The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve sample (...) quizzes and solutions. The Symbolic Logic Study Guide is essential for all instructors and students who use LPL in their symbolic logic classes. (shrink)

"This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with (...) basic syllogisms and deductions." CHOICE connect "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with basic syllogisms and deductions." CHOICE Connect For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results. Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents. Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy. (shrink)

This guide accompanies the following article: ‘Logic and Divine Simplicity’. Philosophy Compass 6/4 : pp. 282–294, doi: Author’s IntroductionFirst‐order formalizations of classical theistic doctrines are increasingly used in contemporary work in philosophy of religion and philosophical theology, as a means for clarifying the conceptual structure of the doctrines and their role in inferential procedures. But there are a variety of different ways in which such doctrines have been formalized, each representing the doctrines as having different conceptual structures. Moreover, the (...) adequacy of such formalizations as such has, at least with respect to some classes of doctrines, been disputed. One reason for disputing their adequacy derives from the conceptual impact of classical theism’s doctrine of divine simplicity.Author RecommendsFrege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. The preface contains interesting remarks about the purpose of formalization as understood by the chief pioneer of modern formal logic. These remarks are also connected by Frege to his views on the relation between thought and language more generally.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press.The preface and first section of the long introduction contain remarks on the purpose and advantages of formalization. Chapter 1 of the introduction contains what is probably one of the first formalizations ever of a theistic doctrine, and is given in terms of a definite description analysis.Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Clear and concise discussion of some of the advantages of formalization in philosophical inquiry, written by a prominent contemporary American philosopher‐logician.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9.A valuable paper that narrates, among other things, the programme of formalizing theistic doctrines that emerged in Poland in the 1920s under the influence of the Lvov‐Warsaw School. Various examples of formalizations are also given.Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press.In Section 27 of this classic study, Quine offers a formalization of theistic doctrines which seeks to avoid the difficulties of earlier formalizations by means of a subtle extensional singleton set analysis. The proposal has not won many adherents, but is worthy of careful study nonetheless.Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.A concise but lucid survey of some attempts to formalize theistic doctrines and some problems besetting these attempts. Woleński also proposes his own method of formalization, which could be described as a simplified version of Quine’s method in Mathematical Logic.Bocheński, Joseph The Logic of Religion. New York: New York University Press.The first book‐length treatment of the relation between modern logic and theism. It covers much ground, and remains very readable.Alston, William P. ‘Religious Language and Verificationism,’ in The Rationality of Theism, eds. Paul Moser and Paul Copan. London: Routledge, pp. 17–34.Identifies some problems with attempts at articulating theistic doctrines by means of subject‐predicate language. Highly relevant to formalizations of theistic doctrines, even though this topic is not dealt with explicitly.Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass.Offers a survey of three main methods of formalizing theistic doctrines, and of some variants of these methods. Argues that certain formalizations of theistic doctrines are bound to be rejected as conceptually inadequate by all who understand the doctrines at hand within the framework provided by the traditional doctrine of divine simplicity.Sample Syllabus Week I: The Idea of Formalization and the Project of Formalizing Theistic Doctrines Reading:Frege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9. Week II: Formalizing Theistic Doctrines: Three Alternative Methods Reading:Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press. Week III: Arguments for and Against Some Formalizations of Theistic Doctrines Reading:Bocheński, Joseph The Logic of Religion. New York: New York University Press. Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass, Vol. 6, No. 4, pp. 282–94.Focus Questions1 What do Frege, Russell and Whitehead, and Suppes understand the purpose or purposes of logical formalization to be, and why do they think formalization can achieve these purposes?2 Woleński sketches some simple ways of formalizing theistic doctrines such as ‘God exists’ or ‘God is almighty’ in terms of 1‐place predicates which he subsequently abandons in favour of other methods. What reasons lead him to abandon these more simple methods of formalization?3 What are the advantages of the definite description formalization of theistic doctrines offered by Russell and Whitehead?4 Quine offers a subtle formalization of the theistic doctrine ‘God exists’ in terms of singleton sets. What problems are Quine’s formalization intended to accommodate, and how does it seek to accommodate them?5 Which relative merits or demerits are there in Bocheński’s and Kraal’s respective arguments for and against the adequacy of certain formalizations of theistic doctrines? (shrink)

Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help ...

Basic course of study of Buddhist logic and dialectrical studies prescribed for Rato Datsang, a monastery at Nyetang in Tibet, China.

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) logic texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

The sources for this volume are the unpublished papers of Reid contained in the Birkwood Colletion. As the title of the volume indicates, Reid’s teaching as a Regent included Logic, Rhetoric, and the Fine Arts. The regenting system assigned cadres of students to a specific teacher who would pace them through the entire curriculum of study. Broadie cites Reid’s own defenses of this system and the important educational and civic aims achieved by it, at the relatively slight cost (...) of unavoidable superficiality. Today’s academic world might benefit from a consideration of current practices as informed by Reid’s ideas on just this point. (shrink)

Moving education to Zoom, Microsoft Teams, and the many alternatives during the COVID19-pandemic raised the question of pedagogical form. In a sense, pandemic education in its two-dimensionality was a frictionless, sanitized reduction of education to pure form; it offered a more efficient transfer of knowledge and was marked by a heightened means-to-an-end logic. This has made the informal, unforming and deformational activity that Stefano Harney and Fred Moten call study even more difficult, if not impossible during pandemic education. (...) In this article, we consider the pitfalls of thinking in terms of pedagogical form and the formalization of education by engaging with Emile Bojesen’s work on education as (de)formation. Via Harney and Moten, we reflect on what the concept/practice of study by way of formless formation teaches us about (pre-)pandemic education and about pedagogical forms that might be in keeping with study in post-pandemic education. (shrink)

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers (...) explore the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

Historical studies convincingly demonstrate that the knowledge process [Erkenntnis] in natural science consists of the gradual adaptation of the thoughts to the facts. This adaptation happens through happy circumstances, which increasingly reveal the more general similarities and subtle differences of the facts. By this, the precision of the representation of the facts by the thoughts grows, so that the latter finally become an image of the former, which for certain intellectual purposes may completely substitute for them. The one who admits (...) this sober view of the meaning of natural science will assign to natural science teaching no other purpose, but to promote the aspired adaptation of thoughts with highest economy of work on shortcuts, by artificially bringing about those favorable circumstances avoiding the unfavorable historical coincidences and delays.One should in teaching first and foremost proceed psychologically; only secondarily and as much logically, as this is enabled through the psychological preparation so that it becomes a need. New concepts, theories, hypotheses, solutions of problems should only be introduced, when the need for this is felt in order to be able to master the topic. For each sentence, which appears during teaching, clarity and explicitness, but in general not indefeasibility from the point of view of the goal of teaching, should be required. (shrink)

A text that would find a place for the realistic formalism of Aristotle, the scientific penetration of Peirce, the pedagogical soundness of Dewey, and the ...

Teaching research methods is especially challenging because we not only wish to convey formal knowledge and encourage critical thinking, as with any course, but also to enable our students dream up meaningful research projects, translate them into logical steps, conduct the research in a professional manner, analyze the data, and write up the project in APA style. We also wish to spark interest in the topics of research papers, and in the intellectual challenge of creating a research report, but we (...) have learned just how difficult these goals can be from teaching undergraduates and from serving as journal reviewers: many submissions contain flaws such as elementary errors of logic (e.g., using a null control condition instead of a placebo or dummy treatment), tangled statistics, a lack of graphs, and ungrammatical, unclear writing that violates APA rules. Yet these manuscripts are written by university faculty, often with doctorates and years of experience. Even published papers may contain egregious faults (Standing & McKelvie, 1986). And although we have both published widely, we still hone our skills. It requires optimism to expect that a typical undergraduate will do better, on the basis of just a year or two of studies in psychology. In this paper, we describe a systematic set of methodology courses and two specific practices that we think can help. Methodology Courses as the Backbone of our Psychology Program How can methodology courses promote undergraduate involvem... (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)

Philosophy is the study of the most general and fundamental problems of human life. The main areas of study in philosophy includes metaphysics, epistemology, logic, ethics and aesthetics etc. there are other several branches of philosophy which characterize different branches of knowledge. Philosophy being a very abstract branch of study, has not much scope of using equipment on a large scale to supplement the normal lecture schedules. However, in some papers/areas there are comparatively better scope to (...) make the lectures more concrete and interesting through proper use of various teaching aids and modes. We include logic, philosophy of science, applied philosophy, applied ethics, social and political philosophy, philosophy of mind, philosophy of cognitive science and history of philosophy etc., we can use various modern aids. In this article my attempt is to draw out an outlines of aids and modes for effective philosophy teaching. (shrink)

Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students (...) in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library. (shrink)

In this important work, Dr. Felipe Fierro offers a comprehensive view on the subject of Introduction to the Study of Law, in which he revives the use of Gnoseology, Philosophy, History and Logic as Auxiliary Sciences; and exposes how the abandonment of such has contributed to the exponential growth of Skepticism and Relativism, currently prevailing in the legal world. The above, through extensive experience in teaching Law from the Aristotelian-Thomistic platform, based on the elementary assumption that we must (...) first prove the existence of the object of study, and contrast main legal branches in topics such as: what is Law?, why is Science?, what are Law, Justice, Facultative rights and the Common Good?; supported by extensive and select bibliography. In addition, the being, nature, concept, essence and properties of the sources, fundamentals and classification are described. But important elements such as knowledge, order, principles, Jurisprudence, and Natural law, fundamental legal concepts, the legislative process, the Constitution, interpretation and others are not absent. Morality and Legal Law are obligatory markers, which although considered in their own field, are not excluded, but different as to object and method. Predominantly, Justice is exposed as one of the great values of the Law, and main theories in order to offer future lawyers the basis regarding the current Science of Law and its significance. (shrink)

A critical study of McPeck's recent book, in which he strengthens and develops his arguments against teaching critical thinking (CT). Accepting McPeck's basic claim that there is no unitary skill of reasoning or thinking, I argue that his strictures on CT courses or programs do not follow. I set out what I consider the proper justification that programs in CT have to meet, and argue both that McPeck demands much more than is required, and also that it is plausible (...) that this deflated justification can be met. Specitically, I argue that it is reasonable to expect transfer of learning for basic logical skills. Additional topics covered include: the relation ofliberal education to critical thinking, argument analysis, testing for CT, and the value of conceptual or linguistic analysis. (shrink)

This anthology opens new perspectives in the domain of history, philosophy, and science teaching research. Its four sections are: first, science, culture and education; second, the teaching and learning of science; third, curriculum development and justification; and fourth, indoctrination. The first group of essays deal with the neglected topic of science education and the Enlightenment tradition. These essays show that many core commitments of modern science education have their roots in this tradition, and consequently all can benefit from a more (...) informed awareness of its strengths and weaknesses. Other essays address research on leaning and teaching from the perspectives of social epistemology and educational psychology. Included here is the first ever English translation of Ernst Mach’s most influential 1890 paper on ‘The Psychological and Logical Moment in Natural Science Teaching’. This paper launched the influential Machian tradition in education. Other essays address concrete cases of the utilisation of history and philosophy in the development and justification of school science curricula. These are instances of the supportive relation of HPS&ST research to curriculum theorising. Finally, two essays address the topic of Indoctrination in science education; a subject long-discussed in philosophy of education, but inadequately in science education. This book is a timely reminder of why history and philosophy of science are urgently needed to support understanding of science. From major traditions such as the Enlightenment to the tensions around cultural studies of science, the book provides a comprehensive context for the scientific endeavour, drawing on curriculum and instructional examples. Sibel Erduran, University of Oxford, UK The scholarship that each of the authors in this volume offers deepens our understanding of what we teach in science and why that understanding matters. This is an important book exploring a wide set of issues and should be read by anyone with an interest in science or science education. Jonathan Osborne, Stanford University, USA This volume presents new and updated perspectives in the field, such as the Enlightenment Tradition, Cultural Studies, Indoctrination in Science Education, and Nature of Science. Highly recommended. Mansoor Niaz, Universidad de Oriente, Venezuela This volume provides an extremely valuable set of insights into educational issues related to the history and philosophy of science. Michael J Reiss, University College London, UK. (shrink)

What is argumentation? -- Building a classroom culture of argumentation -- Structuring classroom discussions to focus on argumentation -- Infusing all instruction with argumentation -- Argumentation for all students -- Argumentation and the mathematical practices -- Technology in teaching and learning argumentation -- Assessing argumentation and proof -- Conclusion.

This paper considers the nature of the changes that took place in logic teaching at the University of Oxford from the beginning of the sixteenth century, when students attended university lectures on Aristotle’s texts as well as studying short works dealing with specifically medieval developments, to the beginning of the eighteenth century when teaching was centred in the colleges, the medieval developments had largely disappeared, and manuals summarizing Aristotelian logic were used. The paper also considers the reasons for (...) these changes, including changes in English society, and the effect of humanism and the more scholarly Aristotelianism that it produced. (shrink)

This paper presents three lessons designed to alert students to the setting in which they are learning (the classroom) and the ways in which this setting provides the context for a discourse which is different than everyday discourse. In the first lesson, students examine empirical studies that illustrate how being in a classroom significantly changes how one reasons about even the most basic logical relationships. In the second lesson, Levi critiques an imaginative way of teaching logic that, while appearing (...) to call on students to use critical reasoning skills they already possess, still fails to take into account its setting. In the final lesson, students translate an editorial into the form of declarative sentences, ordered as premises and a conclusion. Students are prompted to consider what is lost in this rendering and how it distorts the original argument, after which a more successful strategy for paraphrasing and evaluating arguments is attempted. These lessons aim to teach students to think for themselves by encouraging them not to learn logic by wrote, but to see its lessons as tools whose very applicability to real life is something they must critically evaluate. (shrink)

This paper presents three lessons designed to alert students to the setting in which they are learning (the classroom) and the ways in which this setting provides the context for a discourse which is different than everyday discourse. In the first lesson, students examine empirical studies that illustrate how being in a classroom significantly changes how one reasons about even the most basic logical relationships. In the second lesson, Levi critiques an imaginative way of teaching logic that, while appearing (...) to call on students to use critical reasoning skills they already possess, still fails to take into account its setting. In the final lesson, students translate an editorial into the form of declarative sentences, ordered as premises and a conclusion. Students are prompted to consider what is lost in this rendering and how it distorts the original argument, after which a more successful strategy for paraphrasing and evaluating arguments is attempted. These lessons aim to teach students to think for themselves by encouraging them not to learn logic by wrote, but to see its lessons as tools whose very applicability to real life is something they must critically evaluate. (shrink)

Having studied mathematics, in particular foundations and philosophy of mathematics, it happened that I was asked to teach logic to the students in the Faculty of Philosophy of the Radboud University Nijmegen. It was there that I discovered that logic is much more than just a mathematical discipline consisting of definitions, theorems and proofs, and that logic can and should be embedded in a philosophical context. After ten years of teaching logic at the Faculty of Philosophy (...) at the Radboud University Nijmegen, thirty years at the Faculty of Philosophy of Tilburg University and nine years at the Faculty of Philosophy of the Erasmus University Rotterdam, I got many ideas how to improve my LOGIC book which was published twenty five years ago in 1993 by Verlag Peter Lang. Although the amount of work was enormous, I felt I should do it. It is like working on a large painting where you put some extra color in one corner, add a little detail at another place, shed some more light on a particular face, etc. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:502 Feminist Studies 46, no. 2. © 2020 by Feminist Studies, Inc. Jaime Madden Teaching Online: Issues of Equity and Access in Writing-centric Formats The COVID-19 pandemic has turned us all into online teachers. In the context of this crisis, we have quickly learned new technologies and the affordances of asynchronous and synchronous delivery. We have grappled with the challenges of building community and supporting active engagement, and we (...) have turned to adapting our assessment methods for the remote environment. We have done this work at traditional colleges and universities, where online teaching was formerly the purview of graduate students and adjunct instructors. Online learning can no longer be associated with those who struggle to access traditional classrooms, such as disabled students and those who attend for-profit colleges. Instead, access to online learning can now be associated with access to wealth and to health—specifically as relates to avoiding contact with the virus. In K-12 education, we have seen districts that largely enroll white students make the decision to continue online or go hybrid for the fall 2020 semester, whereas those that largely enroll students of color are returning to the classroom.1 Inequalities pervade the teaching landscape as well. Teaching is not a job usually marked as high risk, but within this environment, some 1. The work of activist and artist @bmore_radical shows how these decisions are being made in Baltimore, Maryland. See https://www.instagram.com /bmore_radical/?hl=en. Jaime Madden 503 bodies suffer at higher rates. In a recent article published in this journal, coauthors writing as the Brocher Foundation Feminist Collective describe their experience and knowledge “of the ways that academia produces sickness.”2 The authors are white and cisgender women at Anglo-American and European universities, and even though they acknowledge that they did not experience high levels of racism, classism, linguistic marginalization, and/or illness, they still found themselves—at different stages of their careers—“worn thin” in a system where “bodies are disposable.”3 Commenting on this problem in another context, disability studies scholar Alison Kafer notes that disability is “more fundamental, more inevitable, for some than others.”4 The pandemic has made this much clear: able-bodied people are “temporarily able-bodied,” and those who experience racism and classism are among the most frequently and intensely sickened. In attending to how teachers and students transition online en masse, we need to consider how we are differently positioned within institutions governed by the logics of racialized capitalism. It is important to recognize not only which students can access these online spaces but also which skills such spaces tend to reward. It is also important to ask which teachers are disproportionately impacted by the transition online. In this piece, I describe the challenges of assessment and then wrestle with broader questions of access as a scholar invested in feminist studies and disability studies. The tension in online education between its promise of access and its methods of assessment is, I argue, worthy of urgent attention. The Challenges of Assessment I have taught online courses at four institutions: two private colleges and two public universities. Good teaching and learning can undoubtedly happen across a range of spaces. In online environments, I have found that my best teaching happens in the feedback I give students. 2. Laura Bisaillon, Alana Cattapan, Annelieke Driessen, Esther van Duin, Shannon Spruit, Lorena Anton, and Nancy S. Jecker, “Doing Academia Differently: ‘I Needed Self-Help Less Than I Needed a Fair Society,” Feminist Studies 46, no. 1 (2020): 132. 3. Bisaillon, et al., “Doing Academia Differently,” 136, 140. 4. Alison Kafer, Feminist, Queer, Crip (Bloomington: Indiana University Press, 2013), 26. 504 Jaime Madden This is understandable since assessment practices are important teaching opportunities in all contexts. In online environments, and particularly in asynchronous teaching, I have found that it is while carrying out assessments of student work that my most intense teaching occurs. It is through grading and offering comments on papers and assignments that I am most directly in communication with students as their teacher. When I mark student work, I ask questions of students, I prompt them to consider how our course materials may be placed... (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.

Text with commentary on basic course of study of Buddhist logic and dialectrical studies prescribed for Rato Datsang, a monastery at Nyetang in Tibet, China.

The paper discusses the place and the status of fallacies in Arnauld and Nicole’s Port-Royal Logic, which seems to be the first book to introduce a radical change from the traditional Aristotelian account of fallacies. The most striking innovation is not in the definition of a fallacy but in the publication of a new list of fallacies, dropping some Aristotelian ones and adding more than ten new ones. The first part of the paper deals with the context of the (...) book’s publication. We then show the influence of Cartesian and Augustinian/Pascalian philosophy on the whole book, especially their common critical views about logic, dialectic and their traditional academic teaching. The third part of the paper discusses the two chapters on fallacies. It focuses on their place in the book and their relation with its general orientation, before turning to their content, closely connected with some major concerns of the time. (shrink)

Adding instructional time and holding teachers accountable for teaching social studies are touted as practical, logical steps toward reforming the age-old tradition of marginalization. This qualitative case study of an urban elementary school, examines how nine teachers and one administrator enacted district reforms that added 45 min to the instructional day and implemented a series of formative and summative assessments. Through classroom observations, interviews, time journals, and official school documents, this article describes underlying perceptions and priorities that were barriers (...) to any positive impact time or testing might have afforded social studies. Two recommendations emerge from results: 1) time structures need to provide space for the teaching of and planning for social studies; and 2) testing can have positive outcomes, but these are limited when assessments structures are hierarchical, misaligned, and poorly communicated. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel (...) the many fallacious ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

When it’s time for a game change, you need a guide to the new rules. Helping Students Make Sense of the World Using Next Generation Science and Engineering Practices provides a play-by-play understanding of the practices strand of A Framework for K–12 Science Education (Framework) and the Next Generation Science Standards (NGSS). Written in clear, nontechnical language, this book provides a wealth of real-world examples to show you what’s different about practice-centered teaching and learning at all grade levels. The book (...) addresses three important questions: 1. How will engaging students in science and engineering practices help improve science education? 2. What do the eight practices look like in the classroom? 3. How can educators engage students in practices to bring the NGSS to life? Helping Students Make Sense of the World Using Next Generation Science and Engineering Practices was developed for K–12 science teachers, curriculum developers, teacher educators, and administrators. Many of its authors contributed to the Framework’s initial vision and tested their ideas in actual science classrooms. If you want a fresh game plan to help students work together to generate and revise knowledge—not just receive and repeat information—this book is for you. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Logic Pamphlets of Charles Lutwidge Dodgson and Related PiecesIrving H. AnellisFrancine F. Abeles, editor. The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. The Pamphlets of Lewis Carroll, 4. New York-Charlottesville-London: Lewis Carroll Society of North America-University Press of Virginia, 2010. Pp. xx + 271. Cloth, $75.00.Until William Bartley’s rediscovery and reconstruction of Dodgson’s lost Part II of Symbolic Logic, Lewis Carroll’s reputation (...) in logic, when taken seriously, rested upon his few published articles on logical paradoxes and puzzles, while his published books, The Game of Logic and Symbolic Logic, were regarded as suitable perhaps as pedagogical tools, but dismissed otherwise as amusements, on a par with the Alice works. Richard Braithwaite asserted (“Lewis Carroll as Logician”) that “Carroll regarded formal and symbolic logic not as a corpus of systematic knowledge about valid thought nor yet as an art for teaching a person to think correctly.” He suggested that Dodgson used his pseudonym for his popular and whimsical writings, reserving his legal name only for his serious mathematical products. Philosophers practicing linguistic analysis in their assault on nonsense deriving from misuse of language meanwhile developed an interest in Carroll (e.g. George Pitcher, “Wittgenstein, Nonsense, and Lewis Carroll”). Abeles, on the contrary, stresses the seriousness of Dodgson’s pedagogical and popularizing mission (195–99).Bartley’s discovery opened the door for reevaluating Dodgson as a serious logician, and Abeles has been in the forefront of that reevaluation. Her general introduction and introductions to the main divisions of this collection of Carroll’s publications (and additional material from his Nachlass and a handful of publications of others, composed in response to Carroll’s published articles) place his serious logical work and its significance in historical perspective, providing a deeper, more sophisticated view than found in Bartley’s “Editor’s Introduction” to Lewis Carroll’s Symbolic Logic. Abeles also offers brief introductions to the individual entries, which describe their physical characteristics and circumstances of composition.Dodgson aligned with the majority of those British logicians of his day, starting with George Boole, who understood formal logic to be Aristotelian syllogistic, and symbolic logic to be syllogistic logic expressed algebraically. His notational innovation was employing indices to terms so that, independently of the arrangement of terms, propositions could easily be read; thus, “xy0” can be read as “no x are y” or “no y are x” and “x1y0” as “all x are not y” or “no x are y”. In dealing with the classical elimination problem in the class calculus—to determine the maximum information, without duplications, obtainable from a given set of premises—Dodgson in his later work and unpublished letters anticipated several concepts of automated theorem proving.Central to both geometry and to formal logic are the rules of logical inference that establish the validity of arguments and guarantee that conclusions inferred from true [End Page 506] premises are true. The modern analytic tableaux, or tree method, is a fundamental tool in this regard, both for deriving theorems and for determining the validity or invalidity of the proofs for propositional calculus and first-order predicate calculus.Introducing his reconstruction of Part II of Symbolic Logic, Bartley noted that, along with the logic diagrams that Carroll devised, he also devised a tableau method that strongly resembled Beth’s semantic tableaux. Abeles went more deeply and convincingly into that resemblance in her earlier research. Beth’s tableaux, together with Hintikka’s model sets, were the direct ancestors of Smullyan’s analytic tableaux, which in turn are the theoretical basis for the Robinson resolution method that continues to be central to much work in programming logic.Abeles has also shown that the work in Studies in Logic by Charles Peirce and his logic students at Johns Hopkins University served as a source of inspiration for Dodgson. More critically, she demonstrated that Dodgson devised and employed the tree method for carrying out proofs of syllogisms and chains of syllogisms, or soriteses, in Part II of Symbolic Logic (see her “Lewis Carroll’s Method of Trees: Its Origins in Studies in Logic,” Modern Logic 1 [1990]: 25–34). The tree... (shrink)

Compilation of some important works on basic course of study of elementary Buddhist logic and dialectrical studies of Bkra-śis-lhun-po Monastery, a college of Buddhist studies in Bylakuppe, Karnataka, India.

hese notes don’t reach any conclusions. Their purpose is to point to issues one needs to think through seriously when thinking about logic teaching. They indicate some of the relevant literature where some of these issues are addressed, but they also raise points that seem to have been overlooked. They aim to promote informed discussion. That indeed was their origin: they are descended from an internal discussion document prepared a few years ago when the then Department of Philosophy at (...) the University of Edinburgh was reviewing its logic teaching. (shrink)

The Yogācāra school of logic developed a theory of sign-inferences that has many features of the Stoic and Epicurean logical teachings with small inclusions of Aristotelian ideas. In the Nyāyabindu of Dharmakīrti, we can find the following schemes of formal reasoning: modus Barbara (Figure I) and modus Camenes (Figure IV) of the Aristotelian syllogistic, and all the inference rules of the Stoic logic: modus ponens, modus tollens, modus ponendo tollens, modus tollendo ponens I, modus tollendo ponens II. The (...) three premises of Yogācāra inference (if p, then q; there is an example that p and q occur together; p; then q) corresponds to the Epicurean doctrine of three premises with a necessary exemplification. Thus, the paper is a comparative study of Greek and Buddhist theory of sign-inferences, showing a deep similarity between them. (shrink)

The Introduction outlines, in a concise way, the history of the Lvov-Warsaw School – a most unique Polish school of worldwide renown, which pioneered trends combining philosophy, logic, mathematics and language. The author accepts that the beginnings of the School fall on the year 1895, when its founder Kazimierz Twardowski, a disciple of Franz Brentano, came to Lvov on his mission to organize a scientific circle. Soon, among the characteristic features of the School was its serious approach towards philosophical (...) studies and teaching of philosophy, dealing with philosophy and propagation of it as an intellectual and moral mission, passion for clarity and precision, as well as exchange of thoughts, and cooperation with representatives of other disciplines.The genesis is followed by a chronological presentation of the development of the School in the successive years. The author mentions all the key representatives of the School (among others, Ajdukiewicz, Lesniewski, Łukasiewicz,Tarski), accompanying the names with short descriptions of their achievements. The development of the School after Poland’s regaining independence in 1918 meant part of the members moving from Lvov to Warsaw, thus providing the other segment to the name – Warsaw School of Logic. The author dwells longer on the activity of the School during the Interwar period – the time of its greatest prosperity, which ended along with the outbreak of World War 2. Attempts made after the War to recreate the spirit of the School are also outlined and the names of followers are listed accordingly. The presentation ends with some concluding remarks on the contribution of the School to contemporary developments in the fields of philosophy, mathematical logic or computer science in Poland. (shrink)

This book focuses on logic and logical language. It examines different types of words, terms and propositions in detail. While discussing the nature of propositions, it illustrates the procedures used to determine the truth and falsity of a proposition, and the validity and invalidity of an argument. In addition, the book provides a clear exposition of the pure and mixed form of syllogism with suitable examples. The book encompasses sentential logic, predicate logic, symbolic logic, induction and (...) set theory topics. The book is designed to serve all those involved in teaching and learning courses on logic. It offers a valuable resource for students and researchers in philosophy, mathematics and computer science disciplines. Given its scope, it is an essential read for everyone interested in logic, language, formulation of the hypotheses for the scientific enquiries and research studies, and judging valid and invalid arguments in the natural language discourse. (shrink)

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was (...) essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the formulation of group theory; and geometry, transformed by Riemann, lay at the heart of topology, which in turn transformed much of modern mathematics. Using complex numbers as my case study, I argue that the best way to teach students mathematics is through a repertoire of modes of representation, which is also the best way to make mathematical discoveries. (shrink)

This short work presents a popular fringe theory as a source of case studies for use in teaching informal logic in an introductory course. It puts forward ancient astronaut theory as the candidate source, together with a characterization of why it fits the bill. The televised material associated with that theory is well suited to being used as case studies given that they are easy to follow, contain a surprising number of arguments and fallacies, and keep students reliably engaged. (...) The paper includes an overview of the forms of argumentation and fallacies that these cases may be used to teach, along with a sketch of how to best implement them in the classroom. (shrink)

Taking the Heideggerian critical ontology of technology as its base, this volume looks at postcolonial modernization and development in the global south as the worldwide expansion of the western metaphysical understanding of reality. We live today in an increasingly globalizing technological society that Martin Heidegger described in the middle of the last century as 'the planetary imperialism of technologically organized man.' Consequent upon this cultural-intellectual globalization, the ahistorical, violent, individualistic, calculative and capitalistic logic of the metaphysics of technology is (...) permeating the life-world, even of the world's poorest peoples, in ways they could neither choose nor control. This volume questions the political ethics and justice of post-war development discourse in the light of the egalitarian aims of modern societies, cultural freedom of communities and nations, and the ecological limits of the planet. The final chapters discuss the alternative proposal of development as various conceptions of good life and equitable human flourishing amidst equally flourishing non-human life and non-living beings. This unique volume is the first book-length treatment of the ontology of modernization and development in the global south from a Heideggerian stance. (shrink)

The “dragon” that graces the cover of this volume has a story that goes with it. In the summer of 1980, I was on the teaching staff of the Summer Institute on Medieval Philosophy held at Cornell University under the direction of Norman Kretzmann and the auspices of the Council for Philosophical Studies and the National Endowment for the Humanities. While I was giving a series of lectures there (lectures that contribute to this volume, as it turns out), I went (...) to my office one morning, and there under the door some anonymous wag from the Institute had slid the pen and ink drawing you see in the picture. It represents “Supposition” as a dragon, making a rude face at the viewer. The tail of the dragon is divided — not entirely accurately, as it turns out — into the various branches and subbranches of supposition. If the details are not altogether correct, the spirit is certainly understandable. (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)