An Introduction to Formal Logic: Chapters 1-7
Smith (Peter)
Source: Smith (Peter) - An Introduction to Formal Logic
Paper - Abstract

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Contents

  1. What is deductive logic? 1
    → 1.1 What is an argument? – 1
    → 1.2 Kinds of evaluation – 1
    → 1.3 Deduction vs. induction – 2
    → 1.4 Just a few more examples – 4
    → 1.5 Generalizing – 5
    → 1.6 Summary – 7
    → Exercises 1 – 7
  2. Validity and soundness – 9
    → 2.1 Validity defined again – 9
    → 2.2 Consistency, validity, and equivalence – 11
    → 2.3 Validity, truth, and the invalidity principle – 12
    → 2.4 Inferences and arguments – 14
    → 2.5 ‘Valid’ vs ‘true’ – 15
    → 2.6 What’s the use of deduction? 15
    → 2.7 An illuminating circle? – 17
    → 2.8 Summary – 18
    → Exercises 2 – 18
  3. Forms of inference – 20
    → 3.1 More forms of inference – 20
    → 3.2 Four simple points about the use of schemas – 22
    → 3.3 Arguments can instantiate many patterns – 24
    → 3.4 Summary – 26
    → Exercises 3 – 26
  4. Proofs – 27
    → 4.1 Proofs: first examples – 27
    → 4.2 Fully annotated proofs – 28
    → 4.3 Glimpsing an ideal – 30
    → 4.4 Deductively cogent multi-step arguments – 31
    → 4.5 Indirect arguments – 33
    → 4.6 Summary – 35
    → Exercises 4 – 36
  5. The counterexample method – 37
    → 5.1 ‘But you might as well argue . . . ’ – 37
    → 5.2 The counterexample method, more carefully – 38
    → 5.3 A ‘quantifier shift’ fallacy – 39
    → 5.4 Summary – 41
    → Exercises 5 – 41
  6. Logical validity – 42
    → 6.1 Topic neutrality – 42
    → 6.2 Logical validity, at last – 43
    → 6.3 Logical necessity – 44
    → 6.4 The boundaries of logical validity? 45
    → 6.5 Definitions of validity as rational reconstructions – 46
    → 6.6 Summary – 48
    → Exercises 6 – 48
  7. Propositions and forms – 49
    → 7.1 A definition: Fregean sense – 49
    → 7.2 A distinction: types vs tokens – 49
    → 7.3 A distinction: propositions vs assertions – 50
    → 7.4 Propositions as sentences, naively – 51
    → 7.5 Propositions as truth-relevant contents – 52
    → 7.6 Why we can be indecisive – 52
    → 7.7 Forms of inference again – 53
    → 7.8 Summary – 55
    → Interlude: From informal to formal logic – 56

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2018
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



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