Editing Nominalism (section)

==Criticisms==
===Historical origins of the term===
As a category of late medieval thought, the concept of 'nominalism' has been increasingly queried. Traditionally, the fourteenth century has been regarded as the heyday of nominalism, with figures such as [[John Buridan]] and [[William of Ockham]] viewed as founding figures. However, the concept of 'nominalism' as a movement (generally contrasted with 'realism'), first emerged only in the late fourteenth century,<ref>The classic starting point of nominalism has been the edict issued by [[Louis XI]] in 1474 commanding that realism alone (as contained in scholars such as [[Averroes]], [[Albert the Great]], [[Aquinas]], [[Duns Scotus]] and [[Bonaventure]]) be taught at the University of Paris, and ordering that the books of various 'renovating scholars', including Ockham, [[Gregory of Rimini]], Buridan and [[Peter of Ailly]] be removed. The edict used the word 'nominalist' to describe those students at Paris who 'are not afraid to imitate' the renovators. These students then made a reply to Louis XI, defending nominalism as a movement going back to Ockham, which had been persecuted repeatedly, but which in fact represents the truer philosophy.  See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p. 85.</ref> and only gradually became widespread during the fifteenth century.<ref>For example, when [[Jerome of Prague]] visited the [[University of Heidelberg]] in 1406, he described the nominalists as those who deny the reality of universals outside the human mind, and realists as those who affirm that reality. Also, for instance, in a 1425 document from the [[University of Cologne]] that draws a distinction between the via of Thomas Aquinas, Albert the Great, and the via of the 'modern masters' John Buridan and Marsilius of Inghen. See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p84.</ref> The notion of two distinct ways, a ''via antiqua'', associated with realism, and a ''via moderna'', associated with nominalism, became widespread only in the later fifteenth century – a dispute which eventually dried up in the sixteenth century.<ref name="See Robert Pasnau 2011 p84">See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p84.</ref>

Aware that explicit thinking in terms of a divide between 'nominalism' and 'realism’ emerged only in the fifteenth century, scholars have increasingly questioned whether a fourteenth-century school of nominalism can really be said to have existed. While one might speak of family resemblances between Ockham, Buridan, Marsilius and others, there are also striking differences. More fundamentally, Robert Pasnau has questioned whether any kind of coherent body of thought that could be called 'nominalism' can be discerned in fourteenth century writing.<ref>See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p86.</ref> This makes it difficult, it has been argued, to follow the twentieth century narrative which portrayed late scholastic philosophy as a dispute which emerged in the fourteenth century between the ''via moderna'', nominalism, and the ''via antiqua'', realism, with the nominalist ideas of [[William of Ockham]] foreshadowing the eventual rejection of scholasticism in the seventeenth century.<ref name="See Robert Pasnau 2011 p84"/>

===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>