Introductory Logic PHI 120

1. Presentation: "Natural Deduction – Introduction“ Introductory LogicPHI 120 Bring this book to lecture

2. Homework • Handout • The Rules • Homework First step in learning the rules: • Elimination Rules • What are they? (Literally, can you name them?) • Why are they called "elimination" rules? • Introduction Rules • What are they? (Literally, can you name them?) • Why are they called "introduction rules? Second step in learning the rules: • pp. 19-26 • “primitive rules” • “elimination” and “introduction” rules (only) Important: bring to every class!! Start learning these rules of deduction

3. Homework Exam 1 Being graded by your TA Will be handed back in your section (In lecture, we’re pressing on)

4. New Unit Logical Proofs “Natural Deduction” How it works Worthwhile to turn to page 40.

5. & (ampersand)

6. Simple Valid Argument Forms &E (ampersand elimination)

7. Simple Valid Argument Forms Let’s presume the conjunction is true

8. Simple Valid Argument Forms

9. Simple Valid Argument Forms &E Ampersand-Elimination Given a sentence that is a conjunction, conclude either conjunct

10. Simple Valid Argument Forms &I (ampersand introduction)

11. Simple Valid Argument Forms Let’s presume the two sentences are true

12. Simple Valid Argument Forms

13. Simple Valid Argument Forms &I Ampersand-Introduction Given two sentences, conclude a conjunction of them.

14. v (wedge)

15. Simple Valid Argument Forms vE (wedge elimination) Let’s presume the two sentences are true

16. Simple Valid Argument Forms

17. Simple Valid Argument Forms

18. Simple Valid Argument Forms

19. Simple Valid Argument Forms vE Wedge-Elimination Given a disjunction and another sentence that is the denial of one of its disjuncts, conclude the other disjunct

20. Simple Valid Argument Forms vI (wedge introduction) Let’s presume this premise is true

21. Simple Valid Argument Forms Let’s presume this premise is true

22. Simple Valid Argument Forms

23. Simple Valid Argument Forms vI Wedge-Introduction Given a sentence, conclude any disjunction having it as a disjunct.

24. -> (arrow)

25. Simple Valid Argument Forms ->E (arrow elimination) Let’s presume the two sentences are true

26. Simple Valid Argument Forms

27. Simple Valid Argument Forms

28. Simple Valid Argument Forms ->E Arrow-Elimination Given a conditional and its antecedent, conclude the consequent.

29. Simple Valid Argument Forms ->I (arrow introduction) Let’s presume this premise is true

30. Simple Valid Argument Forms

31. Simple Valid Argument Forms

32. Simple Valid Argument Forms ->I Arrow-Introduction Given any sentence, conclude a conditional with it as the consequent.

33. <-> (double-arrow)

34. Simple Valid Argument Forms <->E (double-arrow elimination)

35. Simple Valid Argument Forms Let’s presume the biconditional is true

36. Simple Valid Argument Forms

37. Simple Valid Argument Forms Antecedent Consequent

38. Simple Valid Argument Forms Antecedent Consequent

39. Simple Valid Argument Forms Antecedent Consequent

40. Simple Valid Argument Forms Antecedent Consequent <->E Double-Arrow Elimination Given a biconditional, conclude one or the other arrow statements

41. Simple Valid Argument Forms Let’s presume these premises are true <->I (double-arrow introduction)

42. Simple Valid Argument Forms

43. Simple Valid Argument Forms

44. Simple Valid Argument Forms

45. Simple Valid Argument Forms

46. Simple Valid Argument Forms

47. Simple Valid Argument Forms

48. Simple Valid Argument Forms 2 conditions

49. Simple Valid Argument Forms 2 conditions <->I Double-Arrow Introduction Given two mirror conditionals, conclude the biconditional

50. Elimination Introduction &Eampersand elimination vEwedge elimination ->Earrow elimination <->Edouble-arrow elimination &Iampersand introduction vIwedge introduction ->Iarrow introduction <->Idouble-arrow introduction Rules of Derivation