Some Deontic Logicians
Lawrence H. Powers · Noûs · 1967
I shall discuss the preceding papers by Aqvist, Sellars, and Anderson, and also Castanfeda's deontic calculus.' Many of the logical properties ascribed to deontic notions in deontic calculi are exhibited in payoff calculi with less problematic interpretations. A preliminary exposition of a payoff calculus will make certain logical points easier to grasp. A payoff machine has a Start lever, a Stop (or Payoff) lever and an array of buttons numbered 1, 2, 3, . . . N. One puts the machine through one cycle by pulling the Start lever, pushing any of the buttons, and finally pulling the Payoff or Stop lever. Then the machine drops money out of a slot to you. The amount is determined solely by which buttons you pushed (and did not push). Each partition of the buttons into pushed and unpushed has its payoff, characteristic of the machine. A canonical description of a payoff machine includes a specification (by numeral) of the number of buttons and a specification (similarly explicit) of the payoff function-i.e. of what payoff accrues to each partition. Consider a machine with three buttons and the following payoff function: