Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features (...) in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided. (shrink)

Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. A central question is how to introduce implication in such a logic. We give a positive answer whenever the orthomodular poset in question is of finite height. The crucial advantage of our solution is that the corresponding algebra, called implication orthomodular poset, i.e. a poset equipped with a binary operator of implication, corresponds to the original orthomodular poset and that its implication operator is everywhere defined. We present here (...) a complete list of axioms for implication orthomodular posets. This enables us to derive an axiomatization in Gentzen style for the algebraizable logic of orthomodular posets of finite height. (shrink)

In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.

Tense operators in effect algebras play a key role for the representation of the dynamics of formally described physical systems. For this, it is important to know how to construct them on a given effect algebra \( E\) and how to compute all possible pairs of tense operators on \( E\) . However, we firstly need to derive a time frame which enables these constructions and computations. Hence, we usually apply a suitable set of states of the effect algebra \( (...) E\) in question. To approximate physical reality in quantum mechanics, we use only the so-called Jauch–Piron states on \( E\) in our paper. To realize our constructions, we are restricted on lattice effect algebras only. (shrink)

A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element (...) of this lattice or poset by using the so-called twist product construction, respectively. We extend this construction of Kleene lattices and Kleene posets by considering a fixed subset instead of a fixed element. Moreover, we show that in some cases, this generating poset can be embedded into the resulting Kleene poset. We investigate the question when a Kleene poset can be represented by a Kleene poset obtained by the mentioned construction. We show that a direct product of representable Kleene posets is again representable and hence a direct product of finite chains is representable. This does not hold in general for subdirect products, but we show some examples where it holds. We present large classes of representable and non-representable Kleene posets. Finally, we investigate two kinds of extensions of a distributive poset $${\textbf{A}}$$ A, namely its Dedekind-MacNeille completion $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) and a completion $$G({\textbf{A}})$$ G ( A ) which coincides with $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) provided $${\textbf{A}}$$ A is finite. In particular we prove that if $${\textbf{A}}$$ A is a Kleene poset then its extension $$G({\textbf{A}})$$ G ( A ) is also a Kleene lattice. If the subset X of principal order ideals of $${\textbf{A}}$$ A is involution-closed and doubly dense in $$G({\textbf{A}})$$ G ( A ) then it generates $$G({\textbf{A}})$$ G ( A ) and it is isomorphic to $${\textbf{A}}$$ A itself. (shrink)

It is well-known that intuitionistic logics can be formalized by means of Heyting algebras, i.e. relatively pseudocomplemented semilattices. Within such algebras the logical connectives implication and conjunction are formalized as the relative pseudocomplement and the semilattice operation meet, respectively. If the Heyting algebra has a bottom element |$0$|⁠, then the relative pseudocomplement with respect to |$0$| is called the pseudocomplement and it is considered as the connective negation in this logic. Our idea is to consider an arbitrary meet-semilattice with |$0$| (...) satisfying only the Ascending Chain Condition (these assumptions are trivially satisfied in finite meet-semilattices) and introduce the operators formalizing the connectives negation |$x^{0}$| and implication |$x\rightarrow y$| as the set of all maximal elements |$z$| satisfying |$x\wedge z=0$| and as the set of all maximal elements |$z$| satisfying |$x\wedge z\leq y$|⁠, respectively. Such a negation and implication is ‘unsharp’ since it assigns to one entry |$x$| or to two entries |$x$| and |$y$| belonging to the semilattice, respectively, a subset instead of an element of the semilattice. Surprisingly, this kind of negation and implication still shares a number of properties of these connectives in intuitionistic logic, in particular the derivation rule Modus Ponens. Moreover, unsharp negation and unsharp implication can be characterized by means of five, respectively seven simple axioms. We present several examples. The concepts of a deductive system and of a filter are introduced as well as the congruence determined by such a filter. We finally describe certain relationships between these concepts. (shrink)

As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics are depending (...) on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)

An assertion is existentially known if and only if: (i) the speaker knows that the sentence she uses to make the assertion expresses a true proposition; (ii) she makes the assertion based on that knowledge; and (iii) she does not believe, have justification for, or know the proposition asserted. Accordingly, if existentially known assertions could be made correctly—as argued by Charlie Pelling in his ‘Assertion and the Provision of Knowledge’—this would show that the norm of assertion cannot be the speaker's (...) belief in, justification for or knowledge of the proposition. In this paper, I try to show that Pelling's argument is inconclusive, as it rests on two assumptions which can be resisted. In turn, I offer a pair of alternative strategies to explain how we can deal with existentially known assertions under the assumption that the speaker's knowledge is the norm of assertion. (shrink)

In this article, we examine the political and educational relevance of Hannah Arendt’s account of friendship. Drawing from Arendt’s central works on friendship, we offer a novel interpretation of the concept by connecting the notion with the idea of educational ‘love for the world’, amor mundi. With this interpretation, we seek to demonstrate that the concept of friendship has both direct educational and indirect political significance. Thereby, we distinguish our interpretation from two previous understandings of the educational relevance of the (...) Arendtian notion of friendship—those by (1) Aaron Schutz and Marie G. Sandy, and (2) Morten T. Korsgaard—in which friendship is either assigned a specifically political role (as in (1)) or its significance to education is narrowly understood (as in (2)). We argue our interpretation of friendship offers both a new contribution to the understanding of the relationship between education and politics in the context of Arendt scholarship, and a novel way of thinking about the educational significance of friendship in the context of contemporary democratic politics, especially the prevailing political polarization. (shrink)

_Epistemic Logic_ studies statements containing verbs such as 'know' and 'wish'. It is one of the most exciting areas in medieval philosophy. Neglected almost entirely after the end of the Middle Ages, it has been rediscovered by philosophers of the present century. This is the first comprehensive study of the subject. Ivan Boh explores the rules for entailment between epistemic statements, the search for the conditions of knowing contingent propositions, the problems of substitutivity in intentional contexts, the relationship between (...) epistemic and modal logic, and the problems of composite and divided senses in authors ranging from Abelard to Frachantian. (shrink)

Introduction 'Indoctrination' belongs to a family of concepts which includes ' teaching', 'education', 'instruction', and 'learning'. ...

_Epistemic Logic_ studies statements containing verbs such as 'know' and 'wish'. It is one of the most exciting areas in medieval philosophy. Neglected almost entirely after the end of the Middle Ages, it has been rediscovered by philosophers of the present century. This is the first comprehensive study of the subject. Ivan Boh explores the rules for entailment between epistemic statements, the search for the conditions of knowing contingent propositions, the problems of substitutivity in intentional contexts, the relationship between (...) epistemic and modal logic, and the problems of composite and divided senses in authors ranging from Abelard to Frachantian. (shrink)

"The medical establishment has become a major threat to health. The disabling impact of professional control over medicine has reached the proportions of an epidemic. Iatrogenesis, the name for this new epidemic, comes from iatros, the Greek word for physician, and genesis, meaning origin. Discussion of the disease of medical progress has moved up on the agendas of medical conferences, researchers concentrate on the sick-making powers of diagnosis and therapy, and reports on paradoxical damage caused by cures for sickness take (...) up increasing space in medical dope-sheets [...] The public has been alerted to the perplexity and uncertainty of the best among its hygienic caretakers [...] This book argues that panic is out of place. Thoughtful public discussion of the iatrogenic pandemic, beginning with an insistence upon demystification of all medical matters, will not be dangerous to the commonweal."-- from Introduction. (shrink)

Lackey’s (2007) class of “selfless assertions” is controversial in at least two respects: it allows propositions that express Moorean absurdity to be asserted warrantedly, and it challenges the orthodox view that the speaker’s belief is a necessary condition for warranted assertibility. With regard to the former point, I critically examine Lackey’s broadly Gricean treatment of Moorean absurdity and McKinnon’s (2015) epistemic approach. With regard to the latter point, I defend the received view by supporting the knowledge account, on which knowledge (...) is the necessary condition for warranted assertion. After examining two defenses of KA, by Montminy and Turri, I propose two alternative approaches. Although I remain neutral between them, I develop in more detail the view which classifies “selfless assertions” as “presentations”, a type of assertives distinct from genuine assertions. This account is motivated further by allowing for the expansion of the normative approach to other assertives, a feature we may be interested in, in the light of a recent wave of normative accounts of speech acts. (shrink)

O utopianismo científico de Neurath é a proposta para que as ciências sociais se envolvam na elaboração, desenvolvimento e comparação de cenários contrafactuais, as ‘utopias’. Tais cenários podem ser entendidos como peças centrais de experimentos de pensamento científicos, isto é, em exercícios da imaginação que não apenas promovem a revisão conceitual, mas também estimulam a criatividade para lidar com problemas vivenciados, já que utopias são esforços para imaginar como o futuro poderia ser. Ademais, experimentos de pensamento utópicos podem oferecer conhecimento (...) científico para informar debates e decisões políticas, contribuindo para formatar a sociedade. Este ensaio reconstrói um evento histórico como um exemplo da metodologia utopianista de Neurath. No final dos anos 1970 e início dos anos 1980, uma comissão científica e política designada pelo parlamento da Alemanha Ocidental inventou e comparou quatro cenários para políticas energético-econômicas futuras. Conclusões da comissão informaram decisões políticas que puseram a Alemanha Ocidental (e depois reunificada) em um caminho para se tornar uma potência industrial verde. Uma parte fundamental do trabalho da comissão envolveu um apelo à imaginação, permitindo a caracterização sob a metodologia de Neurath. (shrink)

The "theory of mind" framework has been the fastest growing body of empirical research in contemporary psychology. It has given rise to a range of positions on what it takes to relate to others as intentional beings. This book brings together disparate strands of ToM research, lays out historical roots of the idea, and indicates better alternatives.

This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. Given that (...) sentential negationparticipates in negative concord, we develop an extension of thepolyadic approach which can deal with non-variable binding operators,treating the contribution of negation in a concord context assemantically empty. Our semantic analysis, incorporated into agrammatical analysis formulated in HPSG, crucially relies on theassumption that quantifiers can be combined in more than one wayupon retrieval from the quantifier store. We also considercross-linguistic variation regarding the participation ofsentential negation in negative concord. (shrink)

"Ivan Illich alights on such topics as education, history, language, politics, and the church. The conversations range over the whole of Illich's published work and public career as a priest, vice-rector of a university, founder of the Centre for Intercultural Documentation in Cuernavaca, Mexico, and author of such classics as Tools for Conviviality, Medical Nemesis, and Deschooling Society.".

An overview on archaeological evidence, provided by Colagè and d’Errico, reveals that the timing, location, and pace of cultural innovations are more consistent with scenarios that take culture, rather than genetic evolutionary processes, as the key driving force for human cognition. The authors elaborate on those mechanisms by which cultural evolution operates, with a specific focus on cultural exaptation and cultural neural reuse.

Conversation analysts have noted that, in psychotherapy, formulations of the client's talk can be a vehicle for offering a psychological interpretation of the client's circumstances. But we notice that not all formulations in psychotherapy offer interpretations. We offer an analysis of formulations that are diagnostic: that is, used by the professional to sharpen, clarify or refine the client's account and make it better able to provide what the professional needs to know about the client's history and symptoms. In doing so, (...) these formulations also have the effect of shepherding the client's account towards subsequent therapeutic interpretation. In a coda, we notice that sometimes the formulations are designed discreetly. We examine one such discreet formulation in detail, and show how its very ambiguity can lead to its failure as a diagnostic probe. (shrink)

Epistemic logic is one of the most exciting areas in medieval philosophy. Neglected almost entirely after the end of the Middle Ages, it has been rediscovered by philosophers of the twentieth century. Epistemic Logic in the Later Middle Ages provides the first comprehensive study of the subject. Ivan Boh explores the contrast between epistemic and alethic conceptions of consequence, the general epistemic rules of consequence, the search for conditions of knowing contingent propositions, the problems of substitutivity in intentional contexts, (...) the considerations of epistemic/doxastic iterated modalities, and the problems of composite and divided senses in authors ranging from Abelard to Frachantian. Boh concludes with a comparison between medieval endeavors and the epistemic logic of our own times. Written in a clear and readable style with minimal symbolic apparatus, this book employs modern symbolism and conceptual frameworks, and complements the studies of the syntacticand semantic dimensions of medieval logic. (shrink)

Statements of degree appear to falsify basic doctrines in Tractatus Logico-Philosophicus. I offer a fresh formulation of the challenge and assess a solution proposed on Wittgenstein’s behalf by Sarah Moss. I find that Moss’s proposal fails. The proposal rides in part on novel interpretations of pronouncements by Wittgenstein on the nature of the elementary proposition. I find that the interpretations cannot be sustained but that Moss’s textual case hints at important and overlooked features of the Tractarian program. I develop Wittgenstein’s (...) comparison of propositions to measuring instruments and apply it throughout, showing that it captures philosophical commitments in Tractatus that otherwise tend to slip from view. (shrink)

Frege's account of indirect proof has been thought to be problematic. This thought seems to rest on the supposition that some notion of logical consequence ? which Frege did not have ? is indispensable for a satisfactory account of indirect proof. It is not so. Frege's account is no less workable than the account predominant today. Indeed, Frege's account may be best understood as a restatement of the latter, although from a higher order point of view. I argue that this (...) ascent is motivated by Frege's conception of logic. (shrink)

Este artículo se ubica en el ámbito de la formación jurídica y expone tres macro estrategias del aprendizaje, que bien pueden, como aquí se afirma, interactuar y complementarse entre sí. En primer lugar, se representa el modelo educativo centrado en la transmisión de conceptos, sin duda el más arraigado y tradicional en el contexto europeo-continental. En segundo lugar, se procede examinando el paradigma formativo por problemas, enfocado en el desarrollo de la capacidad analítica. En tercer lugar, se ilustra el método (...) educativo que entrena el discernimiento, impulsando la capacidad de elección, entre una multitud de opciones posibles, y empoderando la toma de decisiones racionalmente motivadas. En conclusión, se presenta una teoría formativa unitaria que pone en valor la relación funcional, potencialmente existente, entre estas diferentes metodologías formativas. (shrink)

The enigmatic thought of Charles S. Peirce, considered by many to be one of the great philosophers of all time, involves inquiry not only into virtually all branches and sources of modern semiotics, physics, cognitive sciences, and mathematics, but also logic, which he understood to be the only useful approach to the riddle of reality. This book represents an attempt to outline an analytical method based on Charles Peirce’s least explored branch of philosophy, which is his evolutionary cosmology, and his (...) notion that the universe is made of an ‘effete mind.’ The chief argument conceives of human discourse as a giant metaphor in regard to outside reality. The metaphors arise in our imagination as lightning-fast schemes for acting, speaking, or thinking. To illustrate this, each chapter will present a well-known metaphor and explain how it is unfolded and conceptualized according to the new method for revealing meaning. This original work will interest students and scholars in many fields including semiotics, linguistics and philosophy. (shrink)

ARAGÃO, Ivan Rêgo. “ Vinde todas as pessoas, e vede a minha dor ”: A Festa/Procissão ao Nosso Senhor dos Passos como Atrativo Potencial Turístico em São Cristóvão-Sergipe-Brasil. 2012. 198f. Dissertação (Mestrado) Cultura e Turismo – Universidade Estadual de Santa Cruz (UESC), Ilhéus-BA. Palavras-chave: Turismo Cultural-Religioso Católico. Religiosidade Popular. Festa do Senhor dos Passos. Keywords: Catholic Religious-Cultural Tourism. Popular Religiosity. Party of Lord of the Steps.

This paper investigates a limitation of the model of belief and knowledge prevailing in mainstream economics, namely the state-space model. Because of its set-theoretic nature, this model has difficulties in capturing the difference between expressions that designate the same object but have different meanings, i.e., expressions with the same extension but different intensions. This limitation generates puzzling results concerning what individuals believe or know about the world as well as what individuals believe or know about what other individuals believe or (...) know about the world. The paper connects these puzzling results to two issues that are relevant for economic theory beyond the state-space model, namely, framing effects and the distinction between the model-maker and agents that appear in the model. Finally, the paper discusses three possible solutions to the limitations of the state-space model, and concludes that the two alternatives that appear practicable also have significant drawbacks. (shrink)

In the wake of Stalin's death, many Soviet scientists saw the opportunity to promote their methods as tools for the engineering of economic prosperity in the socialist state. The mathematician Leonid Kantorovich (1912–1986) was a key activist in academic politics that led to the increasing acceptance of what emerged as a new scientific persona in the Soviet Union. Rather than thinking of his work in terms of success or failure, we propose to see his career as exemplifying a distinct form (...) of scholarship, as a partisan technocrat, characteristic of the Soviet system of knowledge production. Confronting the class of orthodox economists, many factors were at work, including Kantorovich's cautious character and his allies in the Academy of Sciences. Drawing on archival and oral sources, we demonstrate how Kantorovich, throughout his career, negotiated the relations between mathematics and economics, reinterpreted political and ideological frames, and reshaped the balance of power in the Soviet academic landscape. (shrink)

En esta entrevista, conversamos con el Dr. Alejandro De Oto sobre las potencialidades de los estudios poscoloniales a la hora de comprender la configuración de espacios e imágenes de culto, consagrados, venerados o denostados y su vínculo con la historia, las memorias legitimadas y las subalternas, las identidades y las luchas de poder.