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

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

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.

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: 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.

The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart). In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided: 1. What were the reasons for the philosophers' lack of interest in formal logic? 2. What were the reasons for the mathematicians' interest in logic? 3. What did "logic reform" mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic? 4. Was mathematical logic regarded as art, as science or as both?

SYMBOLIC LOGIC. CHAPTER I. ON THE FORMS OF LOGICAL PROPOSITION. IT has been mentioned in the Introduction that the System of Logic which this work is ...

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.

This introduction to the basic forms of deductive inference as evaluated by methods of modern symbolic logic is de­signed for sophomore-junior-level stu­dents ready to specialize in the study of deductive logic. It can be used also for an introductory logic course. The inde­pendence of many sections allows the instructor utmost flexibility. The text consists of eight chapters, the first six of which are designed to intro­duce the student to basic topics of sen­tence and predicate logic. The last two chapters extend the procedures of the first six to alethic modal logic, the logic of imperatives, and deontic logic. Throughout the text there is an attempt to relate symbolic techniques to issues in the philosophy of logic.

Logic With Trees is a new and original introduction to modern formal logic. It contains discussions on philosophical issues such as truth, conditionals and modal logic, presenting the formal material with clarity, and preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and exercises guide beginners through the book, with answers to selected exercises enabling readers to check their progress. Logic With Trees equips students with: a complete and clear account of the truth-tree system for first order logic; the importance of logic and its relevance to many different disciplines; the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic; the ability to contest claims that "ordinary" reasoning is well represented by formal first order logic.