Logic, Reason and Argument

What the course covers

Logic studies one relation: whether some claims, if true, would force another. The course builds the tools for testing it. First the vocabulary, validity, soundness and form, and the ways ordinary language hides all three. Then the fallacies, which are the patterns that persuade without supporting. Then two formal systems: categorical logic, which is Aristotle’s and still the fastest way to see a syllogism fail, and propositional and predicate logic, which is what a modern paper is set in. Truth tables decide, proofs derive, and models refute. It ends where certainty does, with induction and probability.

What an argument is

1. What an argument is. Reasons offered, not a quarrel.
2. Finding the conclusion. Which claim is being supported.
3. What is not an argument. Explanations, reports, conditionals.
4. Validity. The premises guarantee it, or not.
5. Valid is not true. The four combinations that matter.
6. Soundness. Valid, and the premises are true.
7. Form is everything. Why the content drops out.
8. Forms worth knowing. Five patterns you will reuse.
9. Counterexamples. Same form, true premises, false end.
10. Strength and cogency. Good arguments that are not valid.
11. Reconstructing arguments. Missing premises, fairly supplied.
12. What an argument is review. Everything so far, tested.

Logic and language

13. Saying and suggesting. What a sentence makes you feel.
14. Ambiguity. One sentence, two readings.
15. Vagueness. Borderline cases with no line.
16. Kinds of definition. Five jobs a definition can do.
17. Good and bad definitions. Too broad, too narrow, circular.
18. Definitions in arguments. Winning by fixing the terms.
19. Logic and language review. Words, and the trouble they cause.

Informal fallacies

20. What a fallacy is. Persuades without supporting.
21. Attacking the person. The arguer is not the argument.
22. The straw man. Refuting what nobody said.
23. Appeals to feeling. Fear, pity, and what the crowd says.
24. The red herring. Changing the subject on purpose.
25. Authority and ignorance. Who said it, and what nobody knows.
26. Fallacies of ambiguity. One word quietly doing two jobs.
27. Smuggled assumptions. Assuming what was to be proved.
28. Weak inductive fallacies. Too few cases, and false causes.
29. Informal fallacies review. Naming exactly what went wrong.

Categorical statements

30. The four forms. A, E, I and O, and no more.
31. Quantity and quality. The two dials that make four.
32. Distribution. When a term covers every member.
33. Venn diagrams. Two circles, shading and a bar.
34. The square of opposition. How four forms constrain each other.
35. Existential import. Whether nothing counts as all.
36. Immediate inferences. Conversion, obversion, contraposition.
37. Into standard form. Getting English to behave.
38. Categorical statements review. Four forms and their relations.

Categorical syllogisms

39. Standard form. Major, minor, middle, mood, figure.
40. The Venn test. Three circles settle the question.
41. The rules. Five checks, five named failures.
42. Syllogisms with gaps. Supplying the missing premise.
43. Chains of syllogisms. Several joined end to end.
44. Categorical syllogisms review. Testing a syllogism two ways.

Propositional logic

45. Why symbols. What eyeballing keeps getting wrong.
46. Simple and compound. Atoms, and what joins them.
47. The first three connectives. Not, and, or, with their tables.
48. Two kinds of or. The word logic has to pin down.
49. The conditional. If, and the table nobody likes.
50. The material conditional. Where the table stops matching.
51. The biconditional. If and only if, both ways.
52. Scope and grouping. Brackets, and what is in charge.
53. Other notations. The symbols your textbook uses.
54. Building a truth table. Rows, columns and discipline.
55. Three verdicts. Always, never, or sometimes true.
56. Logical equivalence. Same column, same meaning.
57. Testing arguments. Hunting for the one bad row.
58. The short way. Assume invalid, then try to build it.
59. Propositional logic review. Symbols, tables and verdicts.

Proofs

60. Why proofs. Sixteen rows is fine, a thousand is not.
61. Modus ponens and tollens. The two rules about conditionals.
62. Chaining and eliminating. Hypothetical and disjunctive syllogism.
63. Four more rules. Splitting, joining, weakening, choosing.
64. Rules apply to whole lines. The mistake everybody makes once.
65. Finding the proof. Work backwards from the conclusion.
66. Equivalence rules. Five ways to rewrite a formula.
67. Five more equivalences. Implication, exportation and the rest.
68. Conditional proof. Assume, derive, then discharge.
69. Reductio ad absurdum. Assume the opposite and break it.
70. Proofs review. Rules, strategy and assumptions.

Predicate logic

71. Why letters are not enough. The argument tables cannot touch.
72. Names and predicates. Looking inside a statement.
73. The universal quantifier. All, and why it takes an arrow.
74. The existential quantifier. Some, and why it takes an and.
75. Two standard mistakes. The wrong connective, every time.
76. The four forms again. A, E, I and O, symbolised.
77. Scope and binding. Free variables and bound ones.
78. Relations. Predicates with two places.
79. Order matters. Everyone loves someone, two ways.
80. Interpretations. Building a world to break it.
81. Quantifier rules. Stripping and restoring quantifiers.
82. Identity and descriptions. Only, at most one, and the.
83. Predicate logic review. Quantifiers, models and identity.

Inductive reasoning

84. Strength, not validity. Support that comes in degrees.
85. Statistical syllogism. From most of them to this one.
86. Generalisation. From this sample to all of them.
87. Argument from analogy. Alike here, so alike there.
88. Correlation and cause. Four things a correlation can mean.
89. Mill’s methods. Five ways to isolate a cause.
90. Best explanation. The hypothesis that would explain it.
91. Inductive reasoning review. Evidence that does not compel.

Probability

92. What probability is. Three ways to read a number.
93. The axioms. Between nought and one, always.
94. And. Multiplying, and when you cannot.
95. Or. Adding, minus the overlap.
96. Conditional probability. Given that, what are the odds.
97. Bayes theorem. Updating a belief on evidence.
98. Base rates. Why the accurate test misleads.
99. Probability fallacies. Conjunction, gambler and the rest.
100. Expected value. What a bet is actually worth.
101. Probability review. Rules, updating and traps.

One lesson in full

Valid is not true. The four combinations that matter.

A question to try

All university philosophy courses