This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper (...) is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concerns Åqvist’s system F supplemented with the principle of cautious monotony. It is established that, under the maximality rule, F + is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth . From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F + is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth . Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity. (shrink)

Cliff Landesman provides a vivid description of a case where we have no best outcome available to us. He poses this as a problem for utilitarians who advise us to do the best we can. This does indeed make such advice impractical. I begin by contrasting older versions of utilitarianism with newer ones that have appeared in deontic logic and that were designed precisely to accommodate Landesman's sort of scenario. (I cast matters in terms of the Limit Assumption and world-theoretic (...) versions of utilitarianism.) I then make three points. First, Landesman's problem does not pose any special problem for these newer theories. Secondly, I note that it is an interesting consequence of these newer theories being utilitarian theories, that--contrary to the tradition--utilitarianism isn't automatically a no conflicts theory of obligation. Thirdly, and most importantly, I identify a new, deeper and wider theoretical problem: "The Confinement Problem". This problem infests the newer versions of utilitarianism. Worse still, the infestation spreads to satisficing consequentialism (cf. Scheffler, Slote), the direction Landesman points to for a solution to his problem, and this new problem is one where the theoretical rulings of these theories clearly conflict with intuition. (shrink)

In "Futurc Generations: Further Problems,"‘ and Part Four of Reasons and Persons} Derek Pariit raises many perplexing questions. Although some think his ingenious arguments little more than delightful puzzles, I believe they challenge some of our deepest beliefs. In this article, I examine some of Pariit’s arguments, focusing mainly on "The Mere Addition Paradox." If my analysis is correct, Parfit’s arguments have extremely interesting and important implications that not even Pariit rcalized. In Part I, I present ParHt’s argument for the (...) Merc Addition Paradox, and show that given Pa.rHt’s assumptions, a radical conclusion seems t0 follow; the notion of "bctter th2m"—indced, even the notion of "aH things.. (shrink)

We discuss similarities and residual differences, within the general semantic framework of minimality, between defeasible inference, belief revision, counterfactual conditionals, updating — and also conditional obligation in deontic logic. Our purpose is not to establish new results, but to bring together existing material to form a clear overall picture.

Deontic logic is an area of logic which investigates normative concepts, systems of norms, and normative reasoning. The word ‘deontic’ is derived from the Greek expression ‘déon’, which means ‘what is binding’ or ‘proper’. Thus, Jeremy Bentham used the word ‘deontology’ for “the science of morality,” and the Austrian philosopher Ernst Mally, who developed in the 1920s a system of the “fundamental principles the logic of ought,” called his theory ‘Deontik’. Normative concepts include the concepts of obligation (ought), permission (may), (...) prohibition (may not), and related notions, such as the concept of right. Systems of deontic logic contain, in addition to the usual sentential connectives and quantifiers, logical constants which represent some of these normative concepts. (shrink)

Recently, Bengt Hansson presented a paper about dyadic deontic logic,2 criticizing some purely axiomatic systems of dyadic deontic logic and proposing three purely semantical systems of dyadic deontic logic which he confidently called dyadic standard systems of deontic logic (DSDL1–3). Here I shall discuss the third by far most interesting system DSDL3 which is operating with preference relations. First, I shall describe this semantical system (Sections 1.1–1.3). Then I shall give an axiomatic system (Section 1.4) which is proved to be (...) correct (Section 2) and complete (Section 3) with respect to Hansson's semantics. Finally, in face of these results Hansson's semantics will be discussed from a more intuitive standpoint. After emphasizing its intuitive attractiveness (Section 4.1) I will show that two objections often discussed in connection with preference relations do not apply to it (Section 4.2 and 4.3); more precisely, I will show that the connectedness condition for preference relations can be dropped and that, in a sense, it is not necessary to compare two possible worlds differing in infinitely many respects. (What exactly is meant by this, will become clear later on.) Yet there is a third objection to Hansson's semantics which points to a real intuitive inadequacy of DSDL3. A way of removing this inadequacy, which corresponds to Hansson's own intuitions as well as to familiar metaethical views, is suggested, but not technically realized (Section 4.4). In the last section (section 4.5) I shall briefly show that DSDL3 is decidable, as expected. (shrink)

This paper develops an informal semantics for 'ought to be' and 'ought to be given...' and argues for its plausibility. A feature of the semantics is that it invalidates 'if a entails b, And o(a), Then o(b)' and 'if o(a) & o(b), Then o(a&b)', While validating detachment for conditional obligation.

The main contribution of this paper is a completeness result for an axiomatization of Hansson [13]'s deontic system DSDL2, whose semantics involves a non-necessarily transitive betterness relation. Reference is made to a deductive system put forth by Åqvist [2, 3].