We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...) We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

Chu spaces are a new model for information structure and mathematical structure in general. Their properties are usually developed as a form of category theory. In this note, we show how they may also be viewed as models for a two-sorted first-order language, and we determine the exact flow of information across the natural Chu transforms. Our analysis is akin to that of process graphs via bisimulation and modal formulas.

We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a 'big toy model', in which both quantum and classical systems can be faithfully represented—as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces (...) can be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems—the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hubert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness. (shrink)

This paper proposes a way of navigating the tension between the local and global in Fratelli tutti. The author argues that the encyclical exemplifies and develops an analogical approach for authentic encounter. The analogical approach to God and its use of language emphasize a tensive space between the known and unknown, which the author transposes to human encounter. The encyclical grounds and develops this transposed analogical approach through emphasis on cultural diversity, with a bifocal affirmation of difference and desire for (...) relationship. Francis’s attention to Indigenous peoples grounds attention to the local as disposing toward a global outlook in care for the natural world. Finally, the author applies this approach to reflection on reconciliation between Indigenous peoples and the Church in Canada. Reflection on language is thereby put to the work of engaging the tensive and morally complex space between truth and reconciliation—namely, the space of encount er where healing is ongoing. (shrink)

The concept of the self and its relation to moral action is complex and subject to varying interpretations, not only between different academic disciplines but also across time and space. This paper presents empirical evidence from a cross-cultural study on the Buddhist and Confucian notions of self in SMEs in Vietnam and Taiwan. The study employs Hwang’s Mandala Model of the Self, and its extension into Shiah’s non-self-model, to interpret how these two Eastern philosophical representations of the self, the Confucian (...) relational self and Buddhist non-self, can lead to moral action. By demonstrating the strengths of the model, emphasizing how social and cultural influences constrain the individual self and promote the social person leading to moral action, the paper extends understanding of the self with empirical evidence of the mechanisms involved in organizational contexts. (shrink)

Previous studies provided evidence for a connection between language processing and language change. We add to these studies with an exploration of the influence of lexical-distributional properties of words in orthographic space, semantic space, and the mapping between orthographic and semantic space on the probability of lexical extinction. Through a binomial linear regression analysis, we investigated the probability of lexical extinction by the first decade of the twenty-first century (2000s) for words that existed in the first decade of the nineteenth-century (...) (1800s) in eight data sets for five languages: English, French, German, Italian, and Spanish. The binomial linear regression analysis revealed that words that are more similar in form to other words are less likely to disappear from a language. By contrast, words that are more similar in meaning to other words are more likely to become extinct. In addition, a more consistent mapping between form and meaning protects a word from lexical extinction. A nonlinear time-to-event analysis furthermore revealed that the position of a word in orthographic and semantic space continues to influence the probability of it disappearing from a language for at least 200 years. Effects of the lexical-distributional properties of words under investigation here have been reported in the language processing literature as well. The results reported here, therefore, fit well with a usage-based approach to language change, which holds that language change is at least to some extent connected to cognitive mechanisms in the human brain. (shrink)

A theorem obtained by van Benthem for preservation of formulas under Chu transforms between Chu spaces is strengthened and derived from a general many-sorted interpolation theorem. The latter has been established both by proof-theoretic and model-theoretic methods; there is some discussion as to how these methods compare and what languages they apply to. In the conclusion, several further questions are raised.

There is a remarkable similarity between some mathematical objects used in the Branching Space-Times framework and those appearing in computer science in the fields of event structures for concurrent processing and Chu spaces. This paper introduces the similarities and formulates a few open questions for further research, hoping that both BST theorists and computer scientists can benefit from the project.

To model a (particular kind of) physical system, the perspective that encompasses preparations, tests and the interplay between them is crucial. In this paper, we employ the conceptual and technical framework presented by Buffernoir (2023) to model physical systems through this pivotal lens, utilizing Chu spaces. With some intuitive and operational axioms we manage to reproduce the following fundamental and abstract results, as well as (part of) the involved reasoning: (1) the states corresponding to a property form a (bi-orthogonally) (...) closed set; (2) the properties form an orthomodular lattice. Adding some idealistic axioms, we can derive: (1) the pure states form a quantum Kripke frame in the sense of Zhong (2017, 2021, 2023); (2) the properties form an irreducible propositional system in the sense of Piron (1976), isomorphic to the lattice of closed sets of pure states. Our axioms are different from those in Buffernoir (2023): on the one hand, they say less about the structure of mixed states; on the other hand, they are arguably more intuitive and operational. The work formalizes some important reasoning about quantum systems, reveals some implicit idealization behind the Hilbert space formalism of quantum theory and hints at other possible formalisms. Finally, it is argued that the framework can be applied to classical physics at an abstract level as well as naturally extended with probabilities. (shrink)

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic , which is the linear fragment of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories / of an ambient *-autonomous category . Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models and (...) to present various completeness theorems.As concrete examples, we present a hypercoherence model, using Ehrhard’s hereditary/anti-hereditary objects, a Chu-space model, a double gluing model over our categorical framework, and a model based on iterated double gluing over a *-autonomous category.For the multiplicative fragment of. (shrink)

The definitions of yu 宇 and zhou 宙 in the “Gengsang Chu 庚桑楚” chapter of the Zhuangzi have been cited as the earliest definitions of space and time in the Chinese philosophical tradition. However, careful analysis of chosen modern translations reveals that the definitions entail rather obscure relationships between the Dao and space and time. I argue that the obscurity is not inherent in the text, but arises from the practice of rendering yu and zhou as the conceptual counterparts of (...) space and time or related concepts. Instead, I propose that we leave the terms untranslated. This practice would not only forestall interpretive difficulties concerning the Dao’s relations to space and time, but it would also preserve the Zhuangzist yu and zhou as two distinctive, ontic notions that indicate the Dao’s indeterminate modes of existence, a unique feature of the Zhuangzi. (shrink)

We show that numerous distinctive concepts of constructive mathematics arise automatically from an “antithesis” translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically “constructivize” classical definitions, handling the resulting bookkeeping automatically.

This is a comparative study on the 20th's century's Western philosophy Hannah Arendt(1906-1975) and the 16th century's Eastern Confucian thinker Wang Yang-ming(1472-1529). Wang-ming was a Neoconfucian thinker of the 16th century China. In his time, Chinese intellectual world was dominated by Neoconfucian Ch’eng-Chu School which laid much stress on scholastic work of learning. Yang-ming saw a huge obstacle of intellectualism in Ch’eng-Chu school’s theoretical scholasticism that emphasized overly book-learning to be required on the way to become a genuine person. He (...) recognized this kind of rigidintellectualism as the true reason for the dichotomy in his time between knowledge and action, between learning and life, and between selfcultivation and social practice. According to his view, the dichotomy brought about serious political corruption and oppressed human creativity up to the point of total institutionalization of “truth”. Hannah Arendtwas sickened under the severe totalitarianism of the 20th century, especially as a Jew under the German Nazism. She undertook an extensive analysis of how Western civilization generated totalitarian imperialism, fascism, and communism, going through the modern times, all of which made human beings’ language and action superfluous, erupted, and destroyed. Through these experiences, she became disgusted with traditional Western hierarchy of thinking and doing, philosophy and politics, theory and practice, in short, vita contemplativa and vita activa. Although they both lived far away from each other in space and time and used completely different languages, they both, in my view, shared many common problems and concerns, not only in the contents of their thoughts but also in the way and form of construction of thoughts. To the similar extent that people were warned and judged by both thinkers respectively in their times of the totalitarianism of making human beings superfluous and puppet-like, we human beings in the 21st century are considered to be threatened by the totalitarian nullification caused by modern utilitarianism, automation, consumerism, etc. These principles are practiced limitlessly and boundlessly, so that our whole lives of politics, culture, and education are now suffering from that threat. It is my conviction that we can acquire some guide and wisdom from the twothinkers of East and West, because they discovered possible solutions of how to restore and revive human beings’ capacities of thinking and judging, and how to bring action and doing. (shrink)

This study examines the role of codes of ethics in reducing the extent to which managers act opportunistically in reporting earnings. Corporate codes of ethics, by clarifying the boundaries of ethical corporate behaviors and making relevant social norms more salient, have the potential to deter managers from engaging in opportunistic financial reporting practices. In a sample of international companies, we find that the quality of corporate codes of ethics is associated with higher earnings quality, i.e., lower discretionary accruals. Our results (...) are confirmed for a subsample of firms more likely to be engaging in opportunistic reporting behavior, i.e., firms that just meet or beat analysts’ forecasts. Further, codes of ethics play a greater role in reducing earnings management for firms in countries with weaker investor protection mechanisms. Our results suggest that corporate codes of ethics can be a viable alternative to country-level investor protection mechanisms in curbing aggressive reporting behaviors. (shrink)

Students and teachers of Chinese history and philosophy will not want to miss Daniel Gardner's accessible translation of the teachings of Chu Hsi —a luminary of the Confucian tradition who dominated Chinese intellectual life for centuries. Homing in on a primary concern of our own time, Gardner focuses on Chu Hsi's passionate interest in education and its importance to individual development. For hundreds of years, every literate person in China was familiar with Chu Hsi's teachings. They informed the curricula of (...) private academies and public schools and became the basis of the state's prestigious civil service examinations. Nor was Chu's influence limited to China. In Korea and Japan as well, his teachings defined the terms of scholarly debate and served as the foundation for state ideology. Chu Hsi was convinced that through education anyone could learn to be fully moral and thus travel the road to sagehood. Throughout his life, he struggled with the philosophical questions underlying education: What should people learn? How should they go about learning? What enables them to learn? What are the aims and the effects of learning? Part One of _Learning to Be a Sage_ examines Chu Hsi's views on learning and how he arrived at them. Part Two presents a translation of the chapters devoted to learning in the _Conversations of Master Chu_. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Teaching the Trinity:Scripture and Performance of the Psychological Analogy in Aquinas's Summa TheologiaeZane E. ChuTeaching the Trinity, for St. Thomas Aquinas, takes its point of departure from Sacred Scripture. He makes this explicit at the outset of the Trinitarian treatise in the Summa theologiae, citing Christ's words at John 8:42, "from God I proceeded," and affirming, "divine Scripture in the things of divinity, uses words that pertain to procession."1 (...) The order of teaching then continues through speculative effort to give an account of the scriptural witness to the distinction of persons in God, in order to return to the same Scripture with a deeper grasp of its meaning.2Aquinas is a master of the sacred page, and his basic pedagogy for theology involves the "exercises of Sacred Scripture" of reading, disputing, and preaching.3 Recent scholarship draws attention to his reading of Scripture [End Page 1149] expressed in biblical commentaries as foundational for his teaching and as an interpretive context for his summative works.4 My purpose is to illustrate this basic pedagogy in the Trinitarian treatise of the Summa theologiae, taking the Lectura super Ioannem as an interpretive context for the analogies of word and love—the psychological analogy—for the Trinity. Most scholarly discussion of the psychological analogy elaborates on its theoretical aspects, with some attention to its scriptural foundation.5 I wish to show the priority of Scripture in Aquinas's employment of this analogy in three respects, namely, its foundation in exegesis, performative aspects, and orientation toward preaching.My investigation focuses on question 27 of the prima pars alongside pertinent sections of the Super Ioannem. I argue that citations from the Gospel of John (8:42, 15:26, and 14:16) in the sed contras of articles 1 and 3 function to ground the psychological analogy in scriptural exegesis and to prompt its performance. Turning to the corresponding commentary shows Aquinas leading the student to knowledge of Christ as divine Word and to love of him from the Holy Spirit that both leads to and follows upon such knowledge. This provokes an affective experience of loving Christ in knowing his divinity that is an actual performance of the psychological analogy. The magisterial responses then use this affective experience as a basis to facilitate a grasp of the analogy, the articulation of which is a further guided performance that reflects on this experience. Aquinas teaches the Trinity by exercising the student both affectively and intellectually in its scriptural foundation for a deeper grasp that prepares for preaching. I develop my argument in three [End Page 1150] main steps. First, I specify the place of Scripture in Aquinas's teaching and review the composition of the Trinitarian treatise. Then, I examine the first four articles of question 27 and corresponding sections of the Super Ioannem, in the order of the analogies of word and of love. Lastly, I consider Aquinas's treatment of the Holy Spirit's proper name of Love and subsequent preaching to illustrate Scripture as a point of arrival through performance of the psychological analogy.The Place of Scripture in Aquinas's TeachingFor Aquinas, Scripture is placed within his broader practice of sacra doctrina or holy teaching, attention to which assists in demonstrating how the Johannine citations ground the psychological analogy in Scripture and prompt its performance. Sacra doctrina has a primarily pastoral orientation, namely, to form Dominicans for preaching and hearing confessions.6 Though more speculative than practical, sacra doctrina as speculation or contemplation of the truth of Christian faith contained in Scripture is to be handed on to others.7 This requires training in the scriptural exercises of reading and disputing as preparation for preaching. These may be taken as "spiritual exercises" that engage not only thought, but also affectivity in service of personal transformation for the preacher's way of life.8 Aquinas's practice of sacra doctrina begins with reading Scripture as expressed in biblical commentaries, and develops in the Summa theologiae, which accesses Scripture through citations to offer a summative grasp of the truth contained therein. Here, I review the formal aspects of Aquinas's teaching from Scripture in these texts... (shrink)