Overview of fundamental work in deontic logic.

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...) obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. -/- I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis' V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. -/- My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like "If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated" is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations. (shrink)

“Branching space-times” is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its relativistic theory of spatio-temporal relations; this ability is essential for the representation of local indeterminism. This essay indicates how BST might be seen to grow out of Newton ’s deterministic and (...) non-relativistic theory by two independent moves: Taking account of indeterminism, and attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since and are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and branching space-times indeterminism. (shrink)

Philosophical accounts of collective intentionality typically rely on members to form a personal intention of sorts, viewed as a mental state. This tendency is opposed by recent economic literature on team-directed reasoning, which focuses on the reasoning process leading up to the formation of the members’ intentions. Our formal analysis bridges these paradigms and criticizes the team- directed reasoning account on two counts: first, team-directed reasoning is supposed to transcend traditional game and decision theory by adopting a certain collectivistic reasoning (...) method. However, we show that team-directed reasoning yields the same action recommendations as a certain I-mode we-intention type. Accordingly, an important part of we-mode reasoning can be reduced to I-mode reasoning with certain preferences. Second, contrary to the claims of team-directed-reasoning theorists, we refute that team-directed reasoning surpasses pro-group intentions in selecting cooperatively rational solutions. That is, in some scenarios team-directed reasoning fails to guarantee successful cooperation whereas pro-group intentions succeed in doing so. We therefore propose to revise team-directed reasoning and introduce a third we-intention type, called participatory intentions. We prove that participatory intentions guarantee that a best group action is performed whenever either team-directed reasoning or pro-group intentions do. (shrink)

This paper works within a particular framework for reasoning about actions—sometimes known as the framework of “stit semantics”—originally due to Belnap and Perloff, based ultimately on the theory of indeterminism set out in Prior’s indeterministic tense logic, and developed in full detail by Belnap, Perloff, and Xu [3]. The issues I want to consider arise when certain normative, or decision theoretic, notions are introduced into this framework: here I will focus on the notion of a right action, and so on (...) the formulation of act utilitarianism within this indeterministic setting. The problem is simply that there are two different, and conflicting, ways of defining this notion, both well-motivated, and both carrying intuitive weight. (shrink)

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of (...) the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings. (shrink)

An informal sketch is offered of some chief ideas of the (formal) ``branching histories'' theory of objective possibility, free will and indeterminism. Reference is made to ``branching time'' and to ``branching space-times,'' with emphasis on a theme that they share: Objective possibilities are in Our World, organized by the relation of causal order.

Imperatives occur ubiquitously in natural languages. They produce forces which change the addressee’s cognitive state and regulate her actions accordingly. In real life we often receive conflicting orders, typically, issued by various authorities with different ranks. A new update semantics is proposed in this paper to formalize this idea. The general properties of this semantics, as well as its background ideas are discussed extensively. In addition, we compare our framework with other approaches of deontic logics in the context of normative (...) conflicts. (shrink)