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.
[1]
C. J. Keyser.
Contributions to the Founding of the Theory of Transfinite Numbers
,
1916
.
[2]
Terence Parsons,et al.
Indeterminate Identity: Metaphysics and Semantics
,
2000
.
[3]
Nicholas J. J. Smith.
Why Sense Cannot Be Made of Vague Identity
,
2008
.
[4]
Maciej Wygralak.
Cardinalities of Fuzzy Sets
,
2003
.
[5]
T. Gowers.
Princeton companion to mathematics
,
2008
.
[6]
Nicholas J. J. Smith.
Logic: The Laws of Truth
,
2012
.
[7]
Dominic Hyde.
Vagueness, logic and ontology
,
2008
.
[8]
F. Stephan,et al.
Set theory
,
2018,
Mathematical Statistics with Applications in R.
[9]
T. H. Hildebrandt,et al.
Contributions to the Founding of the Theory of Transfinite Numbers.
,
1916
.
[10]
Nicholas J. J. Smith.
Vagueness and Degrees of Truth
,
2008
.