelty of Newton’s absolute time lay mainly in the use to which he put it. (shrink)

In a nonstandard universe, the κ-saturation property states that any family of fewer than κ internal sets with the finite intersection property has a nonempty intersection. An ordered field F is said to have the λ-Bolzano-Weierstrass property iff F has cofinality λ and every bounded λ-sequence in F has a convergent λ-subsequence. We show that if $\kappa < \lambda$ are uncountable regular cardinals and $\beta^\alpha < \lambda$ whenever $\alpha < \kappa$ and $\beta < \lambda$, then there is a κ-saturated nonstandard (...) universe in which the hyperreal numbers have the λ-Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second order arithmetic. (shrink)

In a nonstandard universe, the $\kappa$-saturation property states that any family of fewer than $\kappa$ internal sets with the finite intersection property has a nonempty intersection. An ordered field $F$ is said to have the $\lambda$-Bolzano-Weierstrass property iff $F$ has cofinality $\lambda$ and every bounded $\lambda$-sequence in $F$ has a convergent $\lambda$-subsequence. We show that if $\kappa < \lambda$ are uncountable regular cardinals and $\beta^\alpha < \lambda$ whenever $\alpha < \kappa$ and $\beta < \lambda$, then there is a $\kappa$-saturated nonstandard (...) universe in which the hyperreal numbers have the $\lambda$-Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second order arithmetic. (shrink)

§0. Introduction. In [16], Barwise described his graduate study at Stanford. He told of his interactions with Kreisel and Scott, and said how he chose Feferman as his advisor. He began working on admissible fragments of infinitary logic after reading and giving seminar talks on two Ph.D. theses which had recently been completed: that of Lopez-Escobar, at Berkeley, on infinitary logic [46], and that of Platek [58], at Stanford, on admissible sets.Barwise's work on infinitary logic and admissible sets is described (...) in his thesis [4], the book [13], and papers [5]—[16]. We do not try to give a systematic review of these papers. Instead, our goal is to give a coherent introduction to infinitary logic and admissible sets. We describe results of Barwise, of course, because he did so much. In addition, we mention some more recent work, to indicate the current importance of Barwise's ideas. Many of the central results are stated without proof, but occasionally we sketch a proof, to indicate how the ideas fit together.Chapters 1 and 2 describe infinitary logic and admissible sets at the time Barwise began his work, circa 1965. From Chapter 3 on, we survey the developments that took place after Barwise appeared on the scene.§1. Background on infinitary logic. In this chapter, we describe the situation in infinitary logic at the time that Barwise began his work. We need some terminology. By a vocabulary, we mean a set L of constant symbols, and relation and operation symbols with finitely many argument places. As usual, by an L-structureM, we mean a universe set M with an interpretation for each symbol of L. (shrink)

The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.

We shall prove quantifier elimination theorems for neocompact formulas, which define neocompact sets and are built from atomic formulas using finite disjunctions, infinite conjunctions, existential quantifiers, and bounded universal quantifiers. The neocompact sets were first introduced to provide an easy alternative to nonstandard methods of proving existence theorems in probability theory, where they behave like compact sets. The quantifier elimination theorems in this paper can be applied in a general setting to show that the family of neocompact sets is countably (...) compact. To provide the necessary setting we introduce the notion of a law structure. This notion was motivated by the probability law of a random variable. However, in this paper we discuss a variety of model theoretic examples of the notion in the light of our quantifier elimination results. (shrink)

The modern corpuscular theory of radiation was born in 1905 when Einstein advanced his light quantum hypothesis; and the steps by which Einstein's hypothesis, after years of profound scepticism, was finally and fully vindicated by Arthur Compton's 1922 scattering experiments constitutes one of the most stimulating chapters in the history of recent physics. To begin to appreciate the complexity of this chapter, however, it is only necessary to emphasize an elementary but very significant point, namely, that while Einstein based his (...) arguments for quanta largely on the behaviour of high-frequency black body radiation or ultra-violet light, Compton experimented with X-rays. A modern physicist accustomed to picturing ultra-violet light and X-radiation as simply two adjacent regions in the electromagnetic spectrum might regard this distinction as hair-splitting. But who in 1905 was sure that X-rays and γ-rays are far more closely related to ultra-violet light than to α-particles, for example? This only became evident after years of painstaking research, so that moving without elaboration from Einstein's hypothesis to Compton's experiments automatically eliminates from consideration an important segment of history—a segment in which a major role was played by William Henry Bragg. (shrink)

Book Information Epistemology: Classic Problems and Contemporary Responses. By Laurence BonJour. Rowman and Littlefield. Lanham MD. 2002. Pp. viii + 289. Hardback, US$75. Paperback, US$23.95.

Starting with the puzzlement M O.C. Drury and Rush Rhees felt about Wittgenstein's admonition that believers ought not to pick and choose among the passages of the bible, this paper seeks to clarify the sense of scriptural authority in the Judeo-Christian traditions. This paper argues that (1) picking and choosing, imposing certain criteria external to the Scripture, is grammatically constitutive of accepting the authority of Scripture and (2) such a picking and choosing is guided by a tradition and its grammar. (...) It notes that Wittgenstein's stance on Scripture is itself based on (1) and (2). (shrink)

A general metatheorem is proved which reduces a wide class of statements about continuous time stochastic processes to statements about discrete time processes. We introduce a strong language for stochastic processes, and a concept of forcing for sequences of discrete time processes. The main theorem states that a sentence in the language is true if and only if it is forced. Although the stochastic process case is emphasized in order to motivate the results, they apply to a wider class of (...) random variables. At the end of the paper we illustrate how the theorem can be used with three applications involving submartingales. (shrink)