This chapter situates both the nominalist and neo-Carnapian approaches to mathematics introduced in Chapter 10 with particular reference to Logicism and Structuralism.

This chapter notes how the potentialist set theory advocated in previous chapters can be naturally extended to a larger philosophy of mathematics, either in a nominalist or a neo-carnapian fashion.

This chapter concludes the book and highlights certain questions for future study.

This chapter discusses challenges to the broadly neo-Carnapian philosophy of language invoked above concerning how to state it without paradox and evaluating metasemantic answers to access worries.

This chapter advocates and defends a broadly neo-Carnapian approach to the philosophy of mathematics more broadly.This approach combines potentialist set theory with platonism about non-set theoretic mathematical objects.

How ontologically committal is common sense? Is the common-sense philosopher beholden to a florid ontology in which all manner of objects, substances, and processes exist and are as they appear to be to common sense, or can she remain neutral on questions about the existence and nature of many things because common sense is largely non-committal? This chapter explores and tentatively evaluates three different approaches to answering these questions. The first applies standard accounts of ontological commitment to common-sense claims. This leads to the surprising and counter-intuitive result that common sense has metaphysically heavyweight commitments. The second approach emphasizes the superficiality and locality of common-sense claims. On this approach, however, common sense comes out as almost entirely non-committal. The third approach questions the seriousness of ontological commitment as such. If ontological commitment is cheap, it becomes possible both to accept the commitments of common sense at face value and to avoid the counter-intuitive consequences of heavyweight metaphysical commitments.