Some Criteria for Acceptable Abstraction

Notre Dame Journal of Formal Logic 52 (3):331-338 (2011)
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Abstract

Which abstraction principles are acceptable? A variety of criteria have been proposed, in particular irenicity, stability, conservativeness, and unboundedness. This note charts their logical relations. This answers some open questions and corrects some old answers

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10.1215/00294527-1435492

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Øystein Linnebo
University of Oslo

Citations of this work

Cardinality and Acceptable Abstraction.Roy T. Cook & Øystein Linnebo - 2018 - Notre Dame Journal of Formal Logic 59 (1):61-74.
Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.
Collective Abstraction.Jon Erling Litland - 2022 - Philosophical Review 131 (4):453-497.
Two-Sorted Frege Arithmetic is Not Conservative.Stephen Mackereth & Jeremy Avigad - 2022 - Review of Symbolic Logic 16 (4):1199-1232.
Conservativeness, Stability, and Abstraction.Roy T. Cook - 2012 - British Journal for the Philosophy of Science 63 (3):673-696.

View all 15 citations / Add more citations

References found in this work

Frege meets dedekind: A neologicist treatment of real analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.
Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
Conservativeness, Stability, and Abstraction.Roy T. Cook - 2012 - British Journal for the Philosophy of Science 63 (3):673-696.
Which abstraction principles are acceptable? Some limitative results.Øystein Linnebo & Gabriel Uzquiano - 2009 - British Journal for the Philosophy of Science 60 (2):239-252.

View all 8 references / Add more references