Review of Symbolic Logic 9 (2): 238-250 (2016)

Authors
Benedikt Löwe
University of Amsterdam
Luca Incurvati
University of Amsterdam
Abstract
Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy's definition. We look at Maddy's formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy's original notion, but fixes the issues raised by Hamkins. Our work brings to light additional structural issues that we also discuss.
Keywords Restrictiveness  Interpretations  Set theory  Mathematical naturalism
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Reprint years 2016
DOI 10.1017/s1755020316000058
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References found in this work BETA

Believing the Axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
Quasi Finitely Axiomatizable Totally Categorical Theories.Gisela Ahlbrandt & Martin Ziegler - 1986 - Annals of Pure and Applied Logic 30 (1):63-82.
Undecidable Theories.Martin Davis - 1959 - Journal of Symbolic Logic 24 (2):167-169.
A Second Glance at Non-Restrictiveness.B. Lowe - 2003 - Philosophia Mathematica 11 (3):323-331.
A First Glance at Non-Restrictivenesst.Benedikt Löwe - 2001 - Philosophia Mathematica 9 (3):347-354.

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Citations of this work BETA

Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.

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