Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction


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.ion 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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DOI 10.1007/s10838-014-9239-7
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References found in this work BETA

Abstract Objects.Bob Hale - 1988 - Blackwell.
Introduction to Phenomenology.Robert Sokolowski - 1999 - Cambridge University Press.
Grundlagen der Arithmetik.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner.

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