This paper applies Dehornoy et al.’s Z theorem and its variant, called the compositional Z theorem, to prove confluence of Parigot’s \-calculi extended by the simplification rules. First, it is proved that Baba et al.’s modified complete developments for the call-by-name and the call-by-value variants of the \-calculus with the renaming rule, which is one of the simplification rules, satisfy the Z property. It gives new confluence proofs for them by the Z theorem. Secondly, it (...) is shown that the compositional Z theorem can be applied to prove confluence of the call-by-name and the call-by-value \-calculi with both simplification rules, the renaming and the \-rules, whereas it is hard to apply the ordinary parallel reduction technique or the original Z theorem by one-pass definition of mappings for these variants. (shrink)

This paper gives new confluence proofs for several lambda calculi with permutation-like reduction, including lambda calculi corresponding to intuitionistic and classical natural deduction with disjunction and permutative conversions, and a lambda calculus with explicit substitutions. For lambda calculi with permutative conversion, naïve parallel reduction technique does not work, and traditional notion of residuals is required as Ando pointed out. This paper shows that the difficulties can be avoided by extending the technique proposed by Dehornoy and van Oostrom, called the (...) Z theorem: existence of a mapping on terms with the Z property concludes the confluence. Since it is still hard to directly define a mapping with the Z property for the lambda calculi with permutative conversions, this paper extends the Z theorem to compositional functions, called compositional Z, and shows that we can adopt it to the calculi. (shrink)

Takahashi translation * is a translation which means reducing all of the redexes in a λ-term simultaneously. In [4] and [5], Takahashi gave a simple proof of the Church–Rosser confluence theorem by using the notion of parallel reduction and Takahashi translation. Our aim of this paper is to give a simpler proof of Church–Rosser theorem using only the notion of Takahashi translation.

A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$ CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$ CPN enjoys strong normalization along with (...) strong confluence (and, hence, uniqueness of normal forms). (shrink)

We introduce a new typed combinatory calculus with a type constructor that, to each type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, associates the star type σ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^*$$\end{document} of the nonempty finite subsets of elements of type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star (...) combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. (shrink)

Dual combinators emerge from the aim of assigning formulas containing ← as types to combinators. This paper investigates formally some of the properties of combinatory systems that include both combinators and dual combinators. Although the addition of dual combinators to a combinatory system does not affect the unique decomposition of terms, it turns out that some terms might be redexes in two ways (with a combinator as its head, and with a dual combinator as its head). We prove a general (...) theorem stating that no dual combinatory system possesses the Church-Rosser property. Although the lack of confluence might be problematic in some cases, it is not a problem per se. In particular, we show that no damage is inflicted upon the structurally free logics, the system in which dual combinators first appeared. (shrink)

1936 was a watershed year for computability. Debates among Gödel, Church and others over the correct analysis of the intuitive concept “human effectively computable”, an analysis at the heart of the Incompleteness Theorems, the Entscheidungsproblem, the question of what a finite computation is, and most urgently—for Gödel—the generality of the Incompleteness Theorems, were definitively set to rest with the appearance, in that year, of the Turing Machine. The question I explore here is, do the mathematical facts exhaust what is to (...) be said about the thinking behind the “confluence of ideas in 1936”? I will argue for a cultural role in Gödel’s, and, by extension, the larger logical community’s absorption of Turing’s 1936 model. As scaffolding I employ a conceptual framework due to the critic Leo Marx of the technological sublime; I also make use of the distinction within the technological sublime due to Caroline Jones, between its iconic and performative modes—a distinction operating within the conceptual art of the 1960s, but serving the history of computability equally well. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...) (ii) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

This essay is a case study concerning the problem of rethinking the relationship between Neo-Confucian (Cheng-Zhu school) and Chan schools of thought. The study builds a comparative perspective on two representative texts assembled during the Song dynasty that concern methods of self-cultivation. My theoretical framework is hermeneutical and involves a twofold articulation of correlatives: “inward-outward” and “procedural morality-substantive morality.” By presenting a comparative interpretation of ideas developed in these texts, this analysis highlights the following two components: first, the existence of (...) explicit confluences between major ideas of the influential Cheng-Zhu Neo-Confucian school, which most virulently criticizes the Buddhist tradition, and Chan’s practical methods of self-cultivation; second, it calls attention to the presence of Chan influences in the Neo-Confucian text. Through comparative analysis, this essay intends not only to bring to light Chan influences insightfully integrated by Neo-Confucians within their own discourse on self-cultivation, but also to understand the multidimensional relation between Song-dynasty Neo-Confucian and Chan practices. (shrink)

We present an extension of the lambda calculus with the letrec construct. In contrast to current theories, which impose restrictions on where the rewriting can take place, our theory is very liberal, e.g., it allows rewriting under lambda abstractions and on cycles. As shown previously, the reduction theory is non-confluent. Thus, we searched for and found a new property that resembles confluence and that is equivalent to uniqueness of infinite normal forms: skew confluence. This notion is based on (...) the intuition that some terms are better than others and that terms reduce to better terms. It states that if a term reduces to two other terms, the second of those terms can always be reduced to a term that is better than the first. Using skew confluence we define the infinite normal form of a term and show that the infinite normal form defines a congruence on the set of terms. We relate the lambda calculus plus letrec to the plain lambda calculus and to one of the infinitary lambda calculi. We also present a variant of our calculus, which follows the tradition of the explicit substitution calculi. (shrink)

The law serves functions that are not often taken seriously enough by ethicists, namely feasibility and practicability. A consequence of feasibility is that most laws do not meet the demands of ideal ethical theory. A consequence of practicability is that law requires elaborated and explicit methodologies that determine how to do things with norms. These two consequences form the core idea behind this book, which employs methods from legal theory to inform and examine debates on methodology in applied ethics, particularly (...) bioethics. It is argued that almost all legal methods have counterparts in applied ethics, which indicates that much can be gained from comparative study of the two. The author first outlines methods as used in legal, focusing on deductive reasoning with statutes as well as analogical reasoning with precedent cases. He then examines three representative kinds of contemporary ethical theories, Beauchamp and Childress’s principlism, Jonsen and Toulmin’s casuistry, and two versions of consequentialism—Singer’s preference utilitarianism and Hooker’s rule-consequentialism—with regards to their methods. These examinations lead to the Morisprudence Model for methods in applied ethics. (shrink)

ExcerptBeing able to sustain the distinction between God’s unknowability and God’s nonexistence is a crucial prerequisite for deepening the coherence of our understanding of Western religion and for the articulation and generation of prospects toward peace. This is true both internationally and domestically—and in terms of intrapsychic peace (peace of mind).

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature (...) is a constant. (shrink)

A system for the modal logic K furnishes a simple mechanical process for proving theorems.

Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans across various disciplines such (...) as economics, political science, philosophy, and computer science. This entry reviews and critically assesses a variety of jury theorems. It first discusses Condorcet's initial jury theorem, and then progressively introduces jury theorems with more appropriate premises and conclusions. It explains the philosophical foundations, and relates jury theorems to diversity, deliberation, shared evidence, shared perspectives, and other phenomena. It finally connects jury theorems to their historical background and to democratic theory, social epistemology, and social choice theory. (shrink)

Since the early 1990s, politicians, policymakers, the media and academics have increasingly focused on religion, noting the significant increase in the number of cases involving religion. As a result, law and religion has become a specific area of study. The work of Professor Norman Doe at Cardiff University has served as a catalyst for this change, especially through the creation of the LLM in Canon Law in 1991 and the Centre for Law and Religion in 1998. Published to mark the (...) twenty-fifth anniversary of the LLM in Canon Law and to pay tribute to Professor Doe's achievements so far, this volume reflects upon the interdisciplinary development of law and religion. (shrink)

Since the early 1990s, politicians, policymakers, the media and academics have increasingly focused on religion, noting the significant increase in the number of cases involving religion. As a result, law and religion has become a specific area of study. The work of Professor Norman Doe at Cardiff University has served as a catalyst for this change, especially through the creation of the LLM in Canon Law in 1991 and the Centre for Law and Religion in 1998. Published to mark the (...) twenty-fifth anniversary of the LLM in Canon Law and to pay tribute to Professor Doe's achievements so far, this volume reflects upon the interdisciplinary development of law and religion. (shrink)

In the following thematic introduction, we seek to situate Confluence within the field of comparative philosophy and substantiate why we deem a new publication necessary. For this purpose, we reconstruct the salient stages in the development of comparative philosophy in Part I, and then proceed to expound the rationale underlying Confluence in Part II. Our reconstruction of these stages pursues an exploratory rather than a documentary approach.

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.

South Africa’s groundbreaking constitution explicitly confers a right of access to sufficient water. But the country is officially ‘water-stressed’ and around 10 % of the population still has no access to on-site or off-site piped or tap water. It is evident that a disconnect exists between this right and the reality for many; however the reasons for the continuation of such discrepancies are not always clear. While barriers to sufficient water are myriad, one significant factor contributing to insufficient and unpredictable (...) access to water is the high percentage of broken water pumps. Previous studies have reported that between 20 and 50 % of all hand operated water pumps installed on the African continent are broken, or out of use. Monitoring and maintenance of pumps, which in South Africa is the responsibility of local municipalities is often ineffective, in part due to the distances between municipal centres and rural communities and the consequent costs of site visits, as well as breakdowns within the local bureaucratic system. The emergence of new telemetry tools that can remotely monitor water applications constitutes a novel and cost-efficient alternative to undertaking regular sites visits. Sustainable, appropriate, low-cost telemetry systems are emerging that could be used to monitor the operational performance of water pumps, or a wide range of other field parameters, and to communicate this information swiftly and cheaply to water service providers, using SMS messages. Data on the performance of water pumps could also be made available to the public online. This is an example of how ICT can be used for water resources management and environmental regulation, as well as in the governance of socio-economic rights: helping to optimize water allocation by improving communication and strengthening accountability. (shrink)

In these highly selective and condensed considerations, I could only offer a comparison of the main sociological themes in Gurwitsch's inaugural dissertation with the corresponding themes in Schutz's first book. Other sociological themes were not discussed, mainly because they were not developed far enough in one or the other or both sources. The crucial theme of explicit and implicit ontological presuppositions had to be ignored because it demands an extensive treatment of its own. The same goes for the proper consideration (...) of the particular conceptions of Husserl mobilized by each author for his purposes.Even so, I hope to have conveyed an idea of the convergences and differences in the early views of Gurwitsch and Schutz, as mirrored in the studies which were compared. This article should be seen as a small beginning of the huge task of studying comprehensively the unique personal and intellectual friendship of two seminal thinkers and the influences they exercised upon each other's work, even though they operated in substantively quite different areas. (shrink)

The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics (...) proposes that all quantum systems be interpreted as dissipative ones and that the theorem be thus derstood. The conclusion is that the continual representation, by force or (gravitational) field between parts interacting by means of it, of a system is equivalent to their mutual entanglement if representation is discrete. Gravity (force field) and entanglement are two different, correspondingly continual and discrete, images of a single common essence. General relativity can be interpreted as a superluminal generalization of special relativity. The postulate exists of an alleged obligatory difference between a model and reality in science and philosophy. It can also be deduced by interpreting a corollary of the heorem. On the other hand, quantum mechanics, on the basis of this theorem and of V on Neumann's (1932), introduces the option that a model be entirely identified as the modeled reality and, therefore, that absolutely reality be recognized: this is a non-standard hypothesis in the epistemology of science. Thus, the true reality begins to be understood mathematically, i.e. in a Pythagorean manner, for its identification with its mathematical model. A few linked problems are highlighted: the role of the axiom of choice forcorrectly interpreting the theorem; whether the theorem can be considered an axiom; whether the theorem can be considered equivalent to the negation of the axiom. (shrink)

Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...) review will lead on average to more reviewers per paper than journal-solicited peer review. Second, due to the wisdom of the crowds, more reviewers will tend to make better judgments than fewer. We make the second claim precise by looking at the Condorcet Jury Theorem as well as two related jury theorems developed specifically to apply to peer review. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement (...) result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

In this book, Canadian scholar David Geoffrey Smith reflects on over thirty years of research and teaching in the human sciences, including education. Written between 1986 and 2018, the essays are organized around three themes: Hermeneutics and the Human Sciences; The Poststructuralist Turn; Globalization and Its Discontents; East/West Encounters and the Search for Wisdom. As a historical guide through the defining discourses in the human sciences, this volume could well serve as an introductory text for graduate students in education and (...) other cognate disciplines like nursing, recreation and cultural studies. The writing can be described as a form of meditative praxis, while the emphasis on interculturality addresses issues in literacy, pedagogy, politics, critical thinking, teacher education, and cultural healing from a geopolitical perspective, drawing on insights from both Western and Eastern traditions and the author's personal experience of being born in China and raised in Central Africa (Northern Rhodesia/Zambia). (shrink)

According to a recent paper by Tim Maudlin, Bell’s theorem has nothing to tell us about realism or the descriptive completeness of quantum mechanics. What it shows is that quantum mechanics is non-local, no more and no less. What I intend to do in this paper is to challenge Maudlin’s assertion about the import of Bell’s proof. There is much that I agree with in the paper; in particular, it does us the valuable service of demonstrating that Einstein’s objections (...) to quantum mechanics have nothing to do with its indeterminism. But I do think that Maudlin’s conclusion is overly cut-and-dried. Quantum mechanics is far from a unified edifice, and what Bell’s theorem shows depends on what version of quantum mechanics you look at. In particular, I’ll try to make the case that there’s an interesting, if ultimately uncompelling anti-realist construal of the import of Bell’s theorem. And I also want to suggest that locality isn’t quite as decisively defeated as Maudlin claims. (shrink)

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. (...) The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists. (shrink)

Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...) - and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...) space formalism of quantum mechanics. In this essay, we first show that identification of mind states with quantum states within the brain is biologically feasible, and then elaborating on the mathematical proofs of two quantum mechanical no-go theorems, we explain why quantum theory might have profound implications for the scientific understanding of one's mental states, self identity, beliefs and free will. (shrink)

What are some of the distinctive virtues of the confluence approach that sets it apart from other attempts to do philosophy across cultural boundaries? First, unlike comparing and contrasting, the confluence approach remains faithful to the dominant conception of philosophy as an intellectual enterprise centered on dialogue and argumentation, in which philosophers pursue unresolved problems by building on the achievements of their acknowledged forbears. Second, confluence philosophy implements a syncretic and creative approach to doing philosophy by drawing (...) on non-Western philosophical sources while using the tools and conceptual resources of analytic philosophy. Third and last, the confluence approach highlights possible tensions when the traditions of thought brought into dialogue are on a diverging path on certain matters. Contemporary philosophy, at least in the Anglophone world and its satellites, is an avowedly secular enterprise, deferring to the sciences for its account of what can be said to exist at the most fundamental level and for its understanding of the processes that realize cognition. Buddhism at its core is often understood as a soteriological project manly concerned with overcoming suffering, which sometimes is taken to entail an insight into the emptiness of all the constitutive elements of existence and/or experience. Confluence philosophy thus makes it possible to ask whether defending a theoretical framework which affirms this truth of emptiness means that one must engage in the very sort of activity, namely, rational self-assertion, that hinders enlightenment. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the (...) basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

This article investigates the origin and the earliest, formative period of one of the major concepts in post-classical Chinese medicine, the concept of phlegm, tan 痰. It is the first study that examines both Chinese- and Sanskrit-language sources in seeking to answer the question whether the development of the concept of phlegm in Chinese medicine is owed to Indic influences. Following traditional Chinese scholarship, it argues that the initial emergence of the substance tan 痰, which later was to become “phlegm,” (...) should be understood as an indigenous development from the fluid yin 飲. The subsequent formation and development of the concept of phlegm in Chinese medicine, however, was influenced by Āyurveda. The influence hinges on the coincidence of Indic and Chinese intuitions about digestion. Previous scholarship on early Chinese Buddhist translations of Indic terms for phlegm and the tridoṣa has either claimed that variations in the terminology betrayed the Chinese translators’ poor understanding of Āyurvedic concepts or that the translators creatively manipulated the terminology with a view to the cultural background of their intended audiences. By contrast, this article argues that the early terminology the Chinese translators crafted was highly accurate and faithful to their Indic source texts. It shows, by going back to the Indic classics, that the variations in Chinese terminology reflect an ancient and long-forgotten temporal shift in the perception of humors in India itself. (shrink)

Conventional agency theory typically focuses on a unidirectional problem, in which an agent behaves opportunistically against the interests of a principal. Yet, this conceptualization is too limited to fully describe all aspects of principal–agent relationships. This article presents a more comprehensive framework explaining a potential three-directional problem—that is, agents behave opportunistically against the interests of principals, principals behave opportunistically against the interests of agents, and relationships between agents and principals representing confluence of interests affect the interests of third-party stakeholders. (...) The article provides evidence of these problems, describes their unique characteristics, and outlines implications for society. It concludes with a discussion focusing on the implications of the proposed framework for purported governance solutions, the ongoing debate between shareholder and stakeholder views of the firm, and business practices. (shrink)

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.

Theorems of hyperarithmetic analysis occupy an unusual neighborhood in the realms of reverse mathematics and recursion-theoretic complexity. They lie above all the fixed iterations of the Turing jump but below ATR $_{0}$. There is a long history of proof-theoretic principles which are THAs. Until the papers reported on in this communication, there was only one mathematical example. Barnes, Goh, and Shore [1] analyze an array of ubiquity theorems in graph theory descended from Halin’s [9] work on rays in graphs. They (...) seem to be typical applications of ACA $_{0}$ but are actually THAs. These results answer Question 30 of Montalbán’s Open Questions in Reverse Mathematics [19] and supply several other natural principles of different and unusual levels of complexity.This work led in [25] to a new neighborhood of the reverse mathematical zoo: almost theorems of hyperarithmetic analysis. When combined with ACA $_{0}$ they are THAs but on their own are very weak. Denizens both mathematical and logical are provided. Generalizations of several conservativity classes are defined and these ATHAs as well as many other principles are shown to be conservative over RCA $_{0}$ in all these senses and weak in other recursion-theoretic ways as well. These results answer a question raised by Hirschfeldt and reported in [19] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong or very strong going up a standard hierarchy and at the end being stronger than full second-order arithmetic. (shrink)

Naive versions of decision theory take probabilities and utilities as primitive and use expected value to give norms on rational decision. However, standard decision theory takes rational preference as primitive and uses it to construct probability and utility. This paper shows how to justify a version of the naive theory, by taking dominance as the most basic normatively required preference relation, and then extending it by various conditions under which agents should be indifferent between acts. The resulting theory can make (...) all the decisions of classical expected utility theory, plus more in cases where expected utilities are infinite or undefined. Although the theory requires similarly strong assumptions to classical expected utility theory, versions of the theory can be developed with slightly weaker assumptions, without having to prove a new representation theorem for the weaker theory. This alternate foundation is particularly useful if probability is prior to preference, as suggested by the recent program to base probabilism on accuracy and alethic considerations rather than pragmatic ones. (shrink)