This paper explores the relationship between informal reasoning, creativity in mathematics, and problem solving. It underscores the importance of environments that promote interaction, hypothesis generation, examination, refutation, derivation of new solutions, drawing conclusions, and reasoning with others, as key factors in enhancing mathematical creativity. Drawing on argumentation logic, the paper proposes a novel approach to uncover specific characteristics in the development of formalized proving using “proof-events.” Argumentation logic can offer reasoning mechanisms that facilitate these environments. This paper proposes how (...) argumentation can be implemented to discover certain characteristics in the development of formalized proving with “proof-events”. The concept of a proof-event was introduced by Goguen who described mathematical proof as a multi-agent social event involving not only “classical” formal proofs, but also other informal proving actions such as deficient or alleged proofs. Argumentation is an integral component of the discovery process for a mathematical proof since a proof necessitates a dialogue between provers and interpreters to clarify and resolve gaps or assumptions. By formalizing proof-events through argumentation, this paper demonstrates how informal reasoning and conflicts arising during the proving process can be effectively simulated. The paper presents an extended version of the proof-events calculus, rooted in argumentation theories, and highlights the intricate relationships among proof, human reasoning, cognitive processes, creativity, and mathematical arguments. (shrink)

Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a "classical" version of the system. They (...) can also be extended to a system with a restricted set of rules for implication: the result is a system of intuitionistic higher-order BCK logic with unrestricted comprehension and without restriction on the rules for disjunction elimination and existential elimination. The result does not extend to the classical version of the BCK logic. (shrink)

It has been persuasively argued that music refers. For example, a passage that resembles the demeanour of people under the sway of emotion E is seen as itself being E and, thus, as referring to E. Yet what is the purpose of such reference? Serious music, I say, works as a proof. A passage that refers to E is cast as a well-formed formula in a calculus. That formula is then creatively developed in accordance with the rules of that (...) calculus (e.g. harmony and counterpoint in classical music). As in scientific proofs, intermediary generated formulae need not have external meaning over and above the character they have due to their role in the formal sequence. Yet finally a formula is derived that does have external meaning; for example, it refers to emotion F. The composer has thus fictionally proved that E is equal to F, e.g. that hope is futile or that love conquers all. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different approaches (...) to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

One of the main motivations for having a compositional semantics is the account of the productivity of natural languages. Formal languages are often part of the account of productivity, i.e., of how beings with finite capaci- ties are able to produce and understand a potentially infinite number of sen- tences, by offering a model of this process. This account of productivity con- sists in the generation of proofs in a formal system, that is taken to represent the way speakers grasp (...) the meaning of an indefinite number of sentences. The informational basis is restricted to what is represented in the lexicon. This constraint is considered as a requirement for the account of productivity, or at least of an important feature of productivity, namely, that we can grasp auto- matically the meaning of a huge number of complex expressions, far beyond what can be memorized. However, empirical results in psycholinguistics, and especially particular patterns of ERP, show that the brain integrates informa- tion of different sources very fast, without any felt effort on the part of the speaker. This shows that formal procedures do not explain productivity. How- ever, formal models are still useful in the account of how we get at the seman- tic value of a complex expression, once we have the meanings of its parts, even if there is no formal explanation of how we get at those meanings. A practice-oriented view of modeling gives an adequate interpretation of this re- sult: formal compositional semantics may be a useful model for some ex- planatory purposes concerning natural languages, without being a good model for dealing with other explananda. (shrink)

In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the derivation indicator position that asserts that the ordinary proofs given in (...) mathematical discourse indicate syntactic derivations in a formal logical system. In particular, we note that several of the arguments against the derivation indicator position would seem to imply that set theorists could gain no benefits from the syntactic representations of concepts indicated by their definitions, yet set theorists clearly do. (shrink)

Extending previous results from work on the complexity of cut elimination for the sequent calculus LK, we discuss the role of quantifier alternations and develop a measure to describe the complexity of cut elimination in terms of quantifier alternations in cut formulas and contractions on such formulas.

To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D. Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D. Deutsch. The idea is to get subjective probabilities from rational decisions related to quantum measurements, showing the non-probabilistic parts of the quantum formalism, plus some rational constraints, ensure the squared modulus of quantum amplitudes play the role of such probabilities. We provide a new presentation of Wallace’s (...) class='Hi'>proof, reorganized to simplify some arguments, and analyze it from a formal perspective. Similarities with classical decision theory are made explicit, to clarify its structure and main ideas. A simpler notation is used, and details are filled in, making it easier to follow and verify. Some problems have been identified, and we suggest possible corrections. (shrink)

An analysis of the role of language in basic and applied science from the semantics of science and the theory of reference requires several steps. First, to specify the field of analysis in the light of several factors: the semantic problems of science; the reference in its triple dimension of relation between language and reality, of referent and of transmission in science; and the link between meaning and reference in science.Second, to consider the central approach to the semantics of (...) science, which forks into two main directions: the semantic line and the pragmatic path. De facto, they lead to different interpretations of the role of language in basic science and in applied science. The semantic line focuses on the content expressed through terms, statements and theories, which has been influential in important philosophical trends and still is prominent in some versions of scientific realism. Meanwhile, the pragmatic path emphasizes the meaning as use, which has influenced philosophers of science of diverse tendencies, such as S. Toulmin, Th. Kuhn, American pragmatists and supporters of the methodological pluralism.Third, to make explicit the leading conceptions regarding the theory of reference, both for the formal sciences and for the empirical sciences. There are a number of options, four of which are analyzed here. The view associated with the semantic role and the semantic value, which connects semantic, epistemological and ontological realms in basic science and in applied science. The causal theory of reference, which has shifted towards internal realism. Anti-realistic semantics, where truth is replaced by proof and the reference is the use made by someone of a term in a context. Kuhn’s approach in his linguistic period, where he rethinks the scientific revolutions taking into account the causal theory of reference.Fourth, to be aware of the consequences of these analyses for basic science and applied science in two ways: on the one hand, for the semantic differences between them, and, on the other, for the perspective of reference. (shrink)

In this article I am concerned with reasoning about matters of justice. There is no doubt that justice-reasoning is a significant mode of ethical reasoning and its importance is therefore generally accepted. But there is a considerable debate concerning the role formal justice can play in reasoning about justice. In this paper, I first provide an analysis of formal justice. I then show that the concept of formal justice is identical to one notion of fairness and I illustrate the (...) function of formal justice in reasoning about issues of fairness. In the third section, I argue that formal justice is an essential component of justice tout court and I demonstrate its value for understanding and assessing reasoning about matters of justice. The overall result of this investigation is that formal justice is an important notion that has a special function in moral thinking, which has not been sufficiently appreciated in the literature. (shrink)

SummaryLooking at proof theory as an attempt to ‘code’ the general pattern of the logical steps of a mathematical proof, the question of what kind of rules can make the meaning of a logical connective completely explicit does not seem to have been answered satisfactorily. The lambda calculus seems to have been more coherent simply because the use of ‘λ’ together with its projection 'apply' is specified by what can be called a 'reduction' rule: β‐conversion. We attempt to (...) analyse the role of proof rules, making use of a set of formal rules designed to capture both the notions of proof theory and those of the lambda‐calculus: Martin‐Löf's Intuitionistic Type Theory.RésuméSi on considère la théorie de la démonstration comme une tentative de ‘codifier’ les pas logiques d'une démonstration mathématique, on se rendra compte qu'on n'a pas répondu de façon satisfaisante à la question suivante: quelles sont les règies qui rendent complètement explicite le sens d'un connecteur logique? Le lambda‐calcul a été apparemment plus cohérent, tout simplement parce que l'utilisation du‘λ’ avec sa projection 'apply' est spécifiée par une regie de 'réduction': β‐conversion. Nous essayons d'analyser le rôle des règies de démonstration, en utilisant un système formel de règies conçu pour englober à la fois les notions de la théorie de la démonstration et celles du lambda‐calcul: la Théorie Intuitionniste des Types de Martin‐Löf.ZusammenfassungWenn man Beweistheorie als einen Versuch, ein allgemeines Muster der logischen Schritte in einem mathematischen Beweis zu kodifizieren, betrachtet, so scheint die Frage nach der Art von Regeln , die die Bedeutung von logischen Operatoren vollständig beschreiben, nicht zufriedenstellend beantwortet. Der Lambda‐Kalkül erscheint, kohärenter, einfach deshalb weil der Gebrauch von ‘λ’ zusammen mit dessen Projektion 'apply' durch Regeln bestimmt wird, die man 'Reduktions'‐Regeln nennen kann: β‐Konversion. Wir versuchen, die Rolle von Beweisregeln zu analysieren, indem wir ein Regelsystem verwenden, das sowohl die Begriffe der Beweistheorie als auch diejenigen des Lambda‐Kalküls erfasst, nämlich die Martin‐Löfsche Typentheorie. (shrink)

This paper reconstructs Sir William Hamilton's argument for thinking that the unconditioned is not an object of thought, a conclusion he abbreviates with the slogan ‘to think is to condition’. The paper describes Hamilton's conception of formal logic as the study of the laws of thought and claims that this conception allows these laws, particularly those of non-contradiction and excluded middle, to play a substantive role in Hamilton's argument.

Aristotle’s way of conceiving the relationship between mathematics and other branches of scientific knowledge is completely different from the way a contemporary scientist conceives it. This is one of the causes of the fact that we look at the mathematical passage we find in Aristotle’s works with the wrong expectation. We expect to find more or less stringent proofs, while for the most part Aristotle employs mere analogies. Indeed, this is the primary function of mathematics when employed in a philosophical (...) context: not a demonstrative tool, but a purely analogical model. In the case of the geometrical examples discussed in this paper, the diagrams are not conceived as part of a formalized proof, but as a work in progress. Aristotle is not interested in the final diagram but in the construction viewed in its process of development; namely in the figure a geometer draws, and gradually modifies, when he tries to solve a problem. The way in which the geometer makes use of the elements of his diagram, and the relation between these elements and his inner state of knowledge is the real feature which interests Aristotle. His goal is to use analogy in order to give the reader an idea of the states of mind involved in a more general process of knowing. (shrink)

This paper examines the role of reason in Shepherd's account of acquiring knowledge of the external world via first principles. Reason is important, but does not have a foundational role. Certain principles enable us to draw the required inferences for acquiring knowledge of the external world. These principles are basic, foundational and, more importantly, self‐evident and thus justified in other ways than by demonstration. Justificatory demonstrations of these principles are neither required, nor possible. By drawing on textual and (...) contextual evidence, I will show that Shepherd should have said that we know the first principles of any science, in general, and that “everything which begins to exist must have a cause”, in particular, via intuition, not via reason. Reasoning about such principles can help their self‐evidence shine through in certain cases; their justification, and our being justified in believing them, does not come from this reasoning, however. (shrink)

The thought system of Qâdî ‘Abd al-Jabbâr, who is a productive intellectual worker in the Mu‘tazilî school, is established on the contingency (imkân) of obligation (taklîf) of the God upon people. In other words he has a universe and order of thought which is built around the term obligation. Therefore, the content of Qâdî’s aforementioned thought which has a very significant place in Mu‘tazilî thought is constituted of responsbilities of human beings. These responsibilities of the human beings are gathered under (...) the title of rational ones (aqliyyât) in terms of being held responsible by reason and the title sem‘iyyât which covers the things that fall under the category of responsibilities that can be only known by revelation (wahy) due to the imposibility of being assigned by the sole reason. In short, aqliyyât corrresponds to the rational field of obligation whereas se‘miyyât corresponds to the legal (shar’i) field of responsibility. The responsibilites under the title aqliyyât are such as tawhîd, justice, and other non-primary premises that serve as instruments for comrehending these two terms. The content of sem‘iyyât, on the other hand, is constituted of the issues that fall outside of the rational obligation (taklîf al-aqlî) and can only be known by means of sam‘ (revelation) such as the knowledge that adultry leads to moral corruption or the knowledge of juristic worships. We can observe that Qâdî ‘Abd al-Jabbâr, did make use of three different kinds of proofs in order to prove, found, and justify the aforementioned issues which lay the foundations for his thought. These are rational (aqlî), revelational (sam‘î) and linguistic (lugawi) proofs, respectively. For each of these kinds of proofs there is an idiosyncratic domain of coverage on which that kind of proof is considered as the unique authority. This research aims to elaborate the domain the only authority of which is the linguistic proofs and also aims to render it comprehensive. So to speak, the motivating factor of this research is to clarify the question of to what extent the language plays a role in Qâdî’s thought and its domain of influence in the simplest way. (shrink)

The main currently unsolved problem in the theory of argumentation concerns the function of logic in argumentation and reasoning. The traditional view simply identified logic with the theory of reasoning. This view is still being echoed in older textbooks of formal logic. In a different variant, the same view is even codified in the ordinary usage of words such as ‘logic’, ‘deduction’, ‘inference’, etc. For each actual occurrence of these terms in textbooks of formal logic, there are hundreds of uses (...) of the same idioms to describe the feats of real or fictional detectives. I have called the idea reflected by this usage the “Sherlock Holmes conception of logic and deduction.” In the history of science, we find no less a thinker than Sir Isaac Newton describing his experimental method as one of analysis or resolution and claiming to have “deduced” at least some of his laws from the “phenomena.”. (shrink)

Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to (...) give a natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs. (shrink)

Henrich and Boyd (2002) were the first to propose a formal model of the role of attraction in cultural evolution. They came to the surprising conclusion that, when both attraction and selection are at work, final outcomes are determined by selection alone. This result is based on a deterministic view of cultural attraction, different from the probabilistic view introduced in Sperber (1996). We defend this probabilistic view, show how to model it, and argue that, when both attraction and selection (...) are at work, both affect final outcomes. (shrink)

PTSD was formalized as a diagnosis by the American Psychiatric Association in 1980 with the publication of the Diagnostic and Statistical Manual of Mental Disorders (DSM), 3rd edition. Since that time, the diagnosis has been widely utilized in the courts including the use in criminal proceedings. PTSD may play a role in the assessment of violent crimes both as a possible contributing factor in the perpetrators as well as a consequence in the victims. There are a number of ethical (...) and clinical considerations in the use of this diagnosis. Importantly, the diagnostic criteria have changed to a degree with subsequent editions of the DSM. This may have an impact on the interpretation of past legal judgments. Moreover, extensive psychiatric comorbidity may complicate the clinical picture, e.g., mood disorders, substance use disorders, or psychosis. The diagnosis of PTSD is still based on clinical, largely subjective criteria, e.g., biological markers are not yet utilized. As such, there may not be consistent agreement about the diagnosis among experts. This paper summarizes some of these relevant issues in adjudicating violent crimes. (shrink)

In this article we strive to provide a detailed and principled analysis of the role of beliefs in goal processing—that is, the cognitive transition that leads from a mere desire to a proper intention. The resulting model of belief-based goal processing has also relevant consequences for the analysis of intentions, and constitutes the necessary core of a constructive theory of intentions, i.e. a framework that not only analyzes what an intention is, but also explains how it becomes what it (...) is. We discuss similarities and differences between our approach and other standard accounts of intention, in particular Bratman’s planning theory. The aim here is to question and refine the conceptual foundations of many theories of intentional action: as a consequence, although our analysis is not formal in itself, it is ultimately meant to have deep consequences for formal models of intentional agency. (shrink)

Doctoral programs at U.S. universities play a critical role in the development of human resources both in the United States and abroad. This volume reports the results of an extensive study of U.S. research-doctorate programs in five broad fields: physical sciences and mathematics, engineering, social and behavioral sciences, biological sciences, and the humanities. Research-Doctorate Programs in the United States documents changes that have taken place in the size, structure, and quality of doctoral education since the widely used 1982 editions. (...) This update provides selected information on nearly 4,000 doctoral programs in 41 subdisciplines at 274 doctorate-granting institutions. This volume also reports the results of the National Survey of Graduate Faculty, which polled a sample of faculty for their views on the scholarly quality of program faculty and the effectiveness of doctoral programs in preparing research scholars/scientists. This much-anticipated update of such an essential reference will be useful to education administrators, university faculty, and students seeking authoritative information on doctoral programs. (shrink)

Avicenna's proof for the existence of God (the Necessary Existent) in the Metaphysics of the Salvation relies on the claim that every possible existent shares a common cause. I argue that Avicenna has good reason to hold this claim given that he thinks that (1) every essentially ordered causal series originates in a first, common cause and that (2) every possible existent belongs to an essentially ordered series. Showing Avicenna's commitment to 1 and 2 allows me to respond to (...) Herbert Davidson's and Richard Swinburne's claim that Avicenna's proof for the Necessary Existent is incomplete and fallacious -/- . (shrink)

Η εύληπτη εκπαιδευτική προσέγγιση ότι «κληρονομιά είναι οτιδήποτε θέλεις “εσύ” να διατηρηθεί για τις επόμενες γενιές» κλονίζεται στην ερώτηση «όλα όσα μας παραδίδονται από τους προγόνους μας αποτελούν μια προς διαφύλαξη κληρονομιά, εφόσον “εσύ” το αποφασίσεις;». Εκφάνσεις «βαρβαρότητας» που διασώζονται σε προγενέστερες εθιμικές πρακτικές θα μπορούσαν άραγε να αποτελέσουν στοιχεία ΑΠΚ προς διαφύλαξη; Η παρούσα εργασία επιχειρεί μια πρώτη ανίχνευση του σύνθετου αυτού θέματος. Περιπτώσεις μελέτης από τον ελληνικό και διεθνή χώρο διερευνώνται με κριτήρια αξιολόγησης τα αναφερόμενα στη Σύμβαση για (...) τη Διαφύλαξη της ΑΠΚ (UNESCO, 2003). Βάσει αυτών δεν γίνονται αποδεκτές εθιμικές πρακτικές ΑΠΚ που αναζωπυρώνουν μνήμες βίαιων συγκρούσεων μεταξύ μελών κοινότητας/κοινοτήτων, αποκλείουν με βίαιο ή/και υποτιμητικό τρόπο μέλη εξαιτίας του φύλου, της ηλικίας, της επαγγελματικής ιδιότητας, ή του σεξουαλικού τους προσανατολισμού, καθώς και εθιμικές πρακτικές που περιλαμβάνουν κακομεταχείριση ή/και βασανισμό ζώων. Η εφαρμογή των παραπάνω στην πράξη παραμένει αχαρτογράφητο πεδίο. Απαραίτητες φάσεις μιας συστηματικής μελέτης αποτελούν α) η αναγνώριση και η ευαισθητοποίηση των τοπικών κοινωνιών και του ευρύτερου κοινωνικού συνόλου για τις αξίες της ΑΠΚ, β) η έρευνα, τεκμηρίωση και αξιολόγηση των επιμέρους στοιχείων της, γ) η υποστήριξη των διαδικασιών μεταβίβασής της στις νεότερες γενιές, μέσω της τυπικής και μη εκπαίδευσης, δ) η ανάδειξη της σημασίας της σε τοπική, περιφερειακή, εθνική ή/και παγκόσμια κλίμακα. Η ΑΠΚ μετεξελίσσεται και μεθερμηνεύεται διαρκώς μέσω σύνθετων κοινωνικών και πολιτισμικών διεργασιών. Απόπειρες εξαναγκασμένης «αναβίωσης» κάποιας «αυθεντικής» ή «γνήσιας» μορφής μιας έκφανσής της συχνά αποτυγχάνουν, ενώ παραμένουν μεθοδολογικά μετέωρες. Ο ρόλος της εκπαιδευτικής διαδικασίας στην ανάπτυξη σχετικών ηθικών αρχών και κριτικής σκέψης είναι κρίσιμης σημασίας. Λέξεις κλειδιά: άυλη πολιτιστική κληρονομιά, κοινότητες, αξίες, ηθικές αρχές, εκπαίδευση For educational purposes, we may claim that heritage is whatever each one of us individually or collectively wishes to preserve and pass on to the next generation. However, should violent or other disturbing forms of expression, preserved in customary practices, be safeguarded, if the whole or part of the ‘community’ decides to do so? The present paper attempts a first approach to this complex issue. Case studies from Greece and worldwide are investigated and appraised on the basis of the Convention for the Safeguarding of the ICH (UNESCO, 2003). According to the Convention criteria, customary practices that refresh memories of violent conflicts between members of the community/communities, or exclude members with an aggressive and pejorative way because of their gender, age, professional status or sexual orientation, as well as practices involving the ill-treatment and/or torture of animals do not deserve safeguarding. The implementation of the above criteria in practice, however, remains an uncharted area. A systematic study, therefore, should: (a) include initiation, recognition and awareness on the part of local communities and societies about the values of the ICH; (b) promote research, documentation and evaluation of heritage components; (c) support the transition to the younger generations through formal and non-formal educational events; (d) highlight its importance on the local, regional, national and international context. ICH is evolving and constantly interpreted through complex social and cultural processes. Any forced attempt to revive an ‘authentic’ or ‘genuine’ version of ICH cultural expression, besides appearing fake, is methodologically challenged. The role of education in developing ethical principles and a critical approach to heritage is undoubtedly crucial. Keywords: Intangible cultural heritage, communities, values, ethical principles, education. (shrink)

I focus on three preoccupations of recent writings on proof. -/- I. The role and possible effects of empirical reasoning in mathematics. Do recent developments (specifically, the computer-assisted proof of the 4CT) point to something essentially new as regards the need for and/or effects of using broadly empirical and inductive reasoning in mathematics? In particular, should we see such things as the computer-assisted proof of the 4CT as pointing to the existence of mathematical truths of which (...) we cannot have a priori knowledge? -/- 2. The role of formalization in proof. What are the patterns ofinference according to which mathematical reasoning naturally proceeds? Are they of 'local' character (i.e. sensitive to the subject-matter of the reasoning concerned) or 'global' character (i.e. invariant across all subject-matters)? Finally, what if any relationship is there (a) between the patterns of inference manifest in a proof and its explanatory capacity and (b) between explanatory capacity and rigor? -/- 3. Diagrams and their role in mathematical reasoning. What essentially is diagrammatic reasoning, and what is the nature and basis of its usefulness? Can it play a justificative role in the development of mathematical knowledge and, more particularly, in genuine proof? Finally, does the use of diagrammatic reasoning force an adjustment either in our conception of rigor or in our view of its importance? (shrink)

Over the last 20+ years, globalization has made international trade and investment more efficient and productive. In the absence of coordinated global regulatory regimes, it has also made multinational corporations (MNCs) impervious to social concerns in the countries where they operate. There is considerable debate in the academic, political, and business arena as to the causes of the apparently inequitable distribution of benefits between labor and capital. Notwithstanding, the relative merits of this debate, and facing tremendous societal pressure, companies have (...) adopted voluntary codes of conduct to ensure that workers making products for them in poor and developing countries are protected from hazardous working conditions and receive wages that meet local laws and market conditions. These codes, however, suffer from a lack of credibility and proof of substantive compliance. A new type of nongovernmental organization (NGO) has emerged that monitors a company's compliance with prespecified standards and provides assurance to the external stakeholders that the company has fulfilled its voluntary obligations. From an historical perspective, this has been an innovative phenomenon where the monitoring organization purports to act as an honest broker to ensure all concerned that the company/industry has fulfilled its obligations. In this article, we undertake a thorough examination of two such organizations, that is, Fair Labor Association, and Social Accountability International, that have played a pioneering role in bridging the gap between societal expectations and corporate performance. We examine their governance structures, operating procedures, monitoring standards, and public disclosure of findings, and above all, their success in improving the level of corporate compliance with their self‐created codes or standards. Unfortunately, our findings and conclusions are disappointing. In our view, the two groups have mostly failed to meet their avowed goals. Rather than using their NGO status to help companies improve their code compliance, they have suffered from managerial capture and have been reduced to corporate apologists. (shrink)

Today, scientific discussions on the specifics of the development of civil society in Russia do not stop. The institutional approach allows us to look at this problem through the prism of formal and informal institutions existing in society. Researchers and practitioners should not focus only on the rule of law, official prescriptions and orders, setting the framework for interactions between authorities and citizens, promoting private initiatives, and realizing the rights and freedoms of the population. If they do not correspond to (...) the prevailing norms, stereotypes, ways of thinking and actions for centuries, then the most useful, at first glance, innovations in the political and social sphere may not take root. This does not mean, however, that informal institutions remain unchanged under any circumstances. They also evolve. This process can be targeted. It is important to understand all the actors involved in the development of civil society in our country. (shrink)

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that (...) nevertheless intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

John Searle raised the question whether all computation is observer-relative. Indeed, all of the common views of computation, be they semantical, functional or causal rely on mapping something onto the states of a physical or abstract process. In order to effectively execute such a mapping, this process would have to be observed in some way. Thus a probably syntactical analysis by an observer seems to be essential for judging whether a given process implements some computation or not. In order to (...) be able to explore the nature of these observers in a more formal way, we look at the Computing by Observing paradigm, a theoretical model of computation that includes an observer. We argue that the observers used there, monadic transducers, are good candidates for formalizing the way in which the syntax of a process must be analysed in order to judge whether it is computational. (shrink)

Coercion in mental health care gives rise to many ethical challenges. Many countries have recently implemented state policy programs or development projects aiming to reduce coercive practices and improve their quality. Few studies have explored the possible role of ethics in such initiatives. This study adds to this subject by exploring health professionals’ descriptions of their ethical challenges and strategies in everyday life to ensure morally justified coercion and best practices. Seven semi-structured telephone interviews were carried out in 2012 (...) with key informants in charge of central development projects and quality-assurance work in mental health services in Norway. No facilities used formal clinical ethics support. However, the informants described five areas in which ethics was of importance: moral concerns as implicit parts of local quality improvement initiatives; moral uneasiness and idealism as a motivational source of change; creating a normative basis for development work; value-based leadership; and increased staff reflexivity on coercive practices. The study shows that coercion entails both individual and institutional ethical aspects. Thus, various kinds of moral deliberation and ethics support could contribute to addressing coercion challenges by offering more systematic ways of dealing with moral concerns. However, more strategic use of implicit and institutional ethics is also needed. (shrink)

In this article, I try to shed some new light onGrundgesetze§10, §29–§31 with special emphasis on Frege’s criteria and proof of referentiality and his treatment of the semantics of canonical value-range names. I begin by arguing against the claim, recently defended by several Frege scholars, that the first-order domain inGrundgesetzeis restricted to value-ranges, but conclude that there is an irresolvable tension in Frege’s view. The tension has a direct impact on the semantics of the concept-script, not least on the (...) semantics of value-range names. I further argue that despite first appearances truth-value names play a distinguished role as semantic “target names” for “test names” in the criteria of referentiality and do not figure themselves as “test names” regarding referentiality. Accordingly, I show in detail that Frege’s attempt to demonstrate that by virtue of his stipulations “regular” value-range names have indeed been endowed with a unique reference, can plausibly be regarded as a direct application of the context principle. In a subsequent section, I turn to some special issues involved in §10. §10 is closely intertwined with §31 and in my and Richard Heck’s view would have been better positioned between §30 and §31. In a first step, I discuss the piecemeal strategy which Frege applies when he attempts to bestow a unique reference on value-range names in §3, §10–§12. In a second step, I critically analyze his tentative, but predictably unsuccessful proposal to identify all objects whatsoever, including those already clad in the garb of value-ranges, with their unit classes. In conclusion, I present two arguments for my claim that Frege’s identification of the True and the False with their unit classes in §10 is illicit even if both the permutation argument and the identifiability thesis that he states in §10 are regarded as formally sound. The first argument is set out from the point of view of the syntax of his formal language. It suggests though that a reorganization of the exposition of the concept-script would have solved at least one of the problems to which the twin stipulations in §10 give rise. The second argument rests on semantic considerations. If it is sound, it may call into question, if not undermine the legitimacy of the twin stipulations. (shrink)

Leszek Kołakowski, who was brought up in the climate of Marxist philosophy, has moved away very considerably from the Marxist position of extreme atheism, but he may not be called a convert. Of the two contrasting attitudes which may be assumed in respect of the existential problems, the attitude of the priest and the attitude of the jester, Kołakowski is closer to the latter. The priest, if he is to perform his role well, should take his duties seriously; he (...) should be convinced of the truth of the deity that he serves. In carrying out his office he is expected to be ceremonious, formal and serious. The jester's position is more comfortable. His task is not to conduct a systematic and serious search for the truth: it is more the role of the critic. He is to observe the faults, the nonsenses, and the blunders, unconcerned for the persons at the butt-end of his critique and how they are to extricate themselves from it. The jester need not be a merry clown at all. Perhaps that is why alongside God, the sub-title of Kołakowski's book mentions things that are sad. Kołakowski is fascinated by the figure of Satan, who wants to be taken seriously but in culture, especially in the folk culture is attributed grotesque forms. Only the devil of the jasełka traditional Polish Christmas play makes audiences laugh hilariously, the real devil is deadly serious, since he is eternally thirsting for the truth and for love. Kołakowski is not pleased with his role of jester. But neither would he be any use as a priest. He has no gospel of his own which he could pass on to other people. He is trapped between two absurdities, which he briefly formulates after Pascal as: „The basic tenets of faith... are absurd, and yet the world image which excludes those tenets is even more absurd". (shrink)

Leszek Kołakowski, who was brought up in the climate of Marxist philosophy, has moved away very considerably from the Marxist position of extreme atheism, but he may not be called a convert. Of the two contrasting attitudes which may be assumed in respect of the existential problems, the attitude of the priest and the attitude of the jester, Kołakowski is closer to the latter. The priest, if he is to perform his role well, should take his duties seriously; he (...) should be convinced of the truth of the deity that he serves. In carrying out his office he is expected to be ceremonious, formal and serious. The jester's position is more comfortable. His task is not to conduct a systematic and serious search for the truth: it is more the role of the critic. He is to observe the faults, the nonsenses, and the blunders, unconcerned for the persons at the butt-end of his critique and how they are to extricate themselves from it. The jester need not be a merry clown at all. Perhaps that is why alongside God, the sub-title of Kołakowski's book mentions things that are sad. Kołakowski is fascinated by the figure of Satan, who wants to be taken seriously but in culture, especially in the folk culture is attributed grotesque forms. Only the devil of the jasełka traditional Polish Christmas play makes audiences laugh hilariously, the real devil is deadly serious, since he is eternally thirsting for the truth and for love. Kołakowski is not pleased with his role of jester. But neither would he be any use as a priest. He has no gospel of his own which he could pass on to other people. He is trapped between two absurdities, which he briefly formulates after Pascal as: „The basic tenets of faith... are absurd, and yet the world image which excludes those tenets is even more absurd". (shrink)

Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the (...) proof contains no substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony. (shrink)

In this paper we consider the relation between beliefs and goals in agent theory. Beliefs play three roles in reasoning about goals: they play a role in the generation of unconditional desires from conditional ones, they play a role in adoption of desires as goals, and they play a role in the selection of plans to achieve goals. In this paper we consider the role of goals in reasoning about beliefs. Though we assume that goals do (...) not play a role in the belief generation problem, we argue that they play a role in the belief selection problem. We show the rationality of the use of goals in belief selection, in the sense that there are cases in which agents that take their goals into account in selecting a belief set from a set of alternatives outperform agents that do not do so. We also formally distinguish between the rational role of goals in belief selection and irrational wishful thinking. (shrink)

For several subsystems of second order arithmetic T we show that the proof-theoretic strength of T + (bar rule) can be characterized in terms of T + (bar induction) □ , where the latter scheme arises from the scheme of bar induction by restricting it to well-orderings with no parameters. In addition, we demonstrate that ACA + 0 , ACA 0 + (bar rule) and ACA 0 + (bar induction) □ prove the same Π 1 1 -sentences.

In this paper we prove some results about the complexity of proofs. We consider proofs in Hilbert-style formal systems such as in [17]. Thus a proof is a sequence offormulas satisfying certain conditions. We can view the formulas as being strings of symbols; hence the whole proof is a string too. We consider the following measures of complexity of proofs: length , depth and number of steps For a particular formal system and a given formula A we consider (...) the shortest length of a proof of A , the minimal depth of a proof of A and the minimal number of steps in a proof of A . The main results are the following: a bound on the depth in terms of the number of steps: Theorem 2.2, a bound on the depth in terms of the length: Theorem 2.3, a bound on the length in terms of the number of steps for restricted systems: Theorem 3.1. These results are applied to obtain several corollaries. In particular we show: a bound on the number of steps in a cut-free proof, some speed-up results, bounds on the number of steps in proofs of Paris-Harrington sentences. Some papers related to our research are listed in the references. We were especially influenced by Parikh's paper [17] on the famous conjecture of Kreisel . Many important problems in this field remain open. We hope that our paper will contribute to progress in this area. It should be noted that some results of this paper can be equally well obtained using unification theory , by translating a complexity-of-proof problem into a unification problem. A unification algorithm solving the unification problem can then be constructed and the complexity of the unification algorithm analyzed. As pointed out by the referee this method can be used to solve the problem stated in Section 3 for some non-simple schematic systems. (shrink)

Education (good teachers and good schools) is crucial for the successful integration of vulnerable groups in the society. Multicultural diversity presents an opportunity to make schools more inclusive, creative and open-minded. Although there are different projects and activities for Roma inclusion in schools, the number of Roma children attending formal education is still very low. Without having attended formal education, the chances for social exclusion are high and minimal for leading a self-defined life. To increase the rate of school registration (...) and the rate for completion, long-term policy interventions and financial support from international donations are needed. This paper aims to analyze the general situation of Roma children and youth the age of pre-school education, primary and secondary education, as well as the engagement of youth in volunteering activities as a significant role in the inclusion of Roma children in schools. Engagement in volunteering activities can help young people to be more integrated into society, as through volunteering they gain valuable experiences, new skills, and competencies that can improve their employability possibilities and enhance their attitudes towards citizenship. (shrink)

Preliminary words One important feature of Poincaré's conventionalism of geometry is linked to the relation between the abstract notion of space geometry and the representations of the free mobility of our bodies. In this sense «the group of rigid motions» identified by Helmholtz and Lie as the foundation of geometries of constant curvature is, according to Poincaré, an idealization of the primitive experience that acquaints us with the properties of space in the first place. 2 Furthermore, since Poincaré thinks that (...) the only adequate candidates for physical geometry – the geometries of constant curvature – are equivalent from a mathematical point of view (they are homeomorphic), we can choose any one of these. Actually, according to Poincaré, the idealization involved in passing from our own local motions to the group of motions makes use of temporal intuition: our notion of the large-space structure of space assumes that our displacements are infinitely iterables and this assumes temporal intuition. 3 Thus, it looks as Poincaré's notion of convention assumes some kind of idealization process. Indeed, the notion of convention involved in this cases seems to assume that in relation to a target system the choice between two idealizations is determined by some kind of equivalence relation, which in our case is displayed 1. (shrink)

Recently, organizational identity is being given more attention than ever before in the business world. This notion has grown substantially in importance in the hospitality industry. Facing increased competition, hospitality companies are driven to project a positive image to their stakeholders. Therefore, these organizations have begun to develop new organizational identity programs as part of their strategies to achieve their desired identities. This study analyzes the role of corporate social responsibility in the definition of the Organizational Identity of these (...) organizations, employing a qualitative research methodology based on an illustrative case study. Particularly, the authors analyze the case of Meliá Hotels International, a leading hotel company in Spain with a presence in 27 countries. The findings indicate that the company has formally integrated CSR into its strategy to align its actual identity with its desired and conceived identity in view of the critics in its local community. Moreover, the interest of the firm toward its stakeholders suggests that the company understands its conceived identity as an important link in understanding its organizational identity. This paper demonstrates that firm’s organizational identity is a set of several elements. When analyzing Meliá Hotels International’s identity, we see that the firm defines this concept as that which is most central, enduring, and distinctive about the organization. In this sense, the company appears to follow the vision-driven approach by referring to the organizational mission and vision statements, organizational philosophy, and core values as the basis of organizational identity. (shrink)

In his well?known paper from 1954, Herbert A. Simon sets out to demonstrate that it is possible, in principle, to make public predictions within the social sciences that will be confirmed by the events. However, Simon's proof by means of the Brouwer fixed?point theorem not only rests on an illegitimate use of continuous variables, it is also founded on the questionable assumption that facts ? even on the level of possibilities ? can be established by purely mathematical means. The (...) ?proof? also appears redundant since we already know from past experience that, for instance, the confirmation of a public election prediction is possible. (shrink)

Any inconsistent theory whose underlying logic is classical encompasses all the sentences of its own language. As it denies everything it asserts, it is useless for explaining or predicting anything. Nevertheless, paraconsistent logic has shown that it is possible to live with contradictions and still avoid the collapse of the theory. The main point of this paper is to show that even if it is formally possible to isolate the contradictions and to live with them, this cohabitation is neither desired (...) by working scientists not desirable for the progress of science. Several cases from the recent history of physics and cosmology are analyzed. (shrink)

This study examines the role of acculturation in shaping consumers’ views of ethics. Specifically, it examines the relationships between the desire to keep one’s original culture, the desire to adopt the host culture, and the four dimensions of the Muncy and Vitell (Journal of Business Research Ethics 24(4), 297, 1992) consumer ethics scale. Using two separate immigrant populations – one of former Middle-Eastern residents now living in the U.S. and the other of Asian immigrants in the U.S. – results (...) indicate that those who want to keep their original culture are less tolerant of unethical consumer activities, while those who are more willing to adopt the host culture are more tolerant of these same consumer activities. Furthermore, the immigrants in both studies who are more tolerant of unethical consumer activities are those who are generally somewhat younger and with less formal education. The relationship between gender and consumer ethics was not significant. (shrink)

Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn into definability results of formal logic. (...) The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible. (shrink)