Introductions to Logic

How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using “truth trees,” as (...) in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. A concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics. (shrink)

O texto fornece distinções conceituais engendradas desde uma perspectiva para o ensino de filosofia que contempla, em seu horizonte, o projeto a construção de uma didática mínima da lógica para o ensino médio. Após a apresentação de alguns aspectos positivos da referida perspectiva são indicadas duas maneiras usuais de compreender e praticar o ensino de lógica. O objetivo central do texto é mostrar como, desde a perspectiva inicialmente esboçada, os esclarecimentos conceituais propostos podem sugerir caminhos interdisciplinares para a didática da (...) lógica sem perda da especificidade da disciplina. The text provides some conceptual distinctions generated from a perspective on teaching philosophy according to which the project of a "didactica minima" for logic in high schools is contemplated. After a brief presentation of some positive aspects of the perspective from which the distinctions are proposed, two common ways of teaching logic are considered. The aim of the paper is to show how the perspective proposed can clarify some topics on the issue of teaching logic in an interdisciplinary way, without losing the specifics of the discipline. (shrink)

In order to decide whether a discursive product of human reason corresponds or not to the logical order, one must analyze it in terms of syntactic correctness, consistency, and validity. The first step in logical analysis is formalization, that is, the process by which logical forms of thoughts are represented in different formal languages or logical systems. Although each thought can be properly formalized in different ways, the formalization variants are not equally adequate. The adequacy of formalization seems to depend (...) on several essential features: parsimony, accuracy, transparency, fertility and reliability. Because there is a partial antinomy between these traits, it is impossible to find a perfectly adequate variant of formalization. However, it is possible and preferable to reach a reasonable compromise by choosing the variant of formalization which satisfies all of these fundamental characteristics. (shrink)

A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.

This is a basic logic text for first-time logic students. Custom-made texts from the chapters is an option as well. And there is a website to go with text too.

This is an introduction to the Isabelle proof assistant aimed at philosophers and their students.

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), translating (formalizing) English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as truth-functional completeness and modal logic. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics) and in LaTeX source code. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

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)

An introduction to informal logic, critical thinking and rhetoric utilizing actual public discourse .

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

Some logic students falter at the transition from the mechanical method of truth tables to the less-mechanical method of natural deduction. This short paper introduces a word game intended to ease that transition.

The book is an undergraduate-level introduction to first-order logic and proposi­tional modal logic. The book presents symbolic logic in a way that is pedagogi­cally attractive and formally rigorous. The main concepts are formally defined, in­formally explained, and illustrated with several examples. The book is aimed at philosophy majors and it includes discussions of several problems in the philosophy of logic.

Introduction to mathematical logic, part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.

On the heels of Franzén's fine technical exposition of Gödel's incompleteness theorems and related topics (Franzén 2004) comes this survey of the incompleteness theorems aimed at a general audience. Gödel's Theorem: An Incomplete Guide to its Use and Abuse is an extended and self-contained exposition of the incompleteness theorems and a discussion of what informal consequences can, and in particular cannot, be drawn from them.

Meaning and Argument shifts introductory logic from the traditional emphasis on proofs to the symbolization of arguments. Another distinctive feature of this book is that it shows how the need for expressive power and for drawing distinctions forces formal language development. This revised edition includes expanded sections, additional exercises, and an updated bibliography. Updated and revised edition includes extended sections, additional exercises, and an updated bibliography. Distinctive approach in that this text is a philosophical, rather than mathematical introduction to logic. (...) Concentrates on symbolization and does all the technical logic simply with truth tables and no derivations at all. Contains numerous exercises and a corresponding answer key. Extensive appendix which allows the reader to explore subjects that go beyond what is usually covered in an introductory logic course. Features accompanying website at www.meaningargument.com. (shrink)

This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small bites that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, (...) relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. (shrink)

An introductory logic textbook where the central concept is not deduction but search and logical form. (Deduction - logical consequence - drops out as a special case. TIt is meant for a class-based rather than a lecture-based course, and for students with general interests.

This book is written for those who wish to learn some basic principles of formal logic but more importantly learn some easy methods to unpick arguments and assess their value for truth and validity. -/- The first section explains the ideas behind traditional logic which was formed well over two thousand years ago by the ancient Greeks. Terms such as ‘categorical syllogism’, ‘premise’, ‘deduction’ and ‘validity’ may appear at first sight to be inscrutable but will easily be understood with examples (...) bringing the subjects to life. Traditionally, Venn diagrams have been employed to test arguments. These are very useful but their application is limited and they are not open to quantification. The mid-section of this book introduces a methodology that makes the analysis of arguments accessible with the use of a new form of diagram, modified from those of the mathematician Leonhard Euler. These new diagrammatic methods will be employed to demonstrate an addition to the basic form of syllogism. This includes a refined definition of the terms ‘most’ and ‘some’ within propositions. This may seem a little obscure at the moment but one will readily apprehend these new methods and principles of a more modern logic. (shrink)

In elementary logic textbooks, Venn diagrams are used to analyze and evaluate the validity of syllogistic arguments. Although the method of Venn diagrams is shown to be a powerful analytical tool in these textbooks, it still has limitations. On the one hand, such method fails to represent singular statements of the form, “a is F.” On other hand, it also fails to represent identity statements of the form, “a is b.” Because of this, it also fails to give an account (...) of the validity of some obviously valid arguments that contain these types of statements as constituents. In this paper, owing to the developments in the literature on Venn diagrams, we offer a way of supplementing the rules of the Venn diagram found in textbooks, and show how this retooled Venn diagram technique could account for the problem cases. (shrink)

- uneducated in the field authors who defend a consensus they are being TOLD when they enter offices of Ed-Sci, teaching and writing works on learning-theory - but never checked the facts, PART I and PART II.

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

The Logic Manual is a clear and concise introduction to logic for beginning philosophy students.

Now much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor.

Greg Restall's Logic provides concise introductions to propositional and first-order predicate logic while showing how formal logic intersects with substantial philosophical issues such as vagueness, conditionals, relevance, propositional attitudes, and opaque contents. The author also examines the ideas behind modal logic, free logic, and other non-standard logics and discusses the nature of logic itself. The book covers both natural deduction and tree methods for proving validity. Each chapter includes excellent suggestions for further reading and both elementary and more advanced exercises, (...) with solutions provided on a website. It is flexibly designed to be useable for half or full-year courses, for courses focusing exclusively on formal logic, or for a variety of approaches that would integrate topics in philosophical logic. Restall examines many of the interesting issues raised by basic logical techniques and will undoubtedly stimulate further study in the discipline. This is a logic book designed principally for philosophers but which will also be of interest to students of computer science, cognitive science, and linguistics. (shrink)

By confining themselves to elementary principles, the authors manage to cover with an appropriate balance of simplicity and rigor a wider range of materials than is common in so readable an introduction. There is an emphasis on logic as a syntax for language. Though not a text book, the work meets very well the authors' aim of "presenting to Spanish speaking readers, in a succinct, clear, and rigorous manner, the fundamental themes of the discipline."--L. K. B.

This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.

This textbook, oriented toward non-majors in philosophy, aims to provide an understanding not merely of forms of valid and invalid inference but also of the cognitive situation, of the methods of successful "problem-solving thought" and of the role of language therein. Great emphasis is thus placed on semiotics, which is integrated with the material from methodology and logic by considerations from general theory of knowledge. The whole presentation is marked by innovations, both pedagogical and theoretical. Most of the material of (...) the usual course in elementary formal logic is crowded into the last part. The author has attempted, with some success, to develop a reformed "traditional" approach to logic in the light of the recent technical advances in semiotic and symbolic logic, without reducing it to a narrow and fragmentary formal exposition of these sciences. --L. K. B. (shrink)

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and (...) their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area. (shrink)

It is made clear what a law of logic is and why the laws of classical logic are true.

Gottlob Frege (1848-1925) invented the discipline of mathematical logic. In this short work, it is clearly stated what Frege did and did not accomplish.

This book clearly explains what an infinite number is, how infinite numbers differ from finite numbers, and how infinite numbers differ from one another. The concept of recursivity is concisely but thoroughly covered, as are the concepts of cardinal and ordinal number. All of Cantor's key proofs are clearly stated, including his epoch-making diagonal proof, whereby he proved that that there are more reals than rationals and, more generally, that there are infinitely large, non-recursive classes. In the final section, Kurt (...) Gödel's celebrated Incompleteness Theorem is shown to be equivalent with a number of the various different theorems proved in this short but profound work. (shrink)

Introducción a la lógica moderna es un libro de texto dedicado al estudio de la lógica simbólica elemental. No presupone familiaridad alguna con la lógica, las matemáticas o la filosofía, y se ha hecho un esfuerzo deliberado por adaptarlo a los intereses de estudiantes provenientes de las más diversas disciplinas. Al mismo tiempo, los conceptos centrales son expuestos de una manera precisa y rigurosa, sin ocultar los detalles y problemas técnicos y filosóficos que hacen de la lógica un área de (...) estudio interesante en sí misma. El libro está dividido en tres partes. La primera se ocupa de la lógica proposicional, la segunda de la lógica de primer orden y la tercera de la lógica modal proposicional. Los tres temas se estudian semánticamente utilizando árboles de verdad, y sintácticamente a través de sistemas de deducción natural. Al final de cada sección hay numerosos ejercicios de práctica, la mitad de los cuales son resueltos en el apéndice. El texto está diseñado para un curso de un año de duración y permite gran flexibilidad en el diseño del mismo. (shrink)

A textobook on classical Aristotelian and Thomistic Logic, with some comparisons with modern authors. Topics: Conceptos, Universals, Predicables, Analogy, Proposition, Syllogism,Sophisms, Scientific Knowledge.