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7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness

[why vagueness matters to philosophy]

7 ideas
Austin revealed many meanings for 'vague': rough, ambiguous, general, incomplete... [Austin,JL, by Williamson]
     Full Idea: Austin's account brought out the variety of features covered by 'vague' in different contexts: roughness, ambiguity, imprecision, lack of detail, generality, inaccuracy, incompleteness. Even 'vague' is vague.
     From: report of J.L. Austin (Sense and Sensibilia [1962], p.125-8) by Timothy Williamson - Vagueness 3.1
     A reaction: Some of these sound the same. Maybe Austin distinguishes them.
Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
     Full Idea: If 'P is red' and 'P is orange' are indefinite, then 'P is red and P is orange' seems false, because red and orange are exclusive. But if two conjoined indefinite sentences are false, that makes 'P is red and P is red' false, when it should be indefinite.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: [compressed] This is the problem of 'penumbral connection', where two indefinite values are still logically related, by excluding one another. Presumably 'P is red and P is of indefinite shape' can be true? Doubtful about this argument.
Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K]
     Full Idea: Vagueness concerns 'local' indeterminacy, such as whether one man in the lineup is bald, and 'global' indeterminacy, applying to a range of cases, as when it is indeterminate how 'bald' applies to the lineup. But how do these relate?
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: This puts the focus either on objects or on predicates which are vague.
Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
     Full Idea: Standard notions of vagueness all accept borderline cases, and presuppose a higher standpoint from which a judgement of being borderline F, rather than simply being F or being not F, can be made.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: He says that the concept of borderline cases is an impediment to understanding vagueness. Proposing a third group when you are struggling to separate two other groups doesn't seem helpful, come to think of it. Limbo cases.
When bivalence is rejected because of vagueness, we lose classical logic [Williamson]
     Full Idea: The principle of bivalence (that every statement is either true or false) has been rejected for vague languages. To reject bivalence is to reject classical logic or semantics.
     From: Timothy Williamson (Vagueness [1994], Intro)
     A reaction: His example is specifying a moment when Rembrandt became 'old'. This is the number one reason why the problem of vagueness is seen as important. Is the rejection of classical logic a loss of our grip on the world?
Vagueness undermines the stable references needed by logic [Williamson]
     Full Idea: Logic requires expressions to have the same referents wherever they occur; vague natural languages violate this contraint.
     From: Timothy Williamson (Vagueness [1994], 2.2)
     A reaction: This doesn't mean that logic has to win. Maybe it is important for philosophers who see logic as central to be always aware of vagueness as the gulf between their precision and the mess of reality. Precision is worth trying for, though.
A vague term can refer to very precise elements [Williamson]
     Full Idea: Both 30° and 60° are clearly acute angles. 'Acute' is precise in all relevant respects. Nevertheless, 30° is acuter than 60°.
     From: Timothy Williamson (Vagueness [1994], 4.11)
     A reaction: A very nice example of something which is vague, despite involving precise ingredients. But then 'bald' is vague, while 'this is a hair on his head' is fairly precise.