Moral dilemmas and nonmonotonic logic

Conclusion From a philosophical standpoint, the work presented here is based on van Fraassen [26]. The bulk of that paper is organized around a series of arguments against the assumption, built into standard deontic logic, that moral dilemmas are impossible; and van Fraassen only briefly sketches his alternative approach. His paper ends with the conclusion that the problem of possibly irresolvable moral conflict reveals serious flaws in the philosophical and semantic foundations of orthodox deontic logic, but also suggests a rich set of new problems and methods for such logic. My goal has been to suggest that some of these methods might be found in current research on nonmonotonic reasoning, and that some of the problems may have been confronted there as well.I have shown that nonmonotonic logics provide a natural framework for reasoning about moral dilemmas, perhaps even more useful than the ordinary modal framework, and that the issues surrounding the treatment of exceptional information within these logics run parallel to some of the problems posed by conditional oughts. However, there is also another way in which deontic logic might benefit from a connection to nonmonotonic reasoning. A familiar criticism among ethicists of work in deontic logic is that it is too abstract, and too far removed from the kind of problems confronted by real agents in moral deliberation. It must be said that similar criticisms of abstraction and irrelevance are often lodged against work in nonmonotonic reasoning by more practically minded researchers in artificial intelligence; but here, at least, the criticisms are taken seriously. Nonmonotonic logic aims at a qualitative account of commonsense reasoning, which can be used to relate planning and action to defeasible goals and beliefs; and at least some of the theories developed in this area have been tested in realistic situations. By linking the subject of deontic logic to this research, it may be possible also to relate the idealized study of moral reasoning typical of the field to a more robust treatment of practical deliberation.     

The Definition of Moral Dilemmas: A Logical Problem

This paper concerns one of the undecided disputes of modern moral philosophy: the possibility of moral dilemmas. Whereas proponents of the possibility of moral dilemmas often appeal to moral experience, many opponents refer to ethical theory and deontic logic. My aim in this paper is to clarify some of the tension between moral experience and ethical theory with respect to moral dilemmas. In Part One I try to show that a number of logical arguments against the possibility of moral dilemmas, though apparently very different, turn out to be basically the same, as they are all based on the following concept of ought: if A ought to be done, doing B is impermissible and doing A itself is permissible. In Part Two I present an overview of several definitions of moral dilemmas that have been given by proponents of moral dilemmas: definitions that define moral dilemmas in terms of oughts and definitions that define them in terms of reasons. I conclude that, while reason is to weak, ought is too strong a concept to define moral dilemmas with. In this way, the arguments from Part One create a logical problem for proponents of the possibility of moral dilemmas to define moral dilemmas.     

Moral dilemmas,disjunctive obligations,and Kant's principle that ‘ought’ implies ‘can’

In moral dilemmas, where circumstances prevent two or more equally justified prima facie ethical requirements from being fulfilled, it is often maintained that, since the agent cannot do both, conjoint obligation is overridden by Kant's principle that ought implies can, but that the agent nevertheless has a disjunctive obligation to perform one of the otherwise obligatory actions or the other. Against this commonly received view, it is demonstrated that although Kant's ought-can principle may avoid logical inconsistency, the principle is incompatible with disjunctive obligation in standard deontic logic, and that it entails paradoxically that none of the conflicting dilemma actions will in fact occur. The principle appears to provide the only plausible safeguard against deontic antinomy, but cannot be admitted because of its collision with considered moral judgments.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

On the non-availability of Dawson-modeling into certain relevance alethic modal logics

This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R _S4or R _M. The technique is to construct an extension of the well known entailment matrix set M ₀and show that the model of the deontic formula P (A v B). PA v PB is excluded.     

Why we need a relevant theory of conditionals

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap's system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis' theory of causation, Lewis' dyadic deontic logic, and Chellas' dyadic deontic logic.I am of course deeply indebted to André Fuhrmann, who co-wrote the paper on which the present effort is based. Perhaps I should also thank the Social Sciences and Humanities Research Council of Canada because the original research for this project was funded by them in the form of a post-doctoral fellowship.     

Is Default Logic a Reinvention of Inductive-Statistical Reasoning?

Currently there is hardly any connection between philosophy of science and Artificial Intelligence research. We argue that both fields can benefit from each other. As an example of this mutual benefit we discuss the relation between Inductive-Statistical Reasoning and Default Logic. One of the main topics in AI research is the study of common-sense reasoning with incomplete information. Default logic is especially developed to formalise this type of reasoning. We show that there is a striking resemblance between inductive-statistical reasoning and default logic. A central theme in the logical positivist study of inductive-statistical reasoning such as Hempels Criterion of Maximal Specificity turns out to be equally important in default logic. We also discuss to what extent the relevance of the results of Logical Positivism to AI research could contribute to a reevaluation of Logical Positivism in general.     

Reasoning to what is true in fiction

The paper discusses the principle by which we reason to what is true in fiction. The focus is David Lewis's article Truth in Fiction (1978) which proposes an analysis in terms of counterfactuals and possible worlds. It is argued thatLewis's account is inadequate in detail and also in principle in that it conflicts radically with basic and familiar tenets of literary criticism. Literary critical reasoning about fiction concerns not the discovery of facts in possible worlds but the recovery of meanings in interpretative frameworks. The model theoretic approach fails to account for common literary or rhetorical devices like unreliable narration, connotation and point of view. And in explaining indeterminacy of content in terms of truth-value gaps it gives too simplistic an account of critical reasoning about character motivation and thematic development. A more adequate account of content-indeterminacy can be provided through a comparison of the interpretation of fiction with the interpretation of human action. A broader motif in the paper is the underlying tension between what is required for the logic of fiction and what is required for the aesthetics of fiction.     

Listening to a different voice: A feminist critique of Gilligan

A critical examination of Carol Gilligan's study of psychological theory and women's development, this essay begins by exploring her concerns about malebiased developmental theorizing. I consider in detail Gilligan's criticisms of Sigmund Freud and her own empirical studies of moral development, as they relate to the work of L. Kohlberg. After defending Freud to some degree, I propose various (less theoretical but intuitively plausible) alternative interpretations of her data-interviews with males and females about hypothetical ethical dilemmas and with females about actual abortion decisions. I contend that Gilligan is too willing to concede the adequacy of Kohlberg's categories for fathoming the moral reasoning of males and that she may, in consequence, exaggerate differences between males and females. Noting the ironic similarities between Gilligan's claims and Schopenhauer's misogyny, I suggest that there may be something undesirably self-limiting about the different course of development she sketches. To move toward a morally preferable, feminism-compatible version of an ethic of care, I recommend that it be extended — by the imagination — beyond the here and now and that it not be restricted to existing webs of personal relationships.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

Intuitionistic Autoepistemic Logic

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.     

Rules of Existential Quantification into "Intensional Contexts"

Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).     

Trying to Resolve the Two-Envelope Problem

After explaining the well-known two-envelope paradox by indicating the fallacy involved, we consider the two-envelope problem of evaluating the factual information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An interpretation is made for statistical science at large.     

The death of Abramo of Montecosaro

In this microhistory from 1553, set in Montecosaro, in east-central Italy, local officials, armed with their lords permission, set out to catch a Jewish banker in sexual traffic with a Christian. To bait their trap, they hire a local woman, who agrees to be found at night in the bankers house. Two years later, the entrappers, arrested, jailed, and tried for high-handed tactics, recount their version of the enterprise, and the lord, also jailed, gives his. The unfortunate banker, meanwhile, has died of prisons rigors, while the lord has pocketed his fat ransom. Though harsh, the state courts aim to punish all those guilty of justices miscarriage, including the rough handling of a Jewish victim. The article explores the attitudes of small-town Christians to the Jewish banker and strives to re-assemble the dialogue across the religious gap as the trap snaps shut. It also offers a well furbished narrative from a period for which few extended Jewish tales survive.     

Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics

Some properties of Kripke-sheaf semantics for super-intuitionistic predicate logics are shown. The concept ofp-morphisms between Kripke sheaves is introduced. It is shown that if there exists ap-morphism from a Kripke sheaf ₁ into ₂ then the logic characterized by ₁ is contained in the logic characterized by ₂. Examples of Kripke-sheaf complete and finitely axiomatizable super-intuitionistic (and intermediate) predicate logics each of which is Kripke-frame incomplete are given. A correction to the author's previous paper Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics (Studia Logica, 49(1990), pp. 289–306 ) is stated.Dedicated to Professor Takeshi Kotake on his 60th birthdayThis research was partially supported by Grant-in-Aid for Encouragement of Young Scientists No. 03740107, Ministry of Educatin, Science and Culture, Japan.     

Syntactical investigations intoBI logic andBB′I logic

In this note, we will study four implicational logicsB, BI, BB and BBI. In [5], Martin and Meyer proved that a formula is provable inBB if and only if is provable inBBI and is not of the form of » . Though it gave a positive solution to theP - W problem, their method was semantical and not easy to grasp. We shall give a syntactical proof of the syntactical relation betweenBB andBBI logics. It also includes a syntactical proof of Powers and Dwyer's theorem that is proved semantically in [5]. Moreover, we shall establish the same relation betweenB andBI logics asBB andBBI logics. This relation seems to say thatB logic is meaningful, and so we think thatB logic is the weakest among meaningful logics. Therefore, by Theorem 1.1, our Gentzentype system forBI logic may be regarded as the most basic among all meaningful logics. It should be mentioned here that the first syntactical proof ofP - W problem is given by Misao Nagayama [6].Presented byHiroakira Ono     

Reasoning and logic

Gilbert Harman, in Logic and Reasoning (Synthese 60 (1984), 107–127) describes an unsuccessful attempt ... to develop a theory which would give logic a special role in reasoning. Here reasoning is psychological, a procedure for revising one's beliefs. In the present paper, I construe reasoning sociologically, as a process of linguistic interaction; and show how both reasoning in the psychologistic sense and logic are related to that process.     

From Brouwerian Counter Examples to the Creating Subject

The original Brouwerian counter examples were algorithmic in nature; after the introduction of choice sequences, Brouwer devised a version which did not depend on algorithms. This is the origin of the creating subject technique. The method allowed stronger refutations of classical principles. Here it is used to show that negative dense subsets of the continuum are indecomposable.     

Why-questions, determinism and circular reasoning

In this article I shall aim at showing that there exists beneath the surface of many why-questions about human behaviour a nest of deterministic assumptions which can preclude their ever being truly answered. A symptom of the presence of these underlying assumptions can be observed in an explanation-seeking dialogue in which the questioner persistently tries to discover why a certain human behaviour occurred. He repeats his why-question until he gets the type of answer he wants, but in the process he effectively reasons in a circle. If the repeated questioning with its implied circular reasoning becomes chronic, then the questioner will beg the question with regards to the answer he desires and consequently run the risk of missing the truth.