Two Senses of 'Ought' in Forrester's Paradox

Introduction to Formal Philosophy, 2018

Deontic logic is the logic of normative concepts such as obligation, permission, and prohibition. This non-technical overview of the area has a strong emphasis on the connections between deontic logic and problems discussed in moral philosophy. Major issues treated are the distinction between ought-to-be and oughtto-do, the various meanings of permissive expressions, the logical relations among norms, the paradoxes of deontic logic, and the nature of moral conflicts and moral dilemmas. It is concluded that deontic logic has resources for precise treatment of important issues in moral philosophy, but in order to make full use of these resources, more cooperation between logicians and moral philosophers is needed.

Normative Multi-agent …, 2007

The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed 'coherent', how to deal with normative conflicts, how contraryto-duty obligations can be appropriately modeled, how dyadic deontic operators may be redefined to relate to sets of norms instead of preference relations between possible worlds, how various concepts of permission can be accommodated, how meaning postulates and counts-as conditionals can be taken into account, and how sets of norms may be revised and merged. The problems are discussed from the viewpoint of input/output logic as developed by van der Torre & Makinson. We argue that norms, not ideality, should take the central position in deontic semantics, and that a semantics that represents norms, as input/output logic does, provides helpful tools for analyzing, clarifying and solving the problems of deontic logic.

2012

The purpose of this paper is to make a suggestion to deontic logic: Respect Hume's Law, the answer to the is-ought problem that says that all ought-talk is completely cut off from is-talk. Most deontic logicians have sought another solution: Namely, the solution that says that we can bridge the is-ought gap. Thus, a century's worth of research into these normative systems of logic has lead to many attempts at doing just that. At the same time, the field of deontic logic has come to be plagued with paradox. My argument essentially depends upon there being a substantive relation between this betrayal of Hume and the plethora of paradoxes that have appeared in two-adic (binary normative operator), oneadic (unary normative operator), and zero-adic (constant normative operator) deontic systems, expressed in the traditions of von Wright, Kripke, and Anderson, respectively. My suggestion has two motivations: First, to rid the philosophical literature of its puzzles and second, to give Hume's Law a proper formalization. Exploring the issues related to this project also points to the idea that maybe we should re-engineer (e.g., further generalize) our classical calculus, which might involve the adoption of many-valued logics somewhere down the line.

IOS Press eBooks, 2021

Inspired by Kelsen's view that norms establish causal-like connections between facts and sanctions, we develop a deontic logic in which a proposition is obligatory iff its complement causes a violation. We provide a logic for normative causality, define non-contextual and contextual notions of illicit and duty, and show that the logic of such duties is well-behaved and solves the main deontic paradoxes.

2004

This paper aims to examine Horty’s proposal of utilitarian deontic logic [7]. It will focus on his dominance operators by way of simplified semantics. An axiomatization of the logic of the simplified semantics will be shown by the construction of a finite countermodel. Analysis of the proof suggests possibilities of further investigations. The presented version of Horty’s proposal does not make essential differences from standard deontic logic: the deontic operators are normal, and thus paradoxes of deontic logic occur. Non-monotonic agency operators should be considered.

The Logics of Formal Inconsistency (LFIs) are paraconsistent logics which internalize the notions of consistency and inconsistency by means of connectives. Based on that idea, in this paper we propose two deontic systems in which contradictory obligations are allowed, without trivializing the system. Thus, from conflicting obligations Oϕ and O¬ϕ contained in (or derived from) an information set, it can be derived that the sentence ϕ is deontically inconsistent. This avoids the logic collapse, and, on the other hand, this allows to "repair" or to refine the given information set. This approach can be used, for instance, for analyzing paradoxes based on contrary-toduty obligations. KEYWORDS: Logics of formal inconsistency, deontic logic, contrary-to-duty obligations.

Abstract The paper presents a new consequentialist deontic logic in which the relation of preference over sets of possible worlds and the relation of conditional dominance are both transitive. This logic validates the principle that absolute ought can be derived from conditional ought in case the conditional statement is the agent's absolute ought. Ought about conditionals is not implied by conditional ought in this logic.

2006

The idea that there are intimate connections between Logic and Ethics might seem rather bizarre, but in fact there are several long-running problems in Ethics which will yield to logical insights. I have already written—albeit briefly—about how Logic takes with one hand by sharpening Hume’s puzzle about deriving an ought from an is in identifying this insight with an intuition of the interpolation lemma, while giving with the other by providing us with the theory of interpretations which allows us to think of oughts as interpretable as is’s. I have nothing to add to that for the moment, and here I shall be concerned with other issues in Logic and Ethics. In this brief note I am concerned to indicate a known and named paradox which–it seems to me—lies at the heart of Ethics as well as in its place of origin. In doing this I am returning to ideas which first struck me when I was a philosophy undergraduate reading—inter alia—Carnap’s Meaning and Necessity, wherein I discovered Carnap’s...

2016

In recent work, Cariani has proposed a semantics for ought that combines two features: (i) it invalidates Inheritance in a principled manner; (ii) it allows for coarseness, which means that ought(φ) can be true even if there are specific ways of making φ true that are (intuitively speaking) impermissible. We present a group of multi-modal logics based on Cariani’s proposal. We study their formal properties and compare them to existing approaches in the deontic logic literature — most notably Anglberger et al.’s logic of obligation as weakest permission, and deontic stit logic.