### Ideas from 'Thinking About Logic' by Stephen Read , by Theme Structure

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###### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
 10987 Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism'
###### 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
 11004 Necessity is provability in S4, and true in all worlds in S5
###### 4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
 11018 There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers
###### 4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
 11011 Same say there are positive, negative and neuter free logics
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
 11020 Realisms like the full Comprehension Principle, that all good concepts determine sets
###### 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
 10986 Not all validity is captured in first-order logic
###### 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
 10972 The non-emptiness of the domain is characteristic of classical logic
###### 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
 11024 Semantics must precede proof in higher-order logics, since they are incomplete
###### 5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
 10985 We should exclude second-order logic, precisely because it captures arithmetic
###### 5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
 10970 A theory of logical consequence is a conceptual analysis, and a set of validity techniques
 10984 Logical consequence isn't just a matter of form; it depends on connections like round-square
###### 5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
 10973 A theory is logically closed, which means infinite premisses
###### 5. Theory of Logic / G. Quantification / 1. Quantification
 11007 Quantifiers are second-order predicates
###### 5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
 10978 In second-order logic the higher-order variables range over all the properties of the objects
###### 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
 10971 A logical truth is the conclusion of a valid inference with no premisses
###### 5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
 10988 Any first-order theory of sets is inadequate
###### 5. Theory of Logic / K. Features of Logics / 6. Compactness
 10975 Compactness does not deny that an inference can have infinitely many premisses
 10974 Compactness is when any consequence of infinite propositions is the consequence of a finite subset
 10976 Compactness makes consequence manageable, but restricts expressive power
 10977 Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite)
###### 5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
 11014 Self-reference paradoxes seem to arise only when falsity is involved
###### 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
 11025 Infinite cuts and successors seems to suggest an actual infinity there waiting for us
###### 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
 10980 Second-order arithmetic covers all properties, ensuring categoricity
 10979 Although second-order arithmetic is incomplete, it can fully model normal arithmetic
###### 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
 10997 Von Neumann numbers are helpful, but don't correctly describe numbers
###### 7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as linguistic
 11016 Would a language without vagueness be usable at all?
###### 7. Existence / D. Theories of Reality / 9. Vagueness / f. Supervaluation for vagueness
 11012 A 'supervaluation' gives a proposition consistent truth-value for classical assignments
 11013 Identities and the Indiscernibility of Identicals don't work with supervaluations
 11019 Supervaluations say there is a cut-off somewhere, but at no particular place
###### 9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
 10995 A haecceity is a set of individual properties, essential to each thing
###### 10. Modality / A. Necessity / 2. Nature of Necessity
 11001 Equating necessity with truth in every possible world is the S5 conception of necessity
###### 10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
 11017 Some people even claim that conditionals do not express propositions
 10989 The standard view of conditionals is that they are truth-functional
 10992 The point of conditionals is to show that one will accept modus ponens
###### 10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
 10983 Knowledge of possible worlds is not causal, but is an ontology entailed by semantics
###### 10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
 10982 How can modal Platonists know the truth of a modal proposition?
###### 10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
 10996 Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions)
###### 10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
 10981 A possible world is a determination of the truth-values of all propositions of a domain
###### 10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
 11000 If worlds are concrete, objects can't be present in more than one, and can only have counterparts
###### 15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
 10998 The mind abstracts ways things might be, which are nonetheless real
###### 19. Language / C. Assigning Meanings / 4. Compositionality
 11005 Negative existentials with compositionality make the whole sentence meaningless
###### 19. Language / D. Propositions / 1. Propositions
 10966 A proposition objectifies what a sentence says, as indicative, with secure references