Journal of Philosophical Logic 49 (2):221-248 (2020)

Susanne Bobzien
Oxford University
Ian Rumfitt
Oxford University
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 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.
Keywords Vagueness  Sorites Paradox  Intuitionistic logic  Modal logic  McKinsey-Tarski translation  Crispin Wright  Higher-order vagueness  McKinsey Axiom  Intuitionistic modal logic  Contingency logic
Categories (categorize this paper)
DOI 10.1007/s10992-019-09507-x
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Wang's Paradox.Michael Dummett - 1975 - Synthese 30 (3-4):201--32.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness.Susanne Bobzien - 2015 - Aristotelian Society Supplementary Volume 89 (1):61-87.
Implicit Versus Explicit Knowledge in Dialogical Logic.Manuel Rebuschi - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag. pp. 229--246.
On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
On Classical Behavior of Intuitionistic Modalities.Sergey Deobyshevich - 2014 - Logic and Logical Philosophy 24 (1):79-104.
Lattice Logic as a Fragment of (2-Sorted) Residuated Modal Logic.Chrysafis Hartonas - 2018 - Journal of Applied Non-Classical Logics 29 (2):152-170.


Added to PP index

Total views
197 ( #42,227 of 2,324,570 )

Recent downloads (6 months)
71 ( #7,836 of 2,324,570 )

How can I increase my downloads?


My notes