1. What makes a Good Argument?

2. Two Characteristics of Good Arguments
1. The premises are true
2. The argument has proper form

3. True Premises
The premises are true when what they say about the world is accurate

4. Proper Form
There is a relationship or connection between the premises and conclusion that make you believe the conclusion is true

5. Deductive Argument
You go from a general principle to a specific example It gives necessity

6. All men are mortal
Socrates is a man
Therefore
(3) Socrates is mortal

7. If all the members of the class of things called MEN have a particular characteristic called MORTALITY And Socrates is a member of that class called MEN Then Socrates MUST have that characteristic called MORTALITY

8. Why? Because we have established a necessary / logical connection between the premises and the conclusion Such that if the premises are true then the conclusion must be true

9. Examples All men are mortal (1) All A has B
Socrates is a man (2) C is A
There: Therefore
(3) Socrates is mortal (3) C has B

10. Valid Deductive Argument
The conclusion follows necessarily from the premises

11. Example All men have brown hair Socrates is a man Therefore
(3) Socrates has brown hair
Is this Valid?
YES!

12. Proper Form Test
Book says that if we assume the premises are true This will help us determine if the argument passes the proper form test This true only for Valid Deductive Arguments Not true for Sound Deductive Argument

13. Sound Deductive Argument
Valid argument with true premises

14. All roses are plants (1) All A’s are B’s
All roses have thorns (2) All A’s are C’s
Therefore Therefore
(3) All plants have thorns (3) All B’s are C’s

15. Improper Form
If all the members of the class of things called ROSES have the characteristic of being PLANTS And if all the members of the class of things called ROSES have the characteristic of having THORNS Then is it necessary that all plants have thorns?

16. No! Why? Because the premises only establish a necessary connection between Roses and Plants Roses and Thorns But not between Plants and Thorns

17. Proper Form
Must establish a necessary connection between the premises and the conclusion

18. Exercises 2.1
Break up into groups
A 1-10

19. 2.1A #1
Oxygen is an element essential for life on Earth as we know it,
Therefore,
(2) If oxygen were to vanish from the Earth’s atmosphere, life as we know it would cease.

20. 2.1A #1
I. Passes both tests.

21. 2.1A #2 All birds can fly. Penguins are birds. Therefore,
(3) Penguins can fly.

22. 2.1A #2
Premise 1 is false, so argument does not pass TP test. If both premises were true, the conclusion would follow, so the argument does pass the PF test. It’s a valid argument.

23. 2.1A #3 All cars are blue. All pigs have wings. Therefore,
(3) All buses have three wheels.

24. 2.1A #3
Fails both tests. Premises are false and irrelevant to conclusion.

25. 2.1A #4 Elephants are mammals. Dogs are mammals. Therefore,
(3) Elephants are dogs.

26. 2.1A #4
Passes TP test This is an invalid deductive argument so it fails the PF test.

27. Elephants are mammals. (1) E = M
Dogs are mammals. (2) D = M
Therefore,
(3) Elephants are dogs. (3) E = D

28. 2.1A #5
(l) Many types of plastic can be recycled. (2) Many types of glass can be recycled. Therefore, (3) Many types of paper can be recycled.

29. 2.1A #5
Argument passes TP test because both premises are true. But it does not pass the PF Inductive argument because of “many” not “all”

30. 2.1A #6 Julia Roberts is either a man or a woman.
Julia Roberts is a man.
Therefore
(3) Julia Roberts isn’t a woman.

31. 2.1A #6
Fails the TP test because premise 2 is false. Passes the PF Test Disjunctive syllogism

32. 2.1A #7 Everyone likes pizza.
Everyone who likes pizza buys it regularly.
Therefore,
(3) Pizza sales will rise over the next six months

33. 2.1A #7
Don’t know about TP (empirical question) Fails PF because if everyone was already buying pizza regularly. Why should sales increase? Wouldn’t they stay the same?

34. 2.1A #8
(1) If you drop wood into water, it floats unless it’s held underwater by a heavy object. (2)Trees are made of wood. Therefore, (3) When trees fall into water, they float unless they’re held underwater by a heavy object.

35. 2.1A #8
Passes both tests.

36. 2.1A #9 The discovery of antibiotics increased life expectancy.
Antibiotics have no effect on viruses,
Therefore,
(3) There must be some causes of reduced life expectancy besides viruses.

37. 2.1A #9
The argument passes the TP test, but the argument does not pass PF test, as stated. Hidden Premises? (viruses reduce life expectancy)

38. 2.1A #10 All cars have three wheels.
Everything with three wheels is blue
Therefore,
(3) All cars are blue.

39. 2.1A #10
The argument fails the TP test because both premises are false. IF they were true, they would prove the conclusion, so this argument passes the PF test. It is a valid (unsound) deductive argument.

40. Audience
The audience of the argument is the group that the person making the argument wants to convince

41. Exercises 2.2
Do as class

42. The Problem of Ignorance
The problem of ignorance is that we don’t know everything

43. Proper Form
If the premises were true, they would provide support for the conclusion
It expresses a relationship between the premises and the conclusion

44. Logical Relationships
In proper form arguments
We are looking for logical relationships
Based upon the premises
What can we determine about the conclusion?

45. All men are mortal
Socrates is a man
Therefore
(3) Socrates is mortal (TP and PF: Sound)
Relationship:
If all members of the class of men have a certain characteristic: mortality
Then all the members of that class MUST also have that characteristic: mortality

46. Valid, but not Sound All men have brown hair Socrates is a man
Therefore
(3) Socrates has brown hair (FP and PF: Valid)
Conclusion follows necessarily from the premises, but premises are NOT TRUE

47. Groups (Fails PT Test) All G1 are G2 (1) All roses are plants
All G1 are G3 (2) All rose have thorns
Therefore
(3) All G2 are G3 Therefore
(3) All plants have thorns

48. Exercise 2.4
Break up into groups
A1-5

49. 2.4A #1 All dogs are mammals All mammals are things with hair
Therefore,
(3) All dogs are things with hair
Form B

50. 2.4A #2 If that’s a car, then I’m a donkey. (2) I’m a donkey.
Therefore,
(3) That’s a car.
Form D
Invalid Modus Ponens

51. 2.4A #3 All children are humans. All humans are mammals Therefore,
(3) All children are mammals.
Form B 
Sound Deductive

52. 2.4A #4 All men are humans All men are under eighteen years of age
Therefore,
(3) All women are under eighteen years of age
Other Form
Not Valid

53. 2.4A #5 If you throw a match on that gas, it will burn.
You will throw a match on that gas.
Therefore
(3) It will burn
Form C
Valid Modus Ponens

54. Deductive Arguments
Claim that the truth of the premises show that the conclusion must be true
Go from a general principle to a specific example
Gives necessity

55. Valid and Sound Deductive Arguments
Valid = Conclusion follows necessarily from the premises
Sound = Validity + true premises

56. If, Then Statements
If A (antecedent), then B (consequent)
A ) B

57. Modus Ponens (MP) Affirm the Antecedent (1) If A, then B (2) We have A
Therefore
(3) We can affirm B

58. Correct Form Example Affirm the Antecedent
(1) If Mary is a mother (A), then she must be a woman (B)
(2) Mary is a mother (A)
(3) Therefore, she must be a woman (B)

59. Incorrect Form Example: Affirm the Consequent
(1) If Mary is a mother (A), then she must be a woman (B)
(2) Mary is a woman (B)
(3) Therefore, she must be a mother (A)

60. You must learn the FORM
1. If it rains tomorrow (A), then I will bring my umbrella (B)
2. I brought my umbrella (B)
3. Therefore what?

61. Correct Form
1. If it rains tomorrow (A), then I will bring my umbrella (B)
2. It rained (A)
3. Therefore?

62. Modus Tollens (MT) Deny the Consequent (1) If A, then B
(2) We do not have B
Therefore
(3) We do not have A

63. Correct Form Example Deny the Consequent
(1) If Mary is a mother (A), then she must be a woman (B)
(2) Mary is not a woman (-B)
(3) Therefore, she must not be a
mother (-A)

64. Incorrect Form Example Deny the Antecedent
(1) If Mary is a mother (A), then she must be a woman (B)
(2) Mary is a not mother (-A)
(3) Therefore, she must not be a
woman (-B)

65. Disjunctive Syllogism (DS)
Deny the Disjunct
Either A or B Either A or B
Not A Not B
Therefore B Therefore A

66. Reductio ad Absurdem (RAA)
Reduce to an absurdity
Reduce to a contradiction

67. Example A = Absolute Truth SA = Statement that are Absolutely True
(1) You have said there are no absolute truth [-A]
(2) But if there is no absolute truth, then no one ever makes a statement that is absolutely true [-A ) -SA]
(3) But you have claimed to state an absolute truth [SA]
(4) Therefore, your statement that there is no absolute truth is not true because it leads to a logical contradiction [-SA and SA]

68. From Specific Examples to
Inductive Arguments
From Specific Examples to
General Principle
Gives Probability

69. Example There are trees on Island 1 (2) There are trees on Island 2
________________________
(4) All Islands have trees

70. Weak vs. Strong Inductive Arguments
The more examples / evidence, the stronger the argument
1,000,000,000 Islands have trees
Therefore all Island have trees

71. GM Example Why use induction? Sometimes we have to
Defective rate of cars!

72. GM Example Why use induction? Sometimes we have to
Defective rate of cars!

73. Strong and Weak Inductive Arguments
Strong Inductive Arguments have many examples (Cogent)
Weak Inductive Arguments have few examples

74. Exercise 2.5
Break up into groups
A 1-10

75. 2.5A #1 If that is a cow, then I am a goat It is a cow Therefore
Deductive and Valid Modus Ponens

76. 2.5A #2
(1)I called Joi and she said she was at the library Therefore, (2) She is probably at the library Inductive

77. (1) The syllabus says that you need to cite three sources
(2) You only cite one source
Therefore,
(3) You won’t get the grade you want.
Deductive and valid.

78. 2.5A #4 Francis had pepperoni and mushroom Therefore,
(2) Francis had pepperoni on her pizza
Deductive and valid.

79. 2.5A #5
Not an argument

80. 2.5A #6 Bret is either in class or in the rec center
Bret is not in class
Therefore,
(3) Bret is in the rec center
Deductive and valid.
Disjunctive Syllogism

81. 2.5A #7
Not an argument. Instructions.

82. 2.5A #8 My son started talking when he was two Therefore,
(2) All children start speaking at two
Inductive and weak because the author only
has one case.

83. 2.5A #9 All human beings are mortal Socrates was a human being
Therefore,
(3) Socrates was mortal 
Deductive and sound

84. 2.5A #10
Not an argument. There are two statements here that would make good premises, but no conclusion is drawn.

85. Quick Review Proper Form Inductive Deductive Weak / Strong
Valid Cogent
Sound
Modus Ponens
Modus Tollens
Disjunctive Syllogism