The Art of Argumentation

Formal Reasoning

  • Deductive by nature
  • Conclusion follows necessarily from premises; if premises are true then conclusion must be true.
  • Conclusion contains no new information, the conclusion is at least implicit in the premises.
  • Analytic in nature - Requires no external 'real-world' reference. Can be completely symbolic.
  • Can be counterfactual (a sound deductive argument, sound meaning the inferences are strong, does not require premises to be true.)
  • Does not add anything to our store of knowledge.
Types of Formal Logic




Syllogism - Structure of 2 or more premises which necessarily lead to a conclusion.
  • Categorical - Categorical statements
    • Universal - All or none (All A are B; No A are B)
    • Partial - Some (Some A are B)
    • Inclusive - Some or all added to another (All A are B; Some A are B)
    • Exclusive - Some or all excluded from another (All A are not B, Some A are not B)
    • Venn Diagrams used to represent categorical Syllogisms
  • Conditional - If/Then clauses. If A then B.
    • 'If Clause' - Antecedent
    • 'Then Clause' - Consequent
    • Affirm or deny one of the two clauses
    • Cannot conclude consequent based on denied antecedent
      • If A then B; not A; cannot conclude not B. (Example: If <Antecedent - I burn this $5 bill> then <Consequent - I will be $5 poorer>; I did not burn the $5 bill. However, I cannot conclude that I am not $5 poorer based solely on the antecedent alone.)
    • Cannot conclude antecedent based on affirming the consequent.
      • If A then B; B; cannot conclude A. (Example: If <Antecedent - I cut my hair> then <Consequent - my hair will be shorter>; My hair is shorter. However, I cannot confirm that I cut my hair based solely on the consequent. Something else may have happened to cause my hair to be shorter.
    • Can only determine validity of one claues based on affirming the antecedent (if A then B; A; So B) or denying the consequent (If A then B; not B; so not A).
  • Disjunctive (Also known as Alternative) 'Either or'
    • Either A or B
      • Not A; therefore B
      • Not B; therefore A
      • What about both?
    • Inclusive Disjunctive - A, B, or Both (Example: You can do A or B, or both if you have time.)
    • Exclusive Disjunctive - Only A or only B; not both. (Example: You only have enough time to perform A or B but not both)
Challenges to Formal Logic

  • Rarely is everyday reasoning performed in syllogistic form.
  • Common reasoning typically deals with specific entities, things that are common in nature.
  • It is important to know matters of degree, not just A or B, what about a superposition between the two?
  • Most reasoning is not represented well when conclusion doesn't contain new information.
  • Reasoning is used to go from something currently known to something not currently known.
  • A leap of faith, or inference is required which deductive reasoning does not account for.
  • Formal reasoning is a specialized subset of reasoning and is not the comprehensive model for all reasoning.
 
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