Mathematical Aspects of Similarity and Quasi-analysis - Order, Topology, and Sheaves

Abstract

The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many empirical sciences can hardly be denied. The aim of this paper is to show that Quine’s and Goodman’s harsh verdicts about this notion are mistaken. The concept of similarity is susceptible to a precise logico-mathematical analysis through which its place in the conceptual landscape of modern mathematical theories such as order theory, topology, and graph theory becomes visible. Thereby it can be shown that a quasi-analysis of a similarity structure S can be conceived of as a sheaf (etale space) over S.

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

In search of radical similarity.Oscar Vilarroya - 2005 - Behavioral and Brain Sciences 28 (1):35-35.
Evolution.Robert N. Brandon - 1978 - Philosophy of Science 45 (1):96-109.
Similarity and cotenability.Vladan Djordjevic - 2013 - Synthese 190 (4):681-691.
The Creation of Similarity: A Discussion of Metaphor in Light of Tversky's Theory of Similarity.Eva Feder Kittay - 1982 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:394 - 405.

Analytics

Added to PP
2013-12-24

Downloads
546 (#29,665)

6 months
84 (#45,321)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Thomas Mormann
Ludwig Maximilians Universität, München (PhD)

Citations of this work

No citations found.

Add more citations

References found in this work

Features of similarity.Amos Tversky - 1977 - Psychological Review 84 (4):327-352.
Problems and projects.Nelson Goodman (ed.) - 1972 - Indianapolis,: Bobbs-Merrill.
Conceptual Spaces: The Geometry of Thought.Peter Gärdenfors - 2000 - Tijdschrift Voor Filosofie 64 (1):180-181.
Category Theory.S. Awodey - 2007 - Bulletin of Symbolic Logic 13 (3):371-372.
Similarity After Goodman.Lieven Decock & Igor Douven - 2011 - Review of Philosophy and Psychology 2 (1):61-75.

View all 15 references / Add more references