Thomas Mormann
University of the Basque Country
This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection.
Keywords Higher-order vagueness, logic of clarity, fixed margin models, similarity structures, graphs, boundary operators, tolerance principles, Galois connection, topology.
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References found in this work BETA

Knowledge and Its Limits.Timothy Williamson - 2000 - Philosophy 76 (297):460-464.
Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
Vagueness.Timothy Williamson - 1997 - Philosophy and Phenomenological Research 57 (4):921-928.
Theories of Vagueness.Rosanna Keefe - 2000 - Cambridge University Press.
Vagueness in Context. [REVIEW]Stewart Shapiro - 2008 - Philosophy and Phenomenological Research 76 (2):471-483.

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