Himelright, Jack, 2023, “A Lewisian Argument Against Platonism, or Why Theses About Abstract Objects Are Unintelligible,” Erkenntnis, 88(7): 3037–3057. doi:10.1007/s10670-021-00489-4.x
However, there are deflationist proposals that run counter to Carnap’s approach, among them, deflationary nominalism (Azzouni 2010) or agnosticism about abstract objects (Bueno 2008a, 2008b, 2020). Additionally, philosophers inspired by Frege’s work have argued for a minimal notion of an object (Rayo 2013, Rayo 2020 [Other Internet Resources]; and Linnebo 2018).
For example, Benacerraf concluded that “numbers are not objects at all, because in giving the properties (that is, necessary and sufficient) of numbers you merely characterize an abstract structure—and the distinction lies in the fact that the ‘elements’ of the structure have no properties other than those relating them to other ‘elements’ of the same structure” (1965, 70).
Though attempts have been made to investigate abstraction principles for sets (Cook 2003), it remains an open question whether something like the mathematical concept of a set can be characterized by a suitably restricted abstraction principle. (See Burgess 2005 for a survey of recent efforts in this direction.)
Our focus will be on individual human action. Readers interested in joint action should consult Roth (2017) and Schweikard and Schmid (2021). We similarly defer on the topic of free will to O’Connor and Franklin (2022).
surprising scientific results continue to challenge commonly held views in philosophy of action (see e.g. Wegner 2002 and Nahmias 2014 for critical discussion of recent findings).