SOPhiA 2022

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programm - Vortrag

Necessitism and Unrestricted Quantification
(Metaphysics/Ontology, Englisch)

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





REFERENCES:



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.


Chair: Youssef Aguisoul
Zeit: 16:50-17:20, 07. September 2022 (Mittwoch)
Ort: SR 1.006
Anmerkung: (Online Talk)

Violeta Conde
(Universidade de Santiago de Compostela, Spanien)



Testability and Meaning deco