Bad company tamed
type: Item
instance of: scholarly article
title: Bad company tamed
zbMATH Open document ID: 1180.03007
author: Øystein Linnebo
published in: Synthese
publication date: 2009-11-04T00:00:00Z
review text: The ``bad company problem'' is a problem plaguing the neo-Fregean project of basing mathematics on abstraction principles. Given the centrality of Hume's Principle (HP) in the foundation of the natural numbers, neo-Fregeans are interested in a broader class of abstraction principles that bear a formal resemblance to HP. However, not all such abstraction principles are acceptable, several of them, the ``bad companions'' of HP, leading to paradoxes, such as Russell's or Burali-Forti's paradox. With the aim of drawing ``a mathematically informative and philosophically well-motivated line between the acceptable abstraction principles and the unacceptable ones'', the author develops ``the idea of individuation as a well-founded process in a modal framework'' and introduces ``a natural and plausible restriction on the individuation of concepts'' which creates ``a safe environment for abstraction, where what used to be the bad companions now re-emerge as perfectly good ones.''
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 5625299
zbMATH Keywords: Hume's Principle
zbMATH Keywords: bad company problem
zbMATH Keywords: abstraction
zbMATH Keywords: Frege
zbMATH Keywords: logicism
zbMATH Keywords: neo-Fregeanism
zbMATH Keywords: paradox
MaRDI profile type: Publication
full work available at URL: s11229-007-9265-7
OpenAlex ID: W1990098392
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DOI: 10.1007/S11229-007-9265-7
description: scientific article; zbMATH DE number 5625299