Teall TB Chapter 04 - Fordham
Chapter 4
All Dogs Are Animals, All Beagles Are Dogs; Therefore, All Beagles Are Animals— Categorical Syllogisms
FILL IN THE BLANK
1. A valid inference in which the subject and predicate of a categorical proposition are switched is a .
Answer: conversion
2. The of the conclusion of a categorical syllogism is the major term.
Answer: predicate
3. The of a categorical syllogism is the predicate of the conclusion.
Answer: major term
4. The of the conclusion of a categorical syllogism is the minor term.
Answer: subject
5. The subject of the conclusion of a categorical syllogism is the .
Answer: minor term
6. The minor term of a categorical proposition is the .
Answer: subject of the conclusion
7. A categorical syllogism is .
Answer: an argument with three categorical proportions (two premises, one conclusion) with three terms each being used twice
8. The middle term of a categorical syllogism is .
Answer: the term that appears in both premises
diagramming
Using Venn diagrams, determine whether the following arguments are valid or invalid.
9. Some A are B.
All B are C.
( Some A are C.
Answer: Valid
[pic]
10. All places of ill repute are bars.
Some places of ill repute are great places to hang out.
( Some bars are great places to hang out.
Answer: Valid
[pic]
11. Some cats are not great pets.
Some great pets are dogs.
( Some dogs are not cats.
Answer: Invalid
[pic]
12. Some plants are not green things.
No frogs are plants.
( Some frogs are not green things.
Answer: Invalid
[pic]
13. Some A are not B.
All B are C.
( Some A are not C.
Answer: Invalid
[pic]
14. Some voters are not students.
No voters are citizens.
( Some citizens are not students.
Answer: Invalid
[pic]
15. All gifts are prizes.
No frogs are prizes.
( No frogs are gifts.
Answer: Valid
[pic]
16. Some anteaters are brown animals.
All brown animals are curious creatures.
( Some anteaters are curious creatures.
Answer: Valid
[pic]
17. Some voters are students.
All voters are citizens.
( Some students are citizens.
Answer: Valid
[pic]
18. No animals are plants.
All frogs are animals.
( No frogs are plants.
Answer: Valid
[pic]
19. All G are I.
No H are I.
( No H are G.
Answer: Valid
[pic]
20. Some X are Y.
All Y are Z.
( Some Z are X.
Answer: Valid
[pic]
21. Some L are M.
No K are M.
( Some K are not L.
Answer: Invalid
[pic]
22. No I are G.
No I are H.
( No H are G.
Answer: Invalid
[pic]
23. Some X are not Y.
All Y are Z.
( Some Z are not X.
Answer: Invalid
[pic]
24. Some M are L.
All M are K.
( Some K are L.
Answer: Valid
[pic]
25. No G are I.
All I are H.
( No H are G.
Answer: Invalid
[pic]
26. Some X are Y.
No Y are Z.
( Some Z are X.
Answer: Invalid
[pic]
27. Some M are not L.
No M are K.
( Some K are not L.
Answer: Invalid
[pic]
28. All G are I.
No I are H.
( No H are G.
Answer: Valid
[pic]
29. Some X are Y.
No Y are Z.
( Some Z are not X.
Answer: Invalid
[pic]
30. Some M are not L.
All M are K.
( Some K are not L.
Answer: Valid
[pic]
31. Some dogs are beagles.
All beagles are animals.
( Some animals are dogs.
Answer: Valid
[pic]
32. Some voters are students.
All voters are citizens.
( All students are citizens.
Answer: Invalid
[pic]
33. Some plants are green things.
No frogs are plants.
( Some frogs are not green things.
Answer: Invalid
[pic]
34. All Y are X.
No Z are Y.
( No Z are X.
Answer: Invalid
[pic]
35. No sinners are saints.
Some angels are saints.
( Some angels are not sinners.
Answer: Valid
[pic]
36. Some men are not actors.
Some actors are academy award winners.
( Some men are not academy award winners.
Answer: Invalid
[pic]
37. Some dogs are not beagles.
All beagles are animals.
( Some animals are not dogs.
Answer: Invalid
[pic]
38. Some A are B.
All B are C.
( Some A are C.
Answer: Valid
[pic]
39. All X are Y.
No Y are Z.
( No Z are X.
Answer: Valid
[pic]
40. Some voters are students.
No voters are citizens.
( Some students are not citizens.
Answer: Valid
[pic]
41. All prizes are gifts.
No frogs are prizes.
( No frogs are gifts.
Answer: Invalid
[pic]
42. No F are G.
Some F are not H.
( Some G are not H.
Answer: Invalid
[pic]
43. No Y are X.
All Z are Y.
( No Z are X.
Answer: Valid
[pic]
Short Answer
Identify the rules or rules violated in the following invalid categorical syllogisms.
10. All grains of salt are small objects.
Some small objects are objects visible to the naked eye.
( Some grains of salt are not objects visible to the naked eye.
Answer: Undistributed middle; if negative conclusion, there must be a negative premise; illicit major
11. Some cats are Persians.
Some terrorists are Persians.
( Some terrorists are cats.
Answer: Undistributed middle
12. Some students are fun people.
Some students are smart people.
( Some smart people are fun people.
Answer: Undistributed middle
13. All Eskimos are Alaskans.
No Russians are Alaskans.
( Some Eskimos are Russians.
Answer: Particular conclusion without particular premise; negative premise with affirmative conclusion
14. All members of Congress are criminals.
Some Republicans are members of Congress.
( Some Republicans are not criminals.
Answer: Illicit major
15. No corporations are entities concerned about human welfare.
Some entities concerned about human welfare are not non-profit organizations.
( Some corporations are non-profit organizations.
Answer: Two negative premises; if negative premise, must be a negative conclusion
16. Some cats are great pets.
Some great pets are dogs.
( Some dogs are not cats.
Answer: Illicit major; undistributed middle
51. Some actors are men.
Some actors are academy award winners.
( Some men are not academy award winners.
Answer: Illicit major; undistributed middle
Matching
Identify the rules or rules violated in the following invalid categorical syllogisms.
Rules
1) Term in both premises must be distributed.
2) Any term distributed in conclusion, must also be distributed in the premise.
3) There cannot be two negative premises.
4) If a premise is negative, the conclusion must be negative.
5) If the conclusion is particular, one of the premises must be particular.
6) The middle term must be distributed at least once.
7) Illicit major
8) Illicit minor
52. All members of Congress are criminals.
Some Democrats are members of Congress.
( Some Democrats are not criminals.
Answer: Rules 2, 7
53. No corporations are entities concerned about human welfare.
Some entities concerned about human welfare are not non-profit organizations.
( Some corporations are non-profit organizations.
Answer: Rules 3, 4
54. All boring people are philosophers.
No logic teachers are boring people.
( No logic teachers are philosophers.
Answer: Rules 3, 7
55. All schizophrenics are freaks.
Some freaks are philosophers.
( All philosophers are schizophrenics.
Answer: Rules 3, 6, 7
56. No grains of salt are small objects.
Some small objects are objects visible to the naked eye.
( Some grains of salt are not objects visible to the naked eye.
Answer: Rules 7, 8
57. No grains of salt are small objects.
Some small objects are objects visible to the naked eye.
( Some grains of salt are not objects visible to the naked eye.
Answer: Rules 2, 7
58. All members of Congress are criminals.
Some Democrats are members of Congress.
( Some Democrats are not criminals.
Answer: Rule 7
59. No philosophers are boring people.
Some logic teachers are not boring people.
( No philosophers are logic teachers.
Answer: Rule 3
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X
A C
B
B P
I
X
X
X
C
D
P
X
F G
X
G
F
X
P
X
C
A
B
C
S
X
V
G
F
P
C
A
X
B
C
S
X
V
P
F
A
I
G
H
X
Z
X
Y
L
K
X
M
G
H
I
X
Z
X
Y
X
L
K
M
G
H
I
X
Z
X
Y
L
K
X
M
G
H
I
X
Z
X
Y
x
L
K
M
D
A
X
B
X
C
S
V
G
F
X
P
X
Z
Y
Sinners
A
X
Saints
X
X
W
M
A
X
D
A
B
X
B
C
A
X
Z
Y
C
S
X
V
G
F
P
X
F
H
G
X
X
Z
Y
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