What is wrong with abstraction’, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their ‘Hale on Caesar’ and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are: To get the character of this objection into sharper focus; To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and (...) about the effects of impredicativity in abstraction principles—which underlie it; and To advance the debate of the issues thereby raised. Thanks for helpful comments to Roy Cook and to an anonymous referee. CiteULike Connotea Del.icio.us What's this? (shrink)

This paper is an exploration of the prospects of rationalist, concept-based epistemologies of modality as far as essentialist and de re modal claims are concerned. I grant certain explanatory power to such epistemologies but, primarily, I identify their limitations. I first explore them in view of the (possible) existence of general as well as of singular modally loaded concepts and find their explanatory scope severely limited. Inspired by the abstractionist's concept-and-entitlement based hybrid model, the paper then explores a similarly hybrid (...) strategy. The outcome of this exploration is that, regardless of its explanatory scope, it would be a misnomer to describe such hybrid view as concept-based. The result generalizes. (shrink)