Carlo Ierna

A widespread view ties the unity and identity of the School of Brentano to Brentano’s well-known thesis that the true method of philosophy is none other than that of the natural sciences. As the story goes, this became the north star of his school and rallied the first students to his flag. However, it is equally well known that few of his students remained orthodox followers of his position and many founded their own schools and movements, to the point of eclipsing their common teacher. It is unclear what remains of Brentano’s original ideal among such diverse approaches as phenomenology, Gestalt psychology, or object-theory. In my contribution, I provide two different perspectives on this issue with the common goal of refining our intuitions about the unity and identity of the School of Brentano. Focusing on the School itself, I will claim that there is a specific unifying element to be found within the overall ideal of philosophy as science, namely, the role of mathematics as foundation for all inductive sciences. Expanding the focus from the School itself and considering it in the context of other philosophers who agreed in general with the ideal of philosophy as science, I will claim that there is a specific interpretation of that ideal shared by the members of the School of Brentano that distinguishes theirs from other closely related positions, such as that of Paulsen.

I examine Brentano’s strategic positioning between German Idealism and British Empiricism, exemplified by Kant and Mill, focusing on the idea of mathematics as foundational science. For Brentano mathematics is both logically and chronologically prior to all other sciences. However, the 1874 Psychologie vom empirischen Standpunkte does not give a complete enough picture of Brentano’s philosophy of mathematics, discussion of which must be based on textual evidence from his lecture notes and manuscripts, particularly Megethologie. Here Brentano clarifies that mathematics is not inductive, but a purely deductive and a priori science. Against Mill, Brentano argues that induction in the sciences is justified by the calculus of probability, which is founded on a priori mathematical deduction. Through the analysis of Brentano’s mathematical foundations of science and comparative analysis of his critique of Kant and Mill, we can better understand Brentano’s project of philosophy as science.

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.

After discussing Husserl’s development from his years as student up to the publication of the _Philosophie der Arithmetik_ in 1891 in Part 1, we will now examine the various authors and theories that influenced Husserl at the time, starting with his mathematical background. Husserl began his studies in 1876 in Leipzig, attending “lectures in mathematics, physics, astronomy and philosophy” and continued with mathematics and philosophy in Berlin, where he studied under Karl Weierstrass and Leopold Kronecker. Subsequently, Husserl obtained his Ph.D in mathematics in Vienna with former Weierstrass-student Leo Königsberger in January 1883, with the technical work _Beiträge zur Variationsrechnung_ (“Contributions to the Calculus of Variations”). Through both his mathematical and philosophical background Husserl learns about and is influenced by Bernard Bolzano. In the years of ÜBZ and PA Husserl was mainly acquainted with Bolzano’s work as a mathematician and logician, especially his _Paradoxien des Unendlichen_, while later on in Husserl’s development Bolzano’s _Wissenschaftslehre_ will become an important influence. One of the most pervasive influences throughout Husserl’s career will remain his Brentanian background. Husserl was converted to philosophy by Franz Brentano himself and continued his studies with Carl Stumpf, a relatively orthodox Brentanist. In Husserl’s _Philosophie der Arithmetik_ we see much attention going out to the endeavours of other members of the School of Brentano, such as Alexius Meinong and Benno Kerry, and in later works also Kazimierz Twardowski and Anton Marty. After having examined these various significant forces in Husserl’s early philosophy, a general conclusion to the discoveries in Part 1 and Part 2 will follow.

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.

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.

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.

Like most of Franz Brentano’s students, Carl Stumpf showed an interest in the philosophy of mathematics. In particular, Stumpf wrote his habilitation thesis On the Foundations of Mathematics, used mathematical examples in central parts of his lectures, and later returned to the topic in the posthumously published Erkenntnislehre. I will try to show the development and the continuity of Stumpf’s position on the basis of his writings and (unpublished) lectures on logic and psychology, taking into account the Brentanist approach to the philosophy of mathematics that developed in the 1880s and 1890s in the School of Brentano.

Christian von Ehrenfels’s foremost contribution to philosophy of mind is undeniably his seminal 1890 article on Gestalt qualities. This work is considered to have been a “watershed” (Smith 1988b, 15) and a “revolution” (Smith 1994, 20). Ehrenfels’ notion of Gestalt resonated not only with his contemporaries, in the School of Brentano and in phenomenology (see e.g. Heinämaa 2009), but it continues to inform cognitive science (see e.g. Wildgen 2001) and philosophy of mind. In this chapter I will outline some of the influences and background of his conception, briefly discuss his notion of Gestalt, explain how it was taken up by others, and then consider how Ehrenfels himself further applied and developed it.

In this article I connect two concepts that played central roles in the School of Meinong: the notion of impossible objects and that of Gestalt. Ehrenfels claims that Widerspruch or incompatibility would be a temporal Gestalt quality, specifically the trying and failing to build an intuitive presentation. Where, when, and how does this process break down exactly? Meinong’s Graz students developed a more detailed production theory for the presentation of Gestalten (Vorstellungsproduktion) which can help to determine how the failure to produce one Gestalt can generate another, which moreover is typical of impossible objects. There are three contributions to Meinong’s 1904 volume Untersuchungen zur Gegenstandstheorie und Psychologie, the ones by Mally, Benussi, and Ameseder, that provide helpful analyses to clarify the incompatibility Gestalt. These suggest three options to refine the analysis of the Gestalt of impossible objects. The conclusion is that the failure of the Vorstellungsproduktion itself is not enough, the incompatibility relation between the foundations must also play a role.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.