Abstract
Logical pluralism is the view that there is more than one right logic. A particular version of the view, what is sometimes called domain-specific logical pluralism, has it that the right logic and connectives depend somehow on the domain of use, or context of use, or the linguistic framework. This type of view has a problem with cross-framework communication, though: it seems that all such communication turns into merely verbal disputes. If two people approach the same domain with different logics as their guide, then they may be using different connectives, and hence talking past each other. In this situation, if we think we are having a conversation about “\(\lnot A\)”, but are using different “\(\lnot \)”s, then we are not really talking about the same thing. The communication problem prevents legitimate disagreements about logic, which is a bad result. In this paper I articulate a possible solution to this problem, without giving up pluralism, which requires adopting a notion of metalinguistic negotiation, and allows people to communicate and disagree across domains/contexts/frameworks.
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Notes
Lynch has particular purposes in labeling some logical pluralisms as domain-specific, and hence attributes a particular meaning to “domain”. We need not be so restrictive here: for our purpose, a domain can be any context in which we can pursue deductive aims.
I do not want to make any claims about how the practice is so guided. It seems this is a normative constraint of some sort, but there are ways to interpret it more or less strongly (see Russell (2018) and Russell and Blake-Turner (forthcoming) for how to interpret it in such a way that it may only be very weakly normative, or normative in a very different sense from what we are used to).
In particular, they will be given by the L-rules of the framework, which are the rules that govern transformations of logically true sentences into logically true sentences. I will not here concern myself with P-rules, which govern transformations of descriptively true sentences into descriptively true sentences. For more information, see (Carnap 1937, pp. 133–135).
There is a rich debate about exactly how to interpret what Carnap was after here, and even whether it is a logical pluralism or a logical nihilism. The exact interpretation of Carnap’s pluralism is unnecessary for the current project, and so I will not pursue it further here.
There is a very important question here about how to individuate domains. It seems domains may come in all shapes and sizes. Some may be very wide in scope (“doing mathematics”, “doing science”), and some very narrow (“doing smooth infinitesimal analysis” and “doing quantum physics”). Further, it seems that in the wide case, multiple logics may be suitable for any given domain, while in the narrow case, there may be only one suitable logic. On the picture described here, there are no restrictions about whether we consider wide or narrow domains. Both count as domains for us. In this sense, we are tolerant. The important point here is that the wider the domain, the more likely deductive pursuits within that domain could be usefully guided by different logics. For this reason, I focus here mostly on wide domains, so that the primary examples are of doing analysis, rather than doing any particular type of analysis.
There is an initial problem here that bears addressing: it seems that in the extant literature, domain-specific pluralism has only been considered as the “narrow” variety. This is certainly how Lynch (2009) discusses the issues, and it seems to be how it is presented in Shapiro (2014). Though this may be a shift from the typical view in the literature, there are two reasons why we do not have to worry. First, Shapiro has recently taken to characterizing his view in this way (“Author Meets Critics” session on Varieties of Logic, Eastern APA 2016), so that more than one logic might be suitable for a particular domain. Second, and more importantly, even in wide domains, the domain itself does a lot of work of ruling out unsuitable logics. So, even though each domain might not select a unique suitable logic, it can still play a role in logical selection. In the example of the analysts, we could be in a situation where the domain of inquiry is “doing analysis” and the deductive aims of each participant are to get as clear about analysis as possible, but where we do not have a unique logic selected by either the domain or aim. So, the domain might rule out dialethic logic, amongst others, as contradictions cannot be tolerated (maybe). The domain of inquiry, then, still plays a role in selecting logics, but doesn’t necessarily select a single unique logic. Thanks to two referees for this journal for pushing me on these issues.
Colin Caret (2017) can also be seen as advocating for a domain-specific logical pluralism, where the domains are contexts, and the right logic in any context is the one which is selected by the deductive standard for that logic. A deductive standard is similar to the standards for knowledge in the literature on contextualism about knowledge. I omitted his view here since it is much more in line with that of Beall and Restall, in that the connectives mean the same thing across all (admissible) logics.
Here, I use “merely verbal dispute” differently from one that might be substantive. A merely verbal dispute is essentially pointless, since the people involved in it are talking past each other.
As an example, suppose two teachers discussing whether Mila, who usually gets A– grades, is an A-student. One says she is, while the other says she is not. Unbeknownst to them, one thinks A-students are students who receive A’s or A+’s, and the other thinks A-students are students who an A– or above. Once they realize this, the debate about whether Mila is an A-student disappears. They can both agree about the grades Mila gets. However, in the case of the analysts above, we cannot expect the debate to disappear once the two participants realize that they are speaking different logical languages. In all likelihood, they will instead continue the debate, each claiming the other is “doing analysis wrong”.
Thanks to a referee for suggesting this issue.
For our purposes here, we do not need any more details about near translational equivalents than is intuitive: they are terms which are very closely related in their meanings, so closely related that they almost mean the same things, and can be interpreted as though they do.
Tony Dardis has suggested to me that this means they are not metalinguistic negotiations, but rather acts of conceptual engineering. This is an interesting point, but I think that it seems likely that metalinguistic negotiations are a method by which we might engineer a concept, and so I do not think that this suggestion goes against anything I say here. Metalinguistic negotiations may just be one way of engineering concepts, by coming to agree about how we want to use a particular term.
Or, perhaps, only resolvable by explicitly making it clear that each participant is speaking a different language, and so no real dispute existed. See footnote 15.
Thanks to Chris Pincock for this example.
It is always difficult to determine exactly what a dispute is about. Here, for example, it might be that Fut and Con are having a dispute about “tautology”, but it could equally be a dispute about the meaning of “or”. Roberts (2012) suggests that one method by which we can determine the topic of a dispute (or, a conversation), is by identifying the questions under discussion of the conversation. We could equally well use that method here. The result would be, I suspect, the Fut and Con were having a metalinguistic negotiation about whatever term we found the dispute to be about. Unfortunately, due to space constraints, I leave this project for another paper. Thanks to Nathan Kellen, Elaine Landry and a referee for this journal for pushing me on this issue.
It is always an option here for Fut and Con to resolve their dispute (or deny that there ever was one) by explicitly admitting that they are using two terms, “tautology\(_{Fut}\)” and “tautology\(_{Con}\)”. Thanks to a referee for suggesting this option, and the following ensuing problem: if they choose this solution, there is nothing metalinguistic about the dispute anymore, and they can both walk away happy. Though admittedly sometimes this is the only response available for some debates, it will not always be the case that it is the best way to resolve the dispute. In effect, what we are concerned with here are the disputes where this is not necessary; we are concerned with those disputes where participants seem to learn from each other. In particular, we are concerned with those disputes where participants can figure out how concepts and terms ought to be deployed. So, though it is possible for Fut and Con to simply assume they are speaking different languages, it is also possible (and perhaps sometimes more charitable) to interpret them as having a normative dispute about how to use “tautology”. As suggested in footnote 5, explicitly interpreting themselves as speaking different languages and working in different domains might be required if the domains are very narrow.
Thanks very much to Colon Caret, Stewart Shapiro and Tony Dardis for reading a commenting on earlier drafts of this work. Additionally, audiences at the 2018 North Carolina Philosophical Association Conferences and the 2018 Society for Exact Philosophy conferences provided helpful feedback. Thanks are also due to two referees for this journal, who gave wonderful feedback and helped greatly improve the paper.
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Kouri Kissel, T. Metalinguistic negotiation and logical pluralism. Synthese 198 (Suppl 20), 4801–4812 (2021). https://doi.org/10.1007/s11229-019-02264-z
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DOI: https://doi.org/10.1007/s11229-019-02264-z