On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture

Bulletin of Symbolic Logic 19 (3):351-393 (2013)
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Abstract

In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the 20th century.

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10.1017/s1079898600010684

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Juliette Kennedy
University of Helsinki

Citations of this work

Epistemic Modality and Hyperintensionality in Mathematics.Timothy Bowen - 2017 - Dissertation, Arché, University of St Andrews

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References found in this work

Varieties of presence.Alva Noë - 2012 - Cambridge, Mass.: Harvard University Press.
Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.

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