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The SEP article on deontic logic mentions at least once or twice that there seem to be two types of permissibility (also a difference between "ought" and "must," to note). Over the years, I've come up with these two ways to introduce the distinction from prior "factoids":

  1. If some a is neither commanded nor countermanded, period, then it is indifferently permitted. But if some a and not-a are disjunctively, but positively, commanded, i.e., "Do a or don't do a," then a is differently permitted.
  2. If some a has no relation to the solution to a moral action-problem, a is indifferently permitted relative to that problem. But if a has an incommensurable relation to the improvement or worsening of a problem, i.e. if it affects the problem's nature without making the problem closer to or further from a solution, then it is differently permitted.

In the SEP article, the sense of "differently permitted" goes with turns-of-phrase like, "You may refrain from attending, but you still ought to." Are definitions (1) and (2) similar enough on some pertinent abstract level, that I could go ahead and maintain them both in a system of deontic logic without further analysis as such, or are they too different to justify the same moment in such logics? I ask in part because (1) seems to cohere easily with a useful characterization of a supererogation operation, whereas (2) so far doesn't seem, on the face of it, to lend itself to understanding supererogation; so there appears to maybe be a deep gap between (1) and (2).

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    In the sense of synthetic a priori, it's hard to sketch or pin down any homo-isomorphism between these two types of permissibility connecting divine/virtue command theory to categorical imperative theory, unless you treat these two types of theories as homo-isomorphic, and there seem strong arguments for such isomorphism on the theory level per rationality argument even the cautious Kant may firmly disagree... Commented Sep 25, 2023 at 6:06

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