One Bald Man … Two Bald Men … Three Bald Men—Aahh Aahh Aahh Aahh Aaaahhhh!

  • Nicholas J. J. Smith
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 33)


In the context of classical (crisp, precise) sets, there is a familiar connection between the notions of counting, ordering and cardinality. When it comes to vague collections, the connection has not been kept in central focus: there have been numerous proposals regarding the cardinality of vague collections, but these proposals have tended to be discussed in isolation from issues of counting and ordering. My main concern in this paper is to draw focus back onto the connection between these notions. I propose a natural generalisation to the vague case of the familiar process of counting precise collections. I then discuss the relationships between this process of counting and various notions of ordering and cardinality for vague sets. Some existing views concerning the cardinality of vague collections fit better than others with my proposal about how to count the members of such a collection. In particular, the idea that we should approach cardinality via certain formulas of a logical language—which has been prominent in the recent literature—is less attractive than other existing proposals.


Vagueness Fuzzy set Counting Ordinal Cardinality 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of SydneySydneyAustralia

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