Chapter 8
Formal Fallacies and Fallacies of Language
This chapter covers formal fallacies, fallacies of language, and three fallacies encountered in
numerical calculations.
A formal fallacy results from failure of form. “Form” is determined by such words as “all,”
“no,” “some,” “not,” “and,” “or,” “if/then,” etc.
We suppose the trick to explaining the common formal fallacies, affirming the consequent,
denying the antecedent, and the undistributed middle fallacy, isn’t to define them (though we
felt obliged to do so in this chapter), but to present examples that are clearly seen as invalid.
For example, “if the dog is pregnant, then it is a female; it isn’t pregnant; therefore it isn’t a
female.”
Equivocation and amphiboly we treat simply as arguments that depend on something’s
being given more than one meaning, the former referring to cases of semantic ambiguity
and the latter to cases of syntactic ambiguity.
The fallacy of composition is the mistake of assuming that what is true of a group of things
taken individually is also true of them taken as a collection; and the mistake of assuming
that what is true of the parts of a thing must be true of the whole thing. When the reverse
assumption is made, the result is the fallacy of division.
Confusing explanations with excuses happens when something that perhaps has been offered
only to explain the cause of something is assumed to have been offered to excuse or justify
it.
Confusing contraries and contradictories happens when we fail to notice that two conflicting
ideas may be contraries rather than contradictories.
Two events are independent, when one event’s happening doesn’t affect the probability of
the second event’s happening. The probability of two independent events’ happening is
obtained by multiplying the probability of each. When we combine the probabilities of
independent events in some other way, such as by adding them, we commit a fallacy.
The gambler’s fallacy happens if we think one event affects the probability of another event
when the two events are in fact independent.
The fallacy, overlooking false positives, seems common. That many dollar bills in Charles’s
wallet have traces of cocaine on them doesn’t prove much if most dollar bills in circulation
have cocaine on them. That most heroin users once used marijuana doesn’t show that
marijuana is a gateway to heroin if most marijuana users don’t take up heroin.
,Somewhat less common is the fallacy overlooking prior probabilities. We define the prior
probability of an attribute in a population as the actual or true proportion of things in the
population with that attribute. The fact you have tested positive for an undesirable medical
condition may not be cause for much concern if the prior probability of that condition is
low. Hal may have a better chance of becoming a professional baseball player than Bill has
of becoming a professional rugby player not because Hall is better at his sport but simply
because the prior probability of becoming a professional baseball player is higher than
becoming a professional rugby player.
Answers to Exercise 9-4 [Note: in the text, items 1, 5, 10, 15, etc. are ▲ exercises.]
1. Equivocation
2. Undistributed middle
3. Affirming the consequent
4. Miscalculating probabilities
5. Composition
6. Division
7. Equivocation
8. Yes, we think so.
9. Denying the antecedent
10. Affirming the consequent
11. Miscalculating probabilities [gambler’s fallacy]
12. Composition
13. Composition
14. Division
15. Undistributed middle
16. Denying the antecedent
17. Denying the antecedent
18. Affirming the consequent
19. Miscalculating probabilities [gambler’s fallacy]
20. Composition
21. Composition
22. Division
23. Equivocation
24. Yes, we think so.
25. Undistributed middle
26. Denying the antecedent
27. Affirming the consequent
28. Miscalculating probabilities
29. Composition
30. Division
31. Equivocation
,32. Yes, we think so.
33. Equivocation
34. Undistributed middle
35. Denying the antecedent
36. Excuse/justification
37. Overlooking prior probabilities
38. No
39. Composition
40. Division
41. Equivocation
42. Yes, we think so.
43. Undistributed middle
44. Denying the antecedent
45. Undistributed middle [The Answers in the text have this one wrong. Sorry.]
46. Overlooking false positives
47. Miscalculating probabilities
48. Composition
49. Equivocation
50. Yes, it is.
51. Yes, it is.
52. Undistributed middle
53. Denying the antecedent
54. Affirming the consequent
55. Denying the antecedent
56. Denying the antecedent
57. Gambler’s fallacy
58. Confusing explanations with excuses
59. Equivocation
60. Division
61. Equivocation
62. Possibly not
63. Equivocation
64. Undistributed middle
65. Undistributed middle [This would be better than answer in Answer Section]
66. Yes, clearly
67. Composition
68. Division
69. Equivocation
70. Overlooking false positives
71. Equivocation
72. Undistributed middle
73. Affirming the consequent
74. Overlooking false positives and prior probabilities
, 75. Not necessarily
76. Division
77. Equivocation (amphiboly)
78. Equivocation
79. Undistributed middle
80. Affirming the consequent
81. Overlooking false positives
82. Confusing explanations with excuses
83. Composition
84. Equivocation
85. Equivocation
86. Undistributed middle
87. Denying the antecedent
88. Miscalculating probabilities [gambler’s fallacy]
89. Composition
90. Miscalculating probabilities
91. Affirming the consequent
92. Confusing explanations with excuses
93. Equivocation
94. Undistributed middle
95. Affirming the consequent
96. Miscalculating probabilities
97. Miscalculating probabilities
98. Composition
99. Division
100. Equivocation
101. No, not clearly
102. Affirming the consequent
103. Denying the antecedent
104. Miscalculating probabilities
105. Division
106. Equivocation
107. Miscalculating probabilities
Chapter 1
What is Critical Thinking, Anyway?
This is a book in “critical thinking” because it is a book about critiquing thinking. Critical
thinking thus (as presented in this book) happens when you evaluate thinking by the
criteria of good reasoning—the criteria of logic and good sense that reasoning adheres to if
it is to be taken seriously by rational individuals. If successful, the book will help readers
Formal Fallacies and Fallacies of Language
This chapter covers formal fallacies, fallacies of language, and three fallacies encountered in
numerical calculations.
A formal fallacy results from failure of form. “Form” is determined by such words as “all,”
“no,” “some,” “not,” “and,” “or,” “if/then,” etc.
We suppose the trick to explaining the common formal fallacies, affirming the consequent,
denying the antecedent, and the undistributed middle fallacy, isn’t to define them (though we
felt obliged to do so in this chapter), but to present examples that are clearly seen as invalid.
For example, “if the dog is pregnant, then it is a female; it isn’t pregnant; therefore it isn’t a
female.”
Equivocation and amphiboly we treat simply as arguments that depend on something’s
being given more than one meaning, the former referring to cases of semantic ambiguity
and the latter to cases of syntactic ambiguity.
The fallacy of composition is the mistake of assuming that what is true of a group of things
taken individually is also true of them taken as a collection; and the mistake of assuming
that what is true of the parts of a thing must be true of the whole thing. When the reverse
assumption is made, the result is the fallacy of division.
Confusing explanations with excuses happens when something that perhaps has been offered
only to explain the cause of something is assumed to have been offered to excuse or justify
it.
Confusing contraries and contradictories happens when we fail to notice that two conflicting
ideas may be contraries rather than contradictories.
Two events are independent, when one event’s happening doesn’t affect the probability of
the second event’s happening. The probability of two independent events’ happening is
obtained by multiplying the probability of each. When we combine the probabilities of
independent events in some other way, such as by adding them, we commit a fallacy.
The gambler’s fallacy happens if we think one event affects the probability of another event
when the two events are in fact independent.
The fallacy, overlooking false positives, seems common. That many dollar bills in Charles’s
wallet have traces of cocaine on them doesn’t prove much if most dollar bills in circulation
have cocaine on them. That most heroin users once used marijuana doesn’t show that
marijuana is a gateway to heroin if most marijuana users don’t take up heroin.
,Somewhat less common is the fallacy overlooking prior probabilities. We define the prior
probability of an attribute in a population as the actual or true proportion of things in the
population with that attribute. The fact you have tested positive for an undesirable medical
condition may not be cause for much concern if the prior probability of that condition is
low. Hal may have a better chance of becoming a professional baseball player than Bill has
of becoming a professional rugby player not because Hall is better at his sport but simply
because the prior probability of becoming a professional baseball player is higher than
becoming a professional rugby player.
Answers to Exercise 9-4 [Note: in the text, items 1, 5, 10, 15, etc. are ▲ exercises.]
1. Equivocation
2. Undistributed middle
3. Affirming the consequent
4. Miscalculating probabilities
5. Composition
6. Division
7. Equivocation
8. Yes, we think so.
9. Denying the antecedent
10. Affirming the consequent
11. Miscalculating probabilities [gambler’s fallacy]
12. Composition
13. Composition
14. Division
15. Undistributed middle
16. Denying the antecedent
17. Denying the antecedent
18. Affirming the consequent
19. Miscalculating probabilities [gambler’s fallacy]
20. Composition
21. Composition
22. Division
23. Equivocation
24. Yes, we think so.
25. Undistributed middle
26. Denying the antecedent
27. Affirming the consequent
28. Miscalculating probabilities
29. Composition
30. Division
31. Equivocation
,32. Yes, we think so.
33. Equivocation
34. Undistributed middle
35. Denying the antecedent
36. Excuse/justification
37. Overlooking prior probabilities
38. No
39. Composition
40. Division
41. Equivocation
42. Yes, we think so.
43. Undistributed middle
44. Denying the antecedent
45. Undistributed middle [The Answers in the text have this one wrong. Sorry.]
46. Overlooking false positives
47. Miscalculating probabilities
48. Composition
49. Equivocation
50. Yes, it is.
51. Yes, it is.
52. Undistributed middle
53. Denying the antecedent
54. Affirming the consequent
55. Denying the antecedent
56. Denying the antecedent
57. Gambler’s fallacy
58. Confusing explanations with excuses
59. Equivocation
60. Division
61. Equivocation
62. Possibly not
63. Equivocation
64. Undistributed middle
65. Undistributed middle [This would be better than answer in Answer Section]
66. Yes, clearly
67. Composition
68. Division
69. Equivocation
70. Overlooking false positives
71. Equivocation
72. Undistributed middle
73. Affirming the consequent
74. Overlooking false positives and prior probabilities
, 75. Not necessarily
76. Division
77. Equivocation (amphiboly)
78. Equivocation
79. Undistributed middle
80. Affirming the consequent
81. Overlooking false positives
82. Confusing explanations with excuses
83. Composition
84. Equivocation
85. Equivocation
86. Undistributed middle
87. Denying the antecedent
88. Miscalculating probabilities [gambler’s fallacy]
89. Composition
90. Miscalculating probabilities
91. Affirming the consequent
92. Confusing explanations with excuses
93. Equivocation
94. Undistributed middle
95. Affirming the consequent
96. Miscalculating probabilities
97. Miscalculating probabilities
98. Composition
99. Division
100. Equivocation
101. No, not clearly
102. Affirming the consequent
103. Denying the antecedent
104. Miscalculating probabilities
105. Division
106. Equivocation
107. Miscalculating probabilities
Chapter 1
What is Critical Thinking, Anyway?
This is a book in “critical thinking” because it is a book about critiquing thinking. Critical
thinking thus (as presented in this book) happens when you evaluate thinking by the
criteria of good reasoning—the criteria of logic and good sense that reasoning adheres to if
it is to be taken seriously by rational individuals. If successful, the book will help readers
