Topics

This is a running list of the course topics—the chunks of presentation and discussion you will want to make sure you have notes on. Make sure, after we’ve covered each topic, you can say something about what it involves. The list might be subject to small changes as we go along, but it probably captures almost exactly our plan for the semester. The topics we cover during each class session will be listed on the main schedule.

  1. What is symbolic logic?
  2. Early logics
  3. Syllogistic/Aristotelian arguments
  4. Axiomatization and formal systems
  5. Arguments and sentences
  6. Truth value
  7. Logical consequence and validity
  8. Cases and possibility
  9. Deductive and inductive reasoning
  10. Sound arguments
  11. Joint possibility (“consistency”)
  12. Necessary truth, necessary falsehood, and contingency
  13. Necessary equivalence
  14. Atomic sentences
  15. Symbolization keys
  16. Negation
  17. Conjunction
  18. Disjunction
  19. Characteristic truth tables
  20. Conditional
  21. Biconditional
  22. Unless
  23. Non-truth-functional connectives
  24. Sentences of TFL
  25. Bracketing conventions
  26. Use/mention
  27. Constructing truth tables
  28. Using truth tables to assess logical properties of sentences
  29. Using truth tables to assess logical properties of sets of sentences
  30. Using truth tables to assess whether arguments are valid/invalid
  31. Natural deduction
  32. The structure of natural deduction proofs
  33. TFL inference rules: reiteration, conjunction introduction, conjunction elimination
  34. TFL inference rules: conditional elimination, conditional introduction
  35. Additional assumptions and subproofs
  36. TFL inference rules: biconditional elimination, biconditional introduction
  37. TFL inference rules: disjunction introduction, disjunction elimination
  38. Reductio ad absurdum
  39. TFL inference rules: negation introduction, negation elimination, indirect proof, explosion
  40. TFL derived inference rules: modus tollens, disjunctive syllogism, double negation elimination, DeMorgan rules
  41. Names and predicates
  42. Quantifiers and variables
  43. Existential quantification
  44. Universal quantification
  45. The scope of quantifiers
  46. Typical constructions for sentences in FOL
  47. Relations and multi-place predicates
  48. Overlapping quantifiers
  49. Symbolizing arguments in FOL
  50. FOL natural deduction rules: universal elimination
  51. FOL natural deduction rules: existential introduction
  52. FOL natural deduction rules: universal introduction
  53. FOL natural deduction rules: existential elimination
  54. FOL natural deduction rules: convert quantifier
  55. Natural deduction with overlapping quantifiers
  56. Identity, maybe?
  57. Logic beyond this course