I have three aims for this book. The first goal is to teach you the vocabulary and grammar of predicate logic
so that you will be able to translate the sentences of English (or other natural languages) into the notation of
this important branch of symbolic logic. The second goal concerns three techniques for evaluating predicate arguments:
formal proofs, counterexamples, and truth trees. I aim to help you become proficient in employing these logical
methods. The third goal of the book is to develop your ability to identify and assess those predicate arguments
you encounter daily as you read books and newspapers, carry on conversations, and watch television. Most of the
examples and exercises in the text involve arguments of this everyday variety.
I enjoyed writing the book. If you enjoy studying it (as I hope you will), I think my goals will be achieved.
Howard Pospesel
University of Miami
Teacher's Preface
This text presupposes familiarity with propositional logic and, in particular, acquaintance with the natural-deduction
approach to formal proofs and the technique of two-sided truth trees. Appendix One contains a review of this material,
but it is too compact to be fully intelligible to the complete novice. A discussion of these techniques is provided
in the companion volume, Introduction to Logic: Propositional Logic, revised third edition.
Predicate logic is developed gradually in this book, starting with the simplest monadic symbolizations and proceeding
through multiple quantification to the logic of relations. Students learn to symbolize and evaluate arguments of
a given degree of complexity before addressing the symbolization of more complex problems.
The formal-proof. system presented here does not include a universal-quantifier introduction rule. The advantages
of this approach are that the quantifier rules can be stated more simply and that proofs (although often longer)
are often easier to devise. A universal-quantifier introduction rule is provided in a footnote at the start of
section 4.2 to accommodate students of teachers who prefer to include this rule.
Most of the examples and exercises center around arguments similar to those encountered by students. The majority
of these arguments are natural, rather than contrived; many are presented by direct quotation from newspapers and
other sources. My purposes in employing natural everyday arguments are (1) to evoke the reader's interest, (2)
to counter the common but mistaken view that formal logic is just an impractical academic diversion, and (3) to
improve students' capacity to notice and assess the arguments they encounter. The final chapter explicitly addresses
the problems that arise when predicate logic is applied to natural arguments.
The second edition has been extensively revised. It differs from the first edition mainly in these ways:
The book has been reorganized to allow students to develop symbolization and proof-construction skills even
more gradually.
There is a chapter on two-sided truth trees. Some instructors prefer to teach one-sided trees; a chapter explaining
that technique is included on the CD-ROM disk packaged with the book.
New sections treat possible-world counterexamples, intensional contexts, quantifier scope, and quantifier order.
There are more exercises, and most of the original exercises and examples have been replaced by better and
more current ones.
The book is accompanied by a tutorial program, "PredLogic," written by Mark Pospesel and me. This
Windows-based software provides an environment in which students symbolize sentences, construct proofs of validity,
devise counterexamples, and create truth trees. The program enables students to catch errors as they are made,
and it offers hints for solving problems.
William G. Lycan has provided an appendix on the metatheory of predicate logic.
This edition uses parenthesis-free quantifier symbols. These symbols have become standard since the first edition
was published, and they are more suitable for doing logic on a computer. Gender-neutral language is used throughout.
The chapter on logic diagrams (that appeared in the first edition) has been moved to the CD-ROM disk that
Summary
For courses in Introduction to Logic and Formal Logic.
This clearly written volume extends to general statements the system developed in Propositional Logic, revised
3/e. It covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps,
beginning with the symbolization of categorical propositions and concluding with the properties of relations. Logic
is applied to materials with which college students will be familiar; both examples and exercises are drawn from
newspapers, television and other popular sources. Logic is made interesting and easier to learn without sacrificing
content or rigor. This new edition includes 'PredLogic,' a CD-ROM-based tutorial for students.
Features
NEW�CD-ROM Tutorial, 'PredLogic'�Windows-based software that helps students learn to symbolize, construct proofs
of validity, devise counterexamples, and create truth trees. The program enables students to catch errors as they
are made, and it offers hints for solving problems.
Helps students gain valuable practice in working additional problems.
NEW�Examples and Exercises�Replaces most of the original exercises and examples with better and more current
content. New sections treat possible-world counterexamples, intentional contexts, and quantifier scope.
Updated examples and exercises, and expanded content in sections, will appeal to a new generation of students.
Reorganized approach�Allows students to develop symbolization and proof-construction skills more gradually
and in tandem.
Enables students to comprehend these challenging techniques more easily and employ them effectively.
Truth Trees�Includes coverage of truth trees.
Teaches students this frequently-employed method of determining validity.
Appendix on metatheory�Includes an appendix on the metatheory of predicate logic written by William G. Lycan.
Students benefit from discussion of this advanced topic.
