The paper examines the roots of Husserlian phenomenology in Weierstrass's approach to analysis. After elaborating on Weierstrass's programme of arithmetization of analysis, the paper examines Husserl's Philosophy of Arithmetic as an attempt to provide foundations to analysis. The Philosophy of Arithmetic consists of two parts; the first discusses authentic arithmetic and the second symbolic arithmetic. Husserl's novelty is to use Brentanian descriptive analysis to clarify the fundamental concepts of arithmetic in the first part. In the second part, he founds the (...) symbolic extension of the authentically given arithmetic with stepwise symbolic operations. In the process of doing so, Husserl comes close to defining the modern concept of computability. The paper concludes with a brief comparison between Husserl and Frege. While Frege chose to subject arithmetic to logical analysis, Husserl wants to clarify arithmetic as it is given to us. Both engage in a kind of analysis, but while Frege analyses within Begriffsschrift, Husserl analyses our experiences. The difference in their methods of analysis is what ultimately grows into two separate schools in philosophy in the 20th century. (shrink)

Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the winter 1901–1902. (...) Husserl’s interest in the Memoir is a continuation of his long-standing concern about analytic geometry and in particular Riemann and Helmholtz’s approach to geometry. Husserl favored a non-metrical approach to geometry; thus the topological nature of Hilbert’s Memoir must have been intriguing to him. The task of phenomenology is to describe the givenness of this logos, hence Husserl needed to develop the notion of eidetic intuition. (shrink)

This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...) the first time. (shrink)

Husserl’s notion of definiteness, i.e., completeness is crucial to understanding Husserl’s view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel’s ‘principle of permanence’. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic, where definiteness serves the purpose of the modern notion of ‘soundness’ and leads Husserl to (...) a ‘computational’ view of logic. Inspired by Gauss and Grassmann Husserl then undertakes a further investigation of theories of manifolds. When Husserl subsequently renounces psychologism and changes his view of logic, his idea of definiteness also develops. The notion of definiteness is discussed most extensively in the pair of lectures Husserl gave in front of the mathematical society in Göttingen (1901). A detailed analysis of the lectures, together with an elaboration of Husserl’s lectures on logic beginning in 1895, shows that Husserl meant by definiteness what is today called ‘categoricity’. In so doing Husserl was not doing anything particularly original; since Dedekind’s ‘Was sind und sollen die Zahlen’ (1888) the notion was ‘in the air’. It also characterizes Hilbert’s (1900) notion of completeness. In the end, Husserl’s view of definiteness is discussed in light of Gödel’s (1931) incompleteness results. (shrink)

This book makes available to the English reader nearly all of the shorter philosophical works, published or unpublished, that Husserl produced on the way to the phenomenological breakthrough recorded in his Logical Investigations of 1900-1901. Here one sees Husserl's method emerging step by step, and such crucial substantive conclusions as that concerning the nature of Ideal entities and the status the intentional `relation' and its `objects'. Husserl's literary encounters with many of the leading thinkers of his day illuminates both the (...) context and the content of his thought. Many of the groundbreaking analyses provided in these texts were never again to be given the thorough expositions found in these early writings. Early Writings in the Philosophy of Logic and Mathematics is essential reading for students of Husserl and all those who enquire into the nature of mathematical and logical knowledge. (shrink)

Heidegger hielt die unter dem Titel Geschichte des Zeitbegriffs angekundigte Vorlesung im Sommer-Semester 1925 in der Marburger Universitat. Er gelangte jedoch nicht mehr zur Ausfuhrung der zentralen Thematik. Der Themenkreis der Vorlesung ist mit der Nennung des Untertitels abgesteckt: Prolegomena zu einer Phanomenologie von Geschichte und Natur. Heideggers thematische Uberlegungen beginnen mit einer Kennzeichnung der Situation von Philosophie und Wissenschaft in der zweiten Halfte des 19. Jahrhunderts und stellen das seiner Deutung nach entscheidende Ereignis dieser Zeit heraus: den Durchbruch der (...) Phanomenologie als philosophische Forschung. Er untersucht ihre wesentlichen Entdeckungen, verteidigt sie gegen Missverstandnisse, um dann seinerseits Kritik vorzubringen, wo die Phanomenologie ihrer Forderung zu den Sachen selbst nicht gerecht wird. (shrink)

THE TITLE OF THIS PAPER calls for clarification. Not only are there several senses in which something may be said to "be," there are also many nuances to the terms "categorial" and "intuition." Taking Aristotle as a guide, let us focus upon the primary sense of "being," that is, substance considered both as first substance and second substance. We may then take "categorial" as referring to what Aristotle calls the "figures of predication," the ways in which predicates characterize subjects, indicating (...) "what" the subject is, its quality, quantity, relation, its "where," its "when," and so forth. The term "intuition" expresses something too primitive to be defined, but Edmund Husserl's metaphorical contrast between the "emptiness" of thought and speech and the "fullness" of intuition successfully highlights its essential characteristic. A couple of examples should suffice to grasp the import of Husserl's distinction. Consider the difference, for instance, between first entertaining vague plans of visiting a foreign city and then experiencing the fulfillment of actually strolling through its streets, or the difference between first reading a manual of instructions for performing some task and then actually executing the task skillfully. Taking Husserl as a guide, let us therefore characterize intuition broadly as the presentation of something in its fullness, as opposed to thinking or talking about it in an empty way. Finally, combining Husserlian and Aristotelian terminologies, we may describe categorial intuition as the presentation of figures of predication. Rather than presenting some particular thing, say a red chair, categorial intuition presents the chair's being red, the red quality's belonging to the chair. In short, categorial intuition makes present the modes of presentation of things. (shrink)