Logical Pluralism from a Pragmatic Perspective

ABSTRACT

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.

KEYWORDS:

• logical pluralism
• questions under discussion
• connectives
• Carnap
• polysemy

Notes

¹ See Bell [1998] for more details.

² It is not clear that the object-level transcription will always be so easy. Field [2009: 346–7] provides an example where translating negation into formal language is quite complicated. I ignore this complication here.

³ Whether does not affect the status of the proposition expressed by as true or false, but only whether the conversational participants are treating it as true for the purposes of the conversation. This means that the theory that I'm giving here is a pragmatic theory. In section 4.2, I will suggest that there is no further theory to provide. Thanks to a referee for pushing me on this issue.

⁴ One possibility not addressed here is that ‘in my system’ is something more like ‘in my book’. In this way, we might liken the debate between Geoffrey and Rudolf to a debate between two historians wondering about the nature of Cleopatra (this example and issue are due to a referee). Certainly, if two historians were disagreeing about Cleopatra, we would not want to interpret them as discussing two distinct historical figures. We might think that the same should be true for the logical cases. However, in the logical cases, we cannot point to historical records or relics, but only to the behaviours of the conversational participants and the rules and/or truth conditions that they profess to associate with each connective. Thus, it makes more sense to let the number of connectives that are (pragmatically) in play be guided by the behaviour of the participants.

⁵ One thing to notice here is that, if this conversation continued, it is distinctly possible that Greg's next utterance would be something like ‘You must mean something different by “proof” than I do.’ In this case, it would be possible that we would have to remove from the common ground, and that it would affect, not the meanings of the logical connectives, but rather the meaning of ‘proof’. This is interesting, since it shows two things. First, it makes explicit the fact that there are two logics in play in the conversation. Second, it shows that does not need to be restricted to just the logical connectives, but can affect much of what is going on in the conversation. One particularly interesting aspect of this lack of restriction is that, rather than different connectives being in operation, it might be different standards of implication (thanks to a referee for this suggestion). Terrés Villalonga [forthcoming] and Caret [forthcoming] each propose a view where the standards of implication might shift in a way that has nothing to do with connective meanings. I have not addressed whether the standards of implication are the same across both conversations. It seems likely that each conversation has two standards of implication in play; but whether both standards in conversation 1 are the same as both standards in conversation 2 is another question. I suspect that we will find that we cannot compare the standards across the conversations without embedding them into the appropriate context. A full examination of this topic is beyond the scope of this paper.

⁶ I need to give a story about what happens in ‘mixed’ conversations—that is, what happens in conversation where cannot be part of the common ground at a certain point, but can be part of the common ground before and after that point. We ought to maintain that, if is removed from the common ground and then ‘added back’, then the meanings of the connectives or ‘proves’ might change throughout the conversation. This means that, at any time when a new goal becomes salient, the status of might change. But this is to be expected. We can account for the purpose of a conversation in terms of the conversational goals. Thus, since we have been maintaining that the right logic and meanings of the connectives are relative to a purpose and a context, so we ought to accept that, when our purpose changes, sometimes the meanings will change.

⁷ Two words are polysemous when they are ambiguous but related. So, while ‘bat’ is ambiguous between the mammal and the baseball equipment, it is not polysemous. On the other hand, ‘wood’ is ambiguous between the thing trees are made of and the thing a lot of trees make up, they are related to each other, and so are polysemous. I will make no claims here about whether all polysemous words are always related by a ‘pre-theoretic’ notion.

⁸ See Steinberger [2016] for an interesting discussion of how to pragmatically select the appropriate linguistic framework.

⁹ Thanks to a referee for raising this concern, and for suggesting that different meanings do not necessarily lead to merely verbal disputes.

¹⁰ For a further development of this point, see Wyatt and Payette [forthcoming].

¹¹ Thanks to a referee for suggesting this line of attack.

¹² This way of thinking about the situation does require us to separate the formal connective meanings from the logical rules. On this picture, the rules in a logic for a particular connective do not necessarily fully specify the meaning of that connective.

¹³ For further work on this ruling-in and ruling-out problem, see Priest [2006], Hjortland [2013], and Kouri [2016].

¹⁴ I owe a debt of gratitude to Stewart Shapiro, who read many early drafts. I am grateful for comments on previous drafts from Ethan Baruer, Roy Cook, Geoffrey Hellman, Hannes Leitgeb, Chris Pincock, Craige Roberts, Marcus Rossberg, Gil Sagi, Giorgio Sbardollini, Kevin Scharp, and Neil Tennant, as well as several referees. Additionally, attentive audiences at The Ohio State Philosophy-Linguistics Workshop (2015), The University of Connecticut Logic Group (2015), Pluralism Week at the Veritas Research Center at Yonsei University (2016), the Buenos Aires Workshop on the Philosophy of Logic (2017), the Logic Seminar at the University of Melbourne (2017), and the Minnesota Center for Philosophy of Science Foundations Interest Group (2016) provided very useful feedback.