Titel
What are Implicit Definitions?
Autor*in
Eduardo N. Giovannini
CONICET and Universidad Nacional del Litoral
Abstract
The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely (1) as specifications of the meaning of the primitive terms of a theory and (2) as definitions of higher-order mathematical concepts or structures. We analyze these two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning.
Stichwort
Modern mathematicsFormal axiomaticsImplicit definitionsStructural definitionsModel-theoretic semanticsInferential semantics
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Erkenntnis
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2019
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2019
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