Brouwer meets Husserl: On the Phenomenology of Choice Sequences (Synthese Library Book 335)

Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? The mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. "It is almost as if one could hear the two rebels arguing their case in a European café or on a terrace, and coming to a common understanding, with both men taking their hat off to the other, in admiration and gratitude. Dr. van Atten has convincingly applied Husserl's method to Brouwer's program, and has equally convincingly applied Brouwer's intuition to Husserl's program. Both programs have come out the better." __Piet Hut, professor of Interdisciplinary Studies, Institute for Advanced Study, Princeton, U.S.A.__ Wittgenstein And The Twentieth Century / Georg Henrik Von Wright -- Wittgenstein On Philosophy And Science / David Pears -- Wittgenstein On Mind And Metaphysics / Anthony J. P. Kenny -- Wittgenstein's Alleged Metaphysics Of Mind / Johannes L. Brandl -- Le Reel Et Son Ombre: La Theorie Wittgensteinienne De La Possibilite / Jacques Bouveresse -- Wittgenstein On The Meaning Of Logical Symbols / Carlo Cellucci -- On Following A Rule / Avrum Stroll -- Fodor And Wittgenstein On Private Language / Diego Marconi -- Mentalesians And Wittgenstein's Private Language / Massimo Dell'utri -- Intentionality In Wittgenstein's Works / Aldo G. Gargani -- Intentional Reference As A Logical Relation: A Variation On A Theme In Moore, Russell, Wittgenstein, And Bergmann / Herbert Hochberg Wittgenstein Between Philosophical Grammar And Psychology / Rosaria Egidi -- Notes On Phenomenology And Visual Space / Roberto Casati -- Disentangling Moore's Paradox / Norman Malcolm -- Malcolm On Moore's Paradox / Eva Picardi -- Wittgenstein's Refutation On Scepticism In 'on Certainty' / Wolfgang Carl -- Was Wittgenstein A Relativist? / Rudolf Haller -- Wittgenstein On Language, Mind And Mythology / S. Stephen Hilmy -- Emotion: Remarks On Wittgenstein And William James / Joachim Schulte -- Wittgenstein And Memory / Guido Frongia -- How Ludwig Wittgenstein Would Have Reacted To Recent Changes In Psychology / Fritz G. Wallner. Edited By Rosaria Egidi. Revised Version [of] The Papers Of The Wittgenstein Conference Held In November 1989 At The University Of Rome La Sapienza--pref. Includes Bibliographical References And Indexes. The essays collected in this volume represent, in a revised version, the pa- pers of the Wittgenstein Conference held in November 1989 at the Univer- sity ofRome 'La Sapienza' to celebrate the centenary ofhis birth. They offer a systematic account ofWittgenstein's philosophy ofmind and contribute to illuminate his later conception of perceptive, emotional and cognitive lan- guage. Some of the reasons why it seemed the right time to promote an am- pIe confrontation ofideas on Wittgenstein's mature perspective are sufficiently c1ear as they derive from the need to sum up the state of research based on the availability of the Nachla and the publication in the last decade of a conspicuous quantity ofwritings dedicated to philosophical psychology; other reasons are more complex as they depend on the already noticed tendency in the recent epistemological debate to interpret Wittgenstein's provocative and controversial theses in a "perverse" way, in a way which has been used as a banner for epistemic relativism, subjectivism, and irrationalism. The intention of this collection of essays is to construct an image of Wittgenstein's thought, which is as faithful as possible to his philosophy of mind and language from both a theoretical and exegetical point of view. The book also strives to assess the continuity and internal coherence of the theses developed throughout the different phases of his research. The work brings together a collection of previously unpublished essays which offer a systematic account of Wittgenstein's philosophy of mind and contribute in an absolutely new and original way to illuminating his later conception of human perceptive, emotional and cognitive language from both a theoretical and a historical point of view. The focus is on the fundamental categories of philosophical grammar, on the analysis of intentionality, of belief and Moore's paradox, on certainty and doubt, on will, memory, sensations and emotions, as well as on the theory of aspects and private language and the relationship with relativism and psychologism. In the recent literature there are undoubtedly numerous qualified publications dedicated to the themes of philosophical psychology as they emerge from Wittgenstein's Nachlass and from his writings on this subject published in the last decade. This book, however, provides the essential points of reference of Wittgenstein's late treatment of psychological concepts in the context of the general features of his early philosophy of science and language and in the framework of the trends of his time. Audience: Scholars and students, philosophers, linguists, psychologists, sociologists, cognitive scientists, logicians, historians of contemporary philosophy and science. l. THE GENERAL PROBLEM OF EPISTEMOLOGY There is a philosophical issue that surely precedes all other possible questions. It concerns the very possibility of our thinking about some­ thing to some purpose. Short of this no philosophy, theory or research would be possible. But it is not immediately clear that we are assured that what purports to be effective thought, and cognition is such in reality. What guarantee is there for instance that when one is under the impression that one is thinking that'the cat is on the mat'it is in fact the case that one is thinking this? One could not be thinking at all, only having a misleading mystic experience. And then even if one was thinking, one might not be really thinking of the cat being on the mat, but only that one wishes there was a cat, and wonders whether if there was it would be on the mat, and yet the subjective impression was that one was thinking:'The cat is on the mat'(the same picture might stand for both the thoughts mentioned). Then one might in some way try to think'the cat is on the mat.'yet be mistaken in that there aren't any material objects at all, and all one does is to inventory god's perceptions. And so on, and so on! These are of course the kind of problem that the layman habitually views with disdainful alarm. Can The Straight Line Be Analysed Mathematically Such That It Does Not Fall Apart Into A Set Of Discrete Points, As Is Usually Done But Through Which Its Fundamental Continuity Is Lost? And Are There Objects Of Pure Mathematics That Can Change Through Time? The Mathematician And Philosopher L. E. J. Brouwer Argued That The Two Questions Are Closely Related And That The Answer To Both Is Yes. To This End He Introduced A New Kind Of Object Into Mathematics, The Choice Sequence. But Other Mathematicians And Philosophers Have Been Voicing Objections To Choice Sequences From The Start. This Book Aims To Provide A Sound Philosophical Basis For Brouwer's Choice Sequences By Subjecting Them To A Phenomenological Critique In The Style Of The Later Husserl.--book Jacket. Preface -- Acknowledgments -- An Informal Introduction -- Introduction -- The Argument -- The Original Positions -- The Phenomenological Incorrectness Of The Original Arguments -- The Constitution Of Choice Sequences -- Application: An Argument For Weak Continuity -- Concluding Remarks. By Mark Van Atten. Includes Bibliographical References (p. 169-180) And Indexes.

The theory presented here represents a radical departure from current treatments of the theory of knowledge. It makes the point that all such work is based on the false assumption that what makes knowledge possible is in itself knowable in some way, whereas in fact it is below the threshold of any cognitive consciousness. It is therefore necessary to seek the basis of the possibility of knowledge on entirely different levels, and in entirely novel ways. To Know or Not to Know is the first presentation of the theory in full, earlier writings being only preliminary and brief. It is aimed at the general philosopher, and the specialist in the field of epistemology, but relevant to anyone who would understand how it is possible to know anything at all.

Can a line be analysed mathematically such a way that it does not fall apart into a set of discrete points? Are there objects of pure mathematics that can change through time? L. E. J. Brouwer argued that the two questions are related and that the answer to both is "yes", introducing the concept of choice sequences. This book subjects Brouwer's choice sequences to a phenomenological critique in the style of Husserl. Front Matter....Pages i-xiii An Informal Introduction....Pages 1-4 Introduction....Pages 5-8 The Argument....Pages 9-10 The Original Positions....Pages 11-52 The Phenomenological Incorrectness of the Original Arguments....Pages 53-83 The Constitution of Choice Sequences....Pages 85-101 Application: An Argument for Weak Continuity....Pages 103-110 Concluding Remarks....Pages 111-111 Back Matter....Pages 113-206 And then even if one was thinking, one might not be really thinking of the cat being on the mat, but only that one wishes there was a cat, and wonders whether if there was it would be on the mat, and yet the subjective impression was that one was thinking: "The cat is on the mat" (the same picture might stand for both the thoughts mentioned).