Introductions to Logic

We show that the partial order of Σ0 3-sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.

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 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)

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.

This outstanding book is a leading text for symbolic or formal logic courses. All techniques and concepts are presented with clear, comprehensive explanations and numerous, carefully constructed examples. Its flexible organization (all chapters are complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.

New features in this edition, in addition to truth tree systems for classical and nonclassical logics, include new and simpler rules for modal logic, deontic ...

This book serves as a concise introduction to some main topics in modern formal logic for undergraduates who already have some familiarity with formal languages. There are chapters on sentential and quantificational logic, modal logic, elementary set theory, a brief introduction to the incompleteness theorem, and a modern development of traditional Aristotelian Logic.

Introduction This is an elementary logic book designed for people who have no technical familiarity with modern logic but who have been reasoning, ...

This review concludes that if the authors know what mathematical logic is they have not shared their knowledge with the readers. This highly praised book is replete with errors and incoherency.

This lively introduction to mathematical logic, easily accessible to non-mathematicians, offers an historical survey, coverage of predicate calculus, model theory, Godel’s theorems, computability and recursivefunctions, consistency and independence in axiomatic set theory, and much more. Suggestions for Further Reading. Diagrams.

No such book currently exists on the market, except for the usual puzzle books, which are an entirely different matter. The book consists of 16 booklets, about 30 pages each. All are written in conversational style, using very simple vocabulary. I explain why logic is about one word, “therefore,” how to use this word correctly, and how to tell when it has not been used correctly. Concepts related to this word are introduced as friends a child can play fun games (...) with. There are frequent breaks to give children time to think, ask questions, and practice what they have learned using examples provided. Children can begin reading these booklets as early as first grade, moving gradually from one to the next at their own place. It should be possible to complete the whole series by fifth grade, though I imagine some will finish much sooner than that. (shrink)

This is a textbook covering the basics of formal logic and elementary metatheory. Its distinguishing feature is that it has more emphasis on metatheory than comparable introductory textbooks. It was originally written to accompany lectures in an introductory to intermediate logic course at the University of Oxford, but it is designed to be used independently.

Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a special appendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, Modern Logic (...) gives equal weight to semantics and proof theory and explains their relationship, and develops in detail techniques for symbolizing natural language in first-order logic. After a general introduction featuring the notion of logical form, the book offers sections on classical sentential logic, monadic predicate logic, and full first-order logic with identity. A concluding section deals with extensions of and alternatives to classical logic, including modal logic, intuitionistic logic, and fuzzy logic. For students of philosophy, mathematics, computer science, or linguistics, Modern Logic provides a thorough understanding of basic concepts and a sound basis for more advanced work. (shrink)

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

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)

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)

What good is logic? -- Seventeen ways this book is different -- The two logics -- All of logic in two pages : an overview -- The three acts of the mind -- I. The first act of the mind : understanding -- Understanding : the thing that distinguishes man from both beast and computer -- Concepts, terms and words -- The problem of universals -- The comprehension and extension of terms -- II. Terms -- Classifying terms -- Categories -- (...) Predicables -- Division -- III. Material fallacies -- Fallacies of language -- Fallacies of diversion -- Fallacies of oversimplification -- Fallacies of argumentation -- Inductive fallacies -- Procedural fallacies -- Metaphysical fallacies -- Short story : love is a fallacy -- IV. Definition -- The nature of definition -- The rules of definition -- The kinds of definition -- The limits of definition -- V. Second act of the mind : judgment -- Judgments, propositions, and sentences -- What is truth? -- The four kinds of categorical propositions -- Logical form -- Euler's circles -- Tricky propositions -- The distribution of terms -- VI. Changing propositions -- Immediate inference -- Conversion -- Obversion -- Contraposition -- VII. Contradiction -- What is contradiction? -- The square of opposition -- Existential import -- Tricky propositions on the square -- Some practical uses of the square of opposition -- VIII. The third act of the mind : reasoning -- What does reason mean? -- The ultimate foundations of the syllogism -- How to detect arguments -- Arguments vs. explanations -- Truth and validity -- IX. Different kinds of arguments -- Three meanings of because -- The four causes -- A classification of arguments -- Simple argument maps -- Deductive and inductive arguments -- Combining deduction and induction : socratic method -- X. Syllogisms -- The structure and strategy of the syllogism -- The skeptics objection to the syllogism -- The empiricist's objection to the syllogism -- Demonstrative syllogisms -- How to construct convincing syllogisms -- XI. Checking syllogisms for validity -- By Euler's circles -- By Aristotle's six rules -- Barbara Celarent : mood and figure -- Venn diagrams -- XII. More difficult syllogisms -- Enthymemes : abbreviated syllogisms -- Sorites : chain syllogisms -- Epicheiremas : multiple syllogisms -- Complex argument maps -- XIII. Compound syllogisms -- Hypothetical syllogisms -- Reductio ad absurdum arguments -- The practical syllogism : arguing about means and ends -- Disjunctive syllogisms -- Conjunctive syllogisms -- Dilemmas -- XIV. Induction -- What is induction? -- Generalization -- Causal induction : Mill's methods -- Scientific hypotheses -- Statistical probability -- Arguments from analogy -- A fortiori and a minore arguments -- XV. Some practical applications of logic -- How to write a logical essay -- How to write a socratic dialogue -- How to have a socratic debate -- How to use socratic method on difficult people -- How to read a book socratically -- XVI. Some philosophical applications of logic -- Logic and theology -- Logic and metaphysics -- Logic and cosmology -- Logic and philosophical anthropology -- Logic and epistemology -- Logic and ethics. (shrink)

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.

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

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)

Famous classic has introduced hundreds of thousands to symbolic logic, via clear, thorough, precise exposition.

"This book is about the basic principles that underlie critical thinking and creativity.

Intended for the first course in logic, The Power of Logic (POL) is written with the conviction that logic is the most important course that college students take. POL preserves the balance between informal and formal logic. Layman;s direct and accessible writing style, along with his plentiful examples, imaginative exercises, and POL;s accompanying Logic Tutor make this the best text for logic classes today.day.