Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity -- Axiomatic set (...) theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

This work contains a full, critical translation of Huai Nan Tzu, Book 9, Chu-shu, which is part of "an important compendium of knowledge and philosophical speculation... presented to the Chinese court of Wu Ti during the first century of the Former Han ". Preceding the translation is a dense philosophical analysis of the treatise, and of its place in a painstakingly reconstructed history of ideas, particular to the development of China up to that date. China had already gone through nearly (...) two millennia of history. (shrink)

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of (...) dialectical argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

Let us begin with the simple observation that applied mathematics can be very tough! It is a common occurrence that basic physical principle instructs us to construct some syntactically simple set of differential equations, but it then proves almost impossible to extract salient information from them. As Charles Peirce once remarked, you can’t get a set of such equations to divulge their secrets by simply tilting at them like Don Quixote. As a consequence, applied mathematicians are often forced to pursue (...) roundabout and shakily rationalized expedients if any useful progress is to be made. Often these provisional and quasi-empirical procedures within applied mathematics loom large in motivating the “anti-realist” or “anti-unificationist” conclusions of Nancy Cartwright and allied authors. (shrink)

This is one of those cases to which Dr. 8 oodhouse's remark applies with all its force, that a method which leads to true results must have its logic — H.S Smith (" On Some of the Methods at Present in Use in Pure Geometry," p. 6) A goodly amount of modern metaphysics has concerned itself, in one form or another, with the question: what attitude should we take in regard to a language whose semantic underpinnings seem less than certain? (...) Since much of standard English is surely of this type, many philosophers have felt driven to extreme and unpalatable resolutions — wholesale rejection of attractive logical rules, radical "antirealism", "minimalism" about truth, and so forth, Scientists, however, have long dealt with analogous foundational insecurities and, under the duress of practicality, have framed a set of shifting attitudes towards language and reasoning that seem far more commonsensical than the extreme positions to which pure philosophy has often been led. Following this lead, this essay will recommend a more nuanced approach to linguistic insecurity that is neither naively optimistic nor mired in the gloomy sloughs of antirealism. (shrink)

There is considerable likelihood that Gottlob Frege began writing his Foundations of Arithmetic with the expectation that he could introduce his numbers, not with sets, but through some algebraic techniques borrowed from earlier writers of the Gottingen school. These rewriting techniques, had they worked, would have required strong philosophical justification provided by Frege's celebrated "context principle," which otherwise serves little evident purpose in the published Foundations.

Current sociological theories appear to have lost their general persuasiveness in part because, unlike the theories of the ‘classical era’, they fail to maintain an integrated stance toward society, and the practical role that sociology plays in society. The authors explore various facets of this failure and possibilities for reconstructing sociological theories as integrated wholes capable of conveying a moral and political immediacy. They discuss the evolution of several concepts (for example, the social, structure, and self) and address the significant (...) disputes (for example, structuralism versus humanism, and individual versus society) that have dominated twentieth-century sociological thought. Their ideas and analyses are directed towards an audience of students and theorists who are coming to terms with the project of sociological theory, and its relationship with moral discourses and political practice. The authors of these essays are sociological theorists from the United States, the United Kingdom and Canada. They are all established, but not ‘establishment’ authors. The book contains no orthodoxies, and no answers. However, the essays do contribute to identifying the range of issues that will constitute the agenda for the next generation of sociological theorists. (shrink)

Stereological techniques allow biologists to create quantitative, three-dimensional descriptions of biological structures from two- dimensional images of tissue viewed under the microscope. For example, they can accurately estimate the size of a particular organelle, the total length of a mass of capillaries, or the number of neurons or synapses in a particular region of the brain. This book provides a practical guide to designing and critically evaluating stereological studies of the nervous system and other tissues. It explains the basic concepts (...) behind design-based stereology and how to get started. Also included are detailed descriptions of how to prepare tissue appropriately, perform pilot studies and decide on the appropriate sampling strategy, and account for phenomena such as tissue shrinkage. Numerous examples of applications of stereological methods that are applicable to studies of the central system and a wide variety of other tissues are explained. The book is therefore essential reading for neurobiologists and cell biologists interested in generating accurate representations of cell and tissue architecture. (shrink)

Together again for the first time, Marx and Durkheim join forces in the pages of Disintegration: Bad Love, Collective Suicide, and the Idols of Imperial Twilight for a dialectical exploration of the moral economy of neoliberalism, animated, as it is not only by the capitalist chase for surplus value, but also by an immortal vortex of sacred powers. Classical sociology and psychoanalysis are reconstituted within Hegelian social ontology and dialectical method that differentiates between the ephemeral and free and the eternal (...) and fixed aspects of modern life. (shrink)

In ancient China, a revered Taoist sage named Zhuangzi told many parables. In Existential Psychology and the Way of the Tao, a selection of these parables will be featured. Following each parable, an eminent existential psychologist will share a personal and scholarly reflection on the meaning and relevance of the parable for psychotherapy and contemporary life. The major tenets of Zhuangzi's philosophy are featured. Taoist concepts of emptiness, stillness, Wu Wei (i.e. intentional non-intentionality), epistemology, dreams and the nature of reality, (...) character building in the midst of pain, meaning and the centrality of relationships, authenticity, self-care, the freedom that can come from one's willingness to confront death, spiritual freedom, and gradations of therapeutic care are topics highlighted in this book. (shrink)

What can we learn about the nature of technology by studying practices of maintenance and repair? This volume addresses this question by bringing together scholarship from philosophers of technology working at the forefront of this emerging and exciting topic. -/- The chapters in this volume explore how attending to maintenance and repair can challenge and complement existing ways of thinking about technology focused on use and design and introduce new philosophical perspectives on the relationship between technology, time and human practice. (...) They examine the significance of maintenance and repair practices at different scales in relation to a diverse range of philosophical traditions and a wide variety of technologies, from urban infrastructure such as bridges and buildings to data technologies such as servers and software systems. Together, the contributions highlight common themes in the philosophical study of maintenance, including the role of skill, the significance of social values and the potential of these practices to transform the technologies to which they are applied. By reflecting on the different ways in which we keep technologies going, from the devices we use in our homes to the large technical systems which surround us, this volume reveals the philosophical significance of practices of maintenance, not only as a source of new insights but also as a resource for enriching our understanding of a variety of existing topics in philosophy. -/- Maintenance and Philosophy of Technology will appeal to scholars and advanced students working in philosophy of technology, philosophy of engineering and science & technology studies. (shrink)

It is time to bring the rich resources of these traditions into the contemporary debate about the nature of self. This volume is the first of its kind.

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)

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)

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)

The logical calculus for SAT are not valid for MaxSAT and MinSAT because they preserve satisfiability but not the number of unsatisfied clauses. To overcome this drawback, a MaxSAT resolution rule preserving the number of unsatisfied clauses was defined in the literature. This rule is complete for MaxSAT when it is applied following a certain strategy. In this paper we first prove that the MaxSAT resolution rule also provides a complete calculus for MinSAT if it is applied following the strategy (...) proposed here. We then describe an exact variable elimination algorithm for MinSAT based on that rule. Finally, we show how the results for Boolean MinSAT can be extended to solve the MinSAT problem of the multiple-valued clausal forms known as signed conjunctive normal form formulas. (shrink)

Taylor focuses on the dramatic presentation of time and self at each state of Kierkegaard's dialectic of the stages of existence.

本书收录《基督教与道教比较论纲》、《天主教成圣观的天人合一幅度》、《论早期基督宗教的性爱伦理观》等20篇论文。.

In his groundbreaking book, Thin Objects, Linnebo (2018) argues for an account of neo-Fregean abstraction principles and thin existence that does not rely on analyticity or conceptual rules. It instead relies on a metaphysical notion he calls “sufficiency”. In this short discussion, I defend the analytic or conceptual rule account of thin existence.

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)

本书是作者的一部遗作。书中对中国国学大师王国维1898-1911年间11种哲学译稿进行了详尽周密考订和主板,可谓王国维研究的可喜成果。作者同时利用加“按”的形式,在许多细微的对比与议论中贯注了自己的审 美意识与世界观,也具有学术价值.

本书主要研究的是心理现象的形式、范围、本质、特征、心身关系、心理内容及其根源等,并对常识心理解释模式和心理学进行哲学反思。.

The inference systems proposed for solving SAT are unsound for solving MaxSAT and MinSAT, because they preserve satisfiability but not the minimum and maximum number of clauses that can be falsified, respectively. To address this problem, we first define a clause tableau calculus for MaxSAT and prove its soundness and completeness. We then define a clause tableau calculus for MinSAT and also prove its soundness and completeness. Finally, we define a complete clause tableau calculus for solving both MaxSAT and MinSAT, (...) in that the minimum number of generated empty clauses provides an optimal MaxSAT solution and the maximum number provides an optimal MinSAT solution. (shrink)