β Scribed by Jc Beall, Shay Allen Logan
No coin nor oath required. For personal study only.
Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as:
Β· mathematical preliminaries
Β· propositional logic
Β· quantified logic (first monadic, then polyadic)
Β· English and standard βsymbolic translationsβ
Β· tableau procedures.
Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of how they can take their knowledge further. With its wealth of exercises (solutions available in the encyclopedic online supplement), Logic: The Basics is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic.
Cover
Half title
Series Page
Title Page
Copyright Page
Dedication
Table of contents
Preface
Acknowledgments
Part I Background Ideas
1 Consequences
1.1 Relations of support
1.2 Logical consequence: the basic recipe
1.3 Valid arguments and truth
1.4 Summary, looking ahead, and further reading
1.5 Exercises
1.6 Notes
2 Models, Modeled, and Modeling
2.1 Models
2.2 Models in science
2.3 Logic as modeling
2.4 A note on notation, metalanguages, and so on
2.5 Summary, looking ahead, and further reading
2.6 Exercises
2.7 Notes
3 Language, Form, and Logical Theories
3.1 Language and formal languages
3.2 Languages: syntax and semantics
3.2.1 Syntax
3.2.2 Semantics
3.3 Atoms, connectives, and molecules
3.4 Connectives and form
3.5 Validity and form
3.6 Logical theories: rivalry
3.7 Summary, looking ahead, and further reading
3.8 Exercises
3.9 Notes
4 Set-theoretic Tools
4.1 Sets
4.1.1 Members
4.1.2 Abstraction and Membership
4.1.3 Criterion of identity
4.1.4 The empty set
4.1.5 Other sets: sets out of sets
4.1.6 A few important relations among sets
4.2 Ordered sets: pairs and n-tuples
4.2.1 Cartesian Product
4.3 Relations
4.3.1 A few features of binary relations
4.4 Functions
4.5 Sets as tools
4.6 Summary, looking ahead, and further reading
4.7 Exercises
4.8 Notes
Part II THE BASIC CLASSICAL THEORY
5 Basic Classical Syntax and Semantics
5.1 Cases: complete and consistent
5.2 Classical truth conditions'
5.3 Basic classical consequence
5.4 Motivation: precision
5.5 Formal picture
5.5.1 Syntax of the basic classical theory
5.5.2 Semantics of the basic classical theory
5.6 Defined connectives
5.7 Some notable valid forms
5.8 Summary, looking ahead, and further reading
5.9 Exercises
5.10 Notes
6 Basic Classical Tableaux
6.1 What are tableaux?
6.1.1 The threefold core of tableaux
6.1.2 What do tableaux look like?
6.2 Tableaux for the basic classical theory
6.2.1 Three steps for specifying tableaux
6.2.2 An example
6.2.3 When a tableau doesn't close
6.3 Summary, looking ahead, and further reading
6.4 Exercises
6.5 Notes
7 Basic Classical Translations
7.1 Atoms, punctuation, and connectives
7.1.1 Connectives
7.1.2 Atomics
7.1.3 Punctuation
7.2 Syntax, altogether
7.3 Semantics
7.4 Consequence
7.5 Summary, looking ahead, and further reading
7.6 Exercises
7.7 Notes
Part III FIRST-ORDER CLASSICAL THEORY
8 Atomic Innards
8.1 Atomic innards: names and predicates
8.2 Truth and falsity conditionsfor atomics
8.3 Cases, domains, and interpretation functions
8.4 Classicality
8.5 A formal picture
8.5.1 Syntax of sentential logic with unary innards
8.5.2 Semantics of sentential logic with unary innards
8.6 Summary, looking ahead, and further reading
8.7 Exercises
8.8 Notes
9 Everything and Something
9.1 Validity involving quantifiers
9.2 Quantifiers: an informal sketch
9.3 Truth and falsity conditions
9.4 A formal picture
9.4.1 Syntax of monadic first-order logic
9.4.2 Semantics of monadic first-order logic
9.5 Summary, looking ahead, and further reading
9.6 Exercises
9.7 Notes
10 First-Order Language with Any-Arity Innards
10.1 Truth and falsity conditions for atomics
10.2 Cases, domains, and interpretation functions
10.3 Classicality
10.4 A formal picture
10.4.1 Syntax of first-order logic
10.4.2 Semantics of first-order logic
10.5 Summary, looking ahead, and further reading
10.6 Exercises
10.7 Notes
11 Identity
11.1 Logical expressions, forms, and sentential forms
11.2 Validity involving identity
11.3 Identity: informal sketch
11.4 Truth conditions: informal sketch
11.5 Formal picture
11.5.1 Syntax of first-order logic with identity
11.5.2 Semantics of first-order logic with identity
11.6 Summary, looking ahead, and further reading
11.7 Exercises
11.8 Notes
12 Tableaux for First-Order Logic with Identity
12.1 A few reminders
12.2 Tableaux for polyadic first-order logic
12.2.1 Examples β No Quantification
12.2.1.1 When not every branch closes
12.2.2 Examples β Monadic Quantification
12.2.2.1 When not every branch closes
12.2.3 Examples β Polyadic quantification and identity
12.2.3.1 When not every branch closes
12.3 Summary, looking ahead, and further reading
12.4 Exercises
12.5 Notes
13 First-Order Translations
13.1 Basic classical theory with innards
13.1.1 Atomics, syntactically
13.1.2 Atomics, semantically
13.2 First-order classical theory
13.2.1 Syntax, semantics, and an example, briefly
13.3 Polyadic innards
13.4 Examples in the polyadic language
13.5 Adding identity
13.5.1 English equivalents of='
13.5.2 An example
13.5.3 A Puzzle About Quantifiers
13.6 Summary, looking ahead, and further reading
13.7 Exercises
13.8 Notes
Part IV NONCLASSICAL THEORIES
14 Alternative Logical Theories
14.1 Apparent unsettledness
14.2 Apparent overdeterminacy
14.3 Options
14.4 Cases
14.5 Truth and falsity conditions
14.5.1 Atomics
14.5.2 Molecular sentences
14.6 Logical consequence
14.6.1 Comparing the β s
14.6.1.1 Paracomplete and classical consequence
14.6.1.2 Paraconsistent and classical consequence
14.6.1.3 Paraconsistent consequence and paracompleteconsequence
14.6.1.4 Paracomplete-and-paraconsistent consequence
14.7 Summary, looking ahead, and further reading
14.8 Exercises
14.9 Notes
15 Nonclassical Sentential Logics
15.1 Syntax
15.2 Semantics, broadly
15.3 Defined connectives
15.4 Some notable forms
15.4.1 Basic K3-forms
15.4.2 Basic LP-forms
15.4.3 Basic FDE-forms
15.5 Summary, looking ahead, and further reading
15.6 Exercises
15.7 Note
16 Nonclassical First-order Theories
16.1 An informal gloss
16.2 A formal picture
16.2.1 Syntax
16.2.2 Semantics
16.3 Summary, looking ahead, and further reading
16.4 Exercises
16.5 Notes
17 Nonclassical Tableaux
17.1 Closure conditions
17.2 Tableaux for nonclassical first-order logics
17.2.1 Three steps for specifying tableaux
17.2.2 Examples
17.2.3 When a tableau doesn't close
17.3 Summary, looking ahead, and further reading
17.4 Exercises
18 Nonclassical Translations
18.1 Syntax and semantics
18.1.1 Nonclassical negation
18.1.1.1 Paraconsistent negation
18.1.2 Nonclassical conditionals
18.2 Consequence
18.3 Summary, looking ahead, and further reading
18.4 Exercises
18.5 Note
19 Speaking Freely
19.1 Speaking of nonexistent `things'
19.2 Existential import
19.3 Freeing our terms, expanding our domains
19.4 Truth conditions: an informal sketch
19.5 Formal picture
19.5.1 Syntax
19.5.2 Semantics
19.5.3 A few remarks
19.6 Summary, looking ahead, and further reading
19.7 Exercises
19.8 Notes
20 Possibilities
20.1 Possibility and necessity
20.2 Towards truth and falsity conditions
20.2.1 Truth at a world
20.2.2 Truth at a world (in a universe): atomics
20.2.3 Truth at a world (in a universe): molecular
20.2.3.1 Basic connectives and quantifiers
20.2.3.2 Modal connectives: possibility and necessity
20.3 Cases and consequence
20.3.1 Exclusion and exhaustion in worlds
20.3.2 Consequence
20.4 Formal picture
20.4.1 Syntax
20.4.2 Semantics
20.4.3 A few notable forms
20.5 Remark on going beyond possibility
20.6 Summary, looking ahead, and further reading
20.7 Exercises
20.8 Notes
21 Free and Modal Tableaux
21.1 Free tableaux
21.1.1 Three steps for specifying tableaux
21.1.2 An example
21.1.3 When a tableau doesn't close
21.2 Modal tableaux
21.2.1 Three steps for specifying tableaux
21.2.2 Example
21.2.3 When a tableau doesn't close
21.3 Summary, looking ahead, and further reading
21.4 Exercises
22 Glimpsing Different Logical Roads
22.1 Other conditionals
22.2 Other negations
22.3 Other alethic modalities: actuality
22.4 Same connectives, different truth conditions
22.5 Another road to difference: consequence
22.6 Summary, looking behind and ahead, and further reading
22.7 Exercises
22.8 Notes
References
Index
Logic
π SIMILAR VOLUMES
Logic: The Basics is a hands-on introduction to the philosophically alive field of logical inquiry. Covering both classical and non-classical theories, it presents some of the core notions of logic such as validity, basic connectives, identity, βfree logicβ and more. This book: introduces som
<P><EM>Logic: The Basics</EM> is a hands-on introduction to the philosophically alive field of logical inquiry. Covering both classical and non-classical theories, it presents some of the core notions of logic such as validity, basic connectives, identity, βfree logicβ and more. This book:</P> <P><
<P><EM>Logic: The Basics</EM> is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: </P> <P>Β· mathematical preliminaries</P> <P>Β· propositional logic</P> <P>Β· quantified logi
Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: mathematical preliminaries, propositional logic, quantified logic (first monadic, then polyadic), Engl
Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as:<br>Β· mathematical preliminaries<br>Β· propositional logic<br>Β· quantified logic (first monadic, then po