antiplatonist

Antiplatonist is a term used in philosophy to describe a position that denies or critiques Platonic realism about abstract entities, especially in mathematics. Antiplatonists argue that mathematical objects do not exist as independent, non-physical entities in a separate realm, as Plato proposed. Instead, they typically view mathematics as grounded in human practices, language, or mental constructs.

Within anti-Platonism, several strands offer different accounts of what mathematical entities are and how mathematical truths are established. Nominalism denies the existence of abstract objects altogether. Fictionalism treats mathematical statements as true or useful within a fictional or pretend domain. Formalism reduces mathematics to the manipulation of symbols within a formal system without commitment to any meaning beyond derivability. Constructivism and intuitionism emphasize constructive proof and mental constructions, resisting the idea that non-constructive existence can be taken as ontological commitment. Although distinct, these views share the core idea that mathematical objects do not inhabit a timeless Platonic realm.

Historical development of anti-Platonism intensified in the 20th century. A landmark articulation is Hartry Field’s Science Without Numbers (1980), which defends nominalism and argues for reducing mathematical commitments to empirical and scientific practice. Philosophers such as Paul Benacerraf raised problems for realism about mathematics, prompting defenses of anti-Platonist positions that appeal to epistemic and methodological considerations. Wittgensteinian and other mainstream anti-metaphysical approaches have also influenced contemporary anti-Platonist thinking.

In contemporary philosophy, anti-Platonism remains a live option in the philosophy of mathematics and the philosophy of language, often connected with formalism, constructivism, or nominalist strategies, and extended to debates about universals and other abstract entities.