mathematical nominalism

Mathematical nominalism is a philosophical stance that denies the existence of abstract entities, including numbers, sets, and other mathematical objects. Unlike mathematical Platonism, which posits that mathematical theorems are true descriptions of abstract objects, nominalism asserts that these objects do not exist.12

There are several versions of mathematical nominalism:
* Paraphrase nominalism suggests that mathematical sentences should not be interpreted literally. Instead, they can be rephrased as conditional statements, such as "If numbers existed, then 4 would be even." This view, also known as "if-thenism" or deductivism, allows for the acceptance of mathematical theories without committing to the existence of abstract objects.2
* Fictionalism posits that mathematical sentences are not literally true. They are considered true within a fictional context, similar to a story, and are useful despite not describing reality.2
* Neo-Meinongianism is a more complex view that claims mathematical sentences should be read at face value, asserting the existence of mathematical objects, yet simultaneously denies the existence of these objects. This leads to the paradoxical conclusion that the sentences are literally true even though their purported subjects do not exist.2

Nominalists often advocate for ontological economy, using Ockham's razor to argue against multiplying entities beyond necessity.1