A simple solution to the collapse argument for logical pluralism

ABSTRACT

Many philosophers have argued that logical pluralism is not compatible with the normativity of logic. They developed different versions of the collapse argument: if two logics are correct, then the weaker one will be normatively irrelevant. In this paper, I argue that the collapse argument is based on a controversial premise: the assumption that every logic can be characterized by the same bridge principle. I provide a solution to the collapse argument based on the modification of this premise, maintaining both logical pluralism and the normativity of logic.

KEYWORDS:

• Normativity of logic
• logical pluralism
• collapse argument
• non-classical logics
• epistemic norms

Acknowledgments

I would like to thank the participants of the IX Workshop on Philosophical Logic (organized by the Buenos Aires Logic Group) and the Tübingen Logic Group for very useful discussions of this material. This research was also funded by the Alexander von Humboldt Foundation.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 In particular, contextualism is affected by the problem of mixed inferences, which is similar, but not identical, to the collapse problem.

2 Most authors propose validity-based principles, but there are some exceptions. In recent papers, Steinberger (2019a), Blake-Turner (2021), and Evershed (2021) proposed invalidity-based principles. If Steinberger is right, invalidity principles have a similar problem (logics collapse into the weakest one). We will discuss Blake–Turner's proposal in Section 5.

3 Blake-Turner (2021, 5) provides a ‘disjunctive’ version of the collapse argument. If the argument is valid only in the stronger logic, then only that logic will matter normatively. If both logics agree, both bridge principles will apply, but the weaker logic ‘makes no normative difference whatsoever’.

4 See Steinberger (2019b) for a similar approach.

5 To be clear, I do not claim that a strict principle such as Wo+ for FDE would be unproblematic. You still have the Preface Paradox, and also the Excessive Demands objection up to a certain degree (clearly not as strong as with classical logic).

6 Blake–Turner also briefly suggests in a footnote (fn. 33) that we may use ‘different principles for different logics’. However, the example he gives is not so useful: he mentions the possitibily of adopting a positive ought-based principle for classical logic, and a negative basing principle for relevant logic. If this is the case, then classical logic will still prevail.

7 In a recent paper, Stei (2020) makes this point. He argues that as far as we know that one logic preserves truth, the collapse argument follows. Even if other properties such as demonstrability may not follow, truth is the basic normative property for beliefs.

8 I would like to thank an anonymous referee for raising these interesting points.