Titlebook: Arbitrary Reference in Logic and Mathematics; Massimiliano Carrara,Enrico Martino Book 2024 Springer Nature Switzerland AG 2024 Arbitrary

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eference. We argue that . is essential for both formal and informal logical deduction, as well as for the semantics of quantifiers. We propose to understand . as direct reference via an ideal act of choice, setting the stage for further developments in later chapters.

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ng mathematician relates to the various possible interpretations in model theory. To this purpose we introduce some .. Additionally, we aim to clarify how one can deduce logical consequences of the axioms by reasoning on a single interpretation, even when a theory has non-equivalent elementary model

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ontological commitment; (b) understanding our semantics does not require any prior mathematical concepts; and (c) although . is not universally applicable, it still offers significant applicability, especially in mathematics. We conclude the chapter arguing that second-order logic, as interpreted t

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a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of .. Finally, in the last section of this chapter we show that, adopting a relativistic notio

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https://doi.org/10.1007/978-3-031-66452-6Arbitrary reference; Plural reference; Second order logic; Plural quantification; Logicality of second o