NDLI: Towards completeness: Husserl on theories of manifolds 1890

Content Provider	Springer Nature Link
Author	Hartimo, Mirja Helena
Copyright Year	2007
Abstract	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.
Starting Page	281
Ending Page	310
Page Count	30
File Format	PDF
ISSN	00397857
Journal	Synthese
Volume Number	156
Issue Number	2
e-ISSN	15730964
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2007-01-31
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Early Husserl Definiteness Completeness Theories of manifolds Philosophy of Language Metaphysics Epistemology Logic Philosophy
Content Type	Text
Resource Type	Article
Subject	Philosophy Social Sciences

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