Logic

1. Section 2 Logic

2. Arguments • An argument is an attempt to establish or prove a conclusion on the basis of one or more premises. Example:

3. Arguments • An argument is an attempt to establish or prove a conclusion on the basis of one or more premises. Example: all historians are golfers, and my buddy Ric is an historian, so he must be a golfer.

4. Arguments • To make it easier to distinguish premises and conclusion, an argument can be put in standard form. • All historians are golfers. • Ric Dias is an historian. Therefore: Ric Dias is an historian.

5. Arguments • In standard form, the premises are each assigned a number, and the conclusion is separated by a horizontal line. • All historians are golfers. • Ric Dias is an historian. Therefore: Ric Dias is an historian.

6. Logical Consistency • A set of claims is logically consistent only if it is conceivable that all the claims are true at the same time.

7. Logical Consistency • Logically consistent: • Logically inconsistent

8. Logical Consistency • Logically consistent: • My grandfather lived in Jonesboro. • My grandfather is dead. • Logically inconsistent

9. Logical Consistency • Logically consistent: • My grandfather lived in Jonesboro. • My grandfather is dead. • Logically inconsistent • My grandfather lives in Jonesboro. • My grandfather is dead.

10. Logical Consistency requires careful thinking • Logically Inconsistent • Abortion is wrong because it is wrong to take a human life. • Capital punishment is right because it is a just punishment for murder.

11. Logical Consistency requires careful thinking • Logically Consistent • Abortion is wrong because it is wrong to take an innocent human life. • Capital punishment is right because it is a just punishment for murder.

12. Supplying Missing Premises • All human beings are mammals. • All mammals are warm blooded. Therefore: Socrates is warm blooded.

13. Supplying Missing Premises • Socrates is a human being. • All human beings are mammals. • All mammals are warm blooded. Therefore: Socrates is warm blooded.

14. Logical Possibility vs. Causal Possibility • A state of affairs is causally possible if it does not violate any of the laws of nature.

15. Logical Possibility vs. Causal Possibility • A state of affairs is causally possible if it does not violate any of the laws of nature. • It is causally possible that the Twins will win the World Series this year.

16. Causal Possibility • A state of affairs is causally impossible if it violates any of the laws of nature. • It is causally possible that the Twins will win the World Series this year. • It is not causally possible for Justin Morneau to hit a baseball into outer space (at least, not quite).

17. Logical Possibilty • A statement is logically impossible if it involves a contradiction.

18. Logical Possibilty • A statement is logically impossible if it involves a contradiction. • It is logically possible that George W. Bush lost the popular vote but was elected President.

19. Logical Possibility • A statement is logically impossible if it involves a contradiction. • It is logically possible that George W. Bush lost the popular vote but was elected President. • It is logically impossible that Bush lost the electoral college vote but was elected President.

20. Logical Possibility • Philosophy is primarily concerned so much with conceptual analysis.

21. Logical Possibility • Philosophy is primarily concerned so much with conceptual analysis. • Proving or ruling out logical possibility is almost always more important than causal possibility.

22. Lexical vs. Philosophical definitions. • A lexical definition tells us how a word is frequently used

23. Lexical vs. Philosophical definitions. • A lexical definition tells us how a word is frequently used • Coke = a soft drink; cocaine

24. Lexical vs. Philosophical definitions. • A philosophically rigorous definition attempts to precisely say what something is and isn’t.

25. Lexical vs. Philosophical definitions. • A philosophically rigorous definition attempts to precisely say what something is and isn’t. • A triangle is a closed figure consisting of three line segments linked end-to-end.

26. Necessary & Sufficient Conditions • A condition in this context means anything that is true of something.

27. Necessary & Sufficient Conditions • A condition in this context means anything that is true of something. • So: being alive is a condition of yourself, if indeed you are reading or hearing this.

28. Necessary & Sufficient Conditions • A condition in this context means anything that is true of something. • So: being alive is a condition of yourself, if indeed you are reading or hearing this. • Being a closed figure is a condition of being a triangle.

29. Necessary Conditions • A condition q is necessary for p if it is impossible for something to be p without being q.

30. Necessary & Sufficient Conditions • A condition q is necessary for p if it is impossible for something to be p without being q. • Here p stands for some concept, and q for some condition that has to be true of that concept.

31. Necessary & Sufficient Conditions • A condition q is necessary for p if it is impossible for something to be p without being q. • Example: • Being an animal is a necessary condition for being a mammal.

32. Necessary Conditions • Being an animal is a necessary condition for being a mammal. • It must be an animal (q) if it is a mammal (p).

33. Necessary Conditions • A condition q is necessary for p if it is impossible for something to be p without being q. • Example: • Being an animal is a necessary condition for being a mammal.

34. Necessary Conditions Animals Mammals

35. Necessary Conditions • A condition q is necessary for p if it is impossible for something to be p without being q. • Notice that the converse is not true • Being a mammal is not a necessary condition for being a animal.

36. Necessary Conditions animal fish mammal fox

37. Sufficient Conditions • A condition q is sufficient for p if it is impossible for something to be q without being p.

38. Sufficient Conditions • A condition q is sufficient for p if it is impossible for something to be q without being p. • Here “sufficient” means enough.

39. Sufficient Conditions • A condition q is sufficient for p if it is impossible for something to be q without being p. • Example: • Being a triangle is sufficient for having three angles.

40. Sufficient Conditions • A condition q is sufficient for p if it is impossible for something to be q without being p. • Example: • Being a triangle is sufficient for having three angles. • Being a mammal is a sufficient condition for being an animal.

41. Sufficient Conditions • If you know that q is a triangle, that’s enough to know that q has condition p (it has three angles.

42. Sufficient Conditions • If you know that q is a triangle, that’s enough to know that q has condition p (it has three angles. • So q is a sufficient condition for p.

43. Sufficient Conditions • If you know that q is a triangle, that’s enough to know that q has condition p (it has three angles. • So q is a sufficient condition for p. • If you know that q is a mammal, that’s enough to know that q is an animal. • So again q is a sufficient condition for p.

44. Necessary Conditions fish fox fern

45. Assignment • Work the Rauhut exercises on page 23.

46. Counterexamples • In philosophy, as in science, all useful concepts must be tested.

47. Counterexamples • In philosophy, as in science, all useful concepts must be tested. • One way of testing a definition is by challenging the necessary and sufficient conditions implied in the definition.

48. A Famous Counterexample • Man is a featherless biped.

49. A Famous Counterexample • Man is a featherless biped. • Counter example: then a plucked chicken would be a man.

50. A Common Counterexample • It is wrong to kill a human being when one can avoid it. • One does not have to execute criminals. Therefore: capital punishment is wrong.