Editing Nominalism (section)

===Nominalist reconstructions in mathematics===
A critique of nominalist reconstructions{{clarification needed|date=January 2023}} in mathematics was undertaken by Burgess (1983) and Burgess and Rosen (1997). Burgess distinguished two types of nominalist reconstructions.  Thus, ''hermeneutic nominalism'' is the hypothesis that science, properly interpreted, already dispenses with mathematical objects (entities) such as numbers and sets.  Meanwhile, ''revolutionary nominalism'' is the project of replacing current scientific theories by alternatives dispensing with mathematical objects (see Burgess, 1983, p.&nbsp;96).  A recent study extends the Burgessian critique to three nominalistic reconstructions: the reconstruction of analysis by [[Georg Cantor]], [[Richard Dedekind]], and [[Karl Weierstrass]] that dispensed with [[infinitesimal]]s; the [[constructivism (mathematics)|constructivist]] re-reconstruction of Weierstrassian analysis by [[Errett Bishop]] that dispensed with the [[law of excluded middle]]; and the hermeneutic reconstruction, by [[Carl Boyer]], [[Judith Grabiner]], and others, of [[Cauchy]]'s foundational contribution to analysis that dispensed with Cauchy's infinitesimals.<ref>{{cite journal | last1 = Usadi Katz | first1 = Karin | author-link2 = Mikhail Katz | last2 = Katz | first2 = Mikhail G. | year = 2011 | title = A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography | journal = [[Foundations of Science]] | volume = 17 | pages = 51–89 | doi = 10.1007/s10699-011-9223-1 | arxiv = 1104.0375 | s2cid = 119250310 }}</ref>