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Vagueness – a nightmare for any scientist? Our author Nora Kluck, a doctor of philosophy of language, asks what value can be attached to vagueness. To answer this question, she has considered clever minds and bald heads.
(Summary based on Nora Kluck's book: Der Wert der Vagheit [the value of vagueness])


Telly Savalas, the actor playing Kojak in the TV series of the same name, is a clear example of a person who his bald. The reggae singer Bob Marley is a clear example of a person who is not. Now let's imagine a row of men whose hair varies in its magnificence, beginning with Bob Marley. The next man in line after Marley has exactly one less hair on his head than Marley himself. Along the line, we might pass the German singer Götz Alsmann, followed by Albert Einstein, Alfred Hitchcock and Homer Simpson, before finally coming to Telly Savalas at the end of the line. The question now is: from what point on the line onwards can we reliably use the word "bald"?

"Bald" is clearly a semantically vague predicate, as there is no clear boundary for its application. Semantic vagueness leads to problems in the application of formal logic. One of these is the sorites paradox. Despite a valid premise, i.e. that "Bob Marley is not bald" and a valid inference, i.e. that "any person with one less hair on his head than a person who is not bald is also not bald", the resulting conclusion, i.e. that "Telly Savalas is not bald", is unacceptable.

A further problem is assignment of the logical value. If we take a man from the middle of our row and state that he is bald, the statement cannot be considered "true" or "false". The person making this judgment may themselves be uncertain, and come to different conclusions at different times.

These are all reasons for semantic vagueness to be considered deficient from the perspective of formal logic. Despite this, vagueness is ubiquitous in everyday language and has not been eliminated during the centuries for which human beings have been using speech.


The justification for vagueness
In fact, observations in memory and cognition psychology suggest that vaguely delimited categories correspond better to the limited sensory and cognitive resources of human beings.

This is particularly the case in the phase of language acquisition. Furthermore, vague predicates promote communication, in that they avoid unnecessary and irrelevant information (this is consistent with Grice's conversational maxims). Vague predicates often lead to more economical and flexible communication and to a better communication result.

Or, in the words of the psychologist Johnson-Laird: "In fact, vagueness is a solution, rather than a problem."