Formal Reasoning
Syllogism - Structure of 2 or more premises which necessarily lead to a conclusion.
- 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.
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)
- Either A or B
- 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.