Abstraction Relations Need Not Be Reflexive | Zendy

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Abstraction Relations Need Not Be Reflexive

Author(s) -

Payne Jonathan

Publication year - 2013

Publication title -

thought: a journal of philosophy

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.429

H-Index - 8

ISSN - 2161-2234

DOI - 10.1002/tht3.82

Subject(s) - reflexivity , abstraction , transitive relation , equivalence relation , relation (database) , computer science , equivalence (formal languages) , wright , epistemology , mathematics , algebra over a field , pure mathematics , programming language , sociology , philosophy , social science , combinatorics , data mining

Neo‐Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non‐reflexive abstraction relations to restricted abstraction principles.

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