Carnapian neo-Fregeanism and the bad company objection

Hume’s Principle, which is the principle on which neo-Fregeans wish to build arithmetic, is an abstraction principle. Many abstraction principles are unacceptable to the neo-Fregean, for instance because they are inconsistent or because they are inconsistent together with Hume’s Principle. What differentiates Hume’s Principle from these unacceptable abstraction principles? This question, which captures the so-called bad company objection, has proved difficult to answer and continues to plague the neo-Fregean programme. In this paper, I draw on the philosophy of Rudolf Carnap to develop a Carnapian neo-Fregeanism. I show how the Carnapian neo-Fregean can deal relatively straightforwardly with the bad company objection. I also consider why a Carnapian should be attracted to the neo-Fregean programme and, finally, argue that some of the pressing problems which have developed from the bad company objection are no issue for the Carnapian neo-Fregean.