Main.VaguenessEpistemic History
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[[Category/LogicAndMaths]]
Changed lines 9-10 from:
!!!Argument from T-schema
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Changed lines 23-26 from:
!!!Margin of error
!!!Higher order vagueness
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!!Margin of error
!!Higher order vagueness
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!Objections
If vague concepts really do have sharp boundaries, what determines where those boundaries lie?
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No sentence that says something is neither true nor false.
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!!!Margin of error
!!!Higher order vagueness
Changed lines 11-20 from:
# u says that p\\
# It is not the case that: u is true or u is false.\\
# If u says that p, then u is true iff p\\
# If u says that p, then u is false iff ¬p\\
# u is true iff p (MP 1,3)\\
# u is false iff ¬p (MP 1,3)\\
# It is not the case that: p or u is false. (Substitution 2,5)\\
# It is not the case that: p or ¬p (Substitution 6,7)\\
# ¬p and ¬¬p (De Morgan 8)\\
to:
# u says that p
# It is not the case that: u is true or u is false.
# If u says that p, then u is true iff p
# If u says that p, then u is false iff ¬p
# u is true iff p (MP 1,3)
# u is false iff ¬p (MP 1,3)
# It is not the case that: p or u is false. (Substitution 2,5)
# It is not the case that: p or ¬p (Substitution 6,7)
# ¬p and ¬¬p (De Morgan 8)
Changed lines 11-20 from:
*1. u says that p\\
*2. It is not the case that: u is true or u is false.\\
*3. If u says that p, then u is true iff p\\
*4. If u says that p, then u is false iff ¬p\\
5. u is true iff p (MP 1,3)\\
6. u is false iff ¬p (MP 1,3)\\
7. It is not the case that: p or u is false. (Substitution 2,5)\\
8. It is not the case that: p or ¬p (Substitution 6,7)\\
9. ¬p and ¬¬p (De Morgan 8)\\
to:
# u says that p\\
# It is not the case that: u is true or u is false.\\
# If u says that p, then u is true iff p\\
# If u says that p, then u is false iff ¬p\\
# u is true iff p (MP 1,3)\\
# u is false iff ¬p (MP 1,3)\\
# It is not the case that: p or u is false. (Substitution 2,5)\\
# It is not the case that: p or ¬p (Substitution 6,7)\\
# ¬p and ¬¬p (De Morgan 8)\\
Changed lines 11-20 from:
*1. u says that p
5. u is true iff p MP 1,3
6. u is false iff ¬p MP 1,3
7. It is not the case that: p or u is false. Substitution 2,5
8. It is not the case that: p or ¬p Substitution 6,7
9. ¬p and ¬¬p DeMorgan 8
to:
*1. u says that p\\
*2. It is not the case that: u is true or u is false.\\
*3. If u says that p, then u is true iff p\\
*4. If u says that p, then u is false iff ¬p\\
5. u is true iff p (MP 1,3)\\
6. u is false iff ¬p (MP 1,3)\\
7. It is not the case that: p or u is false. (Substitution 2,5)\\
8. It is not the case that: p or ¬p (Substitution 6,7)\\
9. ¬p and ¬¬p (De Morgan 8)\\
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to:
!!Arguments for
!!!Argument from T-schema
*1. u says that p
*2. It is not the case that: u is true or u is false.
*3. If u says that p, then u is true iff p
*4. If u says that p, then u is false iff ¬p
5. u is true iff p MP 1,3
6. u is false iff ¬p MP 1,3
7. It is not the case that: p or u is false. Substitution 2,5
8. It is not the case that: p or ¬p Substitution 6,7
9. ¬p and ¬¬p DeMorgan 8
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!The epistemic conception of vagueness
* Stoic logicians?
* Late 1980s and early 1990s - Roy Sorensen and Paul Horwich
* Timothy Williamson
[[Category/Philosophy]]