deontic paradoxes the paradoxes of deontic logic, which typically arise as follows: a certain set of English sentences about obligation or permission appears logically consistent, but when these same sentences are represented in a proposed system of deontic logic the result is a formally inconsistent set. To illustrate, a formulation is provided below of how two of these paradoxes beset standard deontic logic.
The contrary-to-duty imperative paradox, made famous by Chisholm (Analysis, 1963), arises from juxtaposing two apparent truths: first, some of us sometimes do what we should not do; and second, when such wrongful doings occur it is obligatory that the best (or a better) be made of an unfortunate situation. Consider this scenario. Art and Bill share an apartment. For no good reason Art develops a strong animosity toward Bill. One evening Art’s animosity takes over, and he steals Bill’s valuable lithographs. Art is later found out, apprehended, and brought before Sue, the duly elected local punishment-and-awards official. An inquiry reveals that Art is a habitual thief with a history of unremitting parole violation. In this situation, it seems that (1)–(4) are all true (and hence mutually consistent): (1) Art steals from Bill. (2) If Art steals from Bill, Sue ought to punish Art for stealing from Bill. (3) It is obligatory that if Art does not steal from Bill, Sue does not punish him for stealing from Bill. (4) Art ought not to steal from Bill. Turning to standard deontic logic, or SDL, let s stand for ‘Art steals from Bill’ and let p stand for ‘Sue punishes Art for stealing from Bill’. Then (1)–(4) are most naturally represented in SDL as follows: (1a) s. (2a) s / Op. (3a) O(- s / – p). (4a) O – s. Of these, (1a) and (2a) entail Op by propositional logic; next, given the SDL axiom O(A / B) / (OA / OB), (3a) implies O – s / O – p; but the latter, taken in conjunction with (4a), entails O – p by propositional logic. In the combination of Op, O – p, and the axiom OA / – O – A, of course, we have a formally inconsistent set. The paradox of the knower, first presented by Lennart Bqvist (Noûs, 1967), is generated by these apparent truths: first, some of us sometimes do what we should not do; and second, there are those who are obligated to know that such wrongful doings occur. Consider the following scenario. Jones works as a security guard at a local store. One evening, while Jones is on duty, Smith, a disgruntled former employee out for revenge, sets the store on fire just a few yards away from Jones’s work station. Here it seems that (1)–(3) are all true (and thus jointly consistent): (1) Smith set the store on fire while Jones was on duty. (2) If Smith set the store on fire while Jones was on duty, it is obligatory that Jones knows that Smith set the store on fire. (3) Smith ought not set the store on fire. Independently, as a consequence of the concept of knowledge, there is the epistemic theorem that (4) The statement that Jones knows that Smith set the store on fire entails the statement that Smith set the store on fire. Next, within SDL (1) and (2) surely appear to imply: (5) It is obligatory that Jones knows that Smith set the store on fire. But (4) and (5) together yield (6) Smith ought to set the store on fire, given the SDL theorem that if A / B is a theorem, so is OA / OB. And therein resides the paradox: not only does (6) appear false, the conjunction of (6) and (3) is formally inconsistent with the SDL axiom OA / – O – A. The overwhelming verdict among deontic logicians is that SDL genuinely succumbs to the deontic paradoxes. But it is controversial what other approach is best followed to resolve these puzzles. Two of the most attractive proposals are Castañeda’s two-sorted system (Thinking and Doing, 1975), and the agent-and-time relativized approach of Fred Feldman (Philosophical Perspectives, 1990).
See also DEONTIC LOGIC, FORMAL LOGIC, MORAL DILEMMA , SET- THEORETIC PARA – DOXE. J.E.T.