Workbook on Arguments

Link to book

  • Ch1: Short arguments
    • Rule 1: Identify premise and conclusion
    • Rule 2: Develop you ideas in a natural order
    • Rule 3: Start from a reliable premise
    • Rule 4: Be concrete and concise
    • Rule 5: Build on substance, not overtone
    • Rule 6: Use consistent terms
  • Ch 2: Generalizations
    • Rule 7: Use more than one example
    • Rule 8: Use representative examples
    • Rule 9: Background rates may be critical
    • Rule 10: Statistics needs a critical eye
    • Rule 11: Consider counterexample
  • Ch 3: Arguments by analogy
    • Rule 12: Analogies require
  • Ch 4: Sources
    • Rule 13: Cite your sources
    • Rule 14: Seek informed sources
    • Rule 15: Seek impartial sources
    • Rule 16: Cross-check sources
    • Rule 17: Use the web with care
  • Ch 5: Causes
    • Rule 18: Causal arguments start with correlations
    • Rule 19: Correlations may have alternate explanations
    • Rule 20: Work towards the most likely explanations
    • Rule 21: Expect complexity
  • Ch 6: Deductive arguments
    • Rule 22: Modus poneus
    • Rule 23: Modus tollens
    • Rule 24: Hypothetical syllogims
    • Rule 25: Disjunctive syllogims
    • Rule 26: Dillemma
    • Rule 27: Reductio ad absurdum
    • Rule 28: Deductive arguments in several steps
  • Ch 7: Extended arguments
    • Rule 29: Explore the issue
    • Rule 30: Spell out the basic arguments
    • Rule 31: Defend basic premises with arguments of their own
    • Rule 32: Consider objections
    • Rule 33: Consider alternatives
  • Ch 8: Essays
    • Rule 34: Jump right in
    • Rule 35: Make a definite claim or proposal
    • Rule 36: Your argument is your outline
    • Rule 37: Detail objections and meet them
    • Rule 38: Use your feedback
    • Rule 39: Modesty
  • Ch 9: Oral arguments
    • Rule 40: Reach out to your audience
    • Rule 41: Be fully present
    • Rule 42: Signpost your argument
    • Rule 43: Offer something positive
    • Rule 44: Use visual aids sparingly
    • Rule 45: End in style
  • Ch 10: Falacies
  • Ch 11: Definations
    • Rule D1: When terms are unclear, get specific
    • Rule D2: When terms are contested, work from the clear case
    • Rule D3: Definitions don’t replace arguments

Logic 101

Link to course Link to playlist

Operations

  • Negation: ~
  • OR/Disjunction (inclusive): v
  • XOR (exclusive):
  • AND/Conjunction: ^
  • Conditional: P=>Q; P is the antecedent, Q is the consequent
  • Bi-conditional (if and only if): P<=>Q; P is the antecedent, Q is the consequent

Truth Tables

Replacement Rules

Used to replace one expression with another.

  • Double Negation: P <=> ~~P
  • Material Implication: P=>Q <=> ~PvQ
    • Helps convert conditionals to disjunctions
  • Contraposition: P=>Q <=> ~Q=>~P
    • Helps convert conditionals to conditionals
  • De Morgan’s Law: ~(P^Q) <=> ~Pv~Q
    • Helps convert conjunctions to disjunctions
  • Associativity:
    • with conjunction: (P^Q)^R <=> P^(Q^R)
    • with disjunction: (PvQ)vR <=> Pv(QvR)
  • Commutativity
  • Distribution
    • with conjunction: P^(QvR) <=> (P^Q)v(P^R)
    • with disjunction: Pv(Q^R) <=> (PvQ)^(PvR)
  • Idempotence
    • with conjunction: P^P <=> P
    • with disjunction: PvP <=> P

Rules of Inference

Help us draw conclusions from premises

  • Modus Ponens:
    1. P=>Q
    2. P
    3. therefore Q
  • Modus Tollens:
    1. P=>Q
    2. ~Q
    3. therefore ~P
  • Disjunctive Syllogism:
    1. PvQ
    2. ~P
    3. therefore Q
  • Hypothetical Syllogism:
    1. P=>Q
    2. Q=>R
    3. therefore P=>R
  • Dilemma:
    • Constructive:
      1. P=>Q
      2. R=>S
      3. PvR
      4. therefore QvS
    • Destructive:
      1. P=>Q
      2. R=>S
      3. ~Qv~S
      4. therefore ~Pv~R
  • Conjuction introduction
    1. P
    2. Q
    3. therefore P^Q
  • Simplification
    1. P^Q
    2. therefore P
  • Biconditional:
    • Biconditional elimination
      1. P<=>Q
      2. therefore P=>Q and therefore Q=>P
    • Biconditional introduction
      1. P=>Q
      2. Q=>P
      3. therefore P<=>Q
  • Disjuction introduction
    1. P
    2. therefore PvQ

Proofs

  • Styles:
    • Proof by contradiction
    • Conditional proofs
    • Tautologies
    • Nested Proofs
    • Biconditional tautologies
  • Proof strategy:
    1. DeMorgan’s Everything
    2. Working backwards
    3. Proof by cases

Fallacies

  • Affirming the consequent
  • Denying the antecedent