Consider... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John)...

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Consider ... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John)]] = undecided, therefore [[Tall(John) Tall(John)]] = undecided

Transcript of Consider... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John)...

Page 1: Consider... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John) Tall(John)]] = undecided.

Consider ...

[[Tall(John) Tall(John)]]

[[Tall(John)]] = undecided, therefore

[[Tall(John)]] = undecided, therefore

[[Tall(John) Tall(John)]] = undecided

Page 2: Consider... [[Tall(John) Tall(John)]] [[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

Page 3: Consider... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John) Tall(John)]] = undecided.

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.

Page 4: Consider... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John) Tall(John)]] = undecided.

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:

Page 5: Consider... [[Tall(John) Tall(John)]] [[Tall(John)]] = undecided, therefore [[Tall(John) Tall(John)]] = undecided.

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