[PPT] - R OSS S PUZZLE WITH MAY W RONG M ARTIN A HER UM I NTRODUCTION D PowerPoint Presentation

SLIDE 1

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

YOU’RE IN THE WRONG

A VIOLATION-BASED CHALLENGE TO STANDARD SEMANTICS FOR MODALS ▼❛rt✐♥ ❆❤❡r

❚❛rt✉ Ü❧✐❦♦♦❧

✶✼✳✵✺✳✷✵✶✹ ◆❛r✈❛✲❏õ❡s✉✉

SLIDE 2

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

DEONTICS

DEONTIC MODALS

PERMISSION: ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ ❧❛❜♦r❛t♦r②✳ OBLIGATION: ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ ❧❛❜♦r❛t♦r②✳ PROHIBITION: ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ ❧❛❜♦r❛t♦r②✳

SLIDE 3

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

CONJUNCTION

EXAMPLE:

✭✶✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧q ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q

TRUTH TABLE

♣ q ♣ ∧q ❚ ❚ ❚ ❚ ❋ ❋ ❋ ❚ ❋ ❋ ❋ ❋

SLIDE 4

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

CONJUNCTION

EXAMPLE:

✭✷✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧q ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q

PICTORIAL REPRESENTATION

♣q ♣q ♣q ♣q

FIGURE 1: ♣ ∧q

SLIDE 5

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

CONJUNCTION

EXAMPLE:

✭✸✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧q ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q

PICTORIAL REPRESENTATION

♣q ♣q ♣q ♣q

FIGURE 2: ♣ ∧q

SLIDE 6

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

PICTORIAL REPRESENTATION OF ENTAILMENT

EXAMPLE

✭✹✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧q ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q

VIA PICTURES

♣q ♣q ♣q ♣q

FIGURE 3: ♣ ∧q

♣q ♣q ♣q ♣q

FIGURE 4: ♣

SLIDE 7

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

PICTORIAL REPRESENTATION OF ENTAILMENT

EXAMPLE

✭✹✮ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ❛♥❞ ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ∧q ❛✳ ❚❤❡r❡✬s ❛ ♣❤♦♥❡ ♦♥ t❤❡ t❛❜❧❡✳ ♣ ❜✳ ❚❤❡r❡✬s ❛ ❜♦♦❦ ♦♥ t❤❡ t❛❜❧❡✳ q

VIA PICTURES

♣q ♣q ♣q ♣q

FIGURE 3: ♣ ∧q

♣q ♣q ♣q ♣q

FIGURE 4: ♣

SLIDE 8

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ENTAILMENT RULE

ENTAILMENT:

✭✺✮ ϕ ❡♥t❛✐❧s ψ ✐✛ ❛❧❧ ϕ st❛t❡s ❛r❡ ❛❧s♦ ψ st❛t❡s✳

SLIDE 9

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ENTAILMENT RULE

EQUIVALENT RULE FOR ENTAILMENT:

✭✻✮ ϕ ❡♥t❛✐❧s ψ ✐✛ ❛❧❧ ¬ψ st❛t❡s ❛r❡ ❛❧s♦ ¬ϕ st❛t❡s✳

♣ ∧q | = ♣

♣q ♣q ♣q ♣q

FIGURE 5: ¬♣

♣q ♣q ♣q ♣q

FIGURE 6: ¬(♣ ∧q)

SLIDE 10

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ENTAILMENT RULE

EQUIVALENT RULE FOR ENTAILMENT:

✭✻✮ ϕ ❡♥t❛✐❧s ψ ✐✛ ❛❧❧ ¬ψ st❛t❡s ❛r❡ ❛❧s♦ ¬ϕ st❛t❡s✳

♣ ∧q | = ♣

♣q ♣q ♣q ♣q

FIGURE 5: ¬♣

♣q ♣q ♣q ♣q

FIGURE 6: ¬(♣ ∧q)

SLIDE 11

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD MODAL LOGIC

KRIPKE MODELS

◮ P♦ss✐❜❧❡ ✇♦r❧❞s✿ ✭✇ ∈ ❲ ✮✳ ◮ ❘❡❧❛t✐♦♥s ✭✇❘✇′✮✳ ◮ ❱❛❧✉❛t✐♦♥s ✭✈ ∈ ❱ ✮✳

✇✵ ✇✶ ✇✷

FIGURE 7: ▼♦❞❡❧ ✶

SLIDE 12

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD MODAL LOGIC

EXAMPLE:

◮ ✈(♣,✇✶) = ❚ ◮ ✈(♣,✇✷) = ❋

✇✶ ✇✷

FIGURE 8: ❱❛❧✉❛t✐♦♥

SLIDE 13

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD MODAL LOGIC

QUANTIFICATION OVER POSSIBLE WORLDS

◮ ◆❡❝❡ss✐t② ✭♣✮✿ ✉♥✐✈❡rs❛❧ q✉❛♥t✐✜❝❛t✐♦♥

✭∀✇ : ✇′❘✇ : ✇ ∈ ♣✮✳

◮ P♦ss✐❜✐❧✐t② ✭♦♣✮✿ ❡①✐st❡♥t✐❛❧ q✉❛♥t✐✜❝❛t✐♦♥

✭∃✇ : ✇′❘✇ : ✇ ∈ ♣✮✳

EXAMPLE

✭✼✮ ❛✳ ∃✇ : ✇′❘✇ : ✇ ∈ ♣ ❜✳ ♦♣ ✇✵ ✇✶ ✇✷

FIGURE 9: ▼♦❞❡❧ ✶

SLIDE 14

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD MODAL LOGIC

QUANTIFICATION OVER POSSIBLE WORLDS

◮ ◆❡❝❡ss✐t② ✭♣✮✿ ✉♥✐✈❡rs❛❧ q✉❛♥t✐✜❝❛t✐♦♥

✭∀✇ : ✇′❘✇ : ✇ ∈ ♣✮✳

◮ P♦ss✐❜✐❧✐t② ✭♦♣✮✿ ❡①✐st❡♥t✐❛❧ q✉❛♥t✐✜❝❛t✐♦♥

✭∃✇ : ✇′❘✇ : ✇ ∈ ♣✮✳

EXAMPLE

✭✼✮ ❛✳ ∃✇ : ✇′❘✇ : ✇ ∈ ♣ ❜✳ ♦♣ ✇✵ ✇✶ ✇✷

FIGURE 9: ▼♦❞❡❧ ✶

SLIDE 15

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD MODAL LOGIC

EXAMPLE

✭✽✮ ❛✳ ∀✇ : ✇′❘✇ : ✇ ∈ ♣ ❜✳ ♣ ✇✵ ✇✶ ✇✷

FIGURE 10: ▼♦❞❡❧ ✶

SLIDE 16

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD MODAL LOGIC

EXAMPLE

✭✾✮ ❛✳ ∀✇′ : ✇❘✇′ : ✇′ ∈ ♣ ❜✳ ♣ ✇✵ ✇✶

FIGURE 11: ▼♦❞❡❧ ✷

SLIDE 17

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

MONOTONICITY

MONOTONICITIES

UPWARD (UM): ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ DOWNWARD (DM): ❖ ✐s ❉▼ ✐✛ ψ | = ϕ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

EXAMPLE

1. ϕ
2. ϕ |

= ψ

3. ∴ ψ

SLIDE 18

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

MONOTONICITY

MONOTONICITIES

UPWARD (UM): ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ DOWNWARD (DM): ❖ ✐s ❉▼ ✐✛ ψ | = ϕ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

EXAMPLE

1. ϕ
2. ϕ |

= ψ

3. ∴ ψ

SLIDE 19

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ROSS

UM

UM: ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DISJUNCTION

1. ♣ |

= (♣ ∨q)

2. ∴ ♣ |

= (♣ ∨q)

ROSS’S PUZZLE

✭✶✵✮ ❛✳ ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ♣ ❜✳ ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ✐♥✈❛❞❡ ✐ts ♥❡✐❣❤❜♦✉r✳ (♣ ∨q)

SLIDE 20

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ROSS

UM

UM: ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DISJUNCTION

1. ♣ |

= (♣ ∨q)

2. ∴ ♣ |

= (♣ ∨q)

ROSS’S PUZZLE

✭✶✵✮ ❛✳ ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ♣ ❜✳ ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ✐♥✈❛❞❡ ✐ts ♥❡✐❣❤❜♦✉r✳ (♣ ∨q)

SLIDE 21

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ROSS

UM

UM: ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DISJUNCTION

1. ♣ |

= (♣ ∨q)

2. ∴ ♣ |

= (♣ ∨q)

ROSS’S PUZZLE

✭✶✵✮ ❛✳ ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ♣ ❜✳ ❆ ❝♦✉♥tr② ♠✉st ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ✐♥✈❛❞❡ ✐ts ♥❡✐❣❤❜♦✉r✳ (♣ ∨q)

SLIDE 22

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ROSS’S PUZZLE WITH ‘MAY’

UM

UM: ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DISJUNCTION

1. ♣ |

= (♣ ∨q)

2. ∴ ♦♣ |

= ♦(♣ ∨q)

ROSS’S PUZZLE

✭✶✶✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ♦♣ ❜✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ✐♥✈❛❞❡ ✐ts ♥❡✐❣❤❜♦✉r✳ ♦(♣ ∨q)

SLIDE 23

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ROSS’S PUZZLE WITH ‘MAY’

UM

UM: ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DISJUNCTION

1. ♣ |

= (♣ ∨q)

2. ∴ ♦♣ |

= ♦(♣ ∨q)

ROSS’S PUZZLE

✭✶✶✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ♦♣ ❜✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ✐♥✈❛❞❡ ✐ts ♥❡✐❣❤❜♦✉r✳ ♦(♣ ∨q)

SLIDE 24

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ROSS’S PUZZLE WITH ‘MAY’

UM

UM: ❖ ✐s ❯▼ ✐✛ ϕ | = ψ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DISJUNCTION

1. ♣ |

= (♣ ∨q)

2. ∴ ♦♣ |

= ♦(♣ ∨q)

ROSS’S PUZZLE

✭✶✶✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ♦♣ ❜✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ✐♥✈❛❞❡ ✐ts ♥❡✐❣❤❜♦✉r✳ ♦(♣ ∨q)

SLIDE 25

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FREE CHOICE PUZZLE

AN EXAMPLE OF FREE CHOICE

✭✶✷✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ♦(♣ ∨q)

PROPOSED SOLUTION

♦(♣ ∨q) | = ♦♣ ∧♦q

SLIDE 26

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FREE CHOICE PUZZLE

AN EXAMPLE OF FREE CHOICE

✭✶✷✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ♦(♣ ∨q)

PROPOSED SOLUTION

♦(♣ ∨q) | = ♦♣ ∧♦q

SLIDE 27

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FREE CHOICE IS NOT AN ENTAILMENT

PROPERTIES OF CONJUNCTION

1. ♣ ∧q |

= ♣

2. ∴ ♦(♣ ∧q) |

= ♦♣

SLIDE 28

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FREE CHOICE IS NOT AN ENTAILMENT

AN EXAMPLE OF FREE CHOICE

✭✶✸✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ■❢ ♦(♣ ∨q) | = ♦♣ ∧♦q✱ t❤❡♥ ♦(♣ ∨q) | = ♦♣ ❝✳ ■❢ ♦(♣ ∨q) | = ♦♣ t❤❡♥ ¬♦♣ | = ¬♦(♣ ∨q)

FREE CHOICE IS NOT AN ENTAILMENT

✭✶✹✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ❜✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳

SLIDE 29

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FREE CHOICE IS NOT AN ENTAILMENT

AN EXAMPLE OF FREE CHOICE

✭✶✸✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ■❢ ♦(♣ ∨q) | = ♦♣ ∧♦q✱ t❤❡♥ ♦(♣ ∨q) | = ♦♣ ❝✳ ■❢ ♦(♣ ∨q) | = ♦♣ t❤❡♥ ¬♦♣ | = ¬♦(♣ ∨q)

FREE CHOICE IS NOT AN ENTAILMENT

✭✶✹✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ❜✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳

SLIDE 30

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FREE CHOICE IS NOT AN ENTAILMENT

AN EXAMPLE OF FREE CHOICE

✭✶✸✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ■❢ ♦(♣ ∨q) | = ♦♣ ∧♦q✱ t❤❡♥ ♦(♣ ∨q) | = ♦♣ ❝✳ ■❢ ♦(♣ ∨q) | = ♦♣ t❤❡♥ ¬♦♣ | = ¬♦(♣ ∨q)

FREE CHOICE IS NOT AN ENTAILMENT

✭✶✹✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r✳ ❜✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳

SLIDE 31

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD READINGS

NEITHER DISJUNCT IS PERMITTED

✭✶✺✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ¬♦(♣ ∨q)

THE IGNORANCE READING

✭✶✻✮ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✱ ❜✉t ■ ❞♦ ♥♦t ❦♥♦✇ ✇❤✐❝❤✳

SLIDE 32

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STANDARD READINGS

NEITHER DISJUNCT IS PERMITTED

✭✶✺✮ ❛✳ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳ ❜✳ ¬♦(♣ ∨q)

THE IGNORANCE READING

✭✶✻✮ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✱ ❜✉t ■ ❞♦ ♥♦t ❦♥♦✇ ✇❤✐❝❤✳

SLIDE 33

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

KRATZER

WORLDS ARE ORDERED ACCORDING TO HOW CLOSE

THEY ARE TO THE IDEAL WORLD.

✭✶✼✮ ❛✳ ❨♦✉ ♠✉st ✐♥✈✐t❡ ②♦✉r s♣♦✉s❡ t♦ ②♦✉r ♣❛rt②✳ ♣ ❜✳ ❨♦✉ ♠✉st ✐♥✈✐t❡ ②♦✉r ❜r♦t❤❡r t♦ ②♦✉r ♣❛rt②✳ q ♣q ♣q ♣q ♣q

✵ ✈✐♦❧❛t✐♦♥s ✶ ✈✐♦❧❛t✐♦♥ ✷ ✈✐♦❧❛t✐♦♥s

FIGURE 12: ♣ ∧q

SLIDE 34

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

PUZZLE

DEONTIC CONFLICTS

✭✶✽✮ ❛✳ ❨♦✉ ♠✉st ✐♥✈✐t❡ ②♦✉r s♣♦✉s❡ t♦ ②♦✉r ♣❛rt②✳ ♣ ❜✳ ❨♦✉ ♠✉st ✐♥✈✐t❡ ②♦✉r ❜r♦t❤❡r t♦ ②♦✉r ♣❛rt②✳ q ❝✳ ❨♦✉ ♠✉st ♥♦t ✐♥✈✐t❡ ❜♦t❤ ②♦✉r s♣♦✉s❡ ❛♥❞ ②♦✉r ❜r♦t❤❡r t♦ ②♦✉r ♣❛rt②✳ ¬(♣ ∧q) ♣q ♣q ♣q ♣q

✶ ✈✐♦❧❛t✐♦♥ ✷ ✈✐♦❧❛t✐♦♥s

FIGURE 13: ♣ ∧q ∧¬(♣ ∧q)

DEFINITION OF

OBLIGATION

♣ ❤♦❧❞s ✐❢ t❤❡ ❜❡st ✇♦r❧❞s ❛r❡ ❛❧❧ ♣ ✇♦r❧❞s✳

SLIDE 35

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

PROBLEMS WITH PRAGMATIC REASONING

IGNORANCE EXPLORED

✭✶✾✮ ■ ❞♦ ♥♦t ❦♥♦✇ ✇❤❡t❤❡r ✐t✬s tr✉❡ t❤❛t ❛ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳

SLIDE 36

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ALTERNATIVE-BASED SEMANTICS

ALONI [2007]

◮ ❉✐s❥✉♥❝t✐♦♥ ❛❞❞s ❛❧t❡r♥❛t✐✈❡s ✐♥t♦ t❤❡ s❡♠❛♥t✐❝s ◮ ❚❤❡ ❛❧t❡r♥❛t✐✈❡s ❛r❡ t❤❡ ❞❡♥♦t❛t✐♦♥s ♦❢ t❤❡ ❞✐s❥✉♥❝ts ◮ ▼❛②ϕ =❞❢ ∀α♦ϕ ◮ ▼✉stϕ =❞❢ ∃αϕ

A CAVEAT

▲❛✇s ❛r❡ ♥♦t ✐❣♥♦r❛♥t r❡❣❛r❞✐♥❣ ♦❜❧✐❣❛t✐♦♥s✳

SLIDE 37

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

ANDERSON

EXAMPLES

✭✷✵✮ ❛✳ P❛✇♥s ♠❛② ♠♦✈❡ ✷ sq✉❛r❡s ♦♥ t❤❡✐r ✜rst ♠♦✈❡✳ ❜✳ P❛✇♥s ♠✉st ❧✐♠✐t t❤❡✐r ♠♦✈❡♠❡♥t t♦ ✷ sq✉❛r❡s✳

ANDERSONIAN MODALS

✭✷✶✮ ❛✳ ♦ϕ =❞❢ ϕ → ¬✈ ❜✳ ϕ =❞❢ ¬ϕ → ✈

SLIDE 38

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STRENGTHENING THE ANTECEDENT

DM

DM: ❖ ✐s ❉▼ ✐✛ ψ | = ϕ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DM MODALS

1. ♣ ∧q |

= ♣

2. ■❢ ♦♣ ✐s ❉▼✱ t❤❡♥ ♦♣ |

= ♦(♣ ∧q)

IMPLICATION

1. ϕ → χ |

= (ϕ ∧ψ) → χ

2. ♣ → ¬✈ |

= (♣ ∧q) → ¬✈

3. ∴ ✐❢ ♦♣ ≡ ♣ → ¬✈✱ t❤❡♥ ♦♣ |

= ♦(♣ ∧q)

SLIDE 39

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STRENGTHENING THE ANTECEDENT

DM

DM: ❖ ✐s ❉▼ ✐✛ ψ | = ϕ ✐♠♣❧✐❡s ❖ϕ | = ❖ψ

DM MODALS

1. ♣ ∧q |

= ♣

2. ■❢ ♦♣ ✐s ❉▼✱ t❤❡♥ ♦♣ |

= ♦(♣ ∧q)

IMPLICATION

1. ϕ → χ |

= (ϕ ∧ψ) → χ

2. ♣ → ¬✈ |

= (♣ ∧q) → ¬✈

3. ∴ ✐❢ ♦♣ ≡ ♣ → ¬✈✱ t❤❡♥ ♦♣ |

= ♦(♣ ∧q)

SLIDE 40

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

STRENGTHENING THE ANTECEDENT

EXAMPLE

✭✷✷✮ ❨♦✉ ♠❛② ✇❛❧❦ t❤❡ ❞♦❣✳ ♦♣ ✭✷✷✮ ❨♦✉ ♠❛② ✇❛❧❦ t❤❡ ❞♦❣ ❛♥❞ ❦✐❧❧ t❤❡ ♣r❡s✐❞❡♥t✳ ♦(♣ ∧q)

SLIDE 41

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

SEVERAL VIOLATIONS NEEDED

SEVERAL VIOLATIONS (inconsistencies WITH LAW)

✭✷✸✮ ❛✳ ❚❤❡ ❥✉r② ✜♥❞s t❤❡ ❞❡❢❡♥❞❛♥t ✐♥ ✈✐♦❧❛t✐♦♥ ♦❢ ❛rt✐❝❧❡ ✶✳ ❜✳ ❚❤❡ ❥✉r② ✜♥❞s t❤❡ ❞❡❢❡♥❞❛♥t ♥♦t ✐♥ ✈✐♦❧❛t✐♦♥ ♦❢ ❛rt✐❝❧❡ ✷✳

EXAMPLE FROM DSU 344 OF THE WTO

◮ ❚❤❡ ❬❯❙❪ ❛❝t❡❞ ✐♥❝♦♥s✐st❡♥t❧② ✇✐t❤ ❆rt✐❝❧❡ ✷✳✹✳✷ ♦❢ t❤❡

❆♥t✐✲❉✉♠♣✐♥❣ ❆❣r❡❡♠❡♥t ✐♥ t❤❡ ✐♥✈❡st✐❣❛t✐♦♥ ♦♥ ❙t❛✐♥❧❡ss ❙t❡❡❧ ❙❤❡❡t ❛♥❞ ❙tr✐♣ ✐♥ ❈♦✐❧s ❢r♦♠ ▼❡①✐❝♦ ❜② ✉s✐♥❣ ♠♦❞❡❧ ③❡r♦✐♥❣✱

◮ ❚❤❡ ❬❯❙❪ ❞✐❞ ♥♦t ❛❝t ✐♥❝♦♥s✐st❡♥t❧② ✇✐t❤ ❬✳✳✳❪ ❆rt✐❝❧❡s

✷✳✶✱ ✾✳✸ ❛♥❞ ✷✳✹ ♦❢ t❤❡ ❆♥t✐✲❉✉♠♣✐♥❣ ❆❣r❡❡♠❡♥t ❜② ✉s✐♥❣ s✐♠♣❧❡ ③❡r♦✐♥❣ ✐♥ t❤❡ ✜✈❡ ♣❡r✐♦❞✐❝ r❡✈✐❡✇s ♦♥ ❙t❛✐♥❧❡ss ❙t❡❡❧ ❙❤❡❡t ❛♥❞ ❙tr✐♣ ✐♥ ❈♦✐❧s ❢r♦♠ ▼❡①✐❝♦✳

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FURTHER

RESEARCH

ATOMS AND NEGATION

ATOMS

σ | =+ ♣ ✐✛ ∀✇ ∈ σ : ♣ ∈ ✇ σ | =− ♣ ✐✛ ∀✇ ∈ σ : ♣ ∈ ✇

NEGATION

σ | =+ ¬ϕ ✐✛ σ | =− ϕ σ | =− ¬ϕ ✐✛ σ | =+ ϕ ♣q ♣q ♣q ♣q

FIGURE 14: ♣

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RESEARCH

DISJUNCTION

DEFINITION

σ | =+ ϕ ∨ψ ✐✛ σ | =+ ϕ ♦r σ | =+ ψ σ | =− ϕ ∨ψ ✐✛ σ | =− ϕ ❛♥❞ σ | =− ψ

ILLUSTRATION

✭✷✹✮ ❙✉❡ s✐♥❣s ♦r ▼❛r② ❞❛♥❝❡s✳ ❛✳ ❨❡s✱ ❙✉❡ s✐♥❣s✳ ❜✳ ❨❡s✱ ▼❛r② ❞❛♥❝❡s✳ ❝✳ ◆♦✱ ❙✉❡ ✇♦♥✬t s✐♥❣ ❛♥❞ ▼❛r② ✇♦♥✬t ❞❛♥❝❡✳ ♣q ♣q ♣q ♣q

FIGURE 15: ♣ ∨q

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FURTHER

RESEARCH

CONJUNCTION

σ | =+ ϕ ∧ψ ✐✛ σ | =+ ϕ ❛♥❞ σ | =+ ψ σ | =− ϕ ∧ψ ✐✛ σ | =− ϕ ♦r σ | =− ψ

ILLUSTRATION

✭✷✺✮ ❙✉❡ s✐♥❣s ❛♥❞ ▼❛r② ❞❛♥❝❡s✳ ❛✳ ❨❡s✱ ❙✉❡ s✐♥❣s ❛♥❞ ▼❛r② ❞❛♥❝❡s✳ ❜✳ ◆♦✱ ❙✉❡ ✇♦♥✬t s✐♥❣ ❝✳ ◆♦✱ ▼❛r② ✇♦♥✬t ❞❛♥❝❡✳ ♣q ♣q ♣q ♣q

FIGURE 16: ♣ ∧q

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FURTHER

RESEARCH

ALTERNATIVES

MAXIMAL SUPPORTING STATES

▼❆❳[ϕ]+ := {σ ∈ [ϕ]+|¬∃τ ∈ [ϕ]+ : σ ⊂ τ} ♣q ♣q ♣q ♣q

FIGURE 17: ♣ ∨q

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IMPLICATION

σ | =+ ϕ → ψ ✐✛ ∀τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =+ ψ σ | =− ϕ → ψ ✐✛ ∃τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =− ψ

ILLUSTRATION

✭✷✻✮ ■❢ ❙✉❡ s✐♥❣s✱ t❤❡♥ ▼❛r② ✇✐❧❧ ❞❛♥❝❡✳ ❛✳ ❨❡s✱ ✐❢ ❙✉❡ s✐♥❣s✱ t❤❡♥ ▼❛r② ✇✐❧❧ ❞❛♥❝❡✳ ❜✳ ◆♦✱ ✐❢ ❙✉❡ s✐♥❣s✱ t❤❡♥ ▼❛r② ✇♦♥✬t ❞❛♥❝❡✳ ♣q ♣q ♣q ♣q

FIGURE 18: ♣ → q

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RESEARCH

THE GAP IN IMPLICATION

ILLUSTRATION

✭✷✼✮ ■❢ ❙✉❡ s✐♥❣s✱ t❤❡♥ ▼❛r② ✇✐❧❧ ❞❛♥❝❡✳ ❛✳ ❨❡s✱ ✐❢ ❙✉❡ s✐♥❣s✱ t❤❡♥ ▼❛r② ✇✐❧❧ ❞❛♥❝❡✳ ❜✳ ◆♦✱ ✐❢ ❙✉❡ s✐♥❣s✱ t❤❡♥ ▼❛r② ✇♦♥✬t ❞❛♥❝❡✳ ❝✳ ❙✉❡ ✇♦♥✬t s✐♥❣✳ ♣q ♣q ♣q ♣q

FIGURE 19: ♣ → q

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RESEARCH

ALTERNATIVES AND NEGATING IMPLICATION

(♣ ∨q) → r

✭✷✽✮ ■❢ ❙✉❡ s✐♥❣s ♦r ▼❛r② ❞❛♥❝❡s✱ P❡t❡ ✇✐❧❧ ♣❧❛② t❤❡ ♣✐❛♥♦✳ ❛✳ ◆♦✱ ✐❢ ❙✉❡ s✐♥❣s✱ P❡t❡ ✇✐❧❧ ♥♦t ♣❧❛②✳ ❜✳ ◆♦✱ ✐❢ ▼❛r② ❞❛♥❝❡s✱ P❡t❡ ✇✐❧❧ ♥♦t ♣❧❛②✳

IMPLICATION

σ | =− ϕ → ψ ✐✛ ∃τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =− ψ ♣qr ♣qr ♣qr ♣qr ♣qr ♣qr ♣qr ♣qr ♣qr

FIGURE 20: [(♣ ∨q) → r]✲

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RESEARCH

DEONTICS

DEONTIC may

σ | =+ ✈ ϕ ✐✛ ∀τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =− ✈ σ | =− ✈ ϕ ✐✛ ∀τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =+ ✈ ♣✈ ♣✈ ♣✈ ♣✈

FIGURE 21: ♦♣

THREE-FOLD DEONTICS

◮ P❡r♠✐tt❡❞✿ ♦♥❧② ✈

✇♦r❧❞s✳

◮ Pr♦❤✐❜✐t❡❞✿ ♦♥❧② ✈

✇♦r❧❞s✳

◮ ◆❡✉tr❛❧✿ ❜♦t❤ ✈ ❛♥❞ ✈

✇♦r❧❞s✳

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FURTHER

RESEARCH

DEONTIC MODALS DIFFER FROM IMPLICATION

¬♦(♣ ∨q)

✭✷✾✮ ❆ ❝♦✉♥tr② ♠❛② ♥♦t ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳

DEFINITION

σ | =− ✈ ϕ ✐✛ ∀τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =+ ✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 22: [¬♦(♣ ∨q)]✰

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FURTHER

RESEARCH

ENTAILMENT

SUPPORT-ENTAILMENT: ϕ | =+ ψ ✐✛ [ϕ]+ ⊆ [ψ]+ REJECTION-ENTAILMENT: ϕ | =− ψ ✐✛ [ψ]− ⊆ [ϕ]− ENTAILMENT: ϕ | = ψ ✐✛ ϕ | =+ ψ ❛♥❞ ϕ | =− ψ

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RESEARCH

FREE CHOICE

DISJUNCTIVE PERMISSION

✭✸✵✮ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r②✳

DEFINITION

σ | =+ ✈ ϕ ✐✛ ∀τ ∈ ▼❆❳[ϕ]+ : τ ∩σ | =− ✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 23: [♦(♣ ∨q)]✰

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FURTHER

RESEARCH

FREE CHOICE IS NOT ENTAILMENT

ENTAILMENT FACTS

◮ ■❢ ϕ |

=+ ψ t❤❡♥ ¬ψ | =+ ¬ϕ

◮ ■❢ ♦(♣ ∨q) |

=+ ♦♣ t❤❡♥ ¬♦♣ | =+ ¬♦(♣ ∨q) ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 24: [¬♦(♣)]+

♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 25: [¬♦(♣ ∨q)]✰

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FURTHER

RESEARCH

FREE CHOICE IS NOT ENTAILMENT

ENTAILMENT FACTS

◮ ■❢ ϕ |

=+ ψ t❤❡♥ ¬ψ | =+ ¬ϕ

◮ ■❢ ♦(♣ ∨q) |

=+ ♦♣ t❤❡♥ ¬♦♣ | =+ ¬♦(♣ ∨q) ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 24: [¬♦(♣)]+

♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 25: [¬♦(♣ ∨q)]✰

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FURTHER

RESEARCH

FREE CHOICE IS NOT ENTAILMENT

ENTAILMENT FACTS

◮ ■❢ ϕ |

=+ ψ t❤❡♥ ¬ψ | =+ ¬ϕ

◮ ■❢ ♦(♣ ∨q) |

=+ ♦♣ t❤❡♥ ¬♦♣ | =+ ¬♦(♣ ∨q) ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 24: [¬♦(♣)]+

♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 25: [¬♦(♣ ∨q)]✰

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RESEARCH

IGNORANCE READING

DISJUNCTION SCOPING OVER may

✭✸✶✮ ❆ ❝♦✉♥tr② ♠❛② ❡st❛❜❧✐s❤ ❛ r❡s❡❛r❝❤ ❝❡♥t❡r ♦r ❛ ❧❛❜♦r❛t♦r② ❜✉t ■ ❞♦♥✬t ❦♥♦✇ ✇❤✐❝❤✳ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈ ♣q✈

FIGURE 26: [♦♣ ∨♦q]+

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DEONTIC CONFLICTS

CONFLICTS OF OBLIGATION

✭✸✷✮ ❛✳ ❨♦✉ ♠✉st ✐♥✈✐t❡ ②♦✉r s♣♦✉s❡ t♦ ②♦✉r ♣❛rt②✳ ❜✳ ❨♦✉ ♠✉st ✐♥✈✐t❡ ②♦✉r ❜r♦t❤❡r t♦ ②♦✉r ♣❛rt②✳ ❝✳ ❨♦✉ ♠✉st ♥♦t ✐♥✈✐t❡ ❜♦t❤ ②♦✉r s♣♦✉s❡ ❛♥❞ ②♦✉r ❜r♦t❤❡r t♦ ②♦✉r ♣❛rt②✳

REPRESENTATION

ϕ ≡ ¬♦¬ϕ ✭✸✸✮ ❛✳

✈✶ ♣

❜✳

✈✷ q

❝✳

✈✸ ¬(♣ ∧q)

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RESEARCH

CONFLICTS OF OBLIGATION

BROTHER AND SISTER

✭✸✹✮ ❛✳ ▼♦t❤❡r✿ ❨♦✉ ♠✉st ❧❡❛✈❡ ②♦✉r r♦♦♠✳

✈✶ ♣

❜✳ ❋❛t❤❡r✿ ❨♦✉ ♠✉st ♥♦t ❧❡❛✈❡ ②♦✉r r♦♦♠✳

✈✷ ¬♣

♣✈✶✈ ✷ ♣✈ ✶✈ ✷ ♣✈✶✈ ✷ ♣✈ ✶✈ ✷ ♣✈✶✈✷ ♣✈ ✶✈✷ ♣✈ ✶✈✷ ♣✈✶✈✷

FIGURE 27: [ ✈✶ ♣ ∧ ✈✷ ¬♣]✰

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CONDITIONAL OUGHTS

JACKSON’S CONDITIONAL OUGHT’S PUZZLE

✭✸✺✮ ■❢ ❇r✐t♥❡② ❙♣❡❛rs ❞r✐♥❦s ❈♦❦❡✱ t❤❡♥ ❇r✐t♥❡② ❙♣❡❛rs ♠✉st ❞r✐♥❦ ❈♦❦❡✳ ♣ → ♣

REPRESENTATION

1. [♣ → ♣]+ ≡ [♣ → (¬♣ → ✈)+]

♣✈ ♣✈ ♣✈ ♣✈

FIGURE 28: [♣ → ♣❪✰

SLIDE 60

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

CONDITIONAL OUGHTS

JACKSON’S CONDITIONAL OUGHT’S PUZZLE

✭✸✺✮ ■❢ ❇r✐t♥❡② ❙♣❡❛rs ❞r✐♥❦s ❈♦❦❡✱ t❤❡♥ ❇r✐t♥❡② ❙♣❡❛rs ♠✉st ❞r✐♥❦ ❈♦❦❡✳ ♣ → ♣

REPRESENTATION

1. [♣ → ♣]+ ≡ [♣ → (¬♣ → ✈)+]

♣✈ ♣✈ ♣✈ ♣✈

FIGURE 28: [♣ → ♣❪✰

SLIDE 61

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

WHAT GOES WRONG?

ANALYSIS

1. [♣ → ♣]+ ≡ [♣ → (¬♣ → ✈)+]

WHAT HAPPENS WHEN ANTECEDENTS ARE

IMPOSSIBLE?

1. [♣ ∧¬♣]+ = /
2. /

0 | = ϕ

APPLIED TO CONDITIONALS

✭✸✻✮ ❛✳ ■❢ ■ ❛❣r❡❡ ✇✐t❤ ②♦✉✱ ✇❡ ✇✐❧❧ ❜♦t❤ ❜❡ ✇r♦♥❣✳ ❜✳ ■ ❞♦ ♥♦t ❛❣r❡❡ ✇✐t❤ ②♦✉✳ ❝✳ ❄❄❍❡♥❝❡✱ ✐❢ ■ ❛❣r❡❡ ✇✐t❤ ②♦✉✱ ✇❡ ✇✐❧❧ ❜♦t❤ ❜❡ ✇r♦♥❣✳

DEAL WITH THE GAP

❉❡✜♥❡ s✉♣♣♦s✐t✐♦♥s ❛s ❛ t❤✐r❞ ❝♦♠♣♦♥❡♥t ♦❢ ♠❡❛♥✐♥❣✱ s✉❝❤ t❤❛t t❤❡ ❛❧✇❛②s ❝♦♥st✐t✉t❡s s✉♣♣♦s✐t✐♦♥ ❢❛✐❧✉r❡✳

SLIDE 62

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

WHAT GOES WRONG?

ANALYSIS

1. [♣ → ♣]+ ≡ [♣ → (¬♣ → ✈)+]

WHAT HAPPENS WHEN ANTECEDENTS ARE

IMPOSSIBLE?

1. [♣ ∧¬♣]+ = /
2. /

0 | = ϕ

APPLIED TO CONDITIONALS

✭✸✻✮ ❛✳ ■❢ ■ ❛❣r❡❡ ✇✐t❤ ②♦✉✱ ✇❡ ✇✐❧❧ ❜♦t❤ ❜❡ ✇r♦♥❣✳ ❜✳ ■ ❞♦ ♥♦t ❛❣r❡❡ ✇✐t❤ ②♦✉✳ ❝✳ ❄❄❍❡♥❝❡✱ ✐❢ ■ ❛❣r❡❡ ✇✐t❤ ②♦✉✱ ✇❡ ✇✐❧❧ ❜♦t❤ ❜❡ ✇r♦♥❣✳

DEAL WITH THE GAP

❉❡✜♥❡ s✉♣♣♦s✐t✐♦♥s ❛s ❛ t❤✐r❞ ❝♦♠♣♦♥❡♥t ♦❢ ♠❡❛♥✐♥❣✱ s✉❝❤ t❤❛t t❤❡ ❛❧✇❛②s ❝♦♥st✐t✉t❡s s✉♣♣♦s✐t✐♦♥ ❢❛✐❧✉r❡✳

SLIDE 63

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

WHAT GOES WRONG?

ANALYSIS

1. [♣ → ♣]+ ≡ [♣ → (¬♣ → ✈)+]

WHAT HAPPENS WHEN ANTECEDENTS ARE

IMPOSSIBLE?

1. [♣ ∧¬♣]+ = /
2. /

0 | = ϕ

APPLIED TO CONDITIONALS

✭✸✻✮ ❛✳ ■❢ ■ ❛❣r❡❡ ✇✐t❤ ②♦✉✱ ✇❡ ✇✐❧❧ ❜♦t❤ ❜❡ ✇r♦♥❣✳ ❜✳ ■ ❞♦ ♥♦t ❛❣r❡❡ ✇✐t❤ ②♦✉✳ ❝✳ ❄❄❍❡♥❝❡✱ ✐❢ ■ ❛❣r❡❡ ✇✐t❤ ②♦✉✱ ✇❡ ✇✐❧❧ ❜♦t❤ ❜❡ ✇r♦♥❣✳

DEAL WITH THE GAP

❉❡✜♥❡ s✉♣♣♦s✐t✐♦♥s ❛s ❛ t❤✐r❞ ❝♦♠♣♦♥❡♥t ♦❢ ♠❡❛♥✐♥❣✱ s✉❝❤ t❤❛t t❤❡ ❛❧✇❛②s ❝♦♥st✐t✉t❡s s✉♣♣♦s✐t✐♦♥ ❢❛✐❧✉r❡✳

SLIDE 64

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH

FURTHER RESEARCH

FURTHER WORK

❊①t❡♥❞✐♥❣ ▼❆❉ t♦ s✉♣♣♦s✐t✐♦♥❛❧ ✐♥q✉✐s✐t✐✈❡ s❡♠❛♥t✐❝s

APPLICATION

❚❡①t✉❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ❧❡❣❛❧ t❡①ts✳

SLIDE 65

YOU’RE IN THE WRONG MARTIN AHER INTRODUCTION

DEONTICS SOME NOTATION ENTAILMENT MODALITY

PUZZLES

ROSS’S PUZZLE FREE CHOICE KRATZER DEONTIC CONFLICTS

PRIOR PROPOSALS

PRAGMATIC ALTERNATIVES ANDERSON

MADRIS

THE CLAUSES DEONTICS ENTAILMENT

SOLUTIONS

FREE CHOICE DEONTIC CONFLICTS

FURTHER

RESEARCH