Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is much less to (...) be found about mathematics in his published works. Besides Brentano’s own work, it is quite remarkable to see that practically all of his better-known students sooner or later produced a work on the philosophy of mathematics. This also encourages the supposition not just of a common interest in the matter, but of a common theoretical core. All this prompts the question: Can we speak of a Brentanist philosophy of mathematics? (shrink)

In this paper I will discuss Edmund Husserl’s critique of Franz Brentano’s interpretation of categorical judgments as Double Judgments (Doppelurteile). This will be developed mostly as an internal critique, within the framework of the school of Brentano, and not through a direct contrast with Husserl’s own theory of judgment, as presented e.g. in the Fifth Investigation. Already during the 1890s Husserl overcame the psychologistic aspects of Brentano’s approach, advocating the importance of analysing the logical structure underlying language independently from psychology. (...) Moreover, Husserl’s critique seems to be also applicable to Bertrand Russell’s analysis, which shares an important aspect of Brentano’s theory. I will try to avoid going too deep into the various theories of judgment and keep mostly to the issue of double judgments. (shrink)

The article examines the development of Husserl’s early philosophy from his Habilitationsschrift to the Philosophie der Arithmetik . An attempt will be made at reconstructing the lost Habilitationsschrift . The examined sources show that the original version of the Habilitationsschrift was by far broader than the printed version, and included most topics of the PA. The article contains an extensive and detailed comparison of these texts to illustrate the changes in Husserl’s position before and after February 1890. This date is (...) taken as a turning point in his development, because of Husserl’s announcement in a letter to Carl Stumpf that he was mistaken in his basic assumption, i.e. that the analysis of the concept of Anzahl would yield a foundation for arithmetic. Some interesting conclusions in this respect can also be drawn from an unpublished lecture that Husserl held in the WS 1889/90, in which he anticipates aspects of his position hitherto deemed to belong to the last phases of the PA. (shrink)

The article examines the development of Husserl’s early philosophy from his Habilitationsschrift (1887) to the Philosophie der Arithmetik (1891). -/- An attempt will be made at reconstructing the lost Habilitationsschrift (of which only the first chapter survives, which we know as Über den Begriff der Zahl). The examined sources show that the original version of the Habilitationsschrift was by far broader than the printed version, and included most topics of the PA. -/- The article contains an extensive and detailed comparison (...) of these texts to illustrate the changes in Husserl’s position before and after February 1890. This date is taken as a turning point in his development, because of Husserl’s announcement in a letter to Carl Stumpf that he was mistaken in his basic assumption, i.e. that the (psychological) analysis of the concept of Anzahl would yield a foundation for arithmetic. Some interesting conclusions in this respect can also be drawn from an unpublished lecture that Husserl held in the WS 1889/90, in which he anticipates aspects of his position hitherto deemed to belong to the last phases of the PA. (shrink)

Both Alexius Meinong and Edmund Husserl wrote about relations in their early works, in periods in which they were still influenced by Franz Brentano. However, besides the split between Brentano and Meinong, the latter also accused Husserl of plagiarism with respect to the theory of relations. Examining Meinong’s and Husserl’s early works and the Brentanist framework they were written in, we will try to assess their similarities and differences. As they shared other sources besides Brentano, we will consider very carefully (...) whether we should speak at all of influence or plagiarism. Despite Meinong’s accusations it seems that both he and Husserl took over some elements from Brentano and, partially through him, from John Stuart Mill, who appears to be the most probable source on relations. (shrink)

In this article we will address the issue whether and in how far Anton Marty had a significant influence on the development of the phenomenological movement. As “the phenomenological movement” is not a clearly defined and circumscribed notion, we need to provide an appropriate context for any comparison. The phenomenological movement grew out of the School of Brentano and we take this larger whole as our starting point. Since Marty did not found his own school or movement, but remained a (...) Brentanist, it is quite difficult to identify a clear influence of Marty on the phenomenological movement that would not be intermingled with a general Brentanist background. A specifically Martian influence could perhaps mainly be found in the philosophy of language. We will look at Marty’s and Husserl’s shared background, mutual criticisms and common legacy in order to evaluate the significance of any influence there might have been. (shrink)

These five letters from Christian von Ehrenfels to Alexius Meinong contain a written record of how Ehrenfels' dissertation plans came about, based on his reading and commenting on Meinong's work.

Edmund Husserl’s engagement with Bertrand Russell’s paradox stands in a continuum of reciprocal reception and discussions about impossible objects in the School of Brentano. Against this broader context, we will focus on Husserl’s discussion of Russell’s paradox in his manuscript A I 35α from 1912. This highly interesting and revealing manuscript has unfortunately remained unpublished, which probably explains the scant attention it has received. I will examine Husserl’s approach in A I 35α by relating it to earlier discussions of relevant (...) topics in his manuscripts and the broader historical context of the School of Brentano and early phenomenology. (shrink)

The so-called “intentional object” occupies a central position in the debates about intentionality in Brentano and the Brentano School. How does it relate to the correlate, the content, or the intended, possibly external, transcendent object? Does it perhaps even coincide with one of these? There was no clear consensus on this neither in Brentano’s time nor today. In order to develop a new perspective on the problem of the intentional object, I would like to introduce a deliberately radical interpretation and (...) related terminological change: what if we were to avoid any talk of “object” in this context altogether? Perhaps this could help avoid the ambiguities and misunderstandings associated with talk of “intentional objects.” In my contribution I would like to sketch such an interpretation and consider whether this attempt could be useful to reframe the debate. (shrink)

This volume is a broad anthology addressing many if not most major topics in phenomenology and philosophy in general: from foundational and methodological ...

In the article Husserl’s view of the infinite around 1890 is analysed. I give a survey of his mathematical background and other important influences (especially Bolzano). The article contains a short exposition on Husserl's distinction between proper and symbolic presentations in the "Philosophie der Arithmetik" and between finite and infinite symbolic collections. Subsequently Husserl’s conception of surrogate presentations in his treatise "Zur Logik der Zeichen (Semiotik)" is discussed. In this text Husserl gives a detailed account of infinity, using surrogate presentations. (...) The conclusion is that with surrogates we can only operate according to blind psychological rules. (shrink)

In this article I will begin by discussing recent criticism, by Mauro Antonelli and Werner Sauer, of the ontological interpretation of Franz Brentano’s concept of intentionality, as formulated by i.a. Roderick Chisholm. I will then outline some apparent inconsistencies of the positions advocated by Antonelli and Sauer with Brentano’s formulations of his theory in several works and lectures. This new evaluation of (unpublished) sources will then lead to a sketch of a new approach to Brentano’s theory of intentionality. Specifically, it (...) will be argued that the notion of “intentional object” is inherently and un- avoidably ambiguous in every act of external perception, due to the fact that we can only have improper intentions directed at the external world. (shrink)

In this article I will analyse Husserl’s conception of the infinite as ex- pressed in the paragraph Unendliche Mengen of his Philosophie der Arithmetik (PA). I will give a short exposition on his distinction be- tween proper and symbolic presentations and then proceed to the logi- cal distinctions that Husserl makes between finite and infinite symbolic collections. Subsequently (in section 2.3), I will discuss Husserl’s addition of surrogate presentations as a sub-type of symbolic presentations in his short treatise Zur Logik (...) der Zeichen (Semiotik). In this later text (which was originally intended as an appendix to the never published second volume of the PA) Husserl gives a more detailed account of how we can conceive of the infinite, using surrogate presentations. (shrink)

In the second edition of the Logische Untersuchungen Husserl claims to have investigated higher order objects and Gestalt qualities before anyone else in the School of Brentano. Indeed, in the Philosophie der Arithmetik we find a discussion of figural moments and fusion that could lend some support to such a claim. By considering the concepts of Gestalt and Verschmelzung in their relevant historical context, the latter especially in connection to Stumpf, we find that Husserl indeed gave a quite original and (...) interesting account of such higher order phenomena. (shrink)

Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is much less to (...) be found about mathematics in his published works. Besides Brentano’s own work, it is quite remarkable to see that practically all of his better-known students sooner or later produced a work on the philosophy of mathematics. This also encourages the supposition not just of a common interest in the matter, but of a common theoretical core. All this prompts the question: Can we speak of a Brentanist philosophy of mathematics? (shrink)

Among the correspondence between Husserl and Brentano kept at the Houghton Library of Harvard University there is a letter from Husserl to Brentano from 29 XII 1889, whose contents were completely unknown until now. The letter is of some significance, both historically as well as systematically for Husserl’s early development, painting a vivid picture of his relation and indebtedness to his teacher Franz Brentano. As in his letter to Stumpf from February 1890, Husserl describes the issues he had encountered during (...) the elaboration of his habilitation work into the Philosophy of Arithmetic, but also announces that he has finally found "clarity" regarding the arithmetica universalis. (shrink)

On July 14, 1866 Franz Brentano stepped up to the pulpit to defend his thesis that “the true method of philosophy is none other than that of the natural sciences”. This thesis bound his first students to him and became the north star of his school, against the complex background of the progress and specialization of the natural sciences as well as the growth and professionalization of universities. I will discuss the project of the renewal of philosophy as science in (...) the School of Brentano and how this aimed to provide a scientific foundation for the humanities independently from the natural sciences, while preserving the unity of science. Through his well-known re-introduction of the concept of intentionality as criterion to distinguish internal and external perception, Brentano was able to supply an empirical foundation for the Geisteswissenschaften. While philosophy would use the method of natural science, its domain would not be nature, but consciousness: a full-blooded science of the mind that did not require a reduction to the physical in order to be scientific. Brentano’s science of consciousness was empirical, but not experimental, and relied on subjective methods, but was not introspective. Brentano’s students Carl Stumpf, Anton Marty, Alexius Meinong, Christian von Ehrenfels, Edmund Husserl and others came to occupy important chairs in philosophy throughout Europe. While they were certainly not all orthodox followers, they adapted and spread his theories far and wide in the schools and movements they founded and influenced: Gestalt psychology, Prague linguistics, phenomenology, etc.. Moreover, the 19th century idea of scientific research as a collaborative and collective achievement led to a division of labor in Brentano’s school. Each of his students was meant to work out a part of the greater whole: Stumpf, the philosophy of sound and music; Marty, language; Meinong the history of philosophy; Husserl, mathematics; etc. Yet all of them also contributed to the shared project of the renewal of philosophy as science and discussed the (foundational) relation of philosophy to other sciences in programmatic works. Though often forgotten and overlooked due to contingent historical circumstances, the scientific paradigm of the School of Brentano was very fruitful and highly influential in philosophy and the human sciences in general, throughout the second half of the 19th and into the 20th centuries. Yet it is relevant then as now to preserve the independent scientific dignity of the humanities. (shrink)

This book presents a historiographical and theorical analysis of how Husserlian Phenomenology arrived and developed in North America. The chapters analyze the different phases of the reception of Edmund Husserl’s thought in the USA and Canada. The volume discusses the authors and universities that played a fundamental role in promoting Husserlian Phenomenology and clarifies their connection with American Philosophy, Pragmatism, and with Analytic Philosophy. Starting from the analysis of how the first American Scholars of Edmund Husserl's thought opened the door (...) to the reception of his texts, the book explores the first encounters between Pragmatism and Husserlian Phenomenology in American Universities. The study focuses, then, on those Scholars who fled from Europe to America, from 1933 onwards, to escape Nazism - Felix Kaufmann, Alfred Schutz, Aron Gurwitsch, Herbert Spiegelberg, Fritz Kaufmann, among the most notable - and illustrates how their teaching provided the very basis for the spreading of Husserlian Phenomenology in North America. The volume examines, then, the action of the 20th Century North-American Husserl Scholars, together with those places, societies, centers, and journals, specifically created to represent the development of the studies devoted to Husserlian Phenomenology in the U.S., with a focus of the Regional Phenomenological Schools. (shrink)

In this article the author will discuss Franz Brentano’s theory of intentionality and the ontological status of the intentional object specifically with respect to symbolic presentations. The role and function of intentionality are compared to the process of semeiosis. Several interesting parallels can be found between fundamental problems in the interpretation of the Brentanian notion of intentionality and issues in semiotics. In particular, the author focuses on the theory of Charles W. Morris and attempts to apply core notions of his (...) semiotics to clarify Brentano’s ambiguous account of intentional reference, the role of signs in symbolic presentations and how this relates to outer perception. (shrink)

The article introduces and discusses an unpublished manuscript by Edmund Husserl, conserved at the Husserl-Archives Leuven with signature K I 26, pp. 73a–73b. The article is followed by the text of the manuscript in German and in an English translation. The manuscript, titled “The Transition through the Impossible” ( Der Durchgang durch das Unmögliche ), was part of the material Husserl used for his 1901 Doppelvortrag in Göttingen. In the manuscript, the impossible is characterized as the “sphere of objectlessness” ( (...) Sphäre der Gegenstandslosigkeit ) and Husserl addresses the question whether and when it is warranted to perform a transition through the impossible to obtain valid results for the sphere of objectivity. (shrink)

Marx Textor's Brentano's Mind begins with a short, illuminating introduction which clearly sets out the author's main aims. The two questions Textor wants to consider are, "What is the nature of mind?" and, "What is the structure of consciousness?" From the outset, Textor explicitly states that his intent is not to provide a historically plausible exegesis of "Brentano's often dense and difficult texts", but to take his "bold, suggestive, and influential" answers to these questions as an inspiration for new systematic (...) analyses. The book is then divided in two parts, corresponding to the two questions. (shrink)

Obituary for Karl Schuhmann (1941 - 2003), professor and chair of the History of Postmedieval Philosophy at Utrecht University.

Franz Brentano’s 1874 Psychology from an Empirical Standpoint presents us with a framework and methodology for performing scientific research in psychology. Moreover, this project provides the foundation for the more ambitious ideal of the renewal of philosophy as a science, which had been Brentano’s aim ever since defending his habilitation thesis that “the true method of philosophy is none other than that of the natural sciences”. Brentano therefore needs to carefully articulate the precise position and role of his scientific psychology (...) among the Geisteswissenschaften and the Naturwissenschaften. What does his ideal of philosophy as science consist in? What is the relation between his scientific psychology and philosophy? How is psychology related to the natural sciences, in particular psycho-physics and physiology? (shrink)

In 1913, in a draft for a new Preface for the second edition of the Logical Investigations, Edmund Husserl reveals to his readers that "The source of all my studies and the first source of my epistemological difficul­ties lies in my first works on the philosophy of arithmetic and mathematics in general", i.e. his Habilitationsschrift and the Philosophy of Arithmetic: "I carefully studied the consciousness constituting the amount, first the collec­tive consciousness (consciousness of quantity, of multiplicity) in its simplest and (...) higher levels (consciousness of sums, sums of sums etc.). I immediately separated proper (intuitive) and symbolic consciousness, in the characteriza­tion of the former I hit the radical difference of categorial consciousness [...] and sensuous consciousness of unity." Later on, in the Third Investigation, Husserl makes some very specific claims, that are of considerable importance to assess the development of his early works and their relation to his later phenomenology: "This first work of mine (an elaboration of my Habilitationsschrift, [...], 1887) should be compared with all assertions of the present work on compounds, moments of unity, complexes, wholes and objects of higher order. I am sorry that in many recent treatments of the doctrine of "Gestalt-qualities", this work has mostly been ignored, though quite a lot of the thought-content of later treatments by Cornelius, Meinong etc., of questions of analysis, apprehension of plurality and complexion is already to be found, differently expressed, in my Philosophy of Arithmetic. I think it would still be of use today to consult this work on the phenomenological and ontological issues in question, especially since it is the first work that attached importance to acts and objects of higher order and investigated them thoroughly." Hence, at the time of the Ideas, Husserl retrospectively considers his first works4 as being still relevant for phenomenological issues. Not only does Husserl advance a very interesting priority claim with respect to Von Ehrenfels’ development of the notion of Gestalt and Meinong’s development of Gegenstandstheorie, but also a strong affirmation of continuity and coherence of his position from 1887 all the way up to 1913, encompassing the alleged “revolution” in his position from psychologism to anti-psycho­logism in the 1890s. Indeed, according to much of the recent secondary literature, in 1894, right in the middle of the ten “incubation” years between the Philosophy of Arithmetic and the Logical Investigations, Frege’s destruc­tive review would have converted Husserl to antipsychologism practically overnight. This gives us two conflicting interpretations: on the one hand, Husserl himself in 1913 still seems to approve of the Philosophy of Arithmetic and even considers it to contain valuable phenomenological material, on the other, it is routinely dismissed by much of the secondary literature as hope­lessly psychologistic. So which one is it: do we have a phenomenological arithmetic or a psychologistic arithmetic in Husserl’s first book? On balance, I think that Husserl in his Philosophy of Arithmetic developed a position that does not fall prey to the exaggerated and poorly aimed critiques of Frege, while at the same time, as a descriptive psychology of the genesis and constitution of number, it can certainly be considered as providing phenome­nologically meaningful analyses, though of course not made from within an explicitly transcendental phenomenological framework. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s (...) Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

In seiner Kosmogonie bespricht Ehrenfels den Ursprung, die Entwicklung, und das endgültige Schicksal des Universums: die Gestalt der Welt. Einerseits ist sie ein Kosmos, ein Geschöpf des Ordnungsprinzips, andererseits ein Chaos, als Resultat des Prinzips des Zufalls und der Entropie. Diese beiden komplementären kosmischen Prinzipien generieren die Welt, welche nicht aus einem absichtlichen Willen, sondern einem blinden Gestalten hervorkommt. Nach Ehrenfels, nehmen wir Menschen Teil an dem Gestalten der Welt und so kommt allmählich in und durch uns das Ordnungsprinzip zum (...) Selbstbewusstsein. Nur so erhält das blinde Gestalten der Welt ein Ziel und eine Bedeutung. In seinen späteren Schriften zur Religion der Zukunft verdeutlicht Ehrenfels, dass alle Intellekte an dem göttlichen Intellekt mitpartizipieren, was er durch die Theorie der „Supraposition der Bewusstseinseinheiten“ erklärt. Wenn jede Zelle bereits eine Art „Bewusstsein“ hat, dann ist nicht nur jede einzelne meiner Gehirnzellen selbst bewusst, sondern sie konstituieren auch kollektiv mein einheitliches Gesamtbewusstsein als Mensch. Darüber hinaus konstituieren wir kollektiv ebenfalls „Persönlichkeiten höherer Ordnung“: so gestalten wir nicht nur die Welt, sondern auch ihren göttlichen Gestalter. (shrink)

This volume contains an English translation of Edmund Husserl’s first major work, the Philosophie der Arithmetik, (Husserl 1891). As a translation of Husserliana XII (Husserl 1970), it also includes the first chapter of Husserl’s Habilitationsschrift (Über den Begriff der Zahl) (Husserl 1887) and various supplementary texts written between 1887 and 1901. This translation is the crowning achievement of Dallas Willard’s monumental research into Husserl’s early philosophy (Husserl 1984) and should be seen as a companion to volume V of the Husserliana: (...) Collected Works series (Husserl 1994b), which already contained selected translations from Hua XII. As Willard re- marks on the inner cover of the volume, it is “a window on a period of rich and illuminating philosophical activity”, to which I wholeheartedly agree. Willard’s two volumes of translations open this window on the beginnings of Husserl’s philosophy for the English-speaking world. This earliest period of Husserl’s philosophy has often been unjustly ignored and Willard provides the English reader with an excellent starting point. Husserl’s first steps into phenomenology and the philosophy of logic and mathematics contain many promising seeds that will flower later on, in the Logische Untersuchungen and beyond. (shrink)

This present collection of (translations of) reviews is intended to help obtain a more balanced picture of the reception and impact of Edmund Husserl’s first book, the 1891 Philosophy of Arithmetic. One of the insights to be gained from this non-exhaustive collection of reviews is that the Philosophy of Arithmetic had a much more widespread reception than hitherto assumed: in the present collection alone there already are fourteen, all published between 1891 and 1895. Three of the reviews appeared in mathematical (...) journals (Jahrbuch über die Fortschritte der Mathematik, Zeitschrift für Mathematik und Physik, and Zeitschrift für mathema- tischen und naturwissenschaftlichen Unterricht), three were published in English journals (The Philosophical Review, The Monist, Mind), two were written by other members of the School of Brentano (Franz Hillebrand and Alois Höfler). Some of the reviews and notices appear to be very superficial, consisting merely of para- phrases (often without references) and lists of topics taken from the table of con- tents, presenting barely acceptable summaries. Others, among which Höfler might be the most significant, engage much more deeply with the topics and problems that Husserl addresses, analyzing his approach in the context of the mathematics of his time and the School of Brentano. (shrink)

The chapter contains a brief intellectual biography of Herbert Spiegelberg, building on his numerous autobiographical remarks. It provides a survey of Spiegelberg’s early life and works and his German period, focusing more extensively on his American period. The chapter considers in some detail three important themes in Spiegelberg’s works. First, Spiegelberg’s role in spreading and developing the phenomenological method in the United States through the organization of his workshops, based on ideas from his teachers Reinach and Pfänder to phenomenologize “co-subjectively”. (...) Second, his life-long concern with the development of a phenomenological ethics and the detailed development of the core notion of “deontic state of affairs” (Sollverhalt). Last but not least, his monumental contribution to the historiography of phenomenology with his The Phenomenological Movement. The chapter takes a critical look at the early controversies with Farber on the idea of a phenomenological “movement” in order to clarify and qualify Spiegelberg’s own conception of phenomenology. The chapter is meant as a companion piece to the translation of Karl Schuhmann’s unpublished article “Phenomenological Ontology in the Work of Herbert Spiegelberg: Ideas and Ontic and Deontic States of Affairs” which will appear in the second volume. (shrink)

Among the various lecture courses that Edmund Husserl held during his time as a Privatdozent at the University of Halle (1887-1901), there was one on Ausgewählte Fragen aus der Philosophie der Mathematik (Selected Questions from the Philosophy of Mathematics), which he gave twice, once in the WS 1889/90 and again in WS 1890/91. As Husserl reports in his letter to Carl Stumpf of February 1890, he lectured mainly on “spatial-logical questions” and gave an extensive critique of the Riemann-Helmholtz theories. Indeed, (...) in K I 28 many lectures on this subject can be found, which are for the greater part published in Husserliana XXI. The lecture contained in K I 28/4-12 at the Husserl-Archives Leuven, however, was left out of the selection, because the lecture contained “an analysis of the concept of number” whose content is “already known” from the Philosophie der Arithmetik. Indeed, since the lecture is from the WS 1889/90, the manuscript allows a glimpse of Husserl’s ideas halfway between his Habilitationsschrift (1887) and the Philosophie der Arithmetik (1891). From an exam- ple Husserl gives in the lecture: “Der wievielte Januar ist heute?” (The how-many-th of January is it today?), it can be estimated to be from January 1890, placing it in close relation to the letter to Stumpf and the views and doubts expressed therein. The bundle of papers K I 28 is wrapped in a blue cover, bearing only “Vor- lesungen” (Lectures) as a title. The lecture “On the concept of Number” in K I 28/4-12 is contained again in a separate cover, without any title. As in the case of most of his lectures, Husserl folded the paper in half, using the right half as a margin for annotations. Before the lecture there is a single page (K I 28/3) with some annotations on the treatment of imaginary numbers as assumptions in calculation. This text is published here as an Appendix to the lecture, because, while it is not part of the lecture itself, it is closely related to the subjects discussed therein. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s (...) Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

The present article provides a critical analysis of Christian von Ehrenfels’ dissertation Über Grössenrelationen und Zahlen. Eine psychologische Studie. As many other students of Brentano, Ehrenfels engaged repeatedly with the philosophy of mathematics, but until now his dissertation remained nearly completely unknown. Ehrenfels’ dissertation, however, fits perfectly within the Brentanist philosophy of mathematics and actually occupies an important place therein, precisely because it occurs outside of the vertical master - student lineage that goes from Brentano via Stumpf to Husserl. Indeed, (...) Ehrenfels dissertation shows many parallels and anticipations to Husserl’s early works in the philosophy of mathematics. (shrink)

A common analysis of Edmund Husserl’s early works on the philosophy of logic and mathematics presents these writings as the result of a combination of two distinct strands of influence: on the one hand a mathematical influence due to his teachers is Berlin, such as Karl Weierstrass, and on the other hand a philosophical influence due to his later studies in Vienna with Franz Brentano. However, the formative influences on Husserl’s early philosophy cannot be so cleanly separated into a philosophical (...) and a mathematical pathway. Growing evidence indicates that a Brentanist philosophy of mathematics was already in place before Husserl. Rather than an original combination at the confluence of two different streams, his early writings represent an elaboration of topics and problems that were already being discussed in the School of Brentano within a pre-existing framework. The traditional account understandably neglects Brentano’s own work on the philosophy of mathematics and logic, which can be found mostly in his unpublished manuscripts and lectures, and various works by Brentano’s students on the philosophy of mathematics which have only recently emerged from obscurity. Husserl’s early works must be correctly placed in this preceding context in order to be fully understood and correctly assessed. (shrink)

What the present work aimed to achieve is an assessment of the origin an d unity of Husserl s Logical Investigations. My approach was to take the history of its development as fundamental for the determination of its basic structure. Therefore, I proceeded to analyse Husserl s development between the Philosophy of Arithmetic and Logical Investigations with re spect to the fundamental issues in the justification of knowledge in mathematics and logic. In Husserl s own words, one of the concerns (...) that set him on the road to phenomenology was the clarification and analysis of the relation b etween the subjectivity of knowing and the objectivity of knowledge. Fro m my investigations it has, I hope, become apparent how this problem ori ginated in his earliest works and, through various influences and exchanges, led to his theory of intentionality in the first editio n of the Logical Investigations. The Logical Investigations is located between his Brentanist phase and t he ultimate development of transcendental phenomenology. It is the sedim ent of Husserl s logical investigations during the 1890s, which is the m ain period I analysed in the present work. Husserl himself often remarke s on the early origin of some of the issues he tried to deal with in the Logical Investigations. Still in his sketches for a new preface to the second edition of 1913, he took pains to point out the developmental his tory of the work from the Philosophy of Arithmetic onward. Regarding the Philosophy of Arithmetic, more often than not, Husserl remarks that it was just and elaboration of his Habilitationsschrift. Hence, following h is lead, we tried to embrace the whole period of his psychological and l ogical analyses from 1886/7 to 1900/01. Of course, I was certainly not the first, nor will I be the last, to be intrigued by Husserl s development in these years. Numerous books and articles have been written long before mine on precisely these issue s, often dealing with specific topics, such as the uneasy relation of psychology and psychologism in Husserl s work or fundamental inʂ 58;uences such as Bolzano s, which I therefore chose to leave aside. Not simply to duplicate or summarise such pre-existing scholarship, I tried to concentrate on the issues to which I felt I could contribute an orig inal insight, advancing the field. I would like to indicate ᤙ 7;ve points here, where I think I attained this goal: 1. The enduring relevance of Husserl s mathematical ba ckground. 2. Support for an early development of a theory of hig her order objects 3. A better evaluation of Frege s influence 4. A contextualisation of Schuhmann s thesis regarding the relevance of Twardowski for Husserl s notion of intentionality 5. The dependence of the unity of the Logical Investig ations on its historical development. Without understanding its developmental history we would misunderstand i ts internal coherence. In the first part we saw Husserl s early struggle to integrate the mathematical and psychological points of view on the philosophy of math ematics, a struggle that lasted from the Habilitationsschrift at least u p to and including his Doppelvortrag. The basic problem is the justi@ 257;cation of knowledge, in the case of mathematics, the justifica tion of knowledge in formal sciences, obtained with symbolic methods. Su ch problems regarding the subjectivity of knowing and the objectivity of knowledge guided the development of his position from Philosophy of Ari thmetic to Logical Investigations. In articulating his solution Husserl analysed the various relations betw een founding and founded layers of knowledge and whether and how one cou ld pass from on to the other. Already at the time of the Philosophy of A rithmetic he tried to account for higher order acts, relations and objec ts, the mature account of which would have to wait until the Logical Inv estigations and later. Among various influences on his progression towards phenomenology, Frege has been often considered to have provided the conversion to an ti-psychologism with his review of the Philosophy of Arithmetic. I think I have demonstrated that the review is almost entirely irrelevant in th is sense and that we should rather look at a much earlier influenc e on the Philosophy of Arithmetic. By showing that Brentano s conception of intentionality was already more sophisticated than until recently assumed, thanks to some recent public ations of unpublished material from Brentano s and Husserl s Nachlass, I think Schuhmann s thesis is right, but should be reinterpreted as being less radical than it would appear. Both Husserl and Twardowski were in& #64258;uenced by Brentano as his students. Following his and Meinong s l ead, they both elaborated a theory on intentionality, in connection with the other theories of intentionality in his school and the Brentano-Bol zano paradox. Furthermore, by providing a more continuous reading of Hus serl s development through the transcendental turn, I hope to have made clear that his later theory of the noema is not a return to a neo-Twardo wskian triadic position, but a reaffirmation, now in transcendental key, of his 1894 take on the matter. The Logical Investigations are uniquely determined by their historical c ontext in the middle of Husserl s development, falling almost exactly be tween the Habilitationsschrift and the Ideas. Due to their troubled hist ory, including changes in Husserl s earliest position around 1890, the f ailure of the second volume of the Philosophy of Arithmetic, various in& #64258;uences around 1894, and the subsequent reorientation and broadeni ng of his theories to a non-psychologistic logic and mathesis universali s, the Logical Investigations might at first seem to fall apart in two fundamentally disconnected books, the second one of which containin g six heterogeneous studies. It is my contention that it is exactly its troubled history that ties the Logical Investigations together, as Husse rl developed his logical investigations in the 1890s on the basis of a h andful thorny problems, including intentionality as centerpiece. From th e Habilitationsschrift to the Ideas it is the relation between subject a nd object, in all respects, ontological as well as epistemological, that guides his research. The Logical Investigations is a intermediate sedim ent of his struggles, containing an elaboration and improvement of his p osition in his early works and also pointing ahead towards the later pos ition of transcendental phenomenology as an implication and continuation of the solutions he proposes. Furthermore, I tried to address the problem that, while Husserl regarded his Logical Investigations as the breakthrough to phenomenology, many f undamental notions of the later transcendental phenomenology seem to be missing in the first edition of the Logical Investigations. The me thod of the reduction, the notion of a pure ego and a full account of th e noema are at most sketched or implied. Hence, I also looked ahead to t he further development of phenomenology after the Logical Investigations. As Husserl s influence has extended beyond the movement he found ed, I felt I could not bypass his significance for the currently d ominant analytical philosophy. Especially with respect to some of the co re topics of the Logical Investigations, but also earlier themes such as Husserl s semiotics, there is an interest in phenomenology from the ana lytic side. Nevertheless, precisely with regard to the unifying theme of intentionality, analytical philosophy often seems to miss the mark, and spectacularly so. I discussed Searle s influential, but in my opi nion, misguided and flawed approach, and I hope it is clear that I have chosen my method and approach in complete antithesis to his. The central contributions I was able to give, were only possible thanks to solid historical groundwork as necessary prerequisite for systematic analyses. Wherever possible, a reference to the original primary sources was provided, allowing the texts to speak for themselves and providing the reader with the critical instruments to evaluate my interpretations. As Husserl stood in a fruitful exchange with many other scholars, as st udent, colleague, friend and teacher, the intellectual context of his th oughts is essential to a correct understanding of his theories and aims. I hope to have found the right balance in the historical and the system atical aspects of my work to suit the interests of the reader and the re quirements of scholarship. (shrink)

This is the first publication and critical edition of Christian von Ehrenfels' dissertation on "Relations of Magnitude and Numbers. A Psychological Study", based on a new transcription by Reinhard Fabian.

The following pages contain a partial edition of Husserl’s manuscript A I 35, pages 1a-28b. The first few pages are dated on May 1927 and are included mostly for completeness’ sake. The bulk of the manuscript convolute, however, is from 1912. Four pages of the convolute, 31a-34b, have been published as Beilage XII (210, 2–216, 2) in Hua XXXII. The manuscript was excluded from the text selection of Husserliana XXI3 based on its much later date of composition. A I 35/24a (...) is mentioned in Husserliana XXII (p. xxi, n. 4) as confirmation for Zermelo’s 1902 “oral report” to Husserl of his own independent discovery of the paradox. The text presented here for the first time has already been the target of at least three extensive commentaries, while still unpublished, by Claire Ortiz Hill and Guillermo Rosado Haddock. These present a good survey in english of the central issues on the text and contain many translated quotations. (shrink)

History and Philosophy of Logic, Volume 32, Issue 4, Page 399-400, November 2011.

In this article I provide an overview of the many different terms that Brentano sometimes uses as synonyms or as explanations for “intentional inexistence”. The many terms associated with intentional inexistence appear in many different contexts, and we can conclude that Brentano uses these terms primarily to describe a property that is accidental and dependent on the subject from which it arises and with which it passes away. Ontologically, both properties and substances exist, but the former requires a substance (the (...) subject) for its existence. A mental act is to be considered as a first-order property, whereas the content (or part of the mental act) can be understood as an accident of that accident. (shrink)

L’articolo si concentra sull’analisi della filosofia come istituzione affermatasi neutrale che, tuttavia, si rivela sessuata al maschile attraverso la comprensione del concetto di «differenza sessuale» per come teorizzato da Adriana Cavarero. Utilizzando il quadro concettuale della filosofia come «pratica» intrecciata alle pratiche di vita sviluppato da Carlo Sini, e quello di «ordine del discorso» fornito da Michel Foucault, vengono esplicitate le premesse e le conseguenze dell’ordine del discorso nell’elaborazione dei concetti, per poi presentare delle possibilità di un suo ripensamento (...) attraverso la prassi teorica di Adriana Cavarero – di cui viene proposta un’analisi e sono presentati dei risultati rilevanti anche per il contesto attuale. L’ipotesi in esame suggerisce che la pretesa di neutralità e universalità della filosofia sia minata dalla consapevolezza che il pensatore è un essere vivente la cui esperienza di vita, compresa la propria sessuazione, permea sia il mondo della vita che il mondo del sapere. Dunque, la formazione dei concetti filosofici risulta vincolata alla prospettiva sessuata del soggetto che li elabora. Di conseguenza, l’ordine del discorso neutrale rappresenta tanto lo scacco del pensiero delle donne quanto l’occasione di essere ripraticato. Infine, l’articolo propone una riflessione sui cambiamenti istituzionali avvenuti tra gli anni Ottanta, il periodo di riferimento per la formulazione teorica di Cavarero su cui l’articolo si sofferma, e la situazione attuale dell’Università Italiana in relazione alle questioni di genere. (shrink)

Minding Time: A Philosophical and Theoretical Approach to the Psychology of Time offers an innovative philosophical account of the most fundamental kinds of time representation.

This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last (...) century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality. (shrink)

Many of the computing systems programmed using Machine Learning are opaque: it is difficult to know why they do what they do or how they work. Explainable Artificial Intelligence aims to develop analytic techniques that render opaque computing systems transparent, but lacks a normative framework with which to evaluate these techniques’ explanatory successes. The aim of the present discussion is to develop such a framework, paying particular attention to different stakeholders’ distinct explanatory requirements. Building on an analysis of “opacity” from (...) philosophy of science, this framework is modeled after accounts of explanation in cognitive science. The framework distinguishes between the explanation-seeking questions that are likely to be asked by different stakeholders, and specifies the general ways in which these questions should be answered so as to allow these stakeholders to perform their roles in the Machine Learning ecosystem. By applying the normative framework to recently developed techniques such as input heatmapping, feature-detector visualization, and diagnostic classification, it is possible to determine whether and to what extent techniques from Explainable Artificial Intelligence can be used to render opaque computing systems transparent and, thus, whether they can be used to solve the Black Box Problem. (shrink)