Studia Logica

TitleNeologicist nominalism
Publication TypeJournal Article
Year of Publication2010
AuthorsUrbaniak, R
JournalStudia Logica
Volume96
Number2
Pagination149-173
Abstract

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those difficulties while still being able to put abstraction principles to a foundational use.

DOI10.1007/s11225-010-9279-x
Citation KeyUrbaniak2010