Very few sets of data are truly complete or completely accurate. There are nearly always some 'errors and omissions' - as well as cases which fall on borderlines (which are sometimes themselves ill-defined).

Over the years the philosophical community has extensively studied the concept of 'vagueness'.

Vagueness is a major topic of research in philosophical logic, where it serves as a potential challenge to classical logic. Work in formal semantics has sought to provide a compositional semantics for vague expressions in natural language. Work in philosophy of language has addressed implications of vagueness for the theory of meaning, while metaphysicists have considered whether reality itself is vague.

Source : Wikipedia

Vagueness has strong implications in fields as diverse as linguistics (ref.), quantum physics (ref.), law (ref.), fuzzy logic (ref.), computing (ref.), business (ref.) etc..

Some suggest that the concept itself has the problem of a possibly incomplete definition - see : Higher-Order Vagueness and the Vagueness of 'Vague'

Also see : Sorites paradoxplugin-autotooltip__plain plugin-autotooltip_bigSorites paradox

The Sorites paradox is a philosophical problem dating from the time of Ancient Greece.

It relates to the problem of defining groups - specifically large groups. It has implications for the definitions of 'vagueness' 'fuzziness' 'blurriness' etc etc. Which in turn have implications for mathematics, modern computing systems (search algorithms, quantum computers, etc etc )

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