In metaphysics, nominalism is a philosophical view which denies the
existence of universals and abstract objects, but affirms the
existence of general or abstract terms and predicates. There are at
least two main versions of nominalism. One version denies the
existence of universals – things that can be instantiated or
exemplified by many particular things (e.g., strength, humanity). The
other version specifically denies the existence of abstract objects
– objects that do not exist in space and time.
Most nominalists have held that only physical particulars in space and
time are real, and that universals exist only post res, that is,
subsequent to particular things. However, some versions of
nominalism hold that some particulars are abstract entities (e.g.,
numbers), while others are concrete entities – entities that do
exist in space and time (e.g., pillars, snakes, bananas).
Nominalism is primarily a position on the problem of universals, which
dates back at least to Plato, and is opposed to realist philosophies,
such as Platonic realism, which assert that universals do exist over
and above particulars. However, the name "nominalism" emerged from
debates in medieval philosophy with Roscellinus.
The term 'nominalism' stems from the
Latin nomen, "name". For example,
John Stuart Mill
John Stuart Mill once wrote, that "there is nothing general except
names". In philosophy of law, nominalism finds its application in what
is called constitutional nominalism.
1 The problem of universals
2 Varieties of nominalism
Analytic philosophy and mathematics
5 See also
7 References and further reading
8 External links
The problem of universals
Nominalism arose in reaction to the problem of universals,
specifically accounting for the fact that some things are of the same
type. For example, Fluffy and Kitzler are both cats, or, the fact that
certain properties are repeatable, such as: the grass, the shirt, and
Kermit the Frog are green. One wants to know by virtue of what are
Fluffy and Kitzler both cats, and what makes the grass, the shirt, and
The Platonist answer is that all the green things are green in virtue
of the existence of a universal; a single abstract thing that, in this
case, is a part of all the green things. With respect to the color of
the grass, the shirt and Kermit, one of their parts is identical. In
this respect, the three parts are literally one. Greenness is
repeatable because there is one thing that manifests itself wherever
there are green things.
Nominalism denies the existence of universals. The motivation for this
flows from several concerns, the first one being where they might
Plato famously held, on one interpretation, that there is a
realm of abstract forms or universals apart from the physical world
(see theory of the forms). Particular physical objects merely
exemplify or instantiate the universal. But this raises the question:
Where is this universal realm? One possibility is that it is outside
space and time. A view sympathetic with this possibility holds that,
precisely because some form is immanent in several physical objects,
it must also transcend each of those physical objects; in this way,
the forms are "transcendent" only insofar as they are "immanent" in
many physical objects. In other words, immanence implies
transcendence; they are not opposed to one another. (Nor, in this
view, would there be a separate "world" or "realm" of forms that is
distinct from the physical world, thus shirking much of the worry
about where to locate a "universal realm".) However, naturalists
assert that nothing is outside of space and time. Some Neoplatonists,
such as the pagan philosopher
Plotinus and the Christian philosopher
Augustine, imply (anticipating conceptualism) that universals are
contained within the mind of God. To complicate things, what is the
nature of the instantiation or exemplification relation?
Conceptualists hold a position intermediate between nominalism and
realism, saying that universals exist only within the mind and have no
external or substantial reality.
Moderate realists hold that there is no realm in which universals
exist, but rather universals are located in space and time wherever
they are manifest. Now, recall that a universal, like greenness, is
supposed to be a single thing. Nominalists consider it unusual that
there could be a single thing that exists in multiple places
simultaneously. The realist maintains that all the instances of
greenness are held together by the exemplification relation, but this
relation cannot be explained.
Finally, many philosophers prefer simpler ontologies populated with
only the bare minimum of types of entities, or as
W. V. Quine
W. V. Quine said
"They have a taste for 'desert landscapes.'" They try to express
everything that they want to explain without using universals such as
"catness" or "greenness."
Varieties of nominalism
There are various forms of nominalism ranging from extreme to
almost-realist. One extreme is predicate nominalism, which states that
Fluffy and Kitzler, for example, are both cats simply because the
predicate 'is a cat' applies to both of them. And this is the case for
all similarity of attribute among objects. The main criticism of this
view is that it does not provide a sufficient solution to the problem
of universals. It fails to provide an account of what makes it the
case that a group of things warrant having the same predicate applied
Resemblance nominalists believe that 'cat' applies to both cats
because Fluffy and Kitzler resemble an exemplar cat closely enough to
be classed together with it as members of its kind, or that they
differ from each other (and other cats) quite less than they differ
from other things, and this warrants classing them together. Some
resemblance nominalists will concede that the resemblance relation is
itself a universal, but is the only universal necessary. Others argue
that each resemblance relation is a particular, and is a resemblance
relation simply in virtue of its resemblance to other resemblance
relations. This generates an infinite regress, but many argue that it
is not vicious.
Class nominalism argues that class membership forms the metaphysical
backing for property relationships: two particular blue balls share a
property in that they are both members of classes corresponding to
their properties—that of being blue and being balls. A version of
class nominalism that sees some classes as "natural classes" is held
by Anthony Quinton.
Conceptualism is a philosophical theory that explains universality of
particulars as conceptualized frameworks situated within the thinking
mind. The conceptualist view approaches the metaphysical concept of
universals from a perspective that denies their presence in
particulars outside of the mind's perception of them.
Another form of nominalism is trope theory. A trope is a particular
instance of a property, like the specific greenness of a shirt. One
might argue that there is a primitive, objective resemblance relation
that holds among like tropes. Another route is to argue that all
apparent tropes are constructed out of more primitive tropes and that
the most primitive tropes are the entities of complete physics.
Primitive trope resemblance may thus be accounted for in terms of
causal indiscernibility. Two tropes are exactly resembling if
substituting one for the other would make no difference to the events
in which they are taking part. Varying degrees of resemblance at the
macro level can be explained by varying degrees of resemblance at the
micro level, and micro-level resemblance is explained in terms of
something no less robustly physical than causal power. David
Armstrong, perhaps the most prominent contemporary realist, argues
that such a trope-based variant of nominalism has promise, but holds
that it is unable to account for the laws of nature in the way his
theory of universals can.
Ian Hacking has also argued that much of what is called social
constructionism of science in contemporary times is actually motivated
by an unstated nominalist metaphysical view. For this reason, he
claims, scientists and constructionists tend to "shout past each
Analytic philosophy and mathematics
A notion that philosophy, especially ontology and the philosophy of
mathematics should abstain from set theory owes much to the writings
Nelson Goodman (see especially Goodman 1940 and 1977), who argued
that concrete and abstract entities having no parts, called
individuals exist. Collections of individuals likewise exist, but two
collections having the same individuals are the same collection.
Goodman was himself drawing heavily on the work of Stanisław
Leśniewski, especially his mereology, which was itself a reaction to
the paradoxes associated with Cantorian set theory. Leśniewski denied
the existence of the empty set and held that any singleton was
identical to the individual inside it. Classes corresponding to what
are held to be species or genera are concrete sums of their concrete
constituting individuals. For example, the class of philosophers is
nothing but the sum of all concrete, individual philosophers.
The principle of extensionality in set theory assures us that any
matching pair of curly braces enclosing one or more instances of the
same individuals denote the same set. Hence a, b , b, a , a, b, a,
b are all the same set. For Goodman and other nominalists, a, b is
also identical to a, b , b, a, b , and any combination of
matching curly braces and one or more instances of a and b, as long as
a and b are names of individuals and not of collections of
individuals. Goodman, Richard Milton Martin, and
Willard Quine all
advocated reasoning about collectivities by means of a theory of
virtual sets (see especially Quine 1969), one making possible all
elementary operations on sets except that the universe of a quantified
variable cannot contain any virtual sets.
In the foundation of mathematics, nominalism has come to mean doing
mathematics without assuming that sets in the mathematical sense
exist. In practice, this means that quantified variables may range
over universes of numbers, points, primitive ordered pairs, and other
abstract ontological primitives, but not over sets whose members are
such individuals. To date, only a small fraction of the corpus of
modern mathematics can be rederived in a nominalistic fashion.
Plato was perhaps the first writer in
Western philosophy to
clearly state a non-Nominalist position:
...We customarily hypothesize a single form in connection with each of
the many things to which we apply the same name. ... For example,
there are many beds and tables. ... But there are only two forms of
such furniture, one of the bed and one of the table. (Republic 596a-b,
What about someone who believes in beautiful things, but doesn't
believe in the beautiful itself…? Don't you think he is living in a
dream rather than a wakened state? (Republic 476c)
The Platonic universals corresponding to the names "bed" and
"beautiful" were the Form of the Bed and the Form of the Beautiful, or
the Bed Itself and the Beautiful Itself. Platonic Forms were the first
universals posited as such in philosophy.
Our term "universal" is due to the English translation of Aristotle's
technical term katholou which he coined specially for the purpose of
discussing the problem of universals. Katholou is a contraction of
the phrase kata holou, meaning "on the whole".
Aristotle famously rejected certain aspects of Plato's Theory of
Forms, but he clearly rejected
Nominalism as well:
...'Man', and indeed every general predicate, signifies not an
individual, but some quality, or quantity or relation, or something of
that sort. (
Sophistical Refutations xxii, 178b37, trans.
Nominalism redirects the thesis of nominalism to the highest
level of self actualism whereby all individuals are equal and
collectively creates community actualism where everyone is without
Nominalism is thus categorical but without hierarchy and
leads us in directing thought towards the general idea of the
community rather than the individual (Porter, 2006).
In Alice in Wonderland, the problem of nominalism is presented in an
"When I use a word,"
Humpty Dumpty said, in rather a scornful tone,
"it means just what I choose it to mean – neither more nor less."
"The question is," said Alice, "whether you can make words mean so
many different things."
"The question is," said Humpty Dumpty, "which is to be master –
Critique of the 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
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, and only
gradually became widespread during the fifteenth century. 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.
Aware that explicit thinking in terms of a divide between 'nominalism'
and 'realism' only emerged 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. 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
William of Ockham foreshadowing the
eventual rejection of scholasticism in the seventeenth century.
Critique of nominalist reconstructions in mathematics: A critique of
nominalist reconstructions 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. 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 infinitesimals; the constructivist
re-reconstruction of Weiertrassian 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
Ideas Have Consequences
Problem of universals
School of Names
William of Ockham
^ Mill (1872); Bigelow (1998).
^ Rodriguez-Pereyra (2008) writes: "The word 'Nominalism', as used by
contemporary philosophers in the Anglo-American tradition, is
ambiguous. In one sense, its most traditional sense deriving from the
Middle Ages, it implies the rejection of universals. In another, more
modern but equally entrenched sense, it implies the rejection of
abstract objects" (§1).
^ Feibleman (1962), p. 211.
^ An overview of the philosophical problems and an application of the
concept to a case of the Supreme Court of the State of California,
gives Thomas Kupka, 'Verfassungsnominalismus', in: Archives for
Philosophy of Law and Social
Philosophy 97 (2011), 44-77, pdf also on
^ MacLeod & Rubenstein (2006), §3a.
^ MacLeod & Rubenstein (2006), §3b.
^ See, for example, H. H. Price (1953).
^ Quinton, Anthony (1957). "Properties and Classes". Proceedings of
the Aristotelian Society. 58: 33–58. JSTOR 4544588.
^ Strawson, P. F. "Conceptualism." Universals, concepts and qualities:
new essays on the meaning of predicates. Ashgate Publishing, 2006.
^ "Conceptualism." The Oxford Dictionary of Philosophy. Simon
Blackburn. Oxford University Press, 1996. Oxford Reference Online.
Oxford University Press. 8 April 2008.
^ Hacking (1999), pp. 80-84.
^ a b Penner (1987), p. 24.
^ Peters (1967), p. 100.
^ "katholou" in Harvard's Archimedes Project online version of Liddell
& Scott's A Greek-English Lexicon.
^ Caroll, Lewis. (2000). The Annotated Alice: Alice's Adventures in
Wonderland & Through the Looking Glass, p. 213; Young, Laurence
Chisholm. (1980). Lecture on the Calculus of Variations and Optimal
Control Theory, p. 160.
^ The classic starting point of nominalism has been the edict issued
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
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.
^ For example, when
Jerome of Prague
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
University of Cologne
University of Cologne which 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.
^ a b See Robert Pasnau, Metaphysical Themes, 1274-1671, (New York:
OUP, 2011), p84.
^ See Robert Pasnau, Metaphysical Themes, 1274-1671, (New York: OUP,
^ Usadi Katz, Karin; Katz, Mikhail G. (2011). "A Burgessian Critique
of Nominalistic Tendencies in Contemporary Mathematics and its
Historiography". Foundations of Science. arXiv:1104.0375 .
References and further reading
Adams, Marilyn McCord.
William of Ockham
William of Ockham (2 volumes) Notre Dame, IN:
Notre Dame University Press, 1987.
American Heritage Dictionary of the English Language, Fourth Edition,
Borges, Jorge Luis
Borges, Jorge Luis (1960). "De las alegorías a las novelas" in Otras
inquisiciones (pg 153-56).
Burgess, John (1983). Why I am not a nominalist. Notre Dame J. Formal
Logic 24, no. 1, 93–105.
Burgess, John & Rosen, Gideon. (1997). A Subject with no Object.
Princeton University Press.
Courtenay, William J. Adam Wodeham: An Introduction to His Life and
Writings, Leiden: E. J. Brill, 1978.
Feibleman, James K. (1962). "Nominalism" in Dictionary of Philosophy,
Dagobert D. Runes (ed.). Totowa, NJ: Littlefield, Adams, & Co.
Goodman, Nelson (1977) The Structure of Appearance, 3rd ed. Kluwer.
Hacking, Ian (1999). The Social Construction of What?, Harvard
Karin Usadi Katz and Mikhail G. Katz (2011) A Burgessian Critique of
Nominalistic Tendencies in Contemporary Mathematics and its
Historiography. Foundations of Science. doi:10.1007/s10699-011-9223-1
Mill, J. S., (1872). An Examination of William Hamilton's Philosophy,
4th ed., Chapter XVII.
Oberman, Heiko. The Harvest of Medieval Theology:
Gabriel Biel and
Late Medieval Nominalism, Grand Rapids, MI: Baker Academic, 2001.
Penner, T. (1987). The Ascent from Nominalism, D. Reidel Publishing.
Peters, F. (1967). Greek Philosophical Terms, New York University
Porter, R. (2006). The Health
Ethics Typology: Six Domains to Improve
Care. Socratic Publishing. ISBN 0-9786699-0-8
Price, H. H. (1953). "Universals and Resemblance", Ch. 1 of Thinking
and Experience, Hutchinson's University Library.
Quine, W. V. O. (1961). "On What There is," in From a Logical Point of
View, 2nd/ed. N.Y: Harper and Row.
Quine, W. V. O. (1969). Set Theory and Its Logic, 2nd ed. Harvard
University Press. (Ch. 1 includes the classic treatment of virtual
sets and relations, a nominalist alternative to set theory.)
Robson, John Adam,
Wyclif and the Oxford Schools: The Relation of the
"Summa de Ente" to Scholastic Debates at Oxford in the Late Fourteenth
Century, Cambridge, England: Cambridge University Press, 1961.
Utz, Richard, "Literary Nominalism." Oxford Dictionary of the Middle
Ages. Ed. Robert E. Bjork. Oxford: Oxford University Press, 2010. Vol.
III, p. 1000.
Russell, Bertrand (1912). "The World of Universals," in The Problems
of Philosophy, Oxford University Press.
Williams, D. C. (1953). "On the Elements of Being: I", Review of
Metaphysics, vol. 17, pp. 3–18.
Wikisource has the text of the 1905 New International Encyclopedia
Rodriguez-Pereyra, Gonzalo. "
Nominalism in Metaphysics". In Zalta,
Edward N. Stanford Encyclopedia of Philosophy.
Maurin, Anna-Sofia. "Tropes". In Zalta, Edward N. Stanford
Encyclopedia of Philosophy.
Universals entry by Mary C. MacLeod and Eric M. Rubenstein in the
Internet Encyclopedia of Philosophy
Klima, Gyula. "The Medieval Problem of Universals". In Zalta, Edward
N. Stanford Encyclopedia of Philosophy.
Nominalism, Realism, Conceptualism, from The Catholic Encyclopedia.
Nominalism Reconsidered in The Oxford Handbook of
Philosophy of Mathematics and
Nominalism and the Literary Questions: Selected Studies by
Richard Utz, with the assistance of Terry Barakat Perspicuitas, (2004)
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