Abstract
Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus (IPC) and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness.
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Acknowledgements
We thank Peter Fritz, Øystein Linnebo, Christopher Peacocke, Sven Rosenkranz, Timothy Williamson, the participants at the workshop Vagueness and Modality: Philosophical Applications of Modal Logic (Oslo, June 2018), and two anonymous referees. We are especially grateful to Crispin Wright, whose talk in Oxford in November 2016 prompted the discussions that resulted in this paper and who offered both encouragement and insightful comments.
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Bobzien, S., Rumfitt, I. Intuitionism and the Modal Logic of Vagueness. J Philos Logic 49, 221–248 (2020). https://doi.org/10.1007/s10992-019-09507-x
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DOI: https://doi.org/10.1007/s10992-019-09507-x