Moores paradox and hedging with I believe: An attempt. or: I - - PowerPoint PPT Presentation
Moores paradox and hedging with I believe Moores paradox and hedging with I believe: An attempt. or: I believe in a ranking-theoretic analysis of believe Sven Lauer University of Konstanz Questioning Speech Acts
Moore’s paradox and hedging with ‘I believe’
Moore’s paradox and hedging with ‘I believe’: An attempt.
Sven Lauer University of Konstanz Questioning Speech Acts Konstanz, September 14 – 16, 2017
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 1 / 12
Moore’s paradox and hedging with ‘I believe’
A pointwise ranking function
. . . ↓ 4 ↓ 3 ↓ 2 ↓ 1 ↓
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 2 / 12
Moore’s paradox and hedging with ‘I believe’
Another pointwise ranking function
. . . ↓ 4 ↓ 3 ↓ 2 ↓ 1 ↓
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 3 / 12
Moore’s paradox and hedging with ‘I believe’
Numbers matter
. . . ↓ 4 ↓ 3 ↓ 2 ↓ 1 ↓
. . . ↓ 3 ↓ 2 ↓ 1 ↓
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 4 / 12
Moore’s paradox and hedging with ‘I believe’
Lifting to propositions
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
Definition 2: for any non-empty A Ď W : κÒpAq “ mintκpwq | w P Au κÒpIt is not rainingq “ 2 κÒpIt is rainingq “ 0
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 5 / 12
Moore’s paradox and hedging with ‘I believe’
Positive ranks
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
Definition 3: Positive rank = negative rank of complement κ`pIt is not rainingq “ 0 κ`pIt is rainingq “ 2
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 6 / 12
Moore’s paradox and hedging with ‘I believe’
Intersecting propositions
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓ picnic worlds ¬ picnic worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 7 / 12
Moore’s paradox and hedging with ‘I believe’
Positive ranks
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
Definition 3: Positive rank = negative rank of complement κ`pIt is not rainingq “ 0 κ`pIt is rainingq “ 2
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 8 / 12
Moore’s paradox and hedging with ‘I believe’
Hedging explained
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
Suppose β “ 0 and α “ 3. Then the above rating function can satisfy Ca ` Belapφq. But it does not satisfy Ca ` φ.
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 9 / 12
Moore’s paradox and hedging with ‘I believe’
Moore’s paradox explained
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
(1) Rain ^ BelapRainq Suppose: β “ 0, α “ 1 Asserting Rain requires κ`pRainq ą 1 ą 0 Asserting BelapRainq requires κ`pRainq ą 0 Impossible!
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 10 / 12
Moore’s paradox and hedging with ‘I believe’
Strength explained
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
(2) BelapRainq ^ BelapRainq Suppose: β “ 0, α “ 1 Asserting BelapRainq requires κ`pRainq ą 0 Asserting BelapRainq requires κ`pRainq ą 0 Impossible!
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 11 / 12
Moore’s paradox and hedging with ‘I believe’
Closure explained
Rain worlds ¬ Rain worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓ picnic worlds ¬ picnic worlds ↓ 4 ↓ 4 ↓ 3 ↓ 3 ↓ 2 ↓ 2 ↓ 1 ↓
Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 12 / 12