TY - JOUR
T1 - What we talk about when we talk about numbers
AU - Pettigrew, Richard
PY - 2018/12
Y1 - 2018/12
N2 - In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki, and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.
AB - In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki, and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.
KW - Foundations of mathematics
KW - Mathematical structuralism
KW - Nominalism
KW - Philosophy of mathematics
KW - Set-theoretic foundations
UR - http://www.scopus.com/inward/record.url?scp=85051138078&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2018.08.009
DO - 10.1016/j.apal.2018.08.009
M3 - Article
VL - 169
SP - 1437
EP - 1456
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
SN - 0168-0072
IS - 12
ER -