Post on 28-Mar-2015
Consider ...
[[Tall(John) Tall(John)]]
[[Tall(John)]] = undecided, therefore
[[Tall(John)]] = undecided, therefore
[[Tall(John) Tall(John)]] = undecided
Repair by means of supervaluations
Suppose I am uncertain about something(e.g., the exact threshold for ``Tall``)
Suppose p is true regardless of how my uncertainty is resolved ...
Then I can conclude that p
Consider [[Tall(John) Tall(John)]]
The yes/no threshold for ``Tall`` can be anywhere between 165 and 185cm.
Where-ever the threshold is, there are only two possibilities:
1. [[Tall(John)]] = True. In this case[[Tall(John) Tall(John)]] = True.
2. [[Tall(John)]] = False. In this case [[Tall(John)]] = True. Therefore[[Tall(John) Tall(John)]] = True.
The formula must therefore be True.
Partial Logic + supervaluations
• Supervaluations enable Partial Logic to be ``almost Classical`` in its behaviour.
• How good is this as a model of vagueness?
• Like the Classical model that put the threshold at 185cm, the partial model makes a distinction that people could never make:
Partial Logic
This time, we even have
2 such artificial
boundaries:
This still contradicts the
Principle of Tolerance
185.001cm
Tall
Not tall
Gap
165.001cm
184.999cm
164.999cm