Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on (...) structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

We study the logic of strategic ability of coalitions of agents with bounded memory by introducing Alternating-time Temporal Logic with Bounded Memory (ATLBM), a variant of Alternating-time Temporal Logic (ATL). ATLBM accounts for two main consequences of the assumption that agents have bounded memory. First, an agent can only remember a strategy that specifies actions in a bounded number of different circumstances. While the ATL-formula means that coalition C has a joint strategy which will make (...) φ true forever, the ATLBM-formula means that C has a joint strategy which for each agent in C specifies what to do in no more than n different circumstances and which will make φ true forever. Second, an agent has bounded recall—a strategy can only take the last m states of the system into account. We use the logic to study the interaction between strategic ability, bounded number of decisions, bounded recall and incomplete information. We discuss the logical properties and expressiveness of ATLBM, and its relationship to ATL. We show that ATLBM can express properties of strategic ability under bounded memory which cannot be expressed in ATL. (shrink)

This book offers an ideal first reader in ancient Greek. It presents a selection of extracts from a comprehensive range of Greek authors, from Homer to Plutarch, together with generous help with vocabulary and grammar. The passages have been chosen for their intrinsic interest and variety, and brief introductions set them in context. All but the commonest Greek words are glossed as they occur and a general vocabulary is included at the back. Although the book is designed to be used (...) by students who have only completed a beginner's course in Greek, students of all ages will find that it helps them to improve their ability and confidence in reading a wide range of prose and verse texts, while at the same time providing a fascinating and copiously illustrated introduction to the riches and variety of ancient Greek literature over a period of almost a thousand years. (shrink)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, (...) there was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and (...) commonsense reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

In this article, I introduce and analyze the notion of joint abilities; a species of ability possessed by agents who perform joint actions of a certain kind. Joint abilities are abilitie...

This paper considers whether, and if so how, the modelling of joint action in social philosophy – principally in the work of Margaret Gilbert and Michael Bratman – might assist in understanding and applying the concept of concerted practices in European competition law. More specifically, the paper focuses on a well-known difficulty in the application of that concept, namely, distinguishing between concerted practice and rational or intelligent adaptation in oligopolistic markets. The paper argues that although Bratman's model of (...) class='Hi'>joint action is more psychologically plausible and phenomenologically resonant, its less demanding character also makes it less useful than Gilbert's in our understanding of the legal concept of concerted practice and in dealing with the above difficulty. The paper proceeds in two parts: first, a discussion of the concept of concerted practices in European competition law; and second, a discussion of Gilbert and' Bratman's models of joint action, including a comparative assessment of their ability to provide an evidentiary target and an evidentiary platform for conceited practices. (shrink)

Work on 'can' in Action Theory is dichotomized into two styles of analysis: (1) what I call the indeterministic analysis, whereby for x to be able to do A means that there is no obstacle to x's doing A, and (2) the hypothetical analysis, which asserts that x is able to do A if and only if x will do A if x tries (wants, wills, chooses, etc.). This paper explores the general hypothesis that 'can' is two-ways ambiguous, that a (...) sense of opportunity corresponds to (1) and a sense of ability to something after the pattern of (2), and that a general concept of 'can' of the kind often sought after by action theorists requires a certain kind of integration of both concepts into a unified definition. The two previous most well-worked-out attempts to lay out a program along these lines, those of Sellars and Chisholm, are analyzed in detail in the hope of smoothing out some of the technical differences to provide foundations for further work of this type. An attempt is made to integrate the program with some recent developments in the concept of ability in the social sciences. The applicability of this work to some very vexing and significant problems in the social sciences is suggested. (shrink)

A selection function based semantics is offered for the 'can' of ability based on the idea that 'John can run a four minute mile' is true iff John would do so under the right conditions, meaning that he would do so under at least one appropriately chosen test condition. Completeness is proved for an axiom system and semantics based on this idea, and the logic turns out to be interestingly different from any standard system of modal logic.

The basic bimodal systemK/K can be interpreted as an analysis of the logic of ability developed in [1]. Where in [1] we would express the claimI can bring it about that P using the formula, with its non-normal operator, we will now use the formula. Here is a normal alethic possibilitation operator.is a normal necessitation operator, but it is independent of, and not subject to an alethic interpretation. Rather, is interpreted to meanI bring it about that P. The (...) result is a simplification and clarification of a combined logic of ability and action like that in [2], but employing only normal operators.A number of extensions of the basic systemK/K are constructed, first by strengthening the two normal sublogics independently and then by linking the two sublogics via axiom schemata involving both operators. The result is a series of increasingly strong systems which more and more adequately fulfill our expectations for a satisfactory logic of action and ability. (shrink)

The paper critically examines whether the open-endedness of the set concepts mandates the use of intuitionistic logic in set theory, as some philosophers think. [The sequel to this paper is ‘The Open-Endedness of the Set Concept and the Semantics of Set Theory' published in Synthese in 2003.] .

We propose a dynamic-epistemic analysis of the different epistemic operations constitutive of the process of interrogative inquiry, as described by Hintikka’s Interrogative Model of Inquiry (IMI). We develop a dynamic logic of questions for representing interrogative steps, based on Hintikka’s treatment of questions in the IMI, along with a dynamic logic of inferences for representing deductive steps, based on the tableau method. We then merge these two systems into a dynamic logic of interrogative inquiry which articulates a (...) joint treatment of questions and inferences, providing thereby a unified framework representing the informational dynamics of interrogative inquiry. We provide sound and complete axiomatic systems for the three dynamic logics that we introduce, we compare our framework with existing approaches, and we finally propose several directions for further work. (shrink)

The logic of partial terms (LPT) is a variety of negative free logic in which functions, as well as predicates, are strict. A companion paper focused on nonconstructive LPTwith definite descriptions, called LPD, and laid the foundation for tableaux systems by defining the concept of an LPDmodel system and establishing Hintikka's Lemma, from which the strong completeness of the corresponding tableaux system readily follows. The present paper utilizes the tableaux system in establishing an Extended Joint Consistency Theorem (...) for LPDthat incorporates the Robinson Joint Consistency Theorem and the Craig-Lyndon Interpolation Lemma. The method of proof is similar to that originally used in establishing the Extended Joint Consistency Theorem for positive free logic. Proof of the Craig-Lyndon Interpolation Lemma for formulas possibly having free variables is readily had in LPTand its intuitionistic counterpart. The paper concludes with a brief discussion of the theory of definitions in LPD. (shrink)

In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics. We argue that completeness result may be easily regained. Finally, we shortly discuss some issues related to the philosophical intuition behind his approach. This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.

Joint attention is a social-cognitive phenomenon in which two or more agents direct their attention together towards the same object. Definitions range from this rather broad conception to more specific definitions which require that, in addition, attention be directed to the same aspect of that object and that agents need to be mutually aware of their jointly attending. Joint attention is an important coordination mechanism in joint action. The capacity for engaging in joint attention, in particular (...) in the sense of this narrower definition, is frequently taken to indicate the presence of theory of mind in the participating agents, and is also implicated in the development of theory of mind. However, the prominence of sensorimotor components in establishing and sustaining episodes of joint attention — e.g., eye and head movements, pointing and vocalizations — suggests that sensorimotor approaches to social interaction may be well-placed to account for important parts of joint attention without invoking theory-of-mind abilities, and may therefore provide a valuable alternative to approaches emphasizing theory of mind. In particular, sensorimotor accounts may explain aspects of joint attention through the dynamics and regularities in the sensorimotor processes that coordinate the activities of the agents. (shrink)

A critical discussion of Seumas Miller's view on knowing-how and joint abilities.

In the paper, we study the dynamics of coalitional ability by proposing an extension of coalition logic (CL). CL allows one to reason about what a coalition of agents is able to achieve through a joint action, no matter what agents outside of the coalition do. The proposed dynamic extension is inspired by dynamic epistemic logic, and, in particular, by action models. We call the resulting logic coalition action model logic (CAML), which, compared to (...) CL, includes additional modalities for coalitional action models. We investigate the expressivity of CAML, and provide a complexity characterisation of its model checking problem. (shrink)

This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of (...) logic in these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law. (shrink)

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the (...) class='Hi'>logic of the Ramseyan indicative conditional. (shrink)

In the paper the joint Logic of Proofs and Provability is presented that incorporates both the modality □ for provability 287–304) and the proof operator tF representing the proof predicate “t is a proof of F” . The obtained system naturally includes both the modal logic of provability GL and Artemov's Logic of Proofs . The presence of the modality □ requires two new operations on proofs that together with operations of allow to realize all the (...) invariant operations on proofs admitting description in the modal propositional language. Logic is proved to be decidable and complete with the intended provability semantics. (shrink)

In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee \ given \” with a semantics based not on standard epistemic models but on labeled transition systems that represent the agent’s knowledge of his own abilities. The semantics is inspired by conformant planning in AI. A sound (...) and complete proof system is given to capture valid reasoning patterns, which highlights the compositional nature of “knowing how”. The logical language is further extended to handle knowing how to achieve a goal while maintaining other conditions. (shrink)

Abstract Orthodox decision theory presupposes that agency is invested in individuals. An opposing literature allows team agency to be invested in teams whose members use distinctive modes of team reasoning. This paper offers a new conceptual framework, inspired by David Lewis's analysis of common reasons for belief, within which team reasoning can be represented. It shows how individuals can independently endorse a principle of team reasoning which prescribes acting as a team member conditional on assurance that others have endorsed the (...) same principle. It argues that there can be such assurance even when no individual has an obligation to act on team reasoning. *This paper originated in a lecture that I gave at a Colloquium on Collective Intentions at Erasmus University Rotterdam. I thank participants, and particularly Govert den Hartogh, for comments. The analysis presented in this paper is an offshoot of a larger project, which uses David Lewis's work as the starting point for a reconstruction of the foundations of game theory. That project is joint work with Robin Cubitt. The specific idea of using this approach to analyse team reasoning grew out of a discussion with Michael Bratman. My work was supported by the Leverhulme Trust. (shrink)

This article takes its point of departure in Bracha Ettinger’s discussion on the “matrixial borderspace”: the structure of the experience of “the womb,” both from a “mother-pole” and a “fetus-pole”. Ettinger describes this borderspace as a place of differentiation-in-co-emergence, separation-in-jointness, and distance-in-proximity. The question this article poses is what kind of logic this experience is an expression of, as there seems to be a discrepancy in relation to the classical Aristotelian logic of identity. As an alternative to classical (...) Aristotelian logic, Nicholas of Cusa’s logic of the non-aliud is explored as a paradigm more in line with Ettinger’s description of pregnancy specifically and more generally, to an understanding of life as a co-poietic emergence of structures of pactivity and permeability. (shrink)

Aristotle's modal syllogistic has been an object of study ever since the time of Theophrastus; but these studies have been somewhat desultory. Remarkably, in the 1990s several new lines of research have appeared, with series of original publications by Fred Johnson, Richard Patterson and Ulrich Nortmann. Johnson presented for the first time a formal semantics adequate to a de re reading of the apodeictic syllogistic; this was based on a simple intuition linking the modal syllogistic to Aristotelian metaphysics. Nortmann developed (...) an ingenious de dicto analysis. Patterson articulated the links between the modal syllogistic and the metaphysics, using an analysis which strictly speaking is neither de re nor de dicto. My own studies in this field date from 1976, when my colleague Peter Roeper and I jointly wrote a paper "Aristotle's apodeictic syllogisms" for the XXIInd History of Logic Conference in Krakow. This paper contained the disjunctive reading of particular affirmative apodeictic propositions, which I still favour. Nonetheless, I did not consider that paper's results decisive or comprehensive enough to publish, and my 1981 book The Syllogism contained no treatment of the modal syllogism. The paper's ideas lay dormant till 1989, when I read Johnson's and Patterson's initial articles. I began publishing on the topic in 1991. Gradually my thoughts acquired a certain comprehensiveness and systematicity, till in 1993 I was able to take a semester's sabbatical to write up a draft of this book. (shrink)

The educational aims described by educational philosophers rarely embrace the full range of differences in intellectual ability, adaptive behavior, or communication that children exhibit. Because envisioned educational aims have significant consequences for how educational practices, pedagogy, and curricula are conceptualized, the failure to acknowledge and embrace differences in ability leaves open the question of the extent to which students with intellectual disabilities are subject to the same aims as their “typically-developing” peers. In articulating and defending valued aims of (...) education, educational philosophers tacitly or expressly concede that particular aims will be ill suited to many children with intellectual disabilities, and that separate aims will therefore apply to them. This paper evaluates the philosophical reasoning behind this conclusion that some people, by necessity, must be governed by separate educational aims, to be decided separately and secondarily. The author calls this the “deferral stance.” First, the paper outlines concerns about a particular ability-biased social and epistemic context in which theorizing about educational aims takes place. The author then examines assumptions that underpin the logic of deferral, arguing that the logic proves flawed when subjected to conceptual and empirical scrutiny. The paper concludes by outlining an inclusive approach—the affirmative stance—to theorizing about educational aims that resists the logic of exclusion and deferral. (shrink)

We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by (...) LRC and its associated analytic calculus. These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations. (shrink)

Normal systems of modal logic, interpreted as deontic logics, are unsuitable for a logic of conflicting obligations. By using modal operators based on a more complex semantics, however, we can provide for conflicting obligations, as in [9], which is formally similar to a fragment of the logic of ability later given in [2], Having gone that far, we may find it desirable to be able to express and consider claims about the comparative strengths, or degrees of (...) urgency, of the conflicting obligations under which we stand. This paper, building on the formalism of the logic of ability in [2], provides a complete and decidable system for such a language. (shrink)

The work of Luciano Floridi lies at the interface of philosophy, information science and technology, and ethics, an intersection whose existence and significance he was one of the first to establish. His closely related concepts of a philosophy of information (PI), informational structural realism, information logic (IL), and information ethics (IE) provide a new ontological perspective from which moral concerns can be addressed, especially but not limited to those arising in connection with the new information and communication technologies. In (...) this paper, I relate Floridi's approach to another novel perspective, namely, that of an extension of logic to complex real processes, including those of information production and transfer. This non-propositional, non-truth-functional logic (logic in reality (LIR)) is grounded in the fundamental dualism (dynamic opposition) inherent in energy and accordingly present at all levels of reality. The LIR description of the dynamics of processes and their evolution is relevant to what Floridi refers to as the possible non-linguistic aspects of information. It suggests answers to some of Floridi's “outstanding problems” in PI related to the ontological status of information and how it is used in cognition. Floridi's IL retains the formal structure of the doxastic and epistemic logics from which he correctly distinguishes it and is the basis for his conceptual PI. However, LIR fulfills Floridi's implied requirement that logic be regarded as a natural phenomenon dealing with other natural phenomena, recovering its original philosophical function. LIR provides a logical foundation for discussion of ethical questions based on kinds of information that complements IL. Both are reconsiderations of logic that, as Marijuan suggests, may be necessary for the advancement of information technology in an ethical direction (cf. also Brenner). IE focuses on entities as constituted by information in an overall strategy that generalizes the concept of moral agents. LIR and its related ontology naturalize critical aspects of Floridi's theses, especially, the moral value of being as such and a non-separable joint responsibility of individuals and groups. I compare IE to other current approaches to ethics and information technology (e.g., phenomenological and social constructivist). Ethical information is defined “ecologically” in process terms as reality in a physical space (cf. Floridi), with an intentional “valence,” positive and negative, in the morally valued interaction between producer and receiver. LIR is neither topic-neutral nor context independent and can support an ethics involving apparently contradictory perspectives (e.g., internalist and externalist). Ethics involves practical reasoning, and unlike standard logics, LIR supports Magnani's approach to abductive reasoning in rational moral decision making. The basis of moral responsibility and the consequent behavior of individuals involved in information and communications technologies is the same logical–metaphysical principle of dynamic opposition instantiated at other levels of reality. The way moral responsibilities are actively accepted (or not) by individuals supervenes on their primitive psychological structure, which in turn reflects an evolutionary development grounded in the fundamental dualism of the physical world. The paper concludes with some suggestions of areas of philosophical research, such as causality, identity, and the ontological turn, where convergence of the Floridi and LIR approaches might be envisaged. Their overall motivation is the same, namely, the development of strategies for reinforcing and increasing ethical sensitivity wherever possible. The ethical information concept outlined in the paper supports the function of IE, assigned to it by Floridi, of potentially determining what is right and what is wrong. (shrink)

The aim of this paper is to offer a rigorous explication of statements ascribing ability to agents and to develop the logic of such statements. A world is said to be feasible iff it is compatible with the actual past-and-present. W is a P-world iff W is feasible and P is true in W (where P is a proposition). P is a sufficient condition for Q iff every P world is a Q world. P is a necessary condition (...) for Q iff Q is a sufficient condition forP. Each individual property S is shown to generate a rule for an agent X. X heeds S iff X makes all his future choices in accordance with S. (Note that X may heed S and yet fail to have it). S is a P-strategy for X iff X's heeding S together with P is a necessary and sufficient condition for X to have S. (P-strategies are thus rules which X is able to implement on the proviso P).Provisional opportunity: X has the opportunity to A provided P iff there is an S such that S is a P-strategy for X and X's implementing S is a sufficient condition for X's doing A. P is etiologically complete iff for every event E which P reports P also reports an etiological ancestry of E, and P is true. Categorical opportunity: X has the opportunity to A iff there is a P such that P is etiologically complete and X has the opportunity to A provided P. For X to have the ability to A there must not only be an appropriate strategy, but X must have a command of that strategy. X steadfastly intends A iff X intends A at every future moment at which his doing A is not yet inevitable. X has a command of S w.r.t. A and P iff X's steadfastly intending A together with P is a sufficient condition for X to implement S. Provisional ability: X can A provided P iff there is an S such that S is a P-strategy for X, X's implementing S is a sufficient condition for X's doing A, and X has a command of S w.r.t. A and P. Categorical ability: X can A iff there is a P such that P is etiologically complete and X can A provided P. X is free w.r.t. to A iff X can A and X can non- A. X is free iff there is an A such that X is free w.r.t. A. (shrink)

Karl Marx theory of value/labour is primarily based on time. In his theory of value/labour, Marx displays how the economic mechanic of Capital reduces Labour to power and time. Power is the ability to produce, and represent a complex mixture of individual workforce and social cooperation. Time is the general measure of productivity and the partition of labour time gives the units of measure of the value produced. Capitalism is driven by one single linear and universal temporality, signed by (...) the time of production, and by the amount of time/value subtracted to the worker. Within an unorthodox Marxist tradition, Gilles Deleuze and Felix Guattari openly criticised this approach to the production of value. By taking their distance from an image of history as a timeline, Deleuze and Guattari sketched history as a geography, and the capitalist society as an archipelago of temporalities. In this chapter, we will discuss their critique of an idea of linear time. Time is a nexus of lines, flows, segmentations and plateau: it is not merely a subjective experience, nor an objective/quantitative measurement of movement. It rather express a cartography of forms of life, of regimes and assemblages. (shrink)

Malm and colleagues (2008) consider (and reject) five arguments putatively justifying the idea that healthcare workers (HCWs) have a duty to treat (DTT) during a pandemic. We do not have sufficient...

In lieu of an abstract, here is a brief excerpt of the content:Michael Wreen THE LOGIC OF IONESCO'S THE LESSON As men abound in copiousness of language, so they become more wise, or more mad than ordinary. Hobbes, Leviathan, chap. 4 (L a RiTHMETic leads to philology, and philology leads to crime."1 This is both XXthe plot and die pessimism of Ionesco's The Lesson. As the drama unfolds, the spectator watches the world of progress-through-education crumble and a world oflust (...) and murder rise in its ruins. What has gone wrong? In a word, the life oflogic has become the logic oflife. To understand Ionesco's lesson, we must examine the (largely implicit) logic and philosophy of language of his Lesson. Logic, whether die classical syllogistic logic of Aristode, the modern symbolic logic of Russell and Whitehead, or die dialectical logic of Hegel, has two essentia ] components: a syntax, which distinguishes permissible from impermissible combinations and inferences, and a semantics, which allows interpretation and thus fills out the purely formal shell provided by the former. Ionesco's strategy is to show how each of these components as diey have come to be developed philosophically is inadequate to its real content — life, and how, together, they lead, at least metaphorically, to life's devastation. These diree conceptual moments correspond to the three dramatic divisions of the play, marked out by the interruptions of die maid. Ionesco begins with the methodology of logic, syntax, and focuses on arithmetic, which, we are told, "is more a method than a science" (p. 50). Since the time of Descartes, arithmetic, or more generally mathematics, has been the academic discipline par excellence, the study diat all of the empirical sciences have aspired to. So completely has the idea of the mathematical nature of reality impressed itself upon us diat for many people it has acquired the status of an 229 230Philosophy and Literature unquestioned, and even unquestionable, assumption. And for many in this group, including the Professor, it is more dianjust an assumption; it is a way of life. "Let us arithmetize a little," he says to his pupil (p. 51), and his neologism refers not just to a subject matter, arithmetic, but to a way of dealing with subject matters and, ultimately, to a way of dealing with the whole of reality. The noun "arithmetic" has become a verb, and the ascendancy of abstract method has begun. Formal logic, in adi diree of its classic Western forms, is now subjected to sustained and specific criticism. Generally speaking, the Pupil represents Aristotelian and Russellian humanism, a view based on an optimistic belief in man's capacity for direct knowledge, in understanding through analysis by fine distinctions between terms, and in the elimination of paradoxes, both in logic and life. The Professor, again roughly speadcing, represents Hegeliainism, a view based on an optimistic belief in die capacity of reason to unify all oppositions and to overcome, through a higher syndiesis, the fundamentally paradoxical nature of all phenomena, including life itself. Thus, at die level of formal logic and ontology, the Professor amd the Pupil aire diametrically opposed, united only in their uncritical reliatnce upon a method of reason. This philosophical opposition is in turn correlated with a psycho-physical opposition: the Professor is male, old, retiring, and initially lifeless; the Pupil is female, young, forwaurd, amd initiadly vivacious. The confrontation of the two embodied philosophical/ psychological principles over die matter of arithmetic makes dieir opposition manifest and demonstrates, for the first time in the play, die utter inability of bodi philosophical traditions to maintain a grip on reality. This confrontation is also a struggle, one which the fresh, straightforward, vital Pupil begins with great success. She is "magnificent" in addition, and claims she can "count to infinity" — an ability which would vindicate her confident, optimistic belief in man's mental capacities, but an ability, nevertheless, which is logically impossible to possess, since "infinity" is not the name of a particulatrly large number, ais she seems to think. Her claim to understand reveals her as limited and ignorant of the deeper and paradoxical nature of her subject, and thus as in need of further, more abstract lessons. "One must also be able to subtract," die Professor... (shrink)

Some philosophers have recently complained that moral theories almost always portray the distresses of ordinary people in moral predicaments as irrational. In the name of having a minimally realistic picture of ethical thought, these philosophers argue that accounts of morality must allow for strong moral dilemmas, choices involving mutually exclusive all-things-considered requirements or jointly exhaustive all-things-considered prohibitions. In this dissertation I clarify and reject several versions of this argument, which I call the argument from experience. ;In chapters one and two (...) I define strong moral dilemmas as essentially involving conflicts of moral reasons, and reject as premature attempts to reduce questions about strong dilemmas to questions about deontic logic. I accept the goal of representing ordinary experience faithfully, and ask whether a theory will necessarily distort that experience if it employs interpretations of 'ought' and 'prohibited' in ways guaranteeing a priori that there are no strong dilemmas. ;The argument from experience claims that people can have a justifiably high degree of confidence that they are in strong moral dilemmas, and in chapter three I question whether people ever have the needed sorts of confidence about the limits of their abilities, the precise location of their wrongdoing, or the futility of continued moral deliberation. ;In chapter four I reject specific arguments based on regret and guilt. The tendency to feel unavoidable agent-regret or guilt allegedly shows that the agent sees the choice as a strong dilemma, and the appropriateness of such distresses allegedly shows that the agent's way of seeing things is rational. I reply that someone can feel agent-regret without endorsing any moral judgment involving 'ought' or 'prohibited', and that guilt is never unavoidably appropriate. ;In chapter five I trace the failure of the argument from experience to the presence in ordinary thought of a notion of blame which is both conceptually guaranteed always to be avoidable and regarded as an infallible indicator of moral requirement and prohibition. I am led to wonder, finally, why this notion of blame should play a privileged role in philosophical pictures of morality. (shrink)

The book presents the results of the joint annual conference of the four Operations Research Societies DGOR, GM\OR, \GOR and SVOR, held in Vienna in 1990.

A recurring issue in any formal model representing agents' (changing) informational attitudes is how to account for the fact that the agents are limited in their access to the available inference steps, possible observations and available messages. This may be because the agents are not logically omniscient and so do not have unlimited reasoning ability. But it can also be because the agents are following a predefined protocol that explicitly limits statements available for observation and/or communication. Within the broad (...) literature on epistemic logic, there are a variety of accounts that make precise a notion of an agent's "limited access" (for example, Awareness Logics, Justification Logics, and Inference Logics). This paper interprets the agents' access set of formulas as a constraint on the agents' information gathering process limiting which formulas can be observed. (shrink)

We propose a new formalization of legal competences, and in particular for the Hohfeldian categories of power and immunity, through a deontic reinterpretation of dynamic epistemic logic. We argue that this logic explicitly captures the norm-changing character of legal competences while providing a sophisticated reduction of the latter to static normative positions. The logic is completely axiomatizable, and we apply it to a concrete case in German contract law to illustrate that it can capture the distinction between (...) legal ability and legal permissibility. (shrink)

Geary's is the traditional view of the sexes. Yet each part of his argument – the move from sex differences in spatial ability and social preferences to a sex difference in mathematical ability, the claim that the former are biologically primary, and the sociobiological explanation of these differences – requires considerable further work. The notion of a biologically secondary ability is itself problematic.