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)

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)

The paper discusses Husserl’s method of historical reflection, radical Besinnung, as defined and used in Formale und transzendentale Logik (1929). Whereas Formal and Transcendental Logic introduces and displays Husserl’s usage of Besinnung in the context of the exact sciences, the paper seeks to develop it as a more general critical method with which to approach any rational goal-directed activity. Husserl defines Besinnung as a method that enables understanding agents and their actions by explicating agents’ typically implicit goals. It leads to (...) the inclusion of historical-teleological activities as part of Husserl’s natural understanding of the world. The transcendental reflection radicalizes Besinnung by clarifying the kinds of evidence sought for in activities and then suggesting revisions to the concepts and principles used. The result is inner critique, which means that the activities are criticized against the norms that arise from reflection on these activities themselves, and not from a comparison with external standards or measures. (shrink)

This essay presents Husserl’s Formal and Transcendental Logic (1929) in three main sections following the layout of the work itself. The first section focuses on Husserl’s introduction where he explains the method and the aim of the essay. The method used in FTL is radical Besinnung and with it an intentional explication of proper sense of formal logic is sought for. The second section is on formal logic. The third section focuses on Husserl’s “transcendental logic,” which is needed to make (...) Husserl’s conception complete, i.e., to understand what makes Besinnung radical, how the proper sense of formal logic has been reached and how all this relates to transcendental constitution of an object in the world. Husserl’s work is connected to his context (in exact sciences) and the relevance of his views for the contemporary approaches is discussed. (shrink)

Husserl holds that the theoretical sciences should be value-free, i.e., free from the values of extra-scientific practices and guided only by epistemic values such as coherence and truth. This view does not imply that to Husserl the sciences would be immune to all criticism of interests, goals, and values. On the contrary, the paper argues that Husserlian phenomenology necessarily embodies reflection on the epistemic values guiding the sciences. The argument clarifies Husserl’s position by comparing it with the pluralistic position developed (...) in feminist epistemology, according to which sciences may be guided by several competing sets of epistemic values. Further, the existence of alternative epistemic values suggests that choices among such values are social and historically conditioned. Indeed, this is how Husserl’s mature discussion in The Crisis can be understood: his examination of Galileo’s contribution in physics operates as a criticism of the unquestioned dominance of certain set of inherited epistemic values, including the values of accuracy and universal applicability. Indeed, his The Origin of Geometry endorses another set of epistemic values, most importantly that of ontological heterogeneity. Husserl’s analysis demonstrates that the choice of any set of epistemic values is influenced by historical and social factors. Moreover, Husserl argues that we can only avoid biases due to “spells of the time” by continued reflection – Besinnung, in his terms – on the role of values in science. (shrink)

The paper discusses Husserl’s criticism of Frege in Philosophy of Arithmetic (1891) and then his later attitude towards logicism as expressed in Logical Investigations (1900-01). In Philosophy of Arithmetic Husserl holds that logicists offer needless and artificial definitions of notions such as equivalence and number. Frege criticized Husserl’s approach in Philosophy of Arithmetic as psychological, thus shifting the focus of the debate away from logicism. However, Frege’s criticism could be seen to lead Husserl to his later transcendental phenomenological concept of (...) correlation and, with it, to a more developed criticism of logicism. In this regard the division of labor between mathematics and philosophy established in Prolegomena to the Logical Investigations (1900) is central. It implies that in Husserl’s view formal methods fail to shed philosophical insight into the essence of mathematics. In his picture the central notions in need of philosophical clarification are, instead of number and quantity, the notions that are central to abstract structural mathematics. Contrary to Frege who can only elucidate the primitive concepts, Husserl engages in detailed description of their constitution. (shrink)