Carlo Ierna

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.

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?

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.

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?

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). Among other things, in this lecture we find the first documented use of the terms "Gestalt" and "Gestaltmoment" in Husserl.

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.

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

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

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.

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.

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?

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.

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.

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.

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.

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.

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.

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.