On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundation of Number Concepts

Linnebo in 2018 argues that abstract objects like numbers are “thin” because they only required to be referents of singular terms abstraction principles, such as Hume's principle. As the specification existence claims made by analytic truths (the principles), their does not make any substantial demands world; however, notes, there is a potential counter-argument concerning infinite regress against introducing this way. Against this, he vicious avoided account arithmetic based on principle we specifying concept equinumerosity, or its ordinal equivalent. But far from being matter for philosophy, implies distinct empirical prediction: cognitive development, equinumerosity primary number concepts. However, analysing and expanding bootstrapping theory Carey 2009, I argue paper good reasons think development could other way around: possessing numerosity concepts may precede grasping equinumerosity. propose analysis early numerical cognition can also help us understand what thin like, moving away Platonist interpretations.