Journal for General Philosophy of Science

, Volume 45, Issue 1, pp 35–47 | Cite as

Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction

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Abstract

This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege. Abstraction principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account should be construed as putting emphasis on intentionality of human mind towards certain invariant features of the elements of initial domains of discourse that are involved in equivalence relations. Definition of terms like direction, shape, number etc. is achieved by a kind of transformation of those invariants into ideal objects that is involved in intuition. Then the paper argues that at the period of 1926 Weyl’s writings on implicit definitions, he is inclined to endorse symbolic construction as a way to explicate the objectivity of certain processes as those that are carried out in case of implicit definitions.

Keywords

Definition Equivalence relation Intentionality Invariant Intuition Ideal object 
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Notes

Acknowledgments

This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALIS-UOA-Aspects and Prospects of Realism in the Philosophy of Science and Mathematics (APRePoSMa). I thank three anonymous reviewers too for their comments that were very helpful for improvement of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.University of PatrasPatrasGreece
  2. 2.University of AthensAthensGreece

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