Abstract
In this chapter we introduce the distinction between permanentist and temporaryist ontologies and present a non-classical theory of unrestricted quantification and identity that is compatible with either type of view. We discuss and defuse a recent objection that temporaryism cannot accommodate unrestricted quantification. In Sect. 2.1 we use temporal operators and quantification in order to articulate the core tenets of permanentism and temporaryism, and show that static conceptions of reality are committed to permanentism. In Sect. 2.2 we observe that classical quantification theory favours permanentism, and for reasons of neutrality, replace it by a quantification theory that, jointly with corresponding axioms for identity, yields a positive free logic. In Sect. 2.3 we reject T. Williamson’s argument meant to show that temporaryists should endorse the so-called temporal being constraint, lest they be accused of using restricted quantification when articulating their view.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The variable x should of course be required to be distinct from m; and in a formally rigorous presentation we would specify which variable it is, e.g. the first variable distinct from m given a previously defined numbering of the variables. We will henceforth for the most part omit explicit mention of such provisos when we give definitions in such quantificational terms.
- 2.
The intended generalisation to polyadic predicates follows the pattern ‘□∀x □∀x′… □(Φxx′… → ∃y(x = y) & ∃y(x′= y) & …)’.
- 3.
The intended generalisation to polyadic predicates follows the pattern ‘Always, ∀x Always, ∀x′… Always, (Φxx′… → ∃y(x = y) & ∃y(x′ = y) & …)’. Henceforth we will ignore this generalisation. Similarly, we will omit the qualification ‘temporal’ when referring to (3) as ‘the being constraint’ .
- 4.
Notice that irrespective of its logically more complex definiens, ‘is wanting’ is syntactically a predicate.
- 5.
In the contingentists’ case, the corresponding trivialisation could be formulated by saying that (2) holds only for those (predicates expressing) properties that are existence-entailing in the purely modal sense. Although temporaryists may likewise be happy to say that (3) holds for all (predicates expressing) such existence-entailing properties, the relevant trivialisation of (3) allows for a prima facie more general claim: trivially, (3) holds for all substitution instances of ‘Φ’ that something actually only ever satisfies when it exists, even if something could satisfy them without existing. Let ‘@’ rigidly refer to the actual world. Then always for all x, always, if x is identical to @, x exists. However, arguably albeit controversially, @ is such that possibly it is self-identical but does not exist.
- 6.
Note that temporaryists do not claim that sometimes something satisfies the condition denoted by ‘is wanting’. Rather, they merely claim that sometimes something sometimes satisfies that condition. This has a bearing on other things Williamson says in the chapter under discussion. Thus, in an interlude, Williamson observes that contingentists – and by extension, temporaryists – will deny that
(i) Φa → ∃y(a = y)
is logically valid. His subsequent discussion would seem premised on the assumption that in order to argue their case, contingentists (temporaryists) appeal to empty names, of which fictional and mythological names provide stock examples. However, they need have no problem with the idea that all instances of (i) are true. What they will object to is the claim that all instances of (i) necessarily (always) hold. However, if (i) was logically valid, all its instances would necessarily (always) hold. Proponents of GBT, for example, will accept (ii) but, unlike their permanentist opponents, deny (iii):
(ii) Socrates is wanting → ∃y(Socrates = y)
(iii) Always in the past, (Socrates is wanting → ∃y(Socrates = y)).
The truth of (ii) implies that ‘Socrates’ is not an empty name, while the falsity of (iii) in no way requires that whenever Socrates was wanting, ‘Socrates’ was nonetheless among the names then available, even if it then was empty. Thus, temporaryists may concede that ‘we should distrust attempts to use fictional or mythological names to refute metaphysical or logical theses’ (Williamson 2013: 153), but ask back why they should be described as having ever been tempted to undertake such attempts in order to argue their case. Similar considerations apply to contingentism , Williamson’s explicit target.
Bibliography
Broad, C. D. (1923). Scientific thought. London: Routledge.
Correia, F., & Rosenkranz, S. (2011). As time Goes by. Eternal facts in an ageing universe. Paderborn: Mentis.
Correia, F., & Rosenkranz, S. (2015b). Presentism without Presentness. Thought: A Journal of Philosophy, 4, 19–27.
Rosenkranz, S. (2012). In Defence of Ockhamism, Philosophia – Philosophical Quarterly of Israel 40, 617–31, reprinted as ‘In Defense of Ockhamism’ in J. M. Fischer and P. Todd (eds.), Freedom, Fatalism, and Foreknowledge, New York 2015: Oxford University Press, 343–60.
Williamson, T. (2013). Modal logic as metaphysics. Oxford: Oxford University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Correia, F., Rosenkranz, S. (2018). Existence, Quantification and Identity. In: Nothing To Come. Synthese Library, vol 395. Springer, Cham. https://doi.org/10.1007/978-3-319-78704-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-78704-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78703-9
Online ISBN: 978-3-319-78704-6
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)