Nominalist logicians can consistently reject universals while accepting universal statements.
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The retrieved sources discuss nominalism and universals generally, but do not provide sufficient direct evidence to fully support the claim that nominalist logicians can consistently reject universals while accepting universal statements.
division is between particulars and universals. Particulars are unique individual entities, like a specific apple. Universals are general features that different
Metaphysics is the branch of philosophy that examines the basic nature or most fundamental structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of human understanding. Some philosophers, including Aristotle, designate metaphysics as the first philosophy to suggest that it is mor
Universals are general entities, encompassing both properties and relations, that express what particulars are like and how they resemble one another. They are repeatable, meaning that they are not limited to a unique existent but can be instantiated by different particulars at the same time. For example, the particulars Nelson Mandela and Mahatma Gandhi instantiate the universal humanity, similar to how a…
Nominalism in Metaphysics (Stanford Encyclopedia of Philosophy)
Stanford Encyclopedia of Philosophy
# Nominalism in Metaphysics
First published Mon Apr 21, 2025
Nominalism is an exclusionary thesis in ontology. It asserts that there are no entities of certain sorts. Precisely which entities it excludes depends on the relevant variety of nominalism, but nominalist theses typically deny the existence of universals or abstract entities. For those who accept nominalism, a central challenge in metaphysics is to make sense of phenomena that anti-nominalist theories explain via universals or abstract entities. For instance, anti-nominalists often rely upon universals to explain similarity, propositions to explain linguistic meaning, and numbers to explain mathematical truth. Nominalists who reject the existence of such entities must therefore find a credible way to explain how things can be similar without sharing universals, have linguistic meaning without expressing propositions, or be truths of mathematics without the existence of any mathematical entities.
Since nominalists seek to provide metaphysical theories without positing universals or abstract entities, the resulting nomin
How the laws of logic lie about mathematical objects | Synthese | Springer Nature Link
# How the laws of logic lie about mathematical objects
- Published: 07 October 2025
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- Volume 206, article number 201, (2025)
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## Abstract
In ontological debates on the existence of mathematical objects, it has long been taken for granted that if we take our mathematical discourse at face value, it follows from the fact that our true mathematical statements refer to mathematical objects that mathematical objects exists; reference in true statements entails existence. In this paper, I argue that there are positions available in the philosophy of logic that allow us to dislodge this assumption, allowing for a nominalist position according to which statements such as ‘there are four prime numbers between 1 and 10’ are true and genuinely refer to numbers, without a corresponding statement asserting the existence of numbers following from it. Consequently, there is an overlooked nominalist position accordi
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Universalspeer-reviewedsame source L3no side taken