In between impossible worlds

ABSTRACT

The common view has it that there are two families of approaches towards the logical structure of impossible worlds – Australasian and North American. According to the first, impossible worlds are closed under the relation of logical consequence of one of the non-classical logics. The North American approach is more liberal, allowing for impossible worlds where no logic holds. After pointing out the questionable consequences of each view, I propose a third one. While this new perspective allows for worlds where no logical consequence holds, it also imposes some constraints on what worlds are built upon. This renders the proposed view not as restrictive as the Australasian approach and not as liberal as the North American approach. Due to its intermediary nature, I have named this perspective ‘the Pacific’ approach.

KEYWORDS:

• Impossible worlds
• counterpossibles
• dependence
• Humean supervenience

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Thanks to Tadeusz Ciecierski, Daniel Nolan, Jacek Paśniczek, Mariusz Popieluch, David Ripley, Diego Tajer, and the anonymous reviewers for this journal for their helpful comments concerning the earlier versions of the paper. This material is based on the work supported by the National Science Centre (NCN), Poland (Grant No. 2016/20/S/HS1/00125).

2 I use ‘true at a world’ and ‘true in a world’ interchangeably. Both expressions convey the idea that the truth of a formula is evaluated within a specific world.

3 Some, however, claim that discrepancies between the original PWS and proposed modification are crucial enough to consider them two very different approaches (Bjerring and Schwarz 2017).

4 Some have distinguished four notions of impossible worlds, which differ with respect to how broad the domain of worlds is meant to be (Berto and Jago 2019, 31–32). Compared to other notions, the one mentioned above is a moderate one. Thus, for heuristic reasons, I will rely on this characterization.

5 Some call elements of I non-normal, non-standard, or n-worlds (Kripke 1965; Rescher and Brandom 1980; Priest 1992; Paśniczek 1994).

6 Here I assume that the truths of mathematics and metaphysics are necessary. For a view opposite to this see (Rosen 2006; Miller 2009).

7 As a list of advocates of these approaches shows, the mentioned labels may be misleading. Nevertheless, I am going to stick to the terminology introduced by Priest.

8 In order to avoid nuances between various North American approaches, and to unify the terminology, I will assume that truthbearers are formulas and that truthmakers are states. Accordingly, a formula A is true in a given world w if the corresponding state s_A obtains in w. Likewise, formula B is false in w if s_B is an element of w, and does not obtain in w.

9 This interpretation is related to the notion of ‘unreliable narrators’ (Nolan 2007).

10 The above relies on the popular assumption that the story prefix should be understood in terms of counterfactuals. Thus, it should be notice that this argument may be less convincing for those, who favor an alternative analysis of this prefix (Bonomi 2008; Predelli 2008).

11 See also (Bjerring and Schwarz 2017).

12 Notice that this is different than the case of an impossible world where both A and ∼A holds. These kinds of worlds find their place in both Australasian and North American approaches.

13 E.g., some approaches allow for formulas such as ‘w is the actual world’ or ‘nothing is true’ to be evaluated as true or false within a given world (Vander Laan 1997).

14 See Plantinga (1976).

15 While this may raise some worries, it also has some justification. For debates over properties of truthmaking see Restall (1996), Read (2000), Rodriguez-Pereyra (2006); Jago (2009), Tałasiewicz et al. (2013), Fine (2017).

16 For a detailed exposition of the truthmaking theory rejecting the Thesis of Entailment, see Sendłak (2022).

17 See e.g., Adams (1981), Fine (1985), Williamson (2013).

18 The proposed perspective requires acceptance of Humean supervenience in the first place. Like many other philosophical positions, the latter is by no means uncontroversial (Bhogal 2020a). Thus, debates surround the notion of natural properties (Dorr 2019), the explanatory power of such an account of the laws of nature (Lange 2018; Emery 2019; Hicks 2020), and the risk of falling into idealism due to the standards of balance established by human beings (Lewis 1994; Hicks, Jaag, and Loew 2023). However, my intention is not to defend this view here but rather to explore its potential application to the question of the laws of logic.

19 This opens a new perspective on the debate over logical pluralism and revives an old problem of nomic idealism. Both deserve substantial discussion, yet both go beyond the scope of this paper.

20 See e.g., Haack (1978), Resnik (1999), Boghossian (2000), Shapiro (2000), Rush (2014), McSweeney (2019), Peregrin (2024).

21 Likewise, it is justified to say within the object language that ‘The team of Apollo 11 achieved the impossible – they landed on the Moon’, but it is not true that there is no possible world where this happened. This is because the meaning of ‘possible’ within folk language is often taken as having the same meaning as ‘being probable’. In contrast, within possible world semantics, there is no such correlation.

22 For the debate over the plausibility and the role of a distinction between theoretical and common meanings of philosophical terms such as ‘being’, ‘object’, ‘existences’, etc., see Hirsch (2008), van Inwagen (2008), Sider (2011, 171–173), Sendłak (2020).

23 This duality allows also for the analysis of a mixed example such as: ‘If conjunction elimination were invalid and grass were purple, things would be very different’. The antecedent of this counterfactual is represented by such a world w that (i) ‘Grass is purple’ is true at w, and (ii) ‘Conjunction elimination is invalid’ is true about w.

24 It seems that the same methodological observation applies to other accounts of counterfactuals, including the orthodox approaches (Sendłak 2016). Thus, since neither the Australasian nor the North American approaches allow for a world where the law of identity fails to hold, examples such as (7) and (8) should turn vacuously true. For arguments stressing the need for a non-vacuous analysis of examples such as (11), see Sandgren and Tanaka (2020).