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 skillful 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.
Introduces the student reader to the fundamentals of formal logic using the tree method
Clearly and accessibly written but also philosophically sophisticated
Helpful examples and exercises
Author(s): Peter Smith
Publisher: Cambridge University Press
Year: 2003
Language: English
Commentary: better copy available
Pages: C, viii+357, B
Cover
About the Book and the Author
An Introduction to Formal Logic
© Peter Smith 2003
ISBN 978-0-521-80133-3 hardback
ISBN 978-0-521-00804-4 paperback
Contents
Preface
1 What is logic?
1.1 What is an argument?
1.2 What sort of evaluation?
1.3 Deduction vs. induction
1.4 More examples
1.5 The systematic evaluation of arguments
1.6 Summary
Exercises 1
2 Validity and soundness
2.1 Validity and possibility
2.2 What's the use of deduction?
2.3 The invalidity principle
2.4 Inferences and arguments
2.5 What sort of thing are premisses and conclusions?
2.6 Summary
Exercises 2
3 Patterns of inference
3.1 More patterns
3.2 Three simple points about inference patterns
3.3 Generality and topic neutrality
3.4 Arguments instantiate many patterns
3.5 'Logical form'
3.6 'Arguments are reliable in virtue of their form'
3.7 Summary
Exercises 3
4 The counterexample technique
4.1 The technique illustrated
4.2 More illustrations
4.3 The technique described
4.4 More examples
4.5 Countering the counterexample technique?
4.6 Summary
Exercises 4
5 Proofs
5.1 Two sample proofs
5.2 Fully annotated proofs
5.3 Enthymemes
5.4 Reduction arguments
5.5 Limitations
5.6 Summary
Exercises 5
6 Validity and arguments
6.1 Classical validity again
6.2 Sticking with the classical definition
6.3 Multi-step arguments again
6.4 Summary
Interlude: Logic, formal and informal
7 Three propositional connectives
7.1 'And', 'or' and 'not'
7.2 Quirks of the vernacular
7.3 Formalization
7.4 The design brief for PL
7.5 Some simple examples
7.6 Summary
Exercises 7
8 The syntax of PL
8.1 Syntactic rules for PL
8.2 Construction trees
8.3 Main connectives
8.4 Sub formulae and scope
8.5 Bracketing styles
8.6 A final brief remark on symbolism
8.7 Summary
Exercises 8
9 The semantics of PL
9.1 Interpreting atomic wffs
9.2 Interpreting molecular wffs
9.3 Valuations
9.4 Evaluating complex wffs
9.5 Calculating truth-values
9.6 Three points about valuations
9.7 Short working
9.8 Summary
Exercises 9
10 'A's and 'B's, 'P's and 'Q's
10.1 Styles of variable: our conventions
10.2 Basic quotation conventions
10.3 A more complex convention
10.4 Summary
Exercises 10
11 Truth functions
11.1 Truth-functional vs. other connectives
11.2 A very brief word about 'functions'
11.3 Full truth-tables
11.4 'Possible valuations'
11.5 Short cuts
11.6 Truth-functional equivalence
11. 7 Expressive adequacy
11.8 'Disjunctive normal form'
11.9 Other adequate sets of connectives.
11.10 Summary
Exercises 11
12 Tautologies
12.1 Tautologies and contradictions
12.2 Generalizing about tautologies
12.3 A point about 'form'
12.4 Tautologies and necessity
12.5 A philosophical aside about necessity
12.6 Summary
Exercises 12
13 Tautological entailment
13.1 Two introductory examples
13.2 Tautological entailment in PL
13.3 Expressing inferences in PL
13.4 Truth-table testing in PL
13.5 Vernacular arguments again
13.6 'Validity in virtue of form'
13.7 ',,"' and '.'.'
13.8 Some simple metalogical results
13.9 Summary
Exercises 13
Interlude: Propositional logic
14 PLC and the material conditional
14.1 Why look for a truth-functional conditional?
14.2 Introducing the material conditional
14.3 ':J' is conditional-like
14.4 'If', 'only if', and 'if and only if'
14.5 The official syntax and semantics of PLC
14.6 'F, ':.', '::J', '=', and '-'
14.7 Summary
Exercises 14
15 More on the material conditional
15.1 Types of conditional
15.2 In support of the material conditional
15.3 Against identifying vernacular and material conditionals
15.4 Robustness
15.5 'Dutchman' conditionals
15.6 Summary
Exercises 15
16 Introducing PL trees
16.1 'Working backwards'
16.2 Branching cases
16.3 Signed and unsigned trees
16.4 More examples
16.5 Summary
Exercises 16
17 Rules for PL trees
17.1 The official rules
17.2 Tactics for trees
17.3 More examples
17.4 Testing for tautologies
17.5 Comparative efficiency
17.6 Summary
Exercises 17
18 PLC trees
18.1 Rules for PLC trees
18.2 Examples
18.3 An invitation to be lazy
18.4 More translational issues
18.5 Summary
Exercises 18
19 PL trees vindicated
19.1 The tree method is sound
19.2 The tree method is complete
19.3 A corollary and a further result
19.4 Summary
Exercises 19
20 Trees and proofs
20.1 Choices, choices ...
20.2 Trees as arguments in PL
20.3 More natural deductions?
2004 What rules for trees?
20.5 'P and 'r', soundness and completeness
20.6 Summary
Interlude: After propositional logic
21 Quantifiers
21.1 Quantifiers in arguments
21.2 Quantifiers in ordinary language
21.3 Quantifiers and scope
21.4 Expressing quantification unambiguously
21.5 Summary
22 QL introduced
22.1 Names and predicates
22.2 Connectives in QL
22.3 Adding the quantifiers
22.4 Domains, and named vs. nameless things
22.5 Summary
Exercises 22
23 QL explored
23.1 The quantifiers interrelated
23.2 Expressing restricted quantifications
23.3 Existential import
23.4 More on variables
23.5 'Revealing logical form'
23.6 Summary
Exercises 23
24 More QL translations
24.1 Translating English into QL
24.2 Translating from QL
24.3 Moving quantifiers
24.4 Summary
Exercises 24
25 Introducing QL trees
25.1 The V-instantiation rule
25.2 Rules for negated quantifiers
25.3 The 3-instantiation rule
25.4 More examples
25.5 Open and closed trees
25.6 Summary
Exercises 25
26 The syntax of QL
26.1 How not to run out of constants, predicates or variables
26.2 How to introduce quantifiers
26.3 The official syntax
26.4 Some useful definitions
26.5 Summary
Exercises 26
27 Q-valuations
27.1 Q-valuations vs. interpretations
27.2 Q-valuations defined
27.3 The semantics of quantifiers: a rough guide
27.4 The official semantics
27.5 A toy example
27.6 Five results about (extended) q-valuations
27.7 Summary
Exercises 27
28 Q-validity
28.1 Q-validity defined
28.2 Some simple examples of q-validity
28.3 Thinking about trees again
28.4 Validity, q-validity, and 'quantification logical form'
28.5 The undecidability of q-validity
28.6 Countermodels and invalidity
28.7 Summary
Exercises 28
29 More on QL trees
29.1 The official rules
29.2 Further examples of closed trees
29.3 Extending the (V) rule
29.4 What can be learnt from open trees?
29.5 Summary
Exercises 29
30 QL trees vindicated
30.1 Soundness
30.2 Completeness: strateg
30.3 Consistent, saturated sets are satisfiable
30.4 Systematic trees
30.5 Completeness completed
30.6 Summary
Interlude: Developing predicate logic
31 Extensionality
31.1 Interpretations vs. valuations
31.2 Extensional and intensional contexts
31.3 Quotation
31.4 Intentional contexts are intensional
31.5 Modal contexts are intensional
31.6 Summary
32 Identity
32.1 Numerical vs. qualitative identity
32.2 Equivalence relations
32.3 The 'smallest' equivalence relation
32.4 Leibniz's Law
32.5 Leibniz's Law and co-referential designators
32.6 Summary
Exercises 32
33 The language QL =
33.1 Adding identity to QL
33.2 Translating into QL =
33.3 Numerical quantifiers
33.4 Summary
Exercises 33
34 Descriptions and existence
34.1 Definite descriptions
34.2 Descriptions and scope
34.3 More translations
34.4 Existence statements
34.5 Summary
Exercises 34
35 Trees for identity
35.1 Leibniz's Law again
35.2 Self-identity
35.3 Descriptions again
35.4 'One and one make two'
35.5 Soundness and completeness again
35.6 Summary
Exercises 35
36 Functions
36.1 Functions re-introduced
36.2 Adding functions to QL =
36.3 Functions and functional relations
36.4 Partial functions and free logic
36.5 Definite descriptions again
36.6 Summary
Further reading
Matters arising
Other texts
Index
Back Cover
Better Copy Available: http://libgen.org/book/index.php?md5=c7d58ef8901bb486ff0cf780cbfeb673&open=0
