Claire Ortiz Hill

Edmund Husserl was one of the very first to experience the directimpact of challenging problems in set theory and his phenomenology first began to takeshape while he was struggling to solve such problems. Here I study three difficultiesassociated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and “Russell's” paradox.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory andto develop his own theory of manifolds. I define certain issues involved and discuss howHusserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl'stheories about sets and manifolds out of the realm of abstract theorizing and promptfurther exploration of uncharted philosophical territory rich in philosophical implications.

Anna-TeresaTymieniecka writes of a “dynamic skeleton for future fusions of sense” rising from the seemingly disjointed situation of philosophy and details how her phenomenology of life can put flesh on it. Examined here are her efforts to: uncover the deep-lying intelligibility of life by emphasizing the role of the logos of life in connection with meaning structures developed by Husserl; undertake a critique of phenomenological reason; delineate life’s path, not from cognition in isolation, but from within the fullness of human functioning in all its complexity; give Husserl’s phenomenology a metaphysico-existential foundation; analyze the human creative process penetrating the very individualized meanderings of life; show how the creative logos reaches into communal/societal life and opens the way to spiritual and sacral horizons of experience.

In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual consequences of his having done so. To make certain of Frege’s ideas about the inviolability of logical form more tangible, I describe a string of very interrelated consequences that his attempt to transform dependent meanings into independent meanings actually brought in its wake.

E. Husserl, Logik und allgemeine Wissenschaftstheorie. Vorlesungen 1917/18, mit ergänzenden Texten aus der ersten Fassung 1910/11. (Husserliana, 30.) Introduction by U. Panzer. Dordrecht:Kluwer, 1996. lxii + 554 pp. £130. ISBN0 792 33731 X D. Jacquette, Meinongian logic. The semantics of existence and nonexistence. Berlin and New York:Walter de Gruyter, 1996. xiii + 297 pp. DM 198. ISBN 3 11 014865 X M. Beaney (ed. and introduced), The Frege Reader. Blackwell Publishers, 1997. xv + 409 pp. £14.99/$21.95 (pbk). ISBN 0 631 194 452 Elliott Mendelson, Introduction to formal logic, fourth edition. London:Chapman & Hall, 1997. x + 440 pp. £45.00. ISBN 1 412 808307 Samuel Guttenplan, The languages of logic. An introduction to formal logic, second edition. Oxford:Blackwell, 1997. x + 429 pp. No price stated. ISBN 1 55786 988 X A.C. Grayling, An introduction to philosophical logic, third edition. Oxford:Blackwell, 1997. vii + 343 pp. £15.99/$27.99. ISBN 0 631 19982 9 Lewis Carroll, Das Spiel der Logik. Edited with an afterword by P. Good. Translated by M.Zöllner. Cologne:Propen Verlag/frommann-holzboog, 1997. 120pp. 32 DM. ISBN 3 7728 1998 2

Husserl and Cantor were colleagues and close friends during the last 14 years of the nineteenth century, when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which he drew apart from people and writings to whom he owed most of his intellectual training and drew closer to the ideas of thinkers whose writings he had not been able to evaluate properly and had consulted too little. I study ways in which Husserl and Cantor might be said to have been alike, while pointing to dissimilarities between them. In particular, I discuss how their ideas overlapped and crisscrossed with regard to mathematics and philosophy, Platonic idealism, abstraction, empiricism, psychologism, actual consciousness and pure logic, Frege’s reviews of their works, metaphysics and mysticism, sets, arithmetization, strange and imaginary numbers and manifolds. I conclude that Cantor was among those of his mentors from whose ideas Husserl drew away and Lotze and Bolzano were among those to whose ideas he drew closer.

What follows is about Husserl, whose phenomenology, I believe, can be understood as a form of constructivism. However, I generally write about Husserl’s philosophy of logic and mathematics, which he repeatedly said had nothing to do with transcendental phenomenology. So, my aim here is to discuss some things that I believe people interested in constructivism and Husserl’s transcendental phenomenology need to keep in mind. I say that, despite appearances, phenomenology was not everything for Husserl. As much as he loved it, he placed definite limits on what one should do with it and believed that it required an objective complement in the form of pure logic, that it had to be subject to a priori laws to keep phenomenologists from falling into psychologism, naturalism, empiricism, relativism and associated evils. According to this interpretation, Husserl the possible constructivist, Husserl the phenomenologist, Husserl the Platonist, Husserl the realist, Husserl the idealist were one and the same person from the late 1890s until his death, something which is particularly well expressed in the volumes of his lecture courses published since the 1980s, which shed considerable light on his thought.

This book was ten years in the making and it takes as its point of departure work on analytic philosophy and phenomenology done in the late sixties by the authors' professors at Stanford, Jaakko Hintikka and Dagfinn Føllesdal. Subsequent research, though, and notably J. N. Mohanty's work on Husserl and Frege have pointed to the difficulties unearthed as one examines assumptions about ties between Husserl's efforts and the work of Frege and his successors. Husserl was himself a master of the tradition in mathematics and philosophy that produced both him and Frege. He knew Frege's writings and he consciously diverged from them fashioning a distinct philosophical voice from the philosophical legacy they both shared. Any attempt now to interpret and improve Husserl in a Fregean way, adjusting his thought to the needs of contemporary analytic semantics, is misguided and cannot but produce distortions. Though McIntyre and Smith consistently show themselves aware of the criticisms to be levelled against their research, this work cannot, by its very nature, provide an adequate reply to critiques which would destroy the entire fabric of its argument.

Abstract: Groundwork is lain for answering questions as to how to situate Husserl’s theory of functions in relation to Frege’s. I examine Husserl’s ideas about analyticity and mathematics, logic and mathematics, formalization, calculating with concepts and propositions, the foundations of arithmetic, extensions to show that, although he knew, studied and lauded Frege’s ideas about functions and concepts, each man approached the issues from different angles. Seduced by the siren of transcendental phenomenology Husserl did not pursue the issues, implications, and consequences of his ideas about functions. I ask whether so doing could provide new insight into, or even solutions to, the problems involving functions that beset Frege, Russell and have beset their successors.

Evidence is drawn together to connect sources of inconsistency that Frege discerned in his foundations for arithmetic with the origins of the paradox derived by Russell in "Basic Laws" I and then with antinomies, paradoxes, contradictions, riddles associated with modal and intensional logics. Examined are: Frege's efforts to grasp logical objects; the philosophical arguments that compelled Russell to adopt a description theory of names and a eliminative theory of descriptions; the resurfacing of issues surrounding reference, descriptions, identity, substitutivity, paradox in the debates concerning modal and intensional logics; the development of the New Theory of Reference. I consider this to be the philosophical ground upon which the debates regarding that theory should take place

In search of the origins of some of the most fundamental problems that have beset philosophers in English-speaking countries in the past century, Claire Ortiz Hill maintains that philosophers are treating symptoms of ills whose causes lie buried in history. Substantial linguistic hurdles have blocked access to Gottlob Frege's thought and even to Bertrand Russell's work to remedy the problems he found in it. Misleading translations of key concepts like intention, content, presentation, idea, meaning, concept, etc., severed analytic philosophy from its roots. Hill argues that once linguistic and historical barriers are removed, Edmund Husserl's critical study of Frege's logic in his 1891 _Philosophy of Arithmetic_ provides important insights into issues in philosophy now. She supports her conclusions with analyses of Frege's, Husserl's, and Russell's works, including _Principia Mathematica_, and with linguistic analyses of the principal concepts of analytic philosophy. She re-establishes links that existed between English and Continental thought to show Husserl's expertise as a philosopher of mathematics and logic who had been Weierstrass's assistant and had long maintained ties with Cantor, Hilbert, and Zermelo.

Little is known of Edmund Husserl's direct encounter with Georg Cantor's ideas on Platonic idealism and the abstraction of number concepts during the late 19th century, when Husserl's philosophical orientation changed considerably and definitely. Closely analyzing and comparing the two men's writings during that important time in their intellectual careers, I describe the crucial shift in Husserl's views on psychologism and metaphysical idealism as it relates to Cantor's philosophy of arithmetic. I thus establish connections between their ideas which have been until now been virtually unsuspected and contribute to a better understanding of the development of Husserl's thought and of the philosophical and metaphysical ideas within which Cantor chose to frame his theories.

Edmund Husserl was one of the very first to experience the direct impact of challenging problems in set theory and his phenomenology first began to take shape while he was struggling to solve such problems. Here I study three difficulties associated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and 'Russell's paradox'.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory and to develop his own theory of manifolds. I define certain issues involved and discuss how Husserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl's theories about sets and manifolds out of the realm of abstract theorizing and prompt further exploration of uncharted philosophical territory rich in philosophical implications.

Pour projeter de la lumière dans de nombreux coins et recoins obscurs de la logique pure de Husserl et dans les rapports entre sa logique formelle et sa logique transcendantale, et combler des lacunes empêchant qu’on arrive à une appréciation juste de sa Mannigfaltigkeitslehre, ou théorie de multiplicités, on examine comment, en prônant une théorie des systèmes déductifs, ou systèmes d’axiomes, comme tâche suprême de la logique pure, Husserl cherchait à résoudre certains problèmes épineux auxquels il s’était heurté en écrivant Philosophie de l’arithmétique. Ces problèmes sont décrits. Ensuite, on rassemble les éléments nécessaires pour caractériser ce que Husserl, à travers les textes présentement disponibles, voulait dire des Mannigfaltigkeiten. Pour conclure, il est indiqué comment Husserl pouvait considérer que sa théorie représentait une solution aux problèmes qui avaient conduit à son élaboration.To shed light on the numerous dark areas surrounding Husserl’s ideas about pure logic and the relationship between his formal logic and his transcendental logic, and so provide an accurate characterisation of his Mannigfaltigkeitslehre, a close look is taken at how, by advocating a theory of deductive systems, or axiomatic systems as the highest task of pure logic, Husserl sought to resolve certain thorny problems he encountered when writing the Philosophy of Arithmetic. Those problems are described. Then, his ideas about axiomatization and manifolds are drawn together from the various sources now available to provide a more complete picture of his Mannigfaltigkeitslehre. In conclusion, it is shown how Husserl considered his theory to be a solution to the problems leading to its development

Two hundred years ago, J.M.W. Turner packed up two large leatherbound sketchbooks, pencils, and watercolors and set off for the north of England. When he returned from the tour that he regarded as one of the most important of his career, Turner had completed more than two hundred sketches - works that later became the basis of more than fifty major oil paintings and watercolors. For this illustrated book, David Hill has taken photographs of many of the actual sites Turner sketched on his northern tour. The result is an look at the whole of Turner's creative process, from site to exhibited picture, and at the quality and intensity of the artist's experience.

In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual consequences of his having done so. To make certain of Frege’s ideas about the inviolability of logical form more tangible, I describe a string of very interrelated consequences that his attempt to transform dependent meanings into independent meanings actually brought in its wake.

Anna-TeresaTymieniecka writes of a “dynamic skeleton for future fusions of sense” rising from the seemingly disjointed situation of philosophy and details how her phenomenology of life can put flesh on it. Examined here are her efforts to: uncover the deep-lying intelligibility of life by emphasizing the role of the logos of life in connection with meaning structures developed by Husserl; undertake a critique of phenomenological reason; delineate life’s path, not from cognition in isolation, but from within the fullness of human functioning in all its complexity; give Husserl’s phenomenology a metaphysico-existential foundation; analyze the human creative process penetrating the very individualized meanderings of life; show how the creative logos reaches into communal/societal life and opens the way to spiritual and sacral horizons of experience

In letters that Husserl and Frege exchanged during late 1906 and early 1907, when it is thought that Frege abandoned his attempts to solve Russell's paradox, Husserl expressed his views about the "paradox". Studied here are three deep-rooted differences between their approaches to pure logic present beneath the surface in these letters. These differences concern Husserl's ideas about avoiding paradoxical consequences by shunning three potentially para-dox producing practices. Specifically, he saw the need for: 1) correctly drawing the line between meaning analyses and logical analyses; 2) an epistemology of pure logic; 3) a subtler under-standing of the semantics of statements than Frege proposed. This study is part of a project to lend insight into the questions that Russell's paradox raises for logic and epistemology once signaled by Gödel, an admirer of Husserl's work

This chapter deals with the discussion that was going on among set theorists and logicians at the end of the nineteenth century and at the beginning of the twentieth century. Logical experimentation carried out at the intersection of Cantor’s theory of sets and twentieth century attitudes towards metaphysics and logic has unearthed many important questions about the ultimate structure of reality. In particular, the full story of set theory’s role in shaping modern logic and in redrawing the boundaries between metaphysics and logic in both the analytical and the phenomenological traditions is yet to be told and its full implications drawn. The chapter seeks to add new dimensions to standard discussions by going back to where those two logical roads diverged and affording them a look down at the one not taken by mainstream logicians in the last century.

By drawing attention to these facts and to the relationship between Cantor’s and Husserl's ideas, I have tried to contribute to putting Frege's attack on Husserl "in the proper light" by providing some insight into some of the issues underling criticisms which Frege himself suggested were not purely aimed at Husserl's book. I have tried to undermine the popular idea that Frege's review of the Philosophy of Arithmetic is a straightforward, objective assessment of Husserl’s book, and to give some specific reasons for thinking that the uncritical reading of Frege's review has unfairly distorted philosophers' perception of a work they do not know very well.