Moores paradox and hedging with I believe: An attempt. or: I - PowerPoint PPT Presentation

Moore’s paradox and hedging with ‘I believe’ Moore’s 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 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 0 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 0 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 0 ‰ . . . ↓ ↓ ↓ ↓ 3 2 1 0 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 0 Definition 2: for any non-empty A Ď W : κ Ò p A q “ min t κ p w q | w P A u κ Ò p It is not raining q “ 2 κ Ò p It is raining q “ 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 0 Definition 3: Positive rank = negative rank of complement κ ` p It is not raining q “ 0 κ ` p It is raining q “ 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 0 picnic worlds ¬ picnic worlds ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 4 4 3 3 2 2 1 0 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 0 Definition 3: Positive rank = negative rank of complement κ ` p It is not raining q “ 0 κ ` p It is raining q “ 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 0 Suppose β “ 0 and α “ 3 . Then the above rating function can satisfy C a ` Bel a p φ q . But it does not satisfy C a ` 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 0 (1) � Rain ^ Bel a p Rain q Suppose: β “ 0 , α “ 1 Asserting � Rain requires κ ` p� Rain q ą 1 ą 0 Asserting Bel a p Rain q requires κ ` p Rain q 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 0 Bel a p� Rain q ^ Bel a p Rain q Suppose: β “ 0 , α “ 1 (2) Asserting Bel a p� Rain q requires κ ` p� Rain q ą 0 Asserting Bel a p Rain q requires κ ` p Rain q 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 0 picnic worlds ¬ picnic worlds ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 4 4 3 3 2 2 1 0 Sven Lauer (Konstanz) | Questioning Speech Acts, Konstanz, September 14 – 16, 2017 12 / 12