Bad company tamed
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.''
scientific article; zbMATH DE number 5625299