We consider an infinite hierarchy of systems of Alethic Modal Logic with so-called Levels of Perfection, and add to them suitable definitions of such interesting deontic categories as those of supererogation, offence, conditional obligation and conditional permission. We then state three problems concerning the proper characterization of the resulting logic(s) for our defined notions, and discuss two of these problems in some detail.

Recently, a number of philosophers have argued that we can and should “consequentialize” non-consequentialist moral theories, putting them into a consequentialist framework. I argue that these philosophers, usually treated as a group, in fact offer three separate arguments, two of which are incompatible. I show that none represent significant threats to a committed non-consequentialist, and that the literature has suffered due to a failure to distinguish these arguments. I conclude by showing that the failure of the consequentializers’ arguments has implications (...) for disciplines, such as economics, logic, decision theory, and linguistics, which sometimes use a consequentialist structure to represent non-consequentialist ethical theories. (shrink)

AI research is being challenged with ensuring that autonomous agents learn to behave ethically, namely in alignment with moral values. Here, we propose a novel way of tackling the value alignment problem as a two-step process. The first step consists on formalising moral values and value aligned behaviour based on philosophical foundations. Our formalisation is compatible with the framework of (Multi-Objective) Reinforcement Learning, to ease the handling of an agent’s individual and ethical objectives. The second step consists in designing an (...) environment wherein an agent learns to behave ethically while pursuing its individual objective. We leverage on our theoretical results to introduce an algorithm that automates our two-step approach. In the cases where value-aligned behaviour is possible, our algorithm produces a learning environment for the agent wherein it will learn a value-aligned behaviour. (shrink)

Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...) “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

Continuing prior work by the author, a simple classical system for personal obligation is integrated with a fairly rich system for aretaic (agent-evaluative) appraisal. I then explore various relationships between definable aretaic statuses such as praiseworthiness and blameworthiness and deontic statuses such as obligatoriness and impermissibility. I focus on partitions of the normative statuses generated ("normative positions" but without explicit representation of agency). In addition to being able to model and explore fundamental questions in ethical theory about the connection between (...) blame, praise, permissibility and obligation, this allows me to carefully represent schemes for supererogation and kin. These controversial concepts have provided challenges to both ethical theory and deontic logic, and are among deontic logic's test cases. (shrink)

Ethical theorists often assume that the verb ‘ought’ means roughly ‘has an obligation’; however, this assumption is belied by the diversity of ‘flavours’ of ought-sentences in English. A natural response is that ‘ought’ is ambiguous. However, this response is incompatible with the standard treatment of ‘ought’ by theoretical semanticists, who classify ‘ought’ as a member of the family of modal verbs, which are treated uniformly as operators. To many ethical theorists, however, this popular treatment in linguistics seems to elide an (...) important distinction between agential and non-agential ought-statements. The thought is that ‘ought’ must have at least two senses, one implicating agency and connected to obligations, and another covering other uses. In this paper, I pursue some resolution of this tension between semantic theory and ethical theory with respect to the meaning of ‘ought’. To this end, I consider what I believe to be the most linguistically sophisticated argument for the view that the word ‘ought’ is ambiguous between agential and non-agential senses. This argument, due to Mark Schroeder, is instructive but based on a false claim about the syntax of agential ought-sentences—or so I attempt to show by first situating Schroeder's argument in its proper linguistic background and then discussing some syntactic evidence that he fails to appreciate. Then, I use the failure of this argument to motivate some more general reflections on how the standard treatment of ‘ought’ by theoretical semanticists might be refined in the light of the distinction important to ethical theory between agential and non-agential ought-statements, but also on how ethical theory might benefit from more careful study of the dominant treatment of modals as operators in theoretical semantics. (shrink)

The crucial feature of obligation sentences to which the puzzles point is that such sentences, and evaluative sentences more generally, are defeasible. They may be warranted, given some information, only to be defeated by further information. A theory that recognizes this no longer needs to see conditional obligation as anything more than a simple combination of unary obligation and the conditional.

Overview of fundamental work in deontic logic.

There is a growing consensus, long maintained by Derek Parfit, that there is an important distinction between what we have reason to do on the one hand, and what it is rational for us to do on the other. Philosophers are now realising that there is a conceptual distinction between rationality and normativity. Given this distinction, it thus becomes a substantive question whether rationality is genuinely normative; that is, whether there is any reason to do what rationality requires. While some (...) philosophers have argued that we sometimes have reason to do what rationality requires, it is notoriously difficult to show that there are always universal and categorical reasons to do what rationality requires. But if it is not the case that there are always universal and categorical reasons to do what rationality requires, then rationality is not genuinely normative.This dissertation offers a vindication of the normativity of rationality. I maintain that there is a robust relation between rational requirements and normative reasons. In arguing for this claim, I develop what I call the reasons-sensitive view of rationality, according to which rational requirements are normative verdicts: they are second-order claims about what there is conclusive reason of rationality to do. This view explains why there are always universal and categorical reasons to be rational. So while we may not always have most reason to do what it is rational for us to do, there is always some reason—reasons of rationality—to do what it is rational for us to do. I then show how this reasons-sensitive view addresses and responds to what I diagnose to be the major sources of skepticism about the normativity of rationality. (shrink)