In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures hegave in Göttingen in 1901 and other related texts of the same period,a problem that had occupied Husserl since the beginning of 1890, whenhe was planning a never published sequel to Philosophie der Arithmetik(1891). In order to solve the problem of imaginary entities Husserl introduced,independently of Hilbert, two notions of completeness (definiteness in Husserl'sterminology) for a formal axiomatic (...) system. I present and discuss these notionshere, establishing also parallels between Husserl's and Hilbert's notions ofcompleteness. (shrink)

"With provocations on every page, this book is a philosophical feast. The specialist will find familiar ingredients assembled here in a perspicuous and compelling way, while the nonspecialist will discover a Husserl whose philosophy is made of flesh and blood." —Journal of the History of Philosophy In this thorough study of the full body of his writings, Donn Welton uncovers a Husserl very different from the established view. Arguing against established interpretations, The Other Husserl traces Husserl’s move from static to (...) genetic phenomenology and uses accounts of perception, discourse, subjectivity, and world to elaborate the scope of his systematic phenomenology. This serious reflection on the meaning of phenomenology is the first book in English to outline in full Husserl’s phenomenological method and to argue for its cogency. Welton’s stimulating interpretation highlights Husserl’s relevance for current philosophical debates. (shrink)

This is a translation of Edmund HusserI's lecture course from the Summer semester 1907 at the University of Gottingen. The German original was pub lished posthumously in 1973 as Volume XVI of Husserliana, Husserl's opera omnia. The translation is complete, including both the main text and the supplementary texts (as Husserliana volumes are usually organized), except for the critical apparatus which provides variant readings. The announced title of the lecture course was "Main parts of the phenome nology and critique of (...) reason." The course began with five, relatively inde pendent, introductory lectures. These were published on their own in 1947, bearing the title The idea ojphenomenology.l The "Five Lectures" comprise a general orientation by proposing the method to be employed in the subsequent working out of the actual problems (viz., the method of "phenomenological reduction") and by clarifying, at least provisionally, some technical terms that will be used in the labor the subsequent lectures will carry out. The present volume, then, presents that labor, i.e., the method in action and the results attained. As such, this text dispels the abstract impression which could not help but cling to the first five lectures taken in isolation. Accord ingly, we are here given genuine "introductory lectures," i.e., an introduction to phenomenology in the genuine phenomenological sense of engaging in the work of phenomenology, going to the "matters at issue themselves," rather than remaining aloof from them in abstract considerations of standpoint and approach. (shrink)

As this book makes clear, current use of data structures such as frames, scripts, and stereotypes in psychology, artificial intelligence, and all the other disciplines now grouped together as Cognitive Science develop ideas already explored by Husserl who believed that the analysis of mental representations was the proper subject of philosophy, psychology, and other disciplines that deal with the mind. This new anthology will serve as an ideal introduction to phenomenology for analytic philosophers, both as a text and as the (...) single most useful source book on Husserl for cognitive scientists. An MIT Press/Bradford Book. (shrink)

This ambitious work aims to shed new light on the relations between Husserlian phenomenology and the present-day efforts toward a scientific theory of cognition—with its complex structure of disciplines, levels of explanation, and ...

This paper is concerned with the application of constructions from category theory to Smith and McIntyre's interpretation of Husserl's intentionality. 1 Not only did Hussefl's own ideas change in the course of his lifetime 2 but there are a number of interpretations of Husserl's work 3 so that the line of philosophical investigation that Husserl strongly influenced is still in the process of development. In this vein, Smith and McIntyre have recognized the potential for a possible worlds interpretation of intentionality (...) in Hussefl's writing 4 which has led them to extend their interpretation to give a many worlds account of intentionality. 5 Thus, while Smith and McIntyre have refuted interpretations of Husserl's noema in terms of ideal objects, they have been willing to explicate the noerna using possible objects. (shrink)

In Part II of Husserl’s “great last work,” as the Crisis is sometimes called, we find two passages in which he comments upon what he took to be an important and utter failure on the part of “die modernen Logistiker”—or, as Carr well translates it, “modern mathematical logicians.” At the end of subsection 36 he says.

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

In this book Robert Tragesser sets out to determine the conditions under which a realist ontology of mathematics and logic might be justified, taking as his starting point Husserl's treatment of these metaphysical problems. He does not aim primarily at an exposition of Husserl's phenomenology, although many of the central claims of phenomenology are clarified here. Rather he exploits its ideas and methods to show how they can contribute to answering Michael Dummet's question 'Realism or Anti-Realism?'. In doing so he (...) makes a challenging and provocative contribution to the debate. (shrink)

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and (...) Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege. (shrink)

This essay explores an ideal notion of form (mathematical structure) that embraces logical, phenomenological, and ontological form. Husserl envisioned a correlation among forms of expression, thought, meaning, and object—positing ideal forms on all these levels. The most puzzling formal entities Husserl discussed were those he called ‘manifolds’. These manifolds, I propose, are forms of complex states of affairs or partial possible worlds representable by forms of theories (compare structuralism). Accordingly, I sketch an intentionality-based semantics correlating these four Husserlian levels of (...) form—thereby integrating logic, phenomenology, and ontology. (shrink)

The "Cartesian Meditations" translation is based primarily on the printed text, edited by Professor S. Strasser and published in the first volume of Husserliana ...

In this book, which remained unfinished at his death, Husserl attempts to forge a union between phenomenology and existentialism.

the Logische Untersuchungen,l phenomenology has been conceived as a substratum of empirical psychology, as a sphere comprising "imma nental" descriptions of psychical mental processes, a sphere compris ing descriptions that - so the immanence in question is understood - are strictly confined within the bounds of internal experience. It 2 would seem that my protest against this conception has been oflittle avail; and the added explanations, which sharply pinpointed at least some chief points of difference, either have not been understood (...) or have been heedlessly pushed aside. Thus the replies directed against my criticism of psychological method are also quite negative because they miss the straightforward sense of my presentation. My criticism of psychological method did not at all deny the value of modern psychology, did not at all disparage the experimental work done by eminent men. Rather it laid bare certain, in the literal sense, radical defects of method upon the removal of which, in my opinion, must depend an elevation of psychology to a higher scientific level and an extraordinary amplification ofits field of work. Later an occasion will be found to say a few words about the unnecessary defences of psychology against my supposed "attacks. (shrink)

This book clarifies Husserl's notion of perceptual experience as "immediate" or "direct" with respect to its purported object, and outlines his theory of evidence. In particular, it focuses on Husserl's account of our perceptual experience of time, an aspect of perception rarely noted in', recent philosophical literature, yet which must be taken into consideration if an adequate account of perception is to be provided. Perhaps equally important, there is a new wave of work in phenomenology (and intentionality), reflecting a synthesis (...) of phenomenological and analytic philosophy, Miller's book is an important contribution to that "new wave," and has a significant bearing on contemporary issues in cognitive science. (shrink)

For over a decade John Searle's ingenious argument against the possibility of artificial intelligence has held a prominent place in contemporary philosophy. This is not just because of its striking central example and the apparent simplicity of its argument. As its appearance in Scientific American testifies, it is also due to its importance to the wider scientific community. If Searle is right, artificial intelligence in the strict sense, the sense that would claim that mind can be instantiated through a formal (...) program of symbol manipulation, is basically wrong. No set of formal conditions can provide us with the characteristic feature of mind which is the intentionally of its mental contents. Formally regarded, such intentionally is an irreducible primitive. It cannot be analyzed into non-intentional (purely syntactic, symbolic) components. This paper will argue that this objection is based on a misunderstanding. Intentionality is not simply something given which is incapable of further analysis. It only appears so when we mistakenly abstract it from time. When we regard its temporal structure, it shows itself as a rule-governed, synthetic process, one capable of being instantiated both by machines and men. (shrink)

Husserl has finally begun to be recognized as the precursor of current interest in intentionality — the first to have a general theory of the role of mental representations in the philosophy of language and mind. As the first thinker to put directedness of mental representations at the center of his philosophy, he is also beginning to emerge as the father of current research in cognitive psychology and artificial intelligence.

Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...) in the foundational controversy of the 1920s. In addition, they reveal Weyl's hitherto unknown objections to Becker's detailed attempt (Mathematische Existenz, 1927) to ground the transfinite phenomenologically. (shrink)

The presentation of the formal conception of noemata is the main aim of the article. In the first section, three informal approaches to noemata are discussed. The goal of this chapter is specifying main controversies and their sources concerned with different ways of the understanding of noemata. In the second section, basic assumptions determining the proposed way of understanding noemata are presented. The third section is devoted to the formal set-theoretic construction needed for the formal comprehension of noemata. In the (...) fourth section, definitions of noemata and their various kinds, as well as definitions of other phenomenological notions are formulated. In the last section, possibilities of further developing the proposed formal conception are indicated. (shrink)

Science in a new sense arises in the first instance from Plato's establishing of logic, as a place for exploring the essential requirements of "genuine" ...

The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a phenomenological (...) view the relevant evidence is provided by intuition , and this should be the case in either ordinary perceptual knowledge or in mathematical knowledge. Intuition is to be understood in terms of fulfillments of intentions. Knowledge is a product of intuition and intention. In the case of mathematical knowledge it is said that there is a construction for a mathematical statement S if and only if the intention expressed by S is fulfilled . Constructions are thus viewed as intuition processes that could actually or possibly be carried out. In elementary parts of mathematics they might be characterized in terms of certain classes of recursive functions. This view is discussed in the case where S is taken to be a singular statement about natural numbers or finite sets, and also where S is taken to be a general statement about such objects. The distinction between intuition of and intuition that is also investigated in this context. ;It is pointed out how on a phenomenological view a number of central problems about mathematical intuition can be avoided: problems about the analogousness of perceptual and mathematical intuition, about causal accounts of knowledge in mathematics, and about structuralism in mathematics. The bearing of the account on issues concerning constructivism and platonism is also discussed. (shrink)

Most areas of philosopher Edmund Husserl’s thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.

This volume provides an articulate restatement of many of the themes of Husserlian phenomenology.

THE TEXT In the summer semester of 1925 in Freiburg, Edmund Husserl delivered a lecture course on phenomenological psychology, in 1926127 a course on the possibility of an intentional psychology, and in 1928 a course entitled "Intentional Psychology. " In preparing the critical edition of Phiinomeno logische Psychologie (Husserliana IX), I Walter Biemel presented the entire 1925 course as the main text and included as supplements significant excerpts from the two subsequent courses along with pertinent selections from various research manuscripts (...) of Husserl. He also included as larger supplementary texts the final version and two of the three earlier drafts of Husserl's Encyclopedia Britannica article, "Phenomenology"2 (with critical comments and a proposed formulation of the Introduction and Part I of the second draft by Martin Heidegger3), and the text of Husserl's Amsterdam lecture, "Phenomenological Psychology," which was a further revision of the Britannica article. Only the main text of the 1925 lecture course (Husserliana IX, 1-234) is translated here. In preparing the German text for publication, Walter Biemel took as his basis Husserl's original lecture notes (handwritten in shorthand and I Hague: Nijhoff, 1962, 1968. The second impression, 1968, corrects a number of printing mistakes which occur in the 1962 impression. 2 English translation by Richard E. Palmer in Journal o{ the British Society {or Phenomenology, II (1971), 77-90. 3 Heidegger's part of the second draft is available in English as Martin Heidegger, "The Idea of Phenomenology," tr. John N. Deely and Joseph A. (shrink)

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and (...) Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege. (shrink)