Crash Course in Logic is a booklet designed to introduce basic principles of logic and critical thinking to students so they can better express their ideas. Many high school and college students have trouble constructing theoretical arguments and writing clearly because they are not acquainted with the forms of reasoning that are presented in this booklet. Intended as a supplement to other instructional material for a variety of courses, this booklet will guide students through a mini-course (...) on logic that includes many examples and exercises. With knowledge of the basic forms of reasoning, students will have the tools necessary to solve problems and evaluate arguments as well as articulate their own ideas and insights clearly. Crash Course in Logic will be of great value to teachers of any subject who are searching for an accessible way to teach critical thinking and reasoning to their students. (shrink)

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will? Surprisingly (...) little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability. (shrink)

This is a free book, 165 pages. It is for anyone who has had a solid introductory logic course and wants more. Topics covered include soundness and completeness for first-order logic, Tarski's theorem on the undefinability of truth, Gödel's incompleteness theorems, the undecidability of first-order logic, a smattering of second-order logic, and modal logic (both propositional and quantificational). I wrote it for use in my own course, because I thought I could present the (...) most important results and concepts more clearly than the available textbooks. (shrink)

An introductory text in linguistic semantics, uniquely balancing empirical coverage and formalism with development of intuition and methodology. -/- This introductory textbook in linguistic semantics for undergraduates features a unique balance between empirical coverage and formalism on the one hand and development of intuition and methodology on the other. It will equip students to form intuitions about a set of data, explain how well an analysis of the data accords with their intuitions, and extend the analysis or seek an alternative. (...) No prior knowledge of linguistics is required. After mastering the material, students will be able to tackle some of the most difficult questions in the field even if they have never taken a linguistics course before. -/- After introducing such concepts as truth conditions and compositionality, the book presents a basic symbolic logic with negation, conjunction, and generalized quantifiers, to serve as the basis for translation throughout the book. It then develops a detailed compositional semantics, covering quantification (scope and binding), adverbial modification, relative clauses, event semantics, tense and aspect, as well as pragmatic phenomena, notably deictic pronouns and narrative progression. -/- A Course in Semantics offers a large and diverse set of exercises, interspersed throughout the text; those labeled “Important practice and looking ahead” prepare students for material to come; those labeled “Thinking about ” invite students to think beyond the content of the book. (shrink)

A companion to the logic text by the same authors. -- A. R. A.

The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as (...) proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course. (shrink)

In this paper we study 1. the frame-theory of certain bimodal provability logics involving the reflection principle and we study2. certain specific bimodal logics with a provability predicate for a subtheory of Peano arithmetic axiomatized by a non-standardly finite number of axioms.

Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems.

The summary is devoted to the meetings of the Presidium of the Russian Federal Educational and Methodological Association held in September 2018 in Astrakhan and in February 2019 in Moscow. The authors review main educational and methodological issues discussed at the meetings. The summary covers the issues of online courses in philosophy. It also touches upon key issues of religious studies, the specifics of its teaching in Russia and foreign countries, current problems facing religious studies in Russia. The article contains (...) a review of the current state of logic education in Russia, its current problems and possible ways to solve them. Also it outlines issues related to the implementation of the Russian national project “Science” as well as philosophy education at Astrakhan State University and the issues of realization of new educational standards. (shrink)

A clearly written and uncomplicated text, suitable for use with elementary and high school students as well as in college classes. It presents, in thorough detail, the techniques for making deductions, testing for validity, etc., in the logic of sentences and of universal quantification. The exposition rests upon the basic notion of inference according to rules; some fourteen rules of inference are presented and explained. Truth values and truth tables are discussed as means for determining important properties of inferences, (...) e.g., testing for validity of the inference, consistency of the premisses, etc. These techniques are then applied in formulating a simple mathematical system, a set of axioms for addition. The system is then used to illustrate the deduction of theorems with universal quantification.—K. P. F. (shrink)

This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, (...) and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more. (shrink)

In Winter 2017, the first author piloted a course in formal logic in which we aimed to (a) improve student engagement and mastery of the content, and (b) reduce maths anxiety and its negative effects on student outcomes, by adopting student oriented teaching including peer instruction and classroom flipping techniques. The course implemented a partially flipped approach, and incorporated group-work and peer learning elements, while retaining some of the traditional lecture format. By doing this, a wide variety (...) of student learning preferences could be provided for. (shrink)

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 Workbook for Arguments" builds on Anthony Weston's "Rulebook for Arguments" to provide a complete textbook for a course in critical thinking or informal logic. "Workbook" includes: The entire text of "Rulebook," supplemented with extensive further explanations and exercises. Homework exercises adapted from a wide range of arguments from newspapers, philosophical texts, literature, movies, videos, and other sources. Practical advice to help students succeed when applying the "Rulebook's" rules to the examples in the homework exercises. Suggestions for further (...) practice, outlining activities that students can do by themselves or with classmates to improve their skills. Detailed instructions for in-class activities and take-home assignments designed to engage students. An appendix on mapping arguments, giving students a solid introduction to this vital skill in constructing complex and multi-step arguments and evaluating them. Model answers to odd-numbered problems, including commentaries on the strengths and weaknesses of selected sample answers and further discussion of some of the substantive intellectual, philosophical, or ethical issues they raise. (shrink)

In the past three decades there has been a rapid development of the formal machinery for modal logic. Quantified modal logic has developed along with a semantics and model theory that is appropriate to it. With this technical development there has been relatively little discussion of what modality is all about. There are two fundamental questions that have gone unanswered. First, to what does necessity amount? Is this a new logical notion, or is it something that can be (...) further analyzed in terms of other notions that we already have at our disposal? The second question is what makes truths involving necessity true? What is their ontological grounding in the world? This essay is directed at the first of these questions. ;There are three possible reductions of metaphysical modality. First, there is the reduction suggested by the semantics for modal logic: a reduction in terms of possible worlds. Second, there is the reduction in terms of cognition. What is possible is what is conceivable. Third, there is the reduction in terms of language. Necessities arise from the structures of language and/or language use. ;I argue that none of these is successful. All of them suffer either from presupposing some form of metaphysical necessity in the reductive base, rendering them circular and not truly reductive, or they do not do justice to the modality being reduced. ;Since necessity is not reducible to any non-modal features of the world, we need to determine whether we ought to reject it as unacceptable on this basis, or whether we ought to retain it, but treat is as a new primitive that is introduced into a philosophical or logical theory. I urge the latter course is the one that we ought to take because without it too many things will likewise be deemed unacceptable. Causal necessity and explanation, normally accepted theories or knowledge and perception, logic and logical validity, and one common manner of distinguishing sets from properties will be deemed unacceptable if de re necessity is unacceptable. All of these presuppose de re metaphysical necessity in some way. I conclude that de re metaphysical necessity ought to be retained in our theory as primitive, unanalyzable notion. (shrink)

A class in informal logic can be an opportunity to do more than just cover the basic material of the subject. Critical Thinking can also foster civic engagement as experiential learning—in the course’s readings, assignments, in-class activities and discussions, and tests. I favor an inclusive understanding of civic engagement: the course theme is engaging with the concerns of the civis. The argument made throughout here is that the civic engagement theme is a way of doing experiential learning (...) in informal logic. I offer nine ideas for instructors here, which could be adopted wholesale or piecemeal, including how to do CSI. (shrink)

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof (...) techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing. (shrink)

The issue of a logic foundation for African thought connects well with the question of method. Do we need new methods for African philosophy and studies? Or, are the methods of Western thought adequate for African intellectual space? These questions are not some of the easiest to answer because they lead straight to the question of whether or not a logic tradition from African intellectual space is possible. Thus in charting the course of future direction in African (...) philosophy and studies, one must be confronted with this question of logic. The author boldly takes up this challenge and becomes the first to do so in a book by introducing new concepts and formulating a new African culture-inspired system of logic called Ezumezu which he believes would ground new methods in African philosophy and studies. He develops this system to rescue African philosophy and, by extension, sundry fields in African Indigenous Knowledge Systems from the spell of Plato and the hegemony of Aristotle. African philosophers can now ground their discourses in Ezumezu logic which will distinguish their philosophy as a tradition in its own right. On the whole, the book engages with some of the lingering controversies in the idea of African logic before unveiling Ezumezu as a philosophy of logic, methodology and formal system. The book also provides fresh arguments and insights on the themes of decolonisation and Africanisation for the intellectual transformation of scholarship in Africa. It will appeal to philosophers and logicians—undergraduates and post graduate researchers—as well as those in various areas of African studies. (shrink)

"A Workbook for Arguments" builds on Anthony Weston’s "A Rulebook for Arguments" to provide a complete textbook for a course in critical thinking or informal logic. The second edition adds: Updated and improved homework exercises—nearly one third are new—to ensure that the examples continue to resonate with students. Increased coverage of scientific reasoning, demonstrating how scientific reasoning dovetails with critical thinking more generally Two new activities in which students analyze arguments in their original form, as provided in brief (...) selections from the original texts. This edition continues to include The entire text of "Rulebook," supplemented with extensive explanations and exercises. Homework exercises adapted from a wide range of arguments in a wide variety of sources. Practical advice to help students succeed. Model answers to odd-numbered problems, including commentaries on the strengths and weaknesses of selected sample answers and further discussion of some of the substantive intellectual, philosophical, or ethical issues they raise. Detailed instructions for in-class activities and take-home assignments. An appendix on mapping arguments, giving students a solid introduction to this vital skill in constructing complex and multi-step arguments and evaluating them. (shrink)

Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend to be dull knives that mangle reality. If reality is a tomato and predicates are knives, then when these knives divide the tomato, plenty of mush remains unaccounted for. Of course some knives are sharper than others, just as some predicates are less vague than others. “x is water” is certainly (...) sharper than “x is beautiful.” But perfect sharpness, perfect boundaries, and perfect separation seem only to obtain in mathematics. The vagueness inherent in many predicates became particularly evident in the twentieth century. Quantum mechanics, the revival of certain ancient paradoxes, and the philosophy of science all contributed to a growing awareness that vagueness was ineliminable from many predicates. Quantum mechanical superposition seems to allow mutually exclusive simultaneous states. In searching for plausible interpretations of quantum mechanics, some researchers attempted to do away with classical bivalent logic. In its place they substituted multivalent quantum logics. Any logic with more than two values forces its predicates to slice reality into more than two parts. Ancient paradoxes involving heaps and baldness also pointed up the 1 Random Predicate Logic 2.. (shrink)

The European Summer School in Logic, Language and Information (ESSLLI) takes place every year, each time at a different location in Europe. With its focus on the large interdisciplinary area where linguistics, logic and computation converge, it has become very popular since it started in 1989, attracting large crowds of students. ESSLLI is where everyone in the field meets, teaches, takes courses, gives talks, dances all night, and generally has a good time. One of the enjoyable features of (...) the School is its recurring Student Session, organized by students along the lines of a conference. The speakers are students too, who are eager to get a chance to present their work. They face stiff competition to get their talks accepted, as the number of papers that is sent in each year is high and acceptance rates low. -/- In my experience many of the selected talks contain fresh and surprising insights and are a pleasure to attend. But the reader may judge the quality of the Student Session for himself, as this volume contains a selection of papers from its 2008 and 2009 installments, the first held in Hamburg, the second in Bordeaux. The book is divided into four parts. – Semantics and Pragmatics – Mathematical Linguistics – Applied Computational Linguistics – Logic and Computation -/- The first two of these present work in the intersection of logic (broadly conceived) and different parts of linguistics, the third contains papers on the interface of linguistics and computation, while the fourth, as its name suggests, deals with logic and computation. The reader will see a connection with the Venn diagram that functions as ESSLLI’s logo. (shrink)

The European Summer School in Logic, Language and Information is organized every year by the Association for Logic, Language and Information in different sites around Europe. The main focus of ESSLLI is on the interface between linguistics, logic and computation. ESSLLI offers foundational, introductory and advanced courses, as well as workshops, covering a wide variety of topics within the three areas of interest: Language and Computation, Language and Logic, and Logic and Computation. During two weeks, (...) around 50 courses and 10 workshops are offered to the attendants, each of 1.5 hours per day during a five days week, with up to seven parallel sessions. ESSLLI also includes a student session and four evening lectures by senior scientists in the covered areas. The 15 revised full papers presented were carefully reviewed and selected. The papers are organized in topical sections on The papers are organized in topical sections on language and computation; logic and computation; and logic and language. (shrink)

Normal texts and courses in logic are usually so preoccupied with the teaching of techniques that there is little opportunity to discuss some of the interesting and provocative issues in logical theory and the philosophy of logic. This book of readings is designed to supplement a course in symbolic logic. While there are few surprises or novelties here, there is a helpful selection from the writings of Frege, Russell, Strawson, Quine, Carnap, Von Wright, and others. The (...) short introductions to the various selections by the editors are all too brief.—R. J. B. (shrink)

The problem of Galileo's logical methodology has long interested scholars. In this volume William A. Wallace offers a solution that is completely unexpected, yet backed by convincing documentary evidence. His analysis starts with an early notebook Galileo wrote at Pisa, appropriating a Jesuit professor's exposition of the Posterior Analystics of Aristotle, and ends with one of the last letters Galileo wrote, stating that in logic he has been a Peripatetic all his life. Wallace's detective work unearths the complete (...) class='Hi'>logic course from which the notebook was excerpted, then proceeds to show how its terminology and methodology continue to surface in Galileo's later writings in which he founds his new sciences of the heavens and of local motion. The result is a tour de force that commends itself not only to Galileo's scholars and to logicians, philosophers, and historians, but to anyone interested in the epistemic roots of modern science. (shrink)

"We present a proof-theoretic foundation for logic programming in Girard's linear logic. We exploit the permutability properties of two-sided linear sequent calculus to identify appropriate notions of uniform proof, definite formula, goal formula, clause and resolution proof for fragments of linear logic. The analysis of this paper extends earlier work by the present authors to include negative occurrences of [cross] (par) and positive occurences of! (of course!) and? (why not?). These connectives introduce considerable difficulty. We consider (...) briefly some of the issues related to the mechanical implementation of our resolution proofs.". (shrink)

The nature of this book is fourfold: First, it provides comprehensive education in ontology, epistemology, logic, and ethics. From this perspective, it can be treated as a philosophical textbook. Second, it provides comprehensive education in mathematical analysis and analytic geometry, including significant aspects of set theory, topology, mathematical logic, number systems, abstract algebra, linear algebra, and the theory of differential equations. From this perspective, it can be treated as a mathematical textbook. Third, it makes a student and a (...) researcher in philosophy and/or mathematics capable of developing a holistic approach to reality, of undertaking interdisciplinary endeavors, of understanding (and possibly contributing to) advances and research projects in different academic disciplines, and of having more sources of inspiration and pleasure. From this perspective, it can be treated as a contribution to pedagogy and as an attempt to refresh and, indeed, revitalize modern philosophy. Fourth, it seeks to defend, refresh, and enrich philosophical and scientific structuralism and dynamical philosophy (known also as dynamism). From this perspective, this book can be treated as a research monograph on structuralism and dynamism, tackling the fundamental problems of reality, truth, and consciousness. In this context, Nicolas Laos expounds and proposes: (i) the concepts of dynamized time and dynamized space; (ii) a theory and method that he calls the "dialectic of rational dynamicity"; and (iii) his attempt to consider the fundamental problems of philosophy and science from the perspective of the dialectic of rational dynamicity. Thus, this book pertains to every field that is controlled by the function of consciousness, namely, being, knowing, and acting. The philosophy of rational dynamicity, as the author explains in this book, is a way of contemplating the laws of motion of nature, history, and spirit. (shrink)