Online research in philosophy

Gödel’s philosophical rationalism includes a program for “developing philosophy as an exact science.” Gödel believes that Husserl’s phenomenology is essential for the realization of this program. In this article, by analyzing Gödel’s philosophy of idealism, conceptual realism, and his concept of “abstract intuition,” based on clues from Gödel’s manuscripts, I try to investigate the reasons why Gödel is strongly interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. One of the topics that has attracted much attention recently is the development of Gödel’s philosophical thoughts and its connection with other philosophical ideas. For instance, some scholars are searching for the possible connections between Gödel’s philosophy and Husserl’s phenomenology and examining if there is any solid evidence of Husserl’s influence on Gödel from Gödel’s works (Tieszen, Bull Symbolic Logic 4(2):181–203, 1998; Huaser, Bull Symbolic Logic 12(4):529–588, 2006). Why is Gödel’ s interested in Husserl? How should this turn to Husserl be interpreted? Is it a dismissal of Leibnizian philosophy, or a different way to achieve similar goals? Way did Gödel turn specifically to Husserl’s transcendental idealism? (Van Atten and Kennedy, Bull Symbolic Logic 9(4):425–476, 2003) I believe, the reason is that Gödel has a valuable program for “developing philosophy as an exact science” and he believes that Husserl’s phenomenology is relevant to the realization of this program. So far there are no sufficient evidence to show that there is a direct inheritance relation between Gödel’s and Husserl’s thoughts. However, from the clues in Gödel’s idealistic philosophy, conceptual realism, and his concept of “abstract intuition,” we can perhaps explore some similarities between his thoughts and Husserl’s thoughts, and analyze the reason why Gödel is interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished.

In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in "Das Kontinuum". I try to establish how much of the underlying motivation for Weyl's position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl's philosophical ideas in connexion with the work of Husserl, in particular "Logische Untersuchungen" and "Ideen I". I believe that this interpretation of Weyl can clarify the views on mathematical existence and mathematical intuition which are implicit in "Das Kontinuum".

In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in Das Kontinuum. I try to establish how much of the underlying motivation for Weyl''s position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl''s philosophical ideas in connexion with the work of Husserl, in particular Logische Untersuchungen} and Ideen .I believe that this interpretation of Weyl can clarify the views on mathematical existence and mathematical intuition which are implicit in Das Kontinuum.

Husserl is well known for his critique of the “mathematizing tendencies” of modern science, and is particularly emphatic that mathematics and phenomenology are distinct and in some sense incompatible. But Husserl himself uses mathematical methods in phenomenology. In the first half of the paper I give a detailed analysis of this tension, showing how those Husserlian doctrines which seem to speak against application of mathematics to phenomenology do not in fact do so. In the second half of the paper I focus on a particular example of Husserl’s “mathematized phenomenology”: his use of concepts from what is today called dynamical systems theory.

The critique of psychologism -- Phenomenology and other 'eidetic sciences' -- Phenomenology and transcendental philosophy -- The transcendental reduction -- The structure of intentionality -- Intuition, evidence, and truth -- Categorial intuition and ideation (eidetic seeing) -- Time-consciousness -- The ego and selfhood -- Intersubjectivity -- The crisis of the sciences and the idea of the 'lifeworld' -- Conclusion: mastering Husserl.

Introduction: Husserl (1859-1938) -- An introduction to Husserl's ideas I -- Husserl's ideas II: analyses and problems -- A study of Husserl's Cartesian meditations, I-IV -- Husserl's Fifth Cartesian meditation -- Husserl and the sense of history -- Kant and Husserl -- Existential phenomenology -- Methods and tasks of a phenomenology of the will.

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.

In this landmark study, Emmanuel Levinas discusses the aspects and function of intuition in Husserl's thought and its meaning for philosophical self-reflection.

Godel began to seriously study Husserl's phenomenology in 1959, and the Godel Nachlass is known to contain many notes on Husserl. In this paper I describe what is presently known about Godel's interest in phenomenology. Among other things, it appears that the 1963 supplement to "What is Cantor's Continuum Hypothesis?", which contains Godel's famous views on mathematical intuition, may have been influenced by Husserl. I then show how Godel's views on mathematical intuition and objectivity can be readily interpreted in a phenomenological theory of intuition and mathematical knowledge.