What are Implicit Definitions?

GIOVANNINI, EDUARDO N.; SCHIEMER, GEORG

ERKENNTNIS

Springer

Lugar: Munich; Año: 2021 vol. 86 p. 1661 - 1691

0165-0106

[Published 08 November 2019] 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.