Supererogatory acts are those that lie “beyond the call of duty.” There are two standard ways to define this idea more precisely. Although the definitions are often seen as equivalent, I argue that they can diverge when options are infinite, or when there are cycles of better options; moreover, each definition is acceptable in only one case. I consider two ways out of this dilemma.

In this paper, I will discuss some examples of the so-called contrary-to-duty paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us what ought to be the case if something forbidden is true, for example: ‘If she is guilty, she should confess’. Contrary-to-duty obligations are important in our moral and legal thinking. Therefore, we want to be able to find an adequate symbolisation of such obligations in some logical system, a task that has turned out (...) to be difficult. This is shown by the so-called contrary-to-duty paradox. I will investigate and evaluate one kind of solution to this problem that has been suggested in the literature, which I will call the ‘counterfactual solution’. I will use some recent systems that combine not only counterfactual logic and deontic logic, but also temporal logic, in my analysis of the paradox. I will argue that the counterfactual solution has many attractive features and that it can give a fairly satisfactory answer to some examples of the contrary-to-duty paradox, but that it nevertheless has some serious problems. The conclusion is that, notwithstanding the many attractive features of the solution, there seem to be other approaches to the paradox that are more promising. (shrink)

A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. “if you have hurt your friend, you should apologise”, “if he is guilty, he should confess”, and “if she will not keep her promise to you, she ought to call you”. It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic deontic systems, (...) i.e., systems that include temporal, alethic and dyadic deontic operators. We will then show how it is possible to use our formal apparatus to symbolise contrary-to-duty obligations and to solve the so-called contrary-to-duty (obligation) paradox, a problem well known in deontic logic. We will argue that this response to the puzzle has many attractive features. Semantic tableaux are used to characterise our systems proof theoretically and a kind of possible world semantics, inspired by the so-called T× W semantics, to characterise them semantically. Our models contain several different accessibility relations and a preference relation between possible worlds, which are used in the definitions of the truth conditions for the various operators. Soundness results are obtained for every tableau system and completeness results for a subclass of them. (shrink)

According to typical ought-implies-can principles, if you have an obligation to vaccinate me tomorrow, then you can vaccinate me tomorrow. Such principles are uninformative about conditional obligations: what if you only have an obligation to vaccinate me tomorrow if you synthesize a vaccine today? Then maybe you cannot vaccinate me tomorrow ; what you can do instead, I propose, is make it the case that the conditional obligation is not violated. More generally, I propose the ought-implies-can-obey principle: an agent has (...) an obligation only at times at which the agent can obey the obligation. I also propose another principle, which captures the idea that ‘ought’ implies ‘can avoid’. I defend both principles mainly by arguing that they help explain why agents lose obligations, including conditional ones. (shrink)

In Paradoxa Stoicorum, the Roman philosopher Cicero defends six important Stoic theses. Since these theses seem counterintuitive, and it is not likely that the average person would agree with them, they were generally called "paradoxes". According to the third paradox, (P3), (all) transgressions (wrong actions) are equal and (all) right actions are equal. According to one interpretation of this principle, which I will call (P3′), it means that if it is forbidden that A and it is forbidden that B, then (...) not-A is as good as not-B; and if it is permitted that A and it is permitted that B, then A is as good as B. In this paper, I show how it is possible to prove this thesis in dyadic deontic logic. I also try to defend (P3′) against some philosophical counterarguments. Furthermore, I address the claim that (P3′) is not a correct interpretation of Cicero’s third paradox and the assertion that it does not matter whether (P3′) is true or not. I argue that it does matter whether (P3′) is true or not, but acknowledge that (P3′) is perhaps a slightly different principle than Cicero’s thesis. The upshot is that (P3′) seems to be a plausible principle, and that at least one part of paradox III in Cicero’s Paradoxa Stoicorum appears to be defensible. (shrink)

The purpose of this paper is to develop a class of semantic tableau systems for some dyadic deontic logics. We will consider 16 different pure dyadic deontic tableau systems and 32 different alethic dyadic deontic tableau systems. Possible world semantics is used to interpret our formal languages. Some relationships between our systems and well known dyadic deontic logics in the literature are pointed out and soundness results are obtained for every tableau system. Completeness results are obtained for all 16 pure (...) dyadic deontic systems and for 16 alethic dyadic deontic systems. (shrink)

The paper presents an infinite hierarchy of sound and complete axiomatic systems for Two-Dimensional Modal Tense Logic with Historical Necessity, Agents and Acts. A main novelty of these logics is their capacity to represent formally (i) basic action-sentences asserting that such and such an act is performed/omitted by an agent, as well as (ii) causative action-sentences asserting that by performing/omitting a certain act, an agent causes that such and such a state-of-affairs is realized (e.g. comes about/ceases/remains/remains absent). We illustrate how (...) the formal machinery of our systems can be used to reconstruct a number of interesting ideas in the Logic of Agency and Action that have been proposed by authors like von Wright, von Kutschera, Belnap and Segerberg. (shrink)

The Mīmāṃsā school of Indian philosophy has for its main purpose the interpretation of injunctions that are found in a set of sacred texts, the Vedas. In their works, Mīmāṃsā authors provide some of the most detailed and systematic examinations available anywhere of statements with a deontic force; however, their considerations have generally not been registered outside of Indological scholarship. In the present article we analyze the Mīmāṃsā theory of Vedic injunctions from a logical and philosophical point of view. The (...) theory at issue can be regarded as a system of reasoning based on certain fundamental principles, such as the distinction between strong and weak duties, and on a taxonomy of ritual actions. We start by reconstructing the conceptual framework of the theory and then move to a formalization of its core aspects. Our contribution represents a new perspective to study Mīmāṃsā and outlines its relevance, in general, for deontic reasoning. (shrink)

With their book Logical Pluralism, Jc Beall and Greg Restall have elaborated on their previous statements on logical pluralism. Their view of logical pluralism is centred on ways of understanding logical consequence. The essay tries to come to grips with their doctrine of logical pluralism by highlighting some points that might be made clearer, and questioning the force of some of Beall’s and Restall’s central arguments. In that connection seven problems for their approach are put forth: (1) The Informal Common (...) Core Problem, (2) The Formal Common Core Problem, (3) The Superior Judge Problem, (4) The Problem of the Conditional, (6) The Problem of an Unsettled Concept of Consequence, (7) The Methodological Problem, (8) The General Logical Form Problem. It seems that the case for logical pluralism is far from clear. It is even unclear what exactly logical pluralism is and where is stops. It is also unclear if logical pluralism could be stated as it is, if it were true. So far universalism seems to be the better position to take. (shrink)

The purpose of the paper is to present a logical framework that allow to formalize a kind of prima facie duties, defeasible conditional duties, indefeasible conditional duties and actual (indefeasible) duties, as well as to show their logical interconnections.

‘AI & Law’ research has been around since the 1970s, even though with shifting emphasis. This is an overview of the contributions of digital technologies, both artificial intelligence and non-AI smart tools, to both the legal professions and the police. For example, we briefly consider text mining and case-automated summarization, tools supporting argumentation, tools concerning sentencing based on the technique of case-based reasoning, the role of abductive reasoning, research into applying AI to legal evidence, tools for fighting crime and tools (...) for identification. (shrink)

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)

We often use sentences that seem conditional in nature when we reason about normative issues, e.g. ‘If you have promised to do something, you should keep your promise’ and ‘If you have done something bad, you should apologize’. We seem to think that promise-making in some sense commits us to promise-keeping and that acting bad in some sense creates an obligation to apologize. It is, however, not obvious how we should symbolize such sentences in a formal language. The purpose of (...) this essay is to investigate some different possible formalizations of different conditional obligation sentences. I consider seven different interpretations of the concept of commitment or conditional obligation and I say something about the logical properties of these different interpretations. (shrink)

This paper makes an attempt at the conceptual foundation of descriptive ethical theories in terms of evolutionary anthropology. It suggests, first, that what human social actors tend to accept to be morally valid and legitimate ultimately rests upon empirical authority relations and, second, that this acceptance follows an evolved pattern of hierarchical behaviour control in the social animal species. The analysis starts with a brief review of Thomas Hobbes'' moral philosophy, with special emphasis on Hobbes'' authoritarian view of moral validity (...) and of the common political origins and ultimate basis of legitimacy of moral and legal systems. Hobbes'' philosophical conceptions are then put into the context of Max Weber''s influential empirical theory of legitimacy, especially charismatic revelation and authority as the ultimate source of all moral, legal and religious obligations. Weber''s concept of charismatic authority is given a biobehavioural interpretation in terms of ritualised status signals indicating an individual''s superior physical and emotional dispositions to control the social actions of others. Various conclusions are drawn concerning the concept of moral validity and its possible evolutionary interpretations. (shrink)

In a series of articles, P. Vranas recently proposed a new imperative logic. The strong and weak inferences of this logic are motivated by an appeal to a strong and weak ‘support by reasons’ that transfers from the premisses of an argument to its conclusion. They also combine nonmonotonic and monotonic reasoning patterns. I show that for any moral agent, Vranas’s proposal can be simplified enormously.

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.

Using the mathematical frameworks of economic preference ranking, subjective probability, and rational learning through empirical evidence, the epistemological implications of teleological ethical intuitionism are pointed out to the extent to which the latter is based on cognitivist and objectivist concepts of value. The notions of objective value and objective norm are critically analysed with reference to epistemological criteria of intersubjectively shared valuative experience. It is concluded that one cannot meaningfully postulate general material theories of morality that could be tested, confirmed (...) or refuted by intersubjective empirical evidence of preferences and values, however loosely the empirical evidence of values may be interpreted. This situation is explained with reference to the ways in which preceived values become systematically influenced by the concomitants of individual valuative experience, but which have nothing to do with contingent subjective interests. (shrink)