Nominalism

In metaphysics, nominalism posits that universals and abstract objects do not possess actual existence, instead existing solely as names or labels. This philosophical stance encompasses two primary interpretations. One perspective refutes the actual existence of universals, defined as properties or attributes (e.g., strength, humanity) that can be instantiated or exemplified by multiple distinct entities. The alternative interpretation specifically rejects the reality of abstract objects as such, which are entities not situated within spatiotemporal dimensions.

A prevalent view among nominalists posits that only physical particulars existing within space and time possess genuine reality, with universals existing merely post res, or subsequent to specific entities. Nevertheless, certain nominalist interpretations acknowledge that some particulars constitute abstract entities (e.g., numbers), while others are concrete entities, meaning they occupy space and time (e.g., pillars, snakes, bananas). Fundamentally, nominalism addresses the philosophical problem of universals. This perspective contrasts sharply with realist philosophies, such as Platonic realism, which contend that universals exist independently of and prior to particulars, and with Aristotle's hylomorphic substance theory, which maintains that universals are immanently real within particulars. The term "nominalism" itself originated from medieval philosophical discussions involving Roscellinus.

The etymology of the term nominalism traces to the Latin word nomen, signifying 'name'. John Stuart Mill encapsulated the essence of nominalism with his aphorism: "there is nothing general except names". Within the philosophy of law, nominalist principles are applied in the concept known as constitutional nominalism.

History

Ancient Greek philosophy

Plato is arguably the earliest figure in Western philosophy to articulate a distinctly realist, and thus non-nominalist, philosophical stance:

... 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, translated by Grube)

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 associated with the terms "bed" and "beautiful" were conceptualized as the Form of the Bed and the Form of the Beautiful, alternatively referred to as the Bed Itself and the Beautiful Itself. These Platonic Forms represent the initial philosophical postulation of universals in their own right.

The contemporary philosophical term "universal" derives from the English translation of Aristotle's specialized term katholou, which he specifically devised to address the problem of universals. The word katholou itself is a contraction of the Greek phrase kata holou, which translates to "on the whole".

While Aristotle is renowned for his critique of specific elements within Plato's Theory of Forms, he also unequivocally dismissed nominalism:

... '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, translated by Pickard-Cambridge)

The Stoics, particularly Chrysippus, are recognized as the earliest philosophers to articulate explicit nominalist arguments.

Medieval philosophy

In medieval philosophy, Roscellinus (c. 1050 – c. 1125), a French philosopher and theologian, emerged as an early and prominent advocate of nominalism. Nominalist tenets were subsequently explored in the works of Peter Abelard and reached their zenith with William of Ockham, who is recognized as the most influential and comprehensive nominalist. The specific iteration of nominalism advanced by Abelard and Ockham is occasionally termed conceptualism, which positions itself as an intermediate stance between nominalism and realism. This perspective posits that while a commonality is shared among similar individuals, this commonality exists as a mental concept rather than an independently existing real entity. Ockham contended that only individual entities possess existence, and universals merely constitute mental constructs for categorizing sets of individuals. He articulated this view, stating, "I maintain that a universal is not something real that exists in a subject... but that it has a being only as a thought-object in the mind [objectivum in anima]." Consistently, Ockham advocated against positing any entities not essential for explanatory purposes. Consequently, he argued that there is no justification for believing in an entity such as "humanity" residing within, for instance, Socrates, as such a claim provides no further explanatory power. This aligns with the analytical methodology subsequently known as Ockham's razor, a principle asserting that explanations for any phenomenon should rely on the fewest possible assumptions. Critics, however, contend that conceptualist approaches address only the psychological dimension of universals. If a concept is correctly and non-arbitrarily applied to two distinct individuals, an underlying resemblance or shared property must exist between them to justify their categorization under the same concept. This, critics argue, constitutes the very metaphysical problem that universals were introduced to resolve, representing the fundamental issue at stake (MacLeod & Rubenstein, 2006, §3d). Thus, if resemblances between individuals are affirmed, conceptualism converges with moderate realism; if denied, it devolves into nominalism.

Modern and Contemporary Philosophical Perspectives

During the modern philosophical era, nominalism experienced a resurgence through the contributions of Thomas Hobbes and Pierre Gassendi.

Within contemporary analytic philosophy, Rudolf Carnap, Nelson Goodman, H. H. Price, and D. C. Williams have notably championed nominalist positions.

Recent scholarship has increasingly investigated the potential influence of nominalism on the conceptualization of modernity and contemporaneity. Michael Allen Gillespie, for instance, posits that nominalism exerted a profound impact on these two historical periods. He contends that despite their secular character, modernity and contemporaneity possess roots firmly embedded in the sacred. Gillespie further asserts, "Nominalism turned this world on its head," explaining that "For the nominalists, all real being was individual or particular and universals were thus mere fictions."

Victor Bruno, another scholar, echoes this perspective, suggesting that nominalism represents one of the earliest indicators of a fundamental rupture within the medieval system. Bruno elaborates, stating, "The dismembering of the particulars, the dangerous attribution to individuals to a status of totalization of possibilities in themselves, all this will unfold in an existential fissure that is both objective and material. The result of this fissure will be the essays to establish the nation state."

Indian Philosophical Traditions

Indian philosophy incorporates a diverse array of both realist and nominalist traditions. Several orthodox Hindu schools, including Purva Mimamsa, Nyaya, and Vaisheshika, uphold a realist stance. These schools assert that the referent of a word encompasses both the individual object perceived by a knowing subject and the universal class to which that object pertains. From the perspective of Indian realism, both the individual and the universal possess objective existence, with the universal fundamentally underpinning the individual.

In contrast, Buddhist philosophical traditions, particularly the Sautrāntika and Yogācāra schools, adopt a nominalist perspective. They maintained that words do not refer to actual objects but rather to concepts generated within the intellect. These concepts are deemed unreal due to their lack of efficient existence, meaning they possess no causal powers. While words, functioning as linguistic conventions, are acknowledged as valuable tools for thought and discourse, it is nevertheless asserted that they do not apprehend reality in its true form.

Dignāga developed a nominalist theory of meaning, designated as apohavada, or the theory of exclusions. This theory endeavors to elucidate the mechanism by which words can denote categories of objects, notwithstanding the absence of objective existence for such categories. Dignāga posited that categories do not signify inherent positive attributes shared by their constituent members. Instead, universal classifications are defined by exclusions (apoha). Consequently, the category "cow," for instance, comprises all shared exclusions among individual cows, such as being non-horse, non-elephant, and so forth.

The Problem of Universals

Nominalism emerged as a philosophical response to the problem of universals, particularly addressing the phenomenon of objects sharing a common type. For instance, both Fluffy and Kitzler are classified as cats, and certain properties, such as "greenness," are demonstrably repeatable across diverse entities like grass, a shirt, and Kermit the Frog. A fundamental inquiry arises regarding the underlying principle by virtue of what Fluffy and Kitzler are both considered cats, and what confers the attribute of greenness upon the grass, the shirt, and Kermit.

The Platonist perspective posits that all green entities derive their greenness from the existence of a universal: a singular, abstract entity that, in this context, constitutes an inherent component of all green objects. Concerning the coloration of the grass, the shirt, and Kermit, a specific component shared among them is deemed identical. Consequently, these three distinct parts are, in essence, unified. The repeatability of greenness is thus attributed to a singular entity that manifests its presence across all instances of green objects.

Nominalism fundamentally rejects the ontological existence of universals. This philosophical stance is predicated on several concerns, primarily addressing the potential locus of such universals. Plato famously posited, under certain interpretations, the existence of a distinct realm of abstract forms or universals, separate from the material world. Individual physical objects are considered to merely exemplify or instantiate these universals. However, this proposition prompts the critical inquiry: What is the spatial and temporal location of this universal realm? A prominent hypothesis suggests its existence beyond the confines of space and time. A perspective aligned with this possibility contends that, precisely due to a form's immanence within multiple physical objects, it must concurrently transcend each individual object; thus, forms are deemed "transcendent" only to the extent of their "immanence" across numerous physical entities. Consequently, immanence inherently suggests transcendence, indicating that these concepts are not mutually exclusive. Furthermore, this perspective obviates the need for a distinct "world" or "realm" of forms separate from the physical world, thereby mitigating concerns regarding the localization of a "universal realm." Conversely, naturalists maintain that no entity exists independently of space and time. Certain Neoplatonists, including the pagan philosopher Plotinus and the Christian philosopher Augustine, suggested (foreshadowing conceptualism) that universals reside within the mind of God. Further complicating this issue is the fundamental question concerning the nature of the instantiation or exemplification relation itself.

Conceptualists occupy an intermediary philosophical stance between nominalism and realism, asserting that universals possess existence solely within the cognitive domain and lack any external or substantial reality.

Moderate realists contend that universals do not inhabit a separate realm but are instead situated within space and time, manifesting wherever they occur. Consider, for instance, the universal "greenness," posited as a singular entity. Nominalists find it problematic that a singular entity could simultaneously exist in disparate locations. The realist, however, asserts that all manifestations of greenness are unified by an exemplification relation, though the nature of this relation remains unexplained. Furthermore, within lexicology, an argument against color realism emerges concerning the distinction between blue and green. In certain languages, the lexical equivalents for "blue" and "green" may be colexified; moreover, a direct translation may not always exist. For example, in Japanese, "青" (ao), typically rendered as "blue," is occasionally applied to concepts English speakers might categorize as "green," such as green apples.

Ultimately, numerous philosophers advocate for more parsimonious ontologies, comprising only the essential minimum of entity types, a preference W. V. O. Quine famously characterized as a "taste for 'desert landscapes.'" These scholars endeavor to articulate all explanatory concepts without recourse to universals like "catness" or "greenness."

Varieties

Nominalism encompasses a spectrum of theories, ranging from extreme positions to those approaching realism. An extreme manifestation is predicate nominalism, which posits that entities such as Fluffy and Kitzler are categorized as cats solely because the predicate 'is a cat' is applicable to both. This principle extends to all instances of shared attributes among distinct objects. The primary critique leveled against this view is its inadequacy in resolving the problem of universals, as it fails to elucidate the underlying basis for a group of entities warranting the application of the same predicate.

Adherents of resemblance nominalism contend that the term 'cat' applies to multiple felines because, for instance, Fluffy and Kitzler sufficiently resemble an archetypal cat to be classified within its kind. Alternatively, they argue that these entities (and other cats) exhibit significantly less divergence from each other than from other distinct objects, thereby justifying their collective categorization. Some proponents of resemblance nominalism acknowledge that the resemblance relation itself constitutes a universal, albeit the sole necessary one. Conversely, others assert that each resemblance relation is a particular entity, deriving its status as a resemblance relation from its similarity to other resemblance relations. While this latter stance engenders an infinite regress, many philosophers maintain that this regress is not inherently problematic.

Class nominalism posits that class membership provides the metaphysical foundation for property relationships. According to this view, two distinct red balls share the property of redness because both are members of the classes corresponding to their respective properties—namely, the class of red things and the class of balls. Anthony Quinton advocates a variant of class nominalism that incorporates the concept of "natural classes."

Conceptualism is a philosophical theory that accounts for the universality of particulars by positing them as conceptualized frameworks residing exclusively within the thinking mind. This conceptualist perspective addresses the metaphysical notion of universals by rejecting their independent existence in particulars external to mental perception.

Trope nominalism represents an additional form of nominalist thought. A trope is defined as a particular instance of a property, such as the specific hue of green observed in a shirt. One approach within this framework posits the existence of a primitive, objective resemblance relation that obtains among similar tropes. An alternative perspective suggests that all apparent tropes are ultimately constructed from more fundamental tropes, with the most primitive tropes corresponding to the entities described by comprehensive physics. Consequently, primitive trope resemblance can be elucidated through the concept of causal indiscernibility: two tropes are considered exactly resembling if their mutual substitution would not alter the events in which they participate. Differential degrees of macro-level resemblance are thus explained by corresponding variations at the micro-level, where micro-level resemblance is grounded in robustly physical attributes like causal power. David Armstrong, widely recognized as a leading contemporary realist, acknowledges the potential of such a trope-based nominalist variant but maintains that it falls short in explaining the laws of nature as effectively as his own theory of universals.

Ian Hacking has contended that a significant portion of contemporary social constructionism in science is implicitly driven by an unarticulated nominalist metaphysical perspective. He asserts that this underlying philosophical divergence contributes to scientists and constructionists often failing to engage constructively, effectively "shouting past each other."

Mark Hunyadi characterizes the contemporary Western world as embodying a form of "libidinal nominalism." He posits that the emphasis on individual will, which originated in medieval nominalism, has evolved into this "libidinal nominalism," wherein desire and will become indistinguishably conflated.

Mathematical nominalism

The concept that philosophy, particularly ontology and the philosophy of mathematics, should eschew set theory is largely attributable to the writings of Nelson Goodman (Goodman 1940 and 1977), who posited the existence of concrete and abstract entities devoid of parts, termed individuals. Similarly, collections of individuals are deemed to exist, with the stipulation that any two collections comprising identical individuals constitute the same collection. Goodman's perspective was significantly influenced by Stanisław Leśniewski's work, particularly his mereology, which emerged as a response to the paradoxes inherent in Cantorian set theory. Leśniewski rejected the notion of an empty set and maintained that any singleton was indistinguishable from the individual it contained. Classes, often understood as species or genera, are conceptualized as concrete aggregates of their constituent individuals. For instance, the class of philosophers is simply the aggregate of all concrete, individual philosophers.

The principle of extensionality in set theory dictates that any set notation employing curly braces to enclose one or more instances of identical individuals refers to the same set. Consequently, {a, b}, {b, a}, and {a, b, a, b} are considered equivalent sets. However, for Goodman and other advocates of mathematical nominalism, {a, b} is also deemed identical to {a, {b}}, {b, {a, b}}, and any permutation of curly braces containing one or more instances of a and b, provided that a and b represent individuals rather than collections thereof. Goodman, Richard Milton Martin, and Willard Quine collectively championed an approach to reasoning about collectivities through a theory of virtual sets (Quine 1969), which permits all elementary set operations, with the crucial caveat that the domain of a quantified variable cannot encompass any virtual sets.

Within the foundations of mathematics, nominalism is understood as the practice of mathematics without positing the existence of sets in their conventional mathematical sense. Practically, this implies that quantified variables can encompass domains of numbers, points, primitive ordered pairs, and other abstract ontological primitives, but not sets whose constituents are these individuals. Consequently, only a limited portion of contemporary mathematics is amenable to nominalistic reconstruction.

Criticism

Historical Genesis of the Terminology

The conceptualization of 'nominalism' as a distinct category within late medieval thought has faced increasing scrutiny. Historically, the fourteenth century was considered the zenith of nominalism, with prominent figures like John Buridan and William of Ockham often identified as its progenitors. Nevertheless, the notion of 'nominalism' as a coherent philosophical movement, typically juxtaposed with 'realism,' only began to materialize in the late fourteenth century, gaining broader acceptance progressively throughout the fifteenth century. The bifurcation into two distinct intellectual paths, the via antiqua (linked to realism) and the via moderna (associated with nominalism), achieved widespread recognition solely in the latter half of the fifteenth century, with this intellectual contention ultimately subsiding by the sixteenth century.

Acknowledging that the explicit conceptualization of a 'nominalism' versus 'realism' dichotomy only solidified in the fifteenth century, scholars have progressively challenged the premise of a distinct fourteenth-century nominalist school. Although certain thematic similarities may be observed among thinkers such as Ockham, Buridan, and Marsilius, significant divergences also exist. More critically, Robert Pasnau has raised doubts regarding the identifiability of any cohesive intellectual framework warranting the label 'nominalism' within fourteenth-century philosophical discourse. Consequently, it has been contended that adhering to the twentieth-century historical account, which depicted late scholastic philosophy as a fourteenth-century conflict between the via moderna (nominalism) and the via antiqua (realism), becomes problematic, particularly the assertion that William of Ockham's nominalist tenets presaged the eventual repudiation of scholasticism in the seventeenth century.

Nominalistic Reconstructions within Mathematics

A comprehensive critique of nominalist reconstructions in mathematics was conducted by Burgess (1983) and subsequently by Burgess and Rosen (1997). Burgess delineated two distinct categories of nominalist reconstructions: hermeneutic nominalism, which posits that science, when accurately interpreted, inherently operates without mathematical entities such as numbers and sets; and revolutionary nominalism, which aims to substitute existing scientific theories with alternative frameworks that do not rely on mathematical objects (Burgess, 1983, p. 96). A more recent investigation has broadened this Burgessian critique to encompass three specific nominalistic reconstructions: the analytical reconstruction by Georg Cantor, Richard Dedekind, and Karl Weierstrass, which eliminated infinitesimals; Errett Bishop's constructivist re-reconstruction of Weierstrassian analysis, which eschewed the law of excluded middle; and the hermeneutic reconstruction of Cauchy's foundational contributions to analysis, undertaken by Carl Boyer, Judith Grabiner, and others, which dispensed with Cauchy's infinitesimals.

Notes

Notes

References

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