In Defense of Quantifier Generalism: Holism and Infinitary Resources
DOI:
https://doi.org/10.12775/LLP.2025.024Keywords
quantifier generalism, algebraic generalism, individuals, holism, infinitary quantification, arithmetic, non-standard modelsAbstract
According to quantifier generalism, all facts about the world can be expressed in a language devoid of proper names, whose only referential expressions are variables bound by quantifiers. This paper considers and repels some of the recently raised objections against this position. The central part of the paper presents a critical analysis of the claim advanced by Ted Sider that quantifier generalism is inevitably holistic and therefore requires unusually strong expressive resources when applied to infinite domains. Using an example of arithmetic, it is shown that there is a simple generalistic description of natural numbers that does not resort to any infinitary conjunctions or quantifiers. Such generalistic accounts also exist in many cases involving continua (such as descriptions of matter distribution in a continuous space). Moreover, these accounts are arguably superior to their individualistic counterparts due to their parsimony. In addition to that, Sider’s argument alleging that generalism cannot account for the difference between non-isomorphic models of arithmetic is repelled.
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