Understanding Logic and Reasoning for Critical Thinking

1. Review Logic & Reasoning • Deductive Validity—formal • A form such that true premises always  true conclusions • Informal test—imagine an argument in that form • Core vocabulary: if..then.., and, or, not, all, some, none • True premises & false conclusion • Sound = df valid and all true premises • “Conclusions of sound deductive arguments are true” • Sound deduction from definition premises

2. Other Logics • Inductive—valid when good reasons for the conclusion • Not a guarantee • Analogy, induction on example(s), sampling, science • Inference to the best explanation • Practical syllogism: belief-desire to intention • Needs an “ought” in premises

3. Inconsistent Triad (deductive) • If conclusion false then • Either premise(s) false or invalid • Formal test for validity • Then key to Socratic rational doubt • Doubt one of your premises • Also key to science: hypothetical decuction • Take current theory as hypotheses • Measurements, mathematics • Predict experimental outcome • Outcome falsifiessome hypothesis wrong

4. Socrates and Religion Application • Socrates no experimental method • Needs explicit contradiction—harder • Plato cheats a lot • Limits: reveals error not truth • No method to discover truth • Problem of Evil even looser • Needs formal statement unlike the usual • Believer has many options • Accept evil • Best of all possible worlds: Free will • Limited God • Not creator

5. Theodicy • What is the alternative to no-evil? • God does not exist? • Why does it not prove that? • Theodicy: possible solutions to the problem of evil • Limited god (not perfect/omnipotent) • Free will and necessary evil • Necessary for greater good • Human and divine “good” • Or accept the conclusion • Evil is an illusion

6. Questions? Tutorials sign up Start next week 2 quizzes

7. Back to Socrates: Virtue • Use metaphysics model on ethics • Fundamental reality of ‘virtue’, ‘justice’ • Search for definitions using Socratic method • one (conventions many) • unchanging (vs. mores) • knowable (definitions) • rational (Socratic method) and • Real (!) • Why care about those peculiar facts? • No man knowingly does evil

8. Weakness of Socratic Method • No answers—Socrates the skeptic • Dies ignorant • Famous lament—and student response • At least knows he doesn’t know • 知之為知之不知為不知是知也 • Deeper problem • Many different consistent doctrines • Contradiction not easy to prove • Plato the playwright takes control

9. Socrates and Plato Story • Death by legislature—wrong • Plato’s hatred of democracy • Better for policy and choice of leaders • Not for judgment of guilt • separate judiciary rule of law • Socrates as figure in his dialogues • Development of Socratic method • Classic example in Thrasymachus dialogue

10. Plato's Synthesis: • Parmenides: the real world and ethical ideal blend • Real is rational; rational is real • Focus on search for definitions • Socrates origin and geometry • The idea or concept of a thing • Result is the meaning/value = being • Really that being = meaning • Meaning linked to value, purpose • The concept is the thing’s “reality”

11. Are Definitions Important? • Not to knowing how to speak • Vicious circle • Real life and children learning • Examples: true, cute, way, water • Why such emphasis? • Importance to logical method • Socratic method and validity • Problem of evil example • Can’t test validity w/o form

12. Definitions: Concept Reality • Conform to rationalist presuppositions • One – concrete instances are many • Unchanging – remain; things change • Knowable -- beliefs about objects • Heraclitus and Parmenides • Rational -- Socratic method • Hence real • Idealism • Definitions (meanings:ideas) real • Sensible “things" are not

13. Rules for Definitions Implicit in Plato's Socrates • No lists. What is common to all instances • No vagueness. ‘Strong’? • No circularity (or mere synonyms) • Definition so usable in arguments • No hearsay -- test by expert knowledge • Real v. Nominal definitions • Test by reason. Socratic method

14. Conclusion: The Forms • Forms correspond to definitions (meanings) • Meaning “objects” • Provide unified answer to philo questions • Metaphysics: what is real—objective meaning • Real definitions v. Nominal • Epistemology: what is knowable • Like soul/mind--intellectual • Logic: the thinkable objects • Not laws of thought but semantics • Ethics: no man knowingly does evil • Health of the soul • Definitions of virtues • Objects of striving -- teleological account of change

15. Difficulty: Famous Analogies • Cave: sensible appearance v reality • C.f. taking hallucinatory drugs • Meditation or rational insight • Analogy: shadow/object as object/form • Equal difficulty in getting you to accept them • When you "see" them, you will need no more convincing • The character of the object determines your knowledge

16. Line Analogy: • Links metaphysics and epistemology • Knowability depends on nature of object (Parmenides) • Rival view: true belief plus an account (the modern analysis) • X knows that P =df. • P is true • X believes that P • X has justification for believing that P

18. The Sun Analogy • Rule for identification of forms • Logic: there must be a form of forms • It must be “more real” than the forms • The form of the good: of all value • Form of the truth/beauty/good

19. Mystical Result • Absolute one/being • No reason leading to see it • It would blind us • But necessarily there (or nothing exists)

20. Key Political Doctrines • The Republic a political plan • Justice of political structure like that of individual • Same in everything • Rule of the correct ruler—intellect

21. The Philosopher King • Anti-democratic and manipulative • Education and classes • Social ranks: intellectual, spirited, body-like

22. End of Plato and Greek Rationalism • Ancient Chinese idealism next!