SOPhiA 2022

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

Necessitism and Unrestricted Quantification
(Metaphysics and Ontology, English)

A As Williamson (2013) puts it __necessitism__ is the metaphysical view that states the truth of the following principle: (N) &_9633;&_8704;x&_9633;&_8707;y (x = y). Quantifiers in (N) are understood as quantifying over everything whatsoever populates the modal universe, so whoever argues for necessitism should accept (modal) unrestricted quantification as a part of an intelligible discourse. I__ll first present three of the main arguments that have been displayed to cast doubt on the intelligibility of unrestricted quantification, for they can be retrieved in the context of necessitism; namely:

1. Absolutely unrestricted quantification isn__t genuinely absolute, since it depends on the conceptual schema adopted (Hellman, 2006).

2. Our use of first-order quantifiers is unavoidably ambiguous, as the Löwenheim-Skolem theorem shows (Putnam, 1983).

3. Considering the All-in-One-Principle (Rayo & Uzquiano, 2006) together with a plausible principle of recombination (Nolan, 1996) makes modal unrestricted quantification prone to paradox (Sider, 2009).

Then, I__ll suggest some lines of argumentation the necessitist can follow to shield her use of unrestricted quantification for those objections. Regarding 1., I__ll argue that the necessitist can stand for her conceptual schema to be more fundamental than others to characterize the Modal Universe. The key point of my argumentation will be the logical sense of existence held by the necessitist (see Williamson, 2000) since any other schema must start from it by the mere fact that pretends to speak about the world. With respect to 2. the necessitist can proceed by adopting second-order quantification, for that would block the application of the Löwenheim-Skolem theorem. Another option would be trying to defend modal first-order unrestricted quantification even though the ambiguity of our use of quantifiers. That__s because the so-mentioned theorem doesn__t refuse by itself the intelligibility of unrestricted quantification, for it only shows the possibility of having two different models for a first-order language. Concerning 3., I__ll propose different ways to avoid paradoxes: to adopt a plural-talk, to consider an alternative set theory, or to claim that set theory is unable to deal with problems of the metaphysical magnitude like the one presented by a generalist discourse as the necessitist one.

KEYWORDS: necessitism; unrestricted quantification; All-in-One Principle; modality; set-theory


Hellman, G. (2006). __Against __Absolute Everything__!__. In Rayo, A. & Uzquiano, G. (Eds.), Absolute Generality, 75 __ 97. Oxford: Oxford University Press.

Nolan, D. (1996). __Recombination Unbound__, Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 83 (2/3): 239 __ 262. doi: 10.1007/bf00354489

Putnam, H. (1987). The Many Faces of Realism. La Salle, IL: Open Court.

Rayo, A. & Uzquiano, G. (Eds.) (2006). Absolute Generality. Oxford: Oxford University Press.

Sider, T. (2009). __Williamson__s Many Necessary Existents__, Analysis, 69 (2): 250 __ 258. doi: 10.1093/analys/anp010

Williamson, T. (2000). __Existence and Contingency__, Proceedings of the Aristotelian Society, 100 (1): 117 __ 139. doi: 10.1111/1467-9264.00069

Williamson, T. (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press.

Time: 16:50-17:20, 07 September 2022 (Wednesday)
Location: SR 1.006

Violeta Conde 
(Universidade de Santiago de Compostela, Spain)

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