The western fence

Refining Carmo and Jones' system for contrary-to-duty obligations

Bjørn Kjos-Hanssen

University of Hawaii at Manoa

Association for Symbolic Logic

Annual Meeting, UConn, 2016

History of condition 5(e)

  • Proposed by Carmo and Jones (~1994)
  • K-H gives a counterexample (1996)
  • Carmo and Jones defeat the counterexample by weakening condition 5(c) (~2002)
  • K-H gives a new counterexample based on the western fence (2016)
  • The counterexample leads to a natural weakening of 5(e)

Condition 5(e)

O(B|A)\rightarrow B
O(B∣A)→BO(B|A)\rightarrow B

New weaker condition 5(e)

W\in\mathrm{ob}(D)\wedge (\neg\overline{N}\in\mathrm{ob}(D))\wedge (D\cap W\cap N\ne\emptyset)\rightarrow W\in\mathrm{ob}(D\cap N)
W∈ob(D)∧(¬N‾∈ob(D))∧(D∩W∩N≠∅)→W∈ob(D∩N)W\in\mathrm{ob}(D)\wedge (\neg\overline{N}\in\mathrm{ob}(D))\wedge (D\cap W\cap N\ne\emptyset)\rightarrow W\in\mathrm{ob}(D\cap N)

The dog scenario

  • There ought to be no dog
  • If there is a dog, there ought to be a warning sign
  • If there is a dog and no warning sign, there ought to be a fence

The western fence scenario

  • There ought to be no dog
  • If there is a dog, there ought to be a warning sign
  • If there is a dog and no warning sign, there ought to be a western fence and an eastern fence
  • However, if there is no western fence, then there is no need for an eastern fence.
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