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I read subvaluationists think that P can be both true and false (unlike supervaluationists, who think that P is neither true nor false), but it's completely unclear (because I can't read symbolic logic and haven't found an introduction) whether they - or indeed anyone else - claim that borderline cases are both P and not P.

For subvaluationists are logical quantifiers of borderline cases true for both P and not P? e.g. if some people in my family are borderline bald then are some people in my family borderline not bald?

I am asking because I think it likely (won't bother saying why) that my consciousness is vague and necessarily not everything. I am trying to work out whether (for any treatments of vagueness) with borderline cases of consciousness a quantifier is true of both consciousness and its negation.

Because if so, borderline cases of consciousness are necessarily not absent from everything. And I think I find that interesting (and equivalent to saying that borderline states of consciousness necessarily exist), perhaps pending finding out that it also isn't.

forlove1
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  • See [Subvaluationism](https://plato.stanford.edu/entries/vagueness/#Sub): "Whereas the supervaluationist analyzes borderline cases in terms of truth-value gaps the dialetheist analyzes them in terms of truth-value gluts. *A glut is a proposition that is both true and false.* The rule for assigning gluts is the mirror image of the rule for assigning gaps: A statement is true exactly if it comes out true on at least one precisification. The statement is false just if it comes out false on at least one precisification. 1/2 – Mauro ALLEGRANZA Aug 28 '23 at 09:33
  • So if the statement comes out true under one precisification and false under another precisification, the statement is both true and false." 2/2 – Mauro ALLEGRANZA Aug 28 '23 at 09:33
  • I had already read that @MauroALLEGRANZA but thanks – forlove1 Aug 28 '23 at 09:38
  • Yes, borderline cases of vague predicates are one of the standard candidates for dialetheias, a.k.a. truth value gluts, they are both true and false, see [SEP, Other Motivations for Dialetheism](https://plato.stanford.edu/entries/dialetheism/#OtheMotiForDial). In subvaluationism, this is because a statement is true/false when it is so on at least one precisification, and borderline cases, by definition, admit opposite precisifications. – Conifold Aug 28 '23 at 09:50
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    The simple answer is YES, because negation in dialetheical logic works as usual: reversing the truth value. – Mauro ALLEGRANZA Aug 28 '23 at 09:51

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