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I T LOOKS LIKE A DUCK ... CASES OF IMPLICATION M ARTIN A HER M - PowerPoint PPT Presentation

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S OME FUNNY CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT S OME FUNNY CASES OF IMPLICATION T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S

  1. S OME FUNNY CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT S OME FUNNY CASES OF IMPLICATION T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  2. S OME FUNNY I NTRODUCTION CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT I NDICATIVE CONDITIONALS C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY ! K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  3. S OME FUNNY F ALSE ANTECEDENT CASES OF IMPLICATION M ARTIN A HER M ATERIAL | ! = IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION F IGURE 1: IMPLICATION ! F IGURE 2: U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  4. S OME FUNNY T RUE CONSEQUENT CASES OF IMPLICATION M ARTIN A HER | ! = M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY F IGURE 4: ! F IGURE 3: M ORE CONDITIONALS

  5. S OME FUNNY C ONTRAPOSITION CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE ! ! F IGURE 5: F IGURE 6: MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  6. S OME FUNNY C ONTRAPOSITION CASES OF IMPLICATION M ARTIN A HER C ONTRAPOSITION : ! ⌘ ! M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  7. S OME FUNNY C ONTRARIES CASES OF IMPLICATION M ARTIN A HER ! B ROMBERGER ON : M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION ! U PWARD MONOTONIC F IGURE 7: F IGURE 8: N O MORE MONOTONICITY M ORE CONDITIONALS

  8. S OME FUNNY S TRENGTHENING THE A NTECEDENT CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE ANTECEDENT S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  9. S OME FUNNY S TRENGTHENING THE A NTECEDENT CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS F IGURE 9: ! F IGURE 10: ( ^ ) ! A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  10. S OME FUNNY T RANSITIVE LUCK CASES OF IMPLICATION M ARTIN A HER M ATERIAL L OTTERY IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER R EPRESENTATION A LTERNATIVE MODAL LOGICS A NDERSON ! E TERNAL DAMNATION N OT MATERIAL IMPLICATION ! IMPLICATION U PWARD MONOTONIC ! N O MORE MONOTONICITY M ORE CONDITIONALS

  11. S OME FUNNY T RANSITIVE LUCK CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS F IGURE 11: ! ^ ! F IGURE 12: ! A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  12. S OME FUNNY S PLITTING RESPONSIBILITY CASES OF IMPLICATION M ARTIN A HER M ATERIAL C ONJUNCTION TO DISJUNCTION IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS R EPRESENTATION A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION ( ^ ) ! | = ( ! ) _ ( ! ) U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  13. S OME FUNNY S PLITTING RESPONSIBILITY CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS F IGURE 13: ( ^ ) ! F IGURE 14: ( ! ) _ ( ! ) A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  14. S OME FUNNY R AMSEY CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION R AMSEY (1931) P .15 A C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  15. S OME FUNNY S UPPOSITIONAL CONDITIONALS CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION S UPPOSITIONAL CONDITIONALS F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK E DGINGTON (2003) S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  16. S OME FUNNY S TANDARD MODAL LOGIC CASES OF IMPLICATION M ARTIN A HER M ATERIAL IMPLICATION Q UANTIFICATION OVER POSSIBLE WORLDS F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES I S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK I S PLITS R AMSEY K RATZER K RATZER : THE MODAL BASE S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE I MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION I IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  17. S OME FUNNY K RATZER CONDITIONALS CASES OF IMPLICATION M ARTIN A HER M ATERIAL C ONDITIONAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE ! A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER R ESTRICTOR APPROACH S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION ( ⇤ ) U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  18. S OME FUNNY U PWARD MONOTONICITY IN K RATZER CASES OF IMPLICATION SEMANTICS M ARTIN A HER M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT U PWARD MONOTONICITY OF QUANTIFIERS T RANSITIVE LUCK S PLITS 8 ϕ ϕ | = ψ 8 ψ R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER I NHERITANCE (C ARIANI 2012) A LTERNATIVE MODAL LOGICS ϕ | = ψ ⇤ ϕ | = ⇤ ψ A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

  19. S OME FUNNY U PWARD MONOTONICITY PUZZLES CASES OF IMPLICATION M ARTIN A HER R OSS ’ S PUZZLE M ATERIAL IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS A NDERSON E TERNAL DAMNATION N OT MATERIAL IMPLICATION IMPLICATION U PWARD MONOTONIC F IGURE 15: F IGURE 16: _ N O MORE MONOTONICITY M ORE CONDITIONALS

  20. S OME FUNNY P ROF . P ROCRASTINATE CASES OF IMPLICATION M ARTIN A HER M ATERIAL P ROF . P ROCRASTINATE IMPLICATION F ALSE ANTECEDENT T RUE CONSEQUENT C ONTRAPOSITION C ONTRARIES S TRENGTHENING THE A NTECEDENT T RANSITIVE LUCK S PLITS R AMSEY K RATZER S TANDARD MODAL LOGIC R EPRESENTATION P ROBLEMS FOR K RATZER A LTERNATIVE MODAL LOGICS ⇤ ( ^ ) A NDERSON E TERNAL DAMNATION ⇤ N OT MATERIAL IMPLICATION IMPLICATION ⇤ U PWARD MONOTONIC N O MORE MONOTONICITY M ORE CONDITIONALS

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