The article aims at (1) organizing the theoretical ideas of critical thinking on the basis of an overall and systematic conception of education, (2) exposing tensions and contradictions in the various conceptions of critical thinking and (3) suggesting a directing principle for the teaching of critical thinking. In order to achieve these far-reaching aims, the author projects “The Cognitive Map of Instruction” developed by Zvi Lamm on the discourse of critical thinking. Through this “map” it seems that all sub-trends of (...) teaching critical thinking may be divided into three defined “logics,” and that these sub-trends harbor two kinds of internal contradictions: between the different “logics” of teaching, and between their pattern of teaching and the idea of critical thinking. Since none of the three “logics” suggested by Lamm (1976) in “The Cognitive Map of Instruction” suits the purpose of teaching critical thinking, the article turns away from this “map,” that served it so well to locate and expose the various trends of critical thinking. This turn is made on behalf of another idea of Lamm—that of undermining pedagogy. This well-rooted idea may direct the pedagogy of critical thinking toward a coherent and effective instruction. (shrink)

The challenge this book addresses is to demonstrate how, in teaching content knowledge, the development of intellectual and moral dispositions as virtues is not merely a good idea, or peripheral to that content, but deeply embedded in the logic of searching for knowledge and truth. It offers a powerful example of how philosophy of education can be brought to bear on real problems of educational research and practice – pointing the reader to re-envision what it means to educate children (...) by developing the person, instead of simply knowledge and skills. Connected intimately to the practice of teaching and teacher education, the book sets forth an alternative theory of education where the developing person is at the center of education set in a moral space and a political order. To this end, a framework of public and personal knowledge forms the content, to which personal dispositions are integral, not peripheral. The book’s pedagogy is invitational, welcoming its readers as companions in inquiry and thought about the moral aspects of what we teach as knowledge. (shrink)

Teaching and learning in a virtual learning environment poses some difficulties, but also challenges and opportunities to rethink the whole learning process, particularly in abstract subjects like logic or high level mathematics. On the other hand, resources and ways to work, now available in VLEs, might soon extend to all kinds of environments. In this paper, we will present experiences at the Open University of Catalonia , a particular VLE, concerning the whole process of teaching logic and mathematics. (...) In addition, we will discuss some challenges and we will present some innovation projects allowed by the present and near future technologies. (shrink)

In contrast to the conventional fund management industry with a profit-oriented logic based on risk and return, ethical and faith-based funds should follow the religious principles of their investment-style philosophy. Islamic funds should obey the theological teachings of the primary sources of Islam, the Quran and Sunnah, as stakeholders expect these religious teachings to influence the investment decisions of fund managers. In practice, Islamic fund managers use Accounting and Auditing Organization for Islamic Financial Institutions ’s screening criteria, based on (...) secondary sources of Islam, which allow investments that are only partially halal to be included in their portfolios. This study finds that a more religious logic in screening practices, although impairing diversification, does not necessarily harm performance. Thus, Islamic investment funds, and the wider ethical fund management industry, should, and could, adopt stricter screening criteria that match their investment mandates and bring more ethical business practices to the industry. (shrink)

This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.

This paper looks into the contents of the Tractatus suppositionum terminorum by Master Franquera, in the context of the teaching of logic in Salamanca in the fifteenth century. Franquera’s work is characterised by its explicit realist bias and its rejection of Ockhamist theses, i.e., by its recognition of the existence of a natura communis or a universale in re, which is evident in all discussions related to suppositio simplex and the theory of significatio. But, apart from this, Franquera’s discussion (...) of the theory of suppositio stands out as a strange mixture of different doctrines: some of them are derived from thirteenth-century analyses, others from fourteenth-century developments; realist goals are reached by means of instruments that, while not being nominalist, are definitely inspired by terminism. While upholding the theses of realist schools, Franquera adopts the definitions and rules of nominalist authors. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Creativity in Teaching and Building a Meaningful Life as a TeacherDavid T. HansenMy point of departure in this essay is the idea that creativity in teaching often has less to do with inventiveness per se than it does with responsiveness. To draw on terms from John Dewey, creative teachers "rise to the needs of the situation" presented in the educational setting.1 They respond well to circumstances not because they (...) necessarily have the pedagogical equivalent of Twyla Tharp's talent for choreography or B.B. King's brilliance on the blues guitar; rather, I want to suggest that creative teachers, at least in many cases, "rise" and do what is needed because they have learned to pay attention both to students and to the subject(s) at hand. In other words, I propose that we consider the idea that creativity in teaching often manifests itself most vividly, if also subtly, in a kind of ongoing attentiveness, by which I mean a dynamic combination of patience, listening, and initiative.I will begin the discussion by first sketching a conception of creativity in teaching centered around the idea of attentiveness. Then I address two [End Page 57] consequences of this conception. The first is that the most suitable models of good practice for new teachers to start with are not the profession's versions, presuming such exist, of Pablo Picasso, Marie Curie, or Michael Jordan. I do not mean that it is uniformly inappropriate to place such models in front of teacher candidates, any more than it would be wrong to put before art students the work of a Cassatt or Rembrandt. However, I will argue that among the best and most consequential initial models are those experiences in which teacher candidates themselves truly listened to the doings of the world around them and heeded what was said, whether the latter "spoke" in the form of a work of art, a human voice or gesture, or the play of wind in the trees. If new teachers take seriously this kind of experience, they can gain a valuable perspective for approaching the long and often difficult process of appreciating teaching's details and engaging them in educational settings. I illustrate these claims by examining a field-based activity that was part of a teacher education program I used to direct.The second consequence of the conception of creativity in teaching I will put forward points to the title of this essay. If new teachers deepen their ability to pay attention and to engage in creative work, they position themselves to receive one of teaching's primary offerings to its practitioners, namely, a life of meaning."Ordinary" Pedagogical CreativityCreativity in teaching can take many forms. We witness it in the structuring of an artful lesson plan; in the logic, flow, and pacing of a dynamic lecture; or in a timely and evocative example or illustration the teacher employs to clinch a point in the midst of a class. All of this is familiar and an important, indeed indispensable, way to think about good teaching. Creativity in practice is associated here, among other things, with notions of expertise and of knowledge gained through experience.However, I want to add to this portrait the notion that creativity in practice can also spring from responsiveness. Rather than issuing solely from what the teacher brings to the educational setting — consider again terms such as expertise and knowledge — creativity can point to what the teacher is capable of deriving or drawing from it. Creativity as responsiveness denotes a form of openness to the setting, which may or may not complement or fit harmoniously with what is preset, prefigured, or anticipated. Experienced teachers would be the first to say that there are times when it becomes educationally vital to shelve a preset plan. There are times when one form of creativity in teaching, embodied in a well-wrought lesson plan, must give way to another form, embodied in what I am calling responsiveness. The art of teaching consists, in part, of balancing these expressions of pedagogical creativity.Let me share the following vignette as a basis for elucidating this point. One morning in March 2002, during which... (shrink)

By logic I mean the subject Aristotle started in Prior Analytics. Logic studies demonstration and everything necessary for demonstration, and also many things that come to mind in the course of such studies—including axiomatic method as described in my short “Axiomatic method”. By young I mean less than about 40 years old. By logicians I mean people who have dedicated their lives to advancing and criticizing logic: to discovering and establishing new additions and also to clarifying and (...) correcting what has or had been accepted. More specifically, my advice is for people who have already embarked on their careers: from fresh PhDs, instructors, and assistant professors to young professors looking forward to reaping the fruits of their long years of study and research. My advice is for people who have mastered logic and who want to improve their mastery. I would write something very different for students, something along the lines of my “Logic teaching in the 21st century”. Some of the things I recommend you have already done. Please do not think that my recommending something suggests that I think you have not already done it. Moreover, I am fully aware that other retired logicians are as qualified as I to give advice that will help you make the most of your remaining years as an active logician. I hope you seek their advice. I can tell you with certainty that some of their advice will conflict with mine and that some of their advice will serve you better. Temperaments vary; this advice will not be suitable for all temperaments. Be careful whose advice you accept. The lessons of my paper “Critical thinking and pedagogical license” apply here. I recommend that you consider its implications for career decisions. (shrink)

The present paper discusses selected issues of evaluation in the teaching of philosophy. It deals with the issue under consideration on a general level since we do not differentiate between high school and college study performance assessment. Critical reflection focuses on the proper mode of evaluation in teaching the history of philosophy as and in the disciplines of systematic philosophy. In doing so, the close interrelation between the history of philosophy and its disciplines is considered. Three basic evaluative approaches are (...) distinguished. These vary depending on whether the assessment is of the history of philosophy, logic, or other philosophical disciplines. The question of whether a philosopher or a philosophy teacher not directly involved in discussing philosophical issues is better as an evaluator is also investigated. Furthermore, the paper also articulates the reasons for preferring the first option. (shrink)

This paper describes existing and potential short animated presentations that may be helpful in introductory logic courses (particularly in conjunction with Virginia Klenk’s "Understanding Symbolic Logic"), e.g. the progression of a proof, the distinction between inference and replacement rules, propositional variables, the use of truth tables, etc. The author offers reasons why animated presentations of various concepts and derivation rules ought to be short and simple rather than long and complex, provides an overview of some of the technical (...) limitations associated with such presentations, and discusses the prospects for developing future presentations. (shrink)

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, (...) clarity, observationalism, contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. This lecture expands points which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, (...) clarity, observationalism, contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. One rather conspicuous example is that the process of refining logical terminology has been productive. Future logic students will no longer be burdened by obscure terminology and they will be able to read, think, talk, and write about logic in a more careful and more rewarding manner. Closely related is increased use and study of variable-enhanced natural language as in “Every proposition x that implies some proposition y that is false also implies some proposition z that is true”. Another welcome development is the culmination of the slow demise of logicism. No longer is the teacher blocked from using examples from arithmetic and algebra fearing that the students had been indoctrinated into thinking that every mathematical truth was a tautology and that every mathematical falsehood was a contradiction. A fifth welcome development is the separation of laws of logic from so-called logical truths, i.e., tautologies. Now we can teach the logical independence of the laws of excluded middle and non-contradiction without fear that students had been indoctrinated into thinking that every logical law was a tautology and that every falsehood of logic was a contradiction. This separation permits the logic teacher to apply logic in the clarification of laws of logic. This lecture expands the above points, which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

This article outlines the history of logic in China from 1949 to 2019. Firstly, it presents a rough picture of Chinese logic before 1949 using broad brushstrokes. Secondly, it divides the whole process of development into two stages. In the first 30 years from 1949 to 1979, Chinese logic made some achievements, but also went along some detours, and its overall situation was unsatisfactory. In the latter 40 years from 1979 to 2019, due to Deng Xiaoping’s reform (...) and opening up, many Chinese logicians went abroad for academic visits or to study degrees in foreign universities or research institutes, gradually became familiar with and even integrated into the international mainstream of logic teaching and research, and ushered in the great flourishing of logic in China we see today. Finally, it draws four lessons from this process of development, as follows. 1) Let politics and academia live in peace, by respecting and adhering to the idea of academic freedom. 2) Academic advances cannot be achieved in isolation from the world, so we should fully embrace the international academic community, while insisting on our own independent thinking. 3) We should always adhere to the policy of “letting a hundred flowers blossom and a hundred schools of thought contend”, so that different academic viewpoints and tendencies can be improved and developed in their mutual collision. 4) We should culti- vate academic self-confidence, gradually make the change from pure follow-up learning to original work in some fields of logic. (shrink)

Introductory-level undergraduate classes in Logic or Critical Thinking are a staple in the portfolio of many Philosophy programs. A standard approach to these classes is to include teaching and learning activities focused on formal deductive and inductive logic, sometimes accompanied by teaching and learning activities focused on informal fallacies or argument construction. In this article, I discuss a proposal to include an additional element within these classes—namely, teaching and learning activities focused on intellectual virtues. After clarifying the proposal, (...) I identify three reasons in favor of implementing it and I discuss how to implement it, focusing on questions about pedagogical strategies and pedagogical resources. (shrink)

This article examines the attempted reform of education within an emerging audit culture in Australia that has led to the implementation of a high-stakes testing regime known as NAPLAN. NAPLAN represents a machine of auditing, which creates and accounts for data that are used to measure, amongst other things, good teaching. In particular, we address the logics of a policy intervention that aims to improve the quality of education through returning ‘good teaching’. Using Deleuze’s concepts of series, events, copies and (...) simulacra, we suggest that an attempt to return past commonsense logics of ‘good teaching’ as a result of NAPLAN is not possible. In an audit culture as exemplified by NAPLAN, ‘good teaching’ is being reconceptualized through those practices and becomes unrecognizable. Whilst policy claims to improved equity and quality are admirable, this article suggests that the simulacral change to logics of good teaching may actualize something very different. (shrink)

During the nineteenth century, German philosophy developed from a type of general knowledge to an academic discipline at the university. Changes across disciplines to the philosophy of science and psychological surveys created new challenges for the place and purpose of philosophy in the educational system. The content of logic courses for secondary schools (Gymnasiums) was centred on the dissociation of nature and the scale of logic. In this paper, I will examine a number of projects for teaching philosophy (...) at the secondary school level from new humanism to reduce philosophical to philological concerns about different projects offered by Niethammer, Hegel and Herbart. Then, I will focus on the most successful – Adolf Trendelenburg’s Elements of Aristotle’s Logic (1st edition of 1836). This work is a compilation of the logical texts of Aristotle, and for as long as sixty years, it was an official textbook in Prussian secondary schools. The aim of the paper is to show how the rethinking of Aristotle’s heritage affected the theoretical and ideological expectations of propaedeutic courses and transformed the image of logic as a philosophical discipline. (shrink)

British logic teaching in the sixteenth and seventeenth centuries was provided in England by Oxford and Cambridge, both medieval foundations, and in Scotland by the universities of St Andrews and A...

A new idea of ‘contradictory Christology’ has been recently advanced by JC Beall (The contradictory Christ. Oxford University Press, Oxford, 2021a). This paper does not enter the debate whether Christ double nature instantiates a contradiction or does not. It aims to point out a possible view about the Christological problem similar to Beall’s view but more focused on the metaphysical consequences of admitting a treatment of the Christological paradox in dialetheic terms, as a case of ‘true contradiction’. In Beall’s account, (...) the glut-theoretic approach can improve the conception of logic presupposed in theological discussions, giving new suggestions for the development of an updated ‘logic of Christology’. I move in the other direction, exploring whether the philosophical reflection on Christology could give new insights for paraconsistency and the study of inconsistencies in general. More specifically, I claim that the idea of the unity of contradictories in Christ’s being both divine and human may give some support to the idea of conjunctive paraconsistency, whereby true conjunctions of contradictories do not admit of Simplification. After an introduction which presents the main argument, I summarize the theory of conjunctivism in paraconsistency, then I focus on the (pseudo) Athanasian Creed, wherein the two natures – one person principle is defended against monophysism. (shrink)

The first beginnings of modern logic in Croatia are recognizable as early as in the middle of the 19th century in Vatroslav Bertić. At the turn of the 20th century, Albin Nagy, who was teaching in Italy, made contributions to algebraic logic and to the philosophy of logic. At that time, a distinctive author Mate Meršić stood out, also working on algebraic logic. In the Croatian academic philosophy, until the publication of Gajo Petrović's textbook (1964) and (...) the contributions by Heda Festini, a critical or indifferent attitude toward modern logic prevailed. The first comprehensive modern logic textbook in Croatian was written by mathematician Vladimir Devidé (1964), known, for example, for his axiomatizations of natural numbers and classical propositional logic. In the Croatian philosophy of the 1980s and 1990s, influential logicians are Goran Švob and mathematician Zvonimir Šikić. At the turn of the 21st century, logical investigations are being intensified and extended to various branches of the contemporary logic. (shrink)

A course in symbolic logic belongs as a requirement in the undergraduate philosophy major. In this paper, which started life as a letter to my departmental colleagues, I consider and respond to several reasons one might have for excluding Logic from the core requirements. I then give several arguments in favor of keeping Logic. The central—and most important—argument is that the lack of a proper background in logic makes it very difficult to approach many relatively straightforward (...) philosophical arguments, let alone the more technical subliteratures of philosophy. In developing this argument, I consider a few core texts and arguments (e.g., Gettier’s classic paper on the analysis of knowledge) and bring out how a student with some background in formal logic would be able to approach the texts and arguments with much greater ease than a student who lacks such a background. (shrink)

Ordinary textbooks for such a course are purely mathematical in their nature, and students usually find the course difficult, boring and very technical. Our approach motivates the students through reading the classic novel Alice's Adventures in Wonderland, written by Lewis Caroll who was not only one of the best storytellers but also a logician.

Moral education is a core component of ideological and political courses in primary and secondary schools and universities in China, and also an important part of contemporary Chinese Marxist educational theory and practice. In Chinese senior high schools, the main curriculum and platform for moral education is ideological and political courses. The Ideological and Political Curriculum Standards for General Senior High Schools (2017 Edition, 2020 Revised) issued by the Ministry of Education of the People’s Republic of China explicitly includes a (...) course on logical thinking in the ideological and political curriculum in general senior high schools, strengthening the importance of logic in moral education there. In this paper, the authors explain the necessity of intensifying logic training for contemporary Chinese teenagers, introduce and interpret the relevant contents in the Ideological and Political Curriculum Standards for General Senior High Schools (2017 Edition, 2020 Revised), and put forward some theoretical suggestions on how to conduct teaching on the subject of logic. (shrink)

A course in symbolic logic belongs as a requirement in the undergraduate philosophy major. In this paper, which started life as a letter to my departmental colleagues, I consider and respond to several reasons one might have for excluding Logic from the core requirements. I then give several arguments in favor of keeping Logic. The central—and most important—argument is that the lack of a proper background in logic makes it very difficult to approach many relatively straightforward (...) philosophical arguments, let alone the more technical subliteratures of philosophy. In developing this argument, I consider a few core texts and arguments (e.g., Gettier’s classic paper on the analysis of knowledge) and bring out how a student with some background in formal logic would be able to approach the texts and arguments with much greater ease than a student who lacks such a background. (shrink)

In this article, I seek to shed new light on a lesser-known stage of the development of Hans Reichenbach’s thought, namely his research, output and teaching activities at Istanbul University. I argue that the experience of Turkish exile was decisive in the elaboration of Reichenbach’s probability theory of meaning and knowledge. His work Experience and Prediction, produced while in Istanbul, should therefore be put in its Turkish context of elaboration and reception. To this end, I will take into consideration not (...) only Reichenbach’s efforts to popularize and extend the Berlin Group’s program of scientific philosophy in Turkey and throughout Europe in the 1930s, but also the forgotten work of Reichenbach’s students—most of them women—at Istanbul University. (shrink)

Law is known to exist only being articulated in a language and discourse, and the students’ ability to comprehend and use its meta-language is one of the main goals for English for Legal Purposes (ELP) teaching. The knowledge of terminology enables students to fit new information (linguistic, disciplinary, factual, cultural, etc.) into the framework of the legal system they are studying. The acquisition of terminology in a foreign language implies knowledge of both conceptual content and the means of its verbalization. (...) This article argues for a cognitive approach to teaching Legal English, and frame modelling as an effective method of teaching and learning legal terminology. The heterogeneous structure of legal concepts (a permanent core and dynamic periphery) suggests the possibility of framing their verbal representations. From this perspective, legal terminology is viewed as a frame structure. Depending on the instructional objective, frame modelling may be circumscribed around a specific concept or frame level. (shrink)

The paper describes the conception of logic in Polish didactics authored by the Commission of National Education (KEN), an important educational institution of the European Enlightenment. Since the documents of the Commission refer to a vision of science presented by such influential works then as the Encyclopédie ou dictionnaire universel raisonné [Great French Encyclopedia], the paper compares the requirements from the Commission’s programmer with the encyclopaedic entries that entail logical problems broadly understood. It turns out that the Commission, following (...) the Encyclopédie, not only recommended a list of textbooks of logic but also shared its eclectic vision of logic. Although it is characteristic of modernity to take a relative approach to the importance of traditional logic, transformed into science on method, or literally an outline of epistemology, understood according to É. Condillac as a specific form of metaphysics, nevertheless some elements of logic were eclectically made valid. This logic, from the times of I. Kant, has been defined as formal logic. Practical logical skills were preferred to the knowledge of logical theories. At the same time attention was paid to the meaning of natural logical skills, and drills in logical reasoningwhen studying languages and mathematics. Despite preferences for the analytical method they also noticed the importance of synthetic method. It seems also that although the documents of the Commission do not say anything about the teaching of syllogistic issues, in didactic practice inspired by the Encyclopédie in the schools controlled by the Commission, the room was made to teach these problems. Condillac’s book was preferred in the schools controlled by the Commission, nevertheless, it was not, as in the case of other textbooks, a must on the reading list, an obligatory reading matter, therefore it was not published in Poland. The conception of logic presented by the Commission as modelled on the Encyclopédie managed to avoid the one-sidedness of Condillac’s approach, the approach that in fact eliminated the teaching of logic. (shrink)

The roots of the Lvov-Warsaw School can be traced back to Aristotle himself. But in later times we better put them into thinking GW Leibniz and who somehow inherited many of these ways of thinking, such as the philosopher and mathematician Bernhard Bolzano. Since he would pass the key figure of Franz Brentano, who had as one of his disciples to Kazimierz Twardowski, which starts with the brilliant Polish school of mathematics and philosophy dealt with. Among them, one of the (...) most interesting thinkers must be Jan Lukasiewicz, the father of many-valued logic.Jan Łukasiewicz began teaching at the University of Lvov, and then at Warsaw, but after World War II must to continue in Dublin. Some questions may be very astonishing in the CV of Łukasiewicz. For instance, that a firstly Polish Minister of Education in Paderewski cabinet, into the new Polish Republic, and also Rector for two times at Warsaw University, was awarded with a Doctorate ‘Honoris Causa’ in spring 1936, at University of Münster, into the maximum of effervescency of Nazism in Germany. The explanation must be their good relation with a very good friend, the former theologian, and then logician, Heinrich Schölz, who was the first Chairman of Mathematical Logic in German universities.Łukasiewicz firstly studied Law, and then Mathematics and Philosophy in Lvov. His doctoral supervisor was Kazimierz Twardowski, and in 1902 he obtain his Ph. D. title with a very special mention: ‘sub auspiciis Imperatoris’. Also he received a doctorate ring with diamonds from the Kaiser of the Austro-Hungarian Empire, Franz Joseph I.From 1902, Łukasiewicz was employed as a private teacher, and also as a desk in the Universitary Library of Lvov. So it was until 1904 when he obtained a scholarship to study abroad. He defends his ‘Habilitationschrift’ in 1906, entitled “Analysis and construction of the concept of cause”. This permits to give university courses. His first lectures were on the Algebra of Logic, according to the recent translation to Polish of this book of the French logician Louis Couturat.Between 1902 and 1906, Lukasiewicz continued his studies in the universities of Berlin and Leuwen. In 1906, by his ‘Habilitationschrift’, he obtain the qualification as university professor at Lvov. And the, in 1911, he was appointed as associate professor in his ‘alma mater’.Jan Łukasiewicz was also very active in historical research on logic, giving a new and up-to-date interpretation of Aristotle’s syllogism and of the Stoics’ propositional calculus. According to Scholz, the better pages on history of logic are due to him. And also, as Arianna Betti says, “Jan Lukasiewicz is first and foremost associated with the rejection of the Principle of Bivalence and the discovery of Many-Valued Logic.”The discovery of MVL by Lukasiewicz was in 1918, a little earlier than Emil Leon Post. According to Jan Wolenski, “although Post’s remarks were parenthetical and extremely condensed, Lukasiewicz explained his intuitions and motivations carefully and at length. He was guided by considerations about future contingents and the concept of possibility”. So, he introduces, firstly, three-valued logic, then four-valued logic, generalized to logics with an arbitrary finite number of veritative values, and finally, to logics with a countably infinite-valued number of such values.Very noteworthy is his treatment of the history of logic in the light of the new formal logic. Thus, not only he addressed the issue of future contingents departing from Aristotle, but also put in value logic of the Stoics, at least so far taken. In fact, Heinrich Scholz said, rightly, that Lukasiewicz had written the most lucid pages on the history of logic. (shrink)

Recent reflection on the professional knowledge of teachers has been marked by a shift away from more reductive competence and skill-focused models of teaching towards a view of teacher expertise as involving complex context-sensitive deliberation and judgement. Much of this shift has been inspired by an Aristotelian conception of practical wisdom also linked by Aristotle to the development of virtue and character. This has in turn led recent educational philosophers and theorists – inspired by latter-day developments in virtue ethics and (...) virtue epistemology – to investigate the contribution of various forms of virtue to the effective practice of teaching. In this light, the present paper undertakes further exploration of the logical geography of virtue, character and practical deliberation in teaching. (shrink)

This article discusses two well‐known texts that respectively describe learning and teaching, drawn from the work of Freud and Plato. These texts are considered in psychoanalytic terms using a methodology drawn from the philosophy of Luce Irigaray. In particular the article addresses Irigaray's approach to the analysis of speech and utterance as a ‘cohesion between the source of the utterance and the utterance itself’ (Hass, 2000). I apply this approach to ask whether educational tradition has fractured the relationship between pedagogy (...) and the body of the teacher/pupil. Teaching and learning are re‐addressed in ways that challenge the gender‐neutral representation of pedagogy as a systematic technique. (shrink)

The article deals with the issues of comparing the teachings of Tolstoy and Lao-zi according to the criterion of palingenesis, which is the basis for the construction of the entire ideological corpus of the most important treatise of Taoism “Tao de jing”. Lao-zi formulated the lapidary formula of palingenesis in the fortieth zhang of this treatise, recreating a picture of the harmonization of the Middle Kingdom, arguing that return is the movement of the Tao, and weakening is the action of (...) the Tao. The principle of palingenesis is one of the fundamental principles for which Tolstoy uses Christological vocabulary, and Lao-zi uses embryological vocabulary. The choice of the palingenesis criterion for comparative analysis of the teachings is due to the fact that the latter works as an immutable law when setting the task of recreating harmony in social chaos. Based on the assessments of the content of the zhangs of the “Tao de jing” canon, a representative line of palingenesis elements is built: the category of knowledge/truth; the category of ignorance; the category of simplicity; the category of naturalness; the category of “baby”; the category of non-action; the category of nonviolence. The principles of Taoism are not expressed by Tolstoy with a research sequence in logical definitions, but appear as categories and trends, working in the worldview of the Yasnaya Polyana sage. In the works “What is my faith?”, “Sayings of the Chinese sage Lao-Tse”, “Non-doing”, Tolstoy's teaching is presented in its entirety and is therefore convenient for comparison with the Taoist classics. It is noted that Tolstoy's conceptual idea is based on the desire to convert people to the good - unity with all people. This orientation towards the good is nothing else than the return to man of his original nature, on the way to which the principle of palingenesis associated with the boycott of the civilization of violence is realized. The conducted research has shown that in the teachings of Lao-zi and Tolstoy, which record the experience of theoretical exploration of the world, the categories of palingenesis are common to the Russian and Chinese spirit. (shrink)

Over the past century, there has been considerable debate over whether and how anything changes with respect to existence. Most A‐theorists of time (presentists, growing block theorists, and branch theorists) think things come to exist or cease to exist. B‐theorists of time (four‐dimensionalists, in particular) think objects do not change with respect to existence. In my Compass article, I outline a serious difficulty that A‐theorists face in trying to reason about temporary existents. The most straightforward logics for time and existence (...) entail that nothing exists merely temporarily. The problem arises from a set of theorems of the simplest temporal logic – the converse Barcan formulas. But attempts to fix the logic to get rid of the Barcan formulas pressure A‐theorists to abandon an intuitive and widespread assumption about existence. I survey the logical and metaphysical options for solving the problem. (shrink)

Recent students of late medieval intellectual history have treated Oxford theologians' Sentences lectures from the 1320s to 1330s as revealing the interface of the theological, logical, and scientific thinking characteristic of a historically momentous ‘New English Theology’. Its conceptual achievement, historians generally concur, was the casting off of the speculative metaphysics of such thirteenth-century authors as Robert Grosseteste and Roger Bacon; its methodological novelty made it akin to twentieth-century analytic philosophy and seminal for the early Scientific Revolution. Yet the metaphysically (...) cast thirteenth-century sciences of perspectiva and astrologia persisted among scholars long into the early modern period. To show how this apparent paradox may be dissolved, this article details the intersection of thirteenth-century metaphysics and fourteenth-century analysis in the lectures of a controversial and influential proponent of the Oxford theology of the 1330s. (shrink)