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Index
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 reading
2 Language, Form, and Logical Theories
2.1 Language
2.2 Atoms, connectives, and molecules
2.3 Connectives and form
2.4 Validity and form
2.5 Language and formal languages
2.6 Logical theories: rivalry
3 Set-theoretic Tools
3.1 Sets
3.2 Ordered sets: pairs and n -tuples
3.3 Relations
3.4 Functions
3.5 Sets as tools
II BASIC CONNECTIVES
4 Classical Theory
4.1 Cases: complete and consistent
4.2 Classical ‘truth conditions’
4.3 Basic classical consequence
4.4 Motivation: precision
4.5 Formal picture
4.6 Defined connectives
4.7 Some notable valid forms
4.8 Summary and looking ahead
5 A Paracomplete Theory
5.1 Apparent unsettledness
5.2 Cases: incomplete
5.3 Paracomplete truth and falsity conditions
5.4 Paracomplete consequence
5.5 Formal picture
5.6 Defined connectives
5.7 Some notable forms
5.8 Summary and looking ahead
6 A Paraconsistent Theory
6.1 Apparent overdeterminacy
6.2 Cases: inconsistent
6.3 Paraconsistent ‘truth conditions’
6.4 Paraconsistent consequence
6.5 Formal picture
6.6 Defined connectives
6.7 Some notable forms
6.8 Summary and looking ahead
III INNARDS, IDENTITY, AND QUANTIFIERS
7 Atomic Innards
7.1 Atomic innards: names and predicates
7.2 Truth and falsity conditions for atomics
7.3 Cases, domains, and interpretation functions
7.4 Classical, paracomplete and paraconsistent
7.5 A formal picture
7.6 Summary and looking ahead
8 Identity
8.1 Logical expressions and logical form
8.2 Validity involving identity
8.3 Identity: informal sketch
8.4 Truth conditions: informal sketch
8.5 Formal picture
8.6 Summary and looking ahead
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
9.5 Paraconsistent, paracomplete, classical
9.6 Summary and looking ahead
IV FREEDOM, NECESSITY, AND BEYOND
10 Speaking Freely
10.1 Speaking of non-existent ‘things’
10.2 Existential import
10.3 Freeing our terms, expanding our domains
10.4 Truth conditions: an informal sketch
10.5 Formal picture
11 Possibilities
11.1 Possibility and necessity
11.2 Towards truth and falsity conditions
11.3 Cases and consequence
11.4 Formal picture
11.5 Remark on going beyond possibility
12 Glimpsing Different Logical Roads
12.1 Other conditionals
12.2 Other negations
12.3 Other alethic modalities: actuality
12.4 Same connectives, different truth conditions
12.5 Another road to difference: consequence
A List of Common Abbreviations
References
Index
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