In formal logic, sentences and arguments are translated into mathematical languages with well-defined properties. If all goes well, properties of the argument that were hard to discern become clearer. This text describes two formal languages which have been of special importance to philosophers: truth-functional sentential logic and quantified predicate logic. The book covers translation, formal semantics, and proof theory for both languages.This can be used as the textbook for a semester long course in logic, for a unit on logic, or for self-directed study. Each chapter contains practice exercises; solutions to selected exercises appear in an appendix.The author is an assistant professor of philosophy at the University at Albany, SUNY. For more information, see the forall x homepage and the author's homepage. http://www.fecundity.com/logic/

- What is logic?
- Arguments
- Sentences
- Two ways that arguments can go wrong
- Deductive validity
- Other logical notions
- Formal languages
- Practice Exercises

- Sentential logic
- Sentence letters
- Connectives
- Other symbolization
- Sentences of SL
- Practice Exercises

- Truth tables
- Truth-functional connectives
- Complete truth tables
- Using truth tables
- Partial truth tables
- Practice Exercises

- Quantified logic
- From sentences to predicates
- Building blocks of QL
- Quantifiers
- Translating to QL
- Sentences of QL
- Identity
- Practice Exercises

- Formal semantics
- Semantics for SL
- Interpretations and models in QL
- Semantics for identity
- Working with models
- Truth in QL
- Practice Exercises

- Proofs
- Basic rules for SL
- Derived rules
- Rules of replacement
- Rules for quantifiers
- Rules for identity
- Proof strategy
- Proof-theoretic concepts
- Proofs and models
- Soundness and completeness
- Practice Exercises

- Other symbolic notation
- Solutions to selected exercises
- C Quick Reference

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