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.

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

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.

A textbook for an 'advanced introductory' logic class (I used it as a textbook for mathematically capable introductory logic students). The book uses the tableau method, and includes standard results up to a proof of the soundness of predicate logic. Its slightly unusual features include a slightly greater emphasis on decidability than is usual, and more obviously, the presentation of a free logic as standard, alongside a classical alternative. A change of syllabus here means this is no longer under active (...) revision, but I'll leave this archive copy available. (shrink)

This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically ...

Some students in the humanities take fright when introduced to the formal manipulations characteristic of elementary sentential & predicate logic. One way to lessen the pain of initiation is to start with word games, of which Lewis Carroll’s Doublets (section 1) is a familiar example. The paper presents some other games that successively introduce more of the..

In this paper, I argue that ad hominem arguments are not always fallacious. More explicitly, in certain cases of practical reasoning, the circumstances of a person are relevant to whether or not the conclusion should be accepted. This occurs, I suggest, when a person gives advice to others or prescribes certain courses of action but fails to follow her own advice or act in accordance with her own prescriptions. This is not an instance of a fallacious tu quoque provided that (...) such circumstantial ad hominem arguments are construed as rebuttals to appeals (administrative) authority (of expertise), or so I argue. (shrink)

Clearly introduces the major topics in logic and their relation to current philosophical issues.

Deductive Logic is an introductory textbook in formal logic. The book is divided into four parts covering (i) truth-functional logic, (ii) monadic quantifi- cation, (iii) polyadic quantification and (iv) names and identity, and there are exercises for all these topics at the end of the book. In the truth-functional logic part, the reader learns to produce paraphrases of English statements and arguments in logical notation (this subsection is called “analysis”), then about the semantic properties of such paraphrased statements and arguments, (...) such as satisfiability, implication and equivalence (“logical assessment”) and finally (“reflection”) there is an axiomatic proof method and some important extras such as disjunctive normal form and expressive adequacy. Parts two and three mirror this analysis/assessment/reflection structure for monadic and polyadic quantification, though this time the proof system is a natural deduction one, and part three contains a completeness proof for that system. The fourth part of the book introduces names, the identity predicate and descriptions and examines the additional expressive power which these provide. (shrink)

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations ...

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, (...) concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic. (shrink)

This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...