nominalism

Nominalism is a family of philosophical positions concerning the status of universals—properties, kinds, and general terms. In contrast to realism, which holds that universal concepts exist independently of language and minds, nominalism denies such independent existence. According to nominalists, only particular, concrete things exist; general terms are merely names or descriptions that do not correspond to separate abstract entities.

Historically, nominalism emerged in the scholastic debates of medieval Europe. Roscellinus argued that universals are without objective reality and that what we call “the same” across things is a matter of language. William of Ockham offered a systematic defense, insisting that only individuals exist and that universals are substantive abstractions in the mind or in language used for convenience. The term “nominalism” arose as opponents of realism to describe these views. Variants include conceptualism, which situates universals in the mind, and trope nominalism, which treats universals as sets of particularized properties (tropes) rather than abstract entities.

Implications and criticisms: Nominalism challenges the realist assumption underlying mathematics, science, and logic that general forms have independent existence. Critics argue that nominalism must account for the apparent universality of predication and laws of nature. Proponents often invoke mechanisms of language and classification, or reconstruct mathematics and science without referents to abstract objects. In modern philosophy, mathematical nominalism, as defended by thinkers such as Hartry Field, seeks to ground mathematics without abstract universals.

In contemporary use, nominalism remains influential in debates about the nature of properties, truth conditions, and the status of mathematical objects, though most philosophers today align with some form of realism, conceptualism, or structuralist view rather than pure nominalism.