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forallX: an Introduction to Formal Logic


In formal logic, sentences and arguments in English are translated into mathematical languages with well-defined properties. If all goes well, properties that were hard to discern in English become clearer in the formal language. This book covers translation, formal semantics, and proof theory for both sentential logic and quantified logic. Each chapter contains practice exercises, and solutions to selected exercises appear in an appendix. The book is designed to provide a semester’s worth of material for an introductory college course.


1 What is logic?

1.1 Arguments

1.2 Sentences

1.3 Two ways that arguments can go wrong

1.4 Deductive validity

1.5 Other logical notions

1.6 Formal languages

Practice Exercises

2 Sentential logic

2.1 Sentence letters

2.2 Connectives

2.3 Other symbolization

2.4 Sentences of SL

Practice Exercises

3 Truth tables

3.1 Truth-functional connectives

3.2 Complete truth tables

3.3 Using truth tables

3.4 Partial truth tables

Practice Exercises

4 Quanti ed logic

4.1 From sentences to predicates

4.2 Building blocks of QL

4.3 Quanti ers

4.4 Translating to QL

4.5 Sentences of QL

4.6 Identity

Practice Exercises

5 Formal semantics

5.1 Semantics for SL

5.2 Interpretations and models in QL

5.3 Semantics for identity

5.4 Working with models

5.5 Truth in QL

Practice Exercises

6 Proofs

6.1 Basic rules for SL

6.2 Derived rules

6.3 Rules of replacement

6.4 Rules for quanti ers

6.5 Rules for identity

6.6 Proof strategy

6.7 Proof-theoretic concepts

6.8 Proofs and models

6.9 Soundness and completeness

Practice Exercises

A Other symbolic notation

B Solutions to selected exercises

C Quick Reference

P.D. Magnus

P.D. Magnus is a professor and department chair in Philosophy at the University at Albany, State University of New York. He received his PhD from the University of California, San Diego. His primary research is in the philosophy of science, and he has written extensively on topics including the underdetermination of theory by data and natural kinds. His other publications include dozens of journal articles and the book Scientific Enquiry and Natural Kinds: From Planets to Mallards (Palgrave Macmillan, 2012).