Pruss, Alexander and Jerabek, Emil (2025) Counting in Goodman and Quine's constructive nominalism. [Preprint]

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Abstract

It is well-known that one cannot use first-order logic with
identity and the predicates Cat(x) and Dog(x) to say that there are
more cats than dogs. Nonetheless, Goodman and Quine (1947) offered
an ingenious translation of the sentence into a richer but thoroughly
finitist and nominalist language with mereological vocabulary and size
comparison for individuals. However, their translation as it stands fails
in the case of counting comparisons involving overlapping objects (say,
conjoined twin cats). Furthermore, we prove that no general translation
of equinumerosity (and hence of “more”) can be given in the overlapping
object setting using the predicates in Goodman and Quine’s translation,
assuming size comparison can be cashed out by counting mereological
atoms, and we use computational complexity theory to prove a more
general inexpressibility result. We end with some open questions.

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Item Type:	Preprint
Creators:	Creators Email ORCID Pruss, Alexander alexander_pruss@baylor.edu Jerabek, Emil jerabek@math.cas.cz
Keywords:	equinumerosity,Goodman,Quine,mereology
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics General Issues > Reductionism/Holism
Depositing User:	Dr Alexander Pruss
Date Deposited:	05 Dec 2025 13:47
Last Modified:	05 Dec 2025 13:47
Item ID:	27378
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics General Issues > Reductionism/Holism
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/27378

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