The collapse of logical contextualism

ABSTRACT

The most serious objection to Beall and Restall’s case-based logical pluralism is the so-called collapse argument. According to the collapse argument, logical pluralism is not genuinely pluralistic and collapses into a single privileged relation of logical consequence. In response, Caret offered an account of logical contextualism that supposedly maintains the merits of Beall and Restall’s case-based logical pluralism while circumventing the collapse argument. In this paper, I first point out a gap in the collapse argument in that it does not affect pluralists who assume that there is no uniquely strongest admissible consequence relation. This gap, then, is closed by an improved version of the collapse argument, which makes use of Eklund’s classification of types of pluralism. Finally, I discuss how Caret’s logical contextualism cannot hold up against this new formulation of the collapse argument unless implausible assumptions about the contents of normative operators are made. Moreover, by reformulating the collapse argument, I determine the extent to which logical monism and pluralism oppose each other, paving the way for fruitful future discussion.

KEYWORDS:

• Collapse argument
• logical contextualism
• logical pluralism

Disclosure statement

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

Notes

1 B&R’s focus on validity rather than some variation of ‘follows from’ or ‘logical consequence’ has no theoretical bearing. For the rest of this paper, I will follow B&R and Caret to take the terms as describing the same phenomenon in so far as an argument is valid if and only if its conclusion follows from/is a logical consequence of its premises.

2 Exemplary, consider arbitrary claims like ‘Earth is a planet’, ‘2 + 2 = 4’, and ‘The moon is made of cheese’. By the above remarks, there is at least one case γ in which these three claims are true. Now, let Γ be the class of cases that contains γ and, if you so like, any other case in which the three claims are true. Accordingly, the inference from ‘Earth is a planet’ and ‘2 + 2 = 4’ to ‘The moon is made of cheese’ would turn out to be valid, as it is truth preserving in all members of Γ.

3 Sometimes, I will also call a class of cases ‘admissible’, if the consequence relation it determines is admissible.

4 For critical discussions of the formality and necessity constraint, see especially Paseau (2007) and Bueno and Shalkowski (2009).

5 For elaborations on the expression ‘somehow go wrong’ see especially Broome (1999).

6 The general idea of formulating bridging principles in this way stems from MacFarlane (2004), the notation used here is taken from Steinberger (2019).

7 An example of such a drastic adjustment would be to require that one ought to reject the conclusion of a valid argument if one accepts its premises. Satisfying the necessity constraint would then even prevent the normativity constraint from being satisfied. And while this example certainly does not present a plausible bridge principle, it does show that satisfying the necessity constraint in and of itself is not sufficient for satisfying the normativity constraint.

8 Williamson (1988) hinted at a collapse-like problem way before B&R published their works, indicating that the underlying idea is not specific to case-based logical pluralism. The version of the collapse argument I will mainly discuss is due to Keefe (2014) since her work is a generalization of Read’s (2006), Paseau’s (2007) and Priest’s (2005) contributions. For recent alternative presentations, see Stei (2020a, 2020b).

9 Keefe, alongside others, formulates this question as a variant of ‘Should you accept the conclusion?’ (2014, 1385). Considering B&R’s usage of Wo−, I will reformulate the question to be compatible with their conception of normativity.

10 See Russell (2018) for an elaboration on this view.

11 Eklund distinguishes four kinds of logical pluralism of which I will present only two. I will not discuss mapping and indeterminacy pluralism. While mapping pluralism is certainly irrelevant to the discussion of the collapse argument, indeterminacy pluralism may prove resistant to the version of the argument, I will present in this paper. Nevertheless, I will omit a discussion of indeterminacy pluralism here. The reason for this is, on the one hand, that I follow Eklund's judgment that the question of what consequence relation underlies natural language, the question indeterminacy pluralism is concerned with, is primarily linguistic rather than philosophical. On the other hand, the collapse argument seems to be directed against a different version of logical pluralism, as suggested by the discussion in Section 4.

12 Here, ‘best’ should not be understood as implying uniqueness. Rather, ‘best’ applies to a consequence relation if there is no consequence relation that is better.

13 This attitude toward purpose pluralism is not completely uncontroversial. Blake-Turner (2021) and Commandeur (2022) present two publications that focus on defending purpose pluralism as a response to logical monism. If one is close to these positions, the focus on goodness pluralism in this paper may simply be understood as a restriction of the object of research.

14 B&R, for instance, say that we ‘use […] deductive inference in the rational assessment of beliefs and theories, arguments and hypotheses’ (2006, 16), Keefe explicitly claims that ‘[t]he central role of logic is […] to infer truths’ (2014, 1385) and Caret says that ‘we use logic to further our goal of believing true things’ 2017, 743

15 Thanks to an anonymous referee for pointing out this problem.

16 A more detailed justification for the admissibility of the class of possible worlds can be found in B&R (2006, 40–43). While I want to defend the admissibility of a potentially different class of possible worlds here, B&R's argument for the admissibility of ${\mathrm{\Gamma }}_{PW}$ is independent of which worlds one counts as possible worlds.

17 There are certainly reasons to deny the class of possible worlds the satisfaction of the formality constraint. However, using this as a basis for defending against the collapse argument seems a tenuous solution for it would not rule out that there is another class of cases that does possess the required properties. ${\mathrm{\Gamma }}_{PW}$ illustrates a fundamental problem of case-based logical pluralism, and is not itself the problem.

18 I will sometimes be less precise and speak of, for example, a classical deductive standard or of an intuitionistic context.

19 I will not take a position here on whether or not DNE arguments are in fact constructive. Although there are logical systems that validate DNE and that label themselves ‘constructive’ (see e.g. Shulman 2022), DNE is invalid in B&R’s class of construction stages (Beall and Restall 2006, 66). Here, taking DNE arguments to be constructive merely serves illustrative purposes.

20 I would like to emphasize here that this is an interpretation of Caret's account and that he does not put forward this view himself. However, not only do I think that this perspective is helpful for understanding logical contextualism, but it also seems a natural way to explicitly situate purposes within logical contextualism. Thanks to an anonymous referee for suggesting that this previously implicit interpretation be made explicit.

21 I do not wish to contend that Wo-_C is the only way in which the contextualist can formulate their bridge principle. It would also be feasible to have a variant in which the context only appears as a hidden parameter. Another alternative would be that ‘ought’ is not taken to be a context-sensitive expression at all, and that the desired variation in norms arises, for example, from relativization to contextual parameters, such as the purpose pursued. However, understanding ‘ought’ as context-sensitive expression is not only more accessible for discussion, but also more strongly suggested by Caret's remarks, which is why I address it here. Thanks to an anonymous referee for urging me to clarify this point.

22 In fact, the original collapse argument against B&R's logical pluralism merely requires SOG_BR(C), since there too only the content of ‘ought’ relevant for belief regularization needs to be used. Thanks to an anonymous reviewer who pointed out this connection and thus helped to link the two versions of the collapse argument more strongly.

23 BPFp is a modified version of the bridge principle formula (BPF) suggested by MacFarlane (2004). I omit the variants that also allow for propositional attitudes in the antecedent, since not only are they not considered plausible candidates for bridge principles, but they further complicate the current discussion.