Projects per year
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 higherorder 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 modeltheoretic and inferential accounts of meaning.
Original language  English 

Pages (fromto)  16611691 
Number of pages  31 
Journal  Erkenntnis: an international journal of analytic philosophy 
Volume  86 
Issue number  6 
DOIs  
Publication status  Published  Dec 2021 
Austrian Fields of Science 2012
 603113 Philosophy
Keywords
 FREGE
 Formal axiomatics
 HILBERT
 Implicit definitions
 Inferential semantics
 Modeltheoretic semantics
 Modern mathematics
 Structural definitions
Projects
 1 Finished

Structuralism: The Roots of Mathematical Structuralism
Schiemer, G. & Kolowrat, F.
1/03/17 → 28/02/22
Project: Research funding