Abstract
The article presents an overview of the basic ideas of the philosophy of mathematics of C. Wright and B. Hale. The purpose of the article is to characterize one of the main problems of this direction – Bad Company Objection. The author analyzes the main idea of Wright and Hale that the fundamental laws of arithmetic can be derived in the system of second-order logic plus principles of abstraction (Hume's Principle) and analyzes the critics of neologicism, based on the Bad Company Objection. The author makes conclusions characterizing the Bad Company Objection and emphasizing that the success of the program of the philosophy of mathematics of neo-logicism depends on adoption of the problematic ideas and assumptions. However, the project of Wright and Hale is the source of many interesting ideas in contemporary philosophy of mathematics.
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