Abstract
According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original view. It is a major improvement that should be embraced by all logical pluralists.
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Notes
They sometimes refer to intuitionistic logic as constructive logic, but we will use its more familiar name.
According to Carnap (1937), for example, we stipulate a logic when we construct a linguistic framework for our theory, allowing for a high degree of freedom about what can count as logic. Russell (2008) argues that there are different consequence relations over different classes of truth-bearers. Shapiro (2014a, b) has recently developed the view that logic is relative to mathematical structure and that some mathematical structures are intrinsically non-classical. Cook (2014) argues that anti-realists must accept an infinite number of equally good formal codifications of the relation of logical consequence. While each of these is aptly described as a form of logical pluralism, they are quite distinct from the view that concerns us in this paper.
See Beall and Restall (2006, p. 89) for this formulation.
They claim, furthermore, that this does not involve any equivocation with respect to the chosen terms. The ‘correctness’ of, e.g., relevant logic does not depend on attributing a different meaning to negation than that attributed by classical logic. See Beall and Restall (2006, pp. 97–98) and Restall (2002, 2014). I will revisit this topic in the objection and replies.
See Beall and Restall (2006, p. 16) for this commitment. The next section elaborates on the place of normativity within the larger pluralist project.
Thanks to an anonymous referee for pressing me to think more about these issues of normativity.
The class of possible worlds is a class of cases, but not all cases are possible worlds.
For illuminating discussion of this literature, see Steinberger (2015).
MacFarlane never considers the idea, taken up by Field (2009b, 2015), that the objects of logical norms are best construed as credal states (degrees of belief) rather than full belief (or disbelief). As such, all of the principles in MacFarlane’s taxonomy are qualitative rather than quantitative. I will only discuss qualitative formulations of logical norms in this paper because they are the only kind of norms considered by Harman, Beall and Restall, as well as the advocates of the collapse problem. Harman (1986, Chap. 3) actually argues that ordinary agents do not operate with degrees of belief. He considers the notion irrelevant to a theory of reasoning. Beall and Restall (2006, pp. 17–18) take the more conservative line that we often operate with full belief (and disbelief), hence if logic is normative for reasoning, it must pertain to these states.
I always state single-premise formulations of such principles. Technically speaking, this principle Co\(+\) is a special case of MacFarlane’s original principle Co\(+\), which applies to multiple-premise argument forms. MacFarlane does not say anything about norms for multiple-conclusion argument forms, but his taxonomy could easily be extended to them as well. I focus on single-premise arguments because it makes things simpler and it is sufficient to bring out the most interesting skeptical challenges to logical normativity.
What he calls the Logical Implication Principle (Harman 1986, p. 11).
Thanks to an anonymous referee for pointing this out.
Doxastic norms may also underpin appraisals of doxastic conduct.
“To endorse the premises of a valid argument but to reject the conclusion is to contradict yourself in the following sense: There is no case in which those claims could hold true. Your commitments undercut themselves. (Beall and Restall 2006, p. 24)”
When they introduce the criterion of normativity, Beall and Restall (2006, p. 16) give this gloss: “[I]f an argument is valid, then you somehow go wrong if you accept the premises but reject the conclusion.”
Although this strikes me as the right thing to say, it could perhaps be contested. Proponents of situation semantics, e.g. Barwise and Perry (1983), might baulk at this claim. Suffice to say, it is a delicate issue.
Shapiro (2014b) actually has a lot to say about the interaction between contexts, theories, and logics. A whole chapter of his book is devoted to resolving the Quinean charge of ‘meaning change’ between logics by appeal to contexts of intra-theoretic mathematical discourse. When I say that his remarks are made in passing, I am only referring to his remarks about how Beall and Restall’s account of “valid” resembles contextualist treatments of terms like “rude” or “tasty”. Thanks to an anonymous referee for pressing me to clarify this point.
There are some who would not grant this. Goddu (2002) criticizes Beall and Restall for failing to provide sufficiently informative criteria to distinguish acceptable from unacceptable specifications of cases. Griffiths (2013) argues that the appeal to tradition is more of a hindrance than a help. He claims that every one of the features in the ‘historically settled core’ has been contested at some point in the history of logic.
Lewis (1996, p. 559).
Lewis (1996, p. 554).
Field (2009a) also offers something like a contextualist account of logic, but it is rather different from the view on offer here. Field’s view does not explicitly appeal to the context-sensitivity of the concept of logical validity. This could not explain the plurality of logics, according to Field (2015), because the concept of logical validity is primitive and unanalyzable. Field’s view leads to something like attributer-relativity of logic, whereas the grounds of varying deductive standards are not individualized on my view. Field is also highly restrictive about the extent of the plurality, where my view can easily incorporate a large plurality of consequence relations.
Steinberger (forthcoming) argues that for Carnap, the normativity of logic is grounded in the fact that we voluntarily elect a logic as a framework constitutive of a way of thinking. This is an attractive way for someone with pluralistic inclinations to conceive of the grounds of logical normativity. Something akin to Carnapian voluntarism is at work in my contextualist view.
Subjecting us to Quine’s equivocation charge. See Quine (1986, p. 80).
For reservations about minimalism, see Hjortland (2013).
See Dunn (1993) for more on this proposal.
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Acknowledgments
I would like to thank the following people for their helpful comments on earlier drafts of this paper: Jamin Asay, Ben Burgis, Aiste Celkyte, Petr Cintula, Roy Cook, Yasuo Deguchi, Jiwon Kim, Hitoshi Omori, Nikolaj Pedersen, Jisoo Seo, Zach Weber, and Jeremy Wyatt.
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Caret, C.R. The Collapse of Logical Pluralism has been Greatly Exaggerated. Erkenn 82, 739–760 (2017). https://doi.org/10.1007/s10670-016-9841-7
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DOI: https://doi.org/10.1007/s10670-016-9841-7