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- Øystein Linnebo (2009). Bad Company Tamed. Synthese 170 (3).The neo-Fregean project of basing mathematics on abstraction principles faces “the bad company problem,” namely that a great variety of unacceptable abstraction principles are mixed in among the acceptable ones. In this paper I propose a new solution to the problem, based on the idea that individuation must take the form of a well-founded process. A surprising aspect of this solution is that every form of abstraction on concepts is permissible and that paradox is instead avoided by restricting what concepts there are.In my reading list | Discuss this article | Edit | Categorize |My bibliography
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Neo-Fregean logicism seeks to base mathematics on abstraction principles. But the acceptable abstraction principles are surrounded by unacceptable (indeed often paradoxical) ones. This is the “bad company problem.” In this introduction I first provide a brief historical overview of the problem. Then I outline the main responses that are currently being debated. In the course of doing so I provide summaries of the contributions to this special issue.
