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An argument on argument form.
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03 Well-Formed Arguments
Philosophy
All cats are mammals
All mammals are animals
All cats are animals.
Good Argument or Bad?
2
All cats are mammals
All mammals are animals
All cats are animals.
Good Argument or Bad?
By “Good Argument” I mean: do you accept the conclusion on the basis of this argument?
3
All cats are mammals
All mammals are feline
All cats are feline.
Good Argument or Bad?
4
All cats are mammals
Circles are round
All cats are animals.
Good Argument or Bad?
5
All cats are mammals
All mammals are animals
Circles are squares.
Good Argument or Bad?
6
All cats are mammals
All mammals are animals
All cats are animals.
Good Argument
All cats are mammals
All mammals are feline
All cats are feline.
Bad Argument
All cats are mammals
Circles are round
All cats are animals.
Bad Argument
All cats are mammals
All mammals are animals
Circles are squares.
Bad Argument
7
T All cats are mammals
T All mammals are animals
T All cats are animals.
Good Argument
T All cats are mammals
F All mammals are feline
T All cats are feline.
Bad Argument
T All cats are mammals
T Circles are round
T All cats are animals.
Bad Argument
T All cats are mammals
T All mammals are animals
F Circles are squares.
Bad Argument
8
Just to drive home the point...
Truth is not enough to make an argument good!
Truth is not enough to make an argument good!
Truth is not enough to make an argument good!
9
Well-formed
Good Argument
Good Premises
10
Well-formed
Good Argument
???Good Premises
11
When you complain that someone’s conclusion doesn’t “follow” you are picking up on a very sophisticated problem, namely…
…the argument has bad form.
follows = well-formed
doesn’t follow = ill-formed
12
T All cats are mammals
T All mammals are animals
T All cats are animals.
Good Argument
T All cats are mammals
F All mammals are feline
T All cats are feline.
Bad Argument
T All cats are mammals
T Circles are round
T All cats are animals.
Bad Argument
T All cats are mammals
T All mammals are animals
F Circles are squares.
Bad Argument
13
T All cats are mammals
T All mammals are animals
T All cats are animals.
Good Argument
T All cats are mammals
F All mammals are feline
T All cats are feline.
Bad Argument
T All cats are mammals
T Circles are round
T All cats are animals.
Bad Argument
T All cats are mammals
T All mammals are animals
F Circles are squares.
Bad Argument
Set 1: Set 2:
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T All cats are mammals
T All mammals are animals
T All cats are animals.
Good Argument
T All cats are mammals
F All mammals are feline
T All cats are feline.
Bad Argument
Set 1:
15
All A are B .
All B are C .
All A are C .
Good Argument
All A are B .
All B are C .
All A are C .
Bad Argument
Set 1: (Form Only)
16
All A are B .
All B are C .
All A are C .
All A are B .
All B are C .
All A are C .
Set 1: (Form Only)
17
All A are B .
All B are C .
All A are C .
All A are B .
All B are C .
All A are C .
Well-formed
Well-formed
Set 1: (Form Only)
18
All A are B .
All B are C .
All A are C .
All A are B .
All B are C .
All A are C .
Well-formed
Well-formed
Set 1: (Form Only) Set 1: (Form & Content)
T All cats are mammals
T All mammals are animals
T All cats are animals.
Good Argument
T All cats are mammals
F All mammals are feline
T All cats are feline.
Bad Argument
19
20
T All cats are mammals
T All mammals are animals
T All cats are animals.
Good Argument
T All cats are mammals
F All mammals are feline
T All cats are feline.
Bad Argument
T All cats are mammals
T Circles are round
T All cats are animals.
Bad Argument
T All cats are mammals
T All mammals are animals
F Circles are squares.
Bad Argument
Set 1: Set 2:
21
T All cats are mammals
T Circles are round
T All cats are animals.
Bad Argument
T All cats are mammals
T All mammals are animals
F Circles are squares.
Bad Argument
Set 2:
22
Set 2: (Form Only)
All A are B .
C are D .
All A are E .
Bad Argument
All A are B .
All B are C .
D are E .
Bad Argument 23
Set 2: (Form Only)
All A are B .
C are D .
All A are E .
All A are B .
All B are C .
D are E .
24
Set 2: (Form Only)
All A are B .
C are D .
All A are E .
Ill-Formed
All A are B .
All B are C .
D are E .
Ill-Formed 25
Set 2: (Form & Content) Set 2: (Form Only)
All A are B .
C are D .
All A are E .
Ill-Formed
All A are B .
All B are C .
D are E .
Ill-Formed
T All cats are mammals
T Circles are round
T All cats are animals.
Bad Argument
T All cats are mammals
T All mammals are animals
F Circles are squares.
Bad Argument 26
Well-formed
Good Argument
Good Premises
27
Well-formed
“Valid”
or
“Cogent”
Good Argument
Good Premises
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Well-formed Argument = “The conclusion is supported by the premises the premises”; a valid or cogent argument.
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Well-formed Argument = “The conclusion is supported by the premises the premises”; a valid or cogent argument.
Valid Argument = Impossible for the premises to be true and the conclusion false.
30
Well-formed Argument = “The conclusion is supported by the premises the premises”; a valid or cogent argument.
Valid Argument = Impossible for the premises to be true and the conclusion false.
Cogent Argument = It's not impossible for the premises to be true and the conclusion false, but the conclusion is probably true if the premises are true.
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Most dogs are mammals
Sparky is a dog
Sparky is a mammal.
All dogs are mammals
Sparky is a dog
Sparky is a mammal.
32
Valid Argument: Cogent Argument:
Most dogs are mammals
Sparky is a dog
Sparky is a mammal.
All dogs are mammals
Sparky is a dog
Sparky is a mammal.
33
Valid Argument: Cogent Argument:
Most dogs are mammals
Sparky is a dog
Sparky is a mammal.
Most A are B .
b are A .
b are B .
All dogs are mammals
Sparky is a dog
Sparky is a mammal.
All A are B .
c is an A .
c is a B .
34
No pizza is bad
PJ's only serves pizza.
Nothing PJ's serves is
bad.
Most pets are mammals
All mammals are animals
Most pets are animals.
35
Valid Argument: Valid Argument:
No pizza is bad
PJ's only serves pizza.
Nothing PJ's serves is
bad.
Most pets are mammals
All mammals are animals
Most pets are animals.
36
Valid Argument: Valid Argument:
No pizza is bad
PJ's only serves pizza.
Nothing PJ's serves is
bad.
No A is B .
All C are A .
No C are B .
Most pets are mammals
All mammals are animals
Most pets are animals.
Most A are B .
All B are C .
Most A are C .
37
Most dogs are mammals
Sparky is a mammal
Sparky is a dog.
Most rocks are purple
I have a rock
I have something purple.
38
Cogent Argument: Ill-formed Argument:
Most dogs are mammals
Sparky is a mammal
Sparky is a dog.
Most rocks are purple
I have a rock
I have something purple.
39
Cogent Argument: Ill-formed Argument:
Most dogs are mammals
Sparky is a mammal
Sparky is a dog.
Most A are B .
b are B .
b are A .
Most rocks are purple
I have a rock
I have something purple.
Most A are B .
C is a A .
C is B .
40
Practice with identifying valid, cogent, and ill-formed arguments.
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A .
A or B .
Most A are B .
c are B .
c are A .
If A then B .
A .
B .
If A then B .
B .
A .
A and B .
A .
Most A are B .
All B are C .
Most A are C .
Valid, Cogent, or Ill-formed?
42
~A .
~A or B .
If A then B .
~B .
~A .
A if and only if B .
~B .
~A .
If A then ~B .
~B .
A .
A or B .
A .
All A are B .
All B are C .
All A are C .
Valid, Cogent, or Ill-formed?
43
Possible combinations with valid, cogent, and ill-formed arguments.
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VALID INVALID
True Premises + True Conclusion
True Premises + False Conclusion
False Premises + True Conclusion
False Premises + False Conclusion
Valid Argument = Impossible for the premises to be true and the conclusion false.
What combinations are possible and which are not?45
VALID INVALID
True Premises + True Conclusion
Possible Possible
True Premises + False Conclusion
Impossible Possible
False Premises + True Conclusion
Possible Possible
False Premises + False Conclusion
Possible Possible
Valid Argument = Impossible for the premises to be true and the conclusion false.
What combinations are possible and which are not?46
COGENT NOT COGENT
True Premises + True Conclusion
True Premises + False Conclusion
False Premises + True Conclusion
False Premises + False Conclusion
Cogent Argument = It's not impossible for the premises to be true and the conclusion false, but the conclusion is probably true if the premises are true.
What combinations are possible and which are not?47
COGENT NOT COGENT
True Premises + True Conclusion
Possible Possible
True Premises + False Conclusion
Possible Possible
False Premises + True Conclusion
Possible Possible
False Premises + False Conclusion
Possible Possible
What combinations are possible and which are not?
Cogent Argument = It's not impossible for the premises to be true and the conclusion false, but the conclusion is probably true if the premises are true.
48
COGENT NOT COGENT
True Premises + True Conclusion
Possible(Likely)
Possible
True Premises + False Conclusion
Possible(Unlikely)
Possible
False Premises + True Conclusion
Possible Possible
False Premises + False Conclusion
Possible Possible
What combinations are possible and which are not?
Cogent Argument = It's not impossible for the premises to be true and the conclusion false, but the conclusion is probably true if the premises are true.
49
Reconstructing an Argument and Identifying its Form
50
Argument Reconstruction:
Men can reproduce successfully with minimal energy. Natural selection chooses for traits and behaviors that maximize an organism’s reproductive success. Promiscuous behavior maximizes the reproductive success of males. Therefore, natural selection has selected men to be promiscuous.
51
Argument Reconstruction:
1. Men can reproduce successfully with minimal energy.
2. Natural selection chooses for traits and behaviors that maximize an organism’s reproductive success.
3. Promiscuous behavior maximizes the reproductive success of males.
4. Natural selection has selected men to be promiscuous.
52
Argument Reconstruction:
1. Men can reproduce successfully with minimal energy.
2. Natural selection chooses for traits and behaviors that maximize an organism’s reproductive success.
3. Promiscuous behavior maximizes the reproductive success of males.
4. Natural selection has selected men to be promiscuous.
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“Promiscuous behavior maximizes the reproductive success of males.”
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“Promiscuous behavior maximizes the reproductive success of males.”
1. Men can reproduce successfully with minimal energy costs.
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1. P.
“Promiscuous behavior maximizes the reproductive success of males.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
56
1. P.
2. If P, then Q.
“Promiscuous behavior maximizes the reproductive success of males.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
57
1. P.
2. If P, then Q.
3. Q.
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
58
1. P.
2. If P, then Q.
3. Q.
“Promiscuous behavior maximizes the reproductive success of males.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
4. If promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs, then promiscuous behavior maximizes the reproductive success of males.
59
1. P.
2. If P, then Q.
3. Q.
4. If Q, then R.
“Promiscuous behavior maximizes the reproductive success of males.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
4. If promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs, then promiscuous behavior maximizes the reproductive success of males.
5. Promiscuous behavior maximizes the reproductive success of males.
60
1. P.
2. If P, then Q.
3. Q.
4. If Q, then R.
5. R.
“Promiscuous behavior maximizes the reproductive success of males.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
4. If promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs, then promiscuous behavior maximizes the reproductive success of males.
5. Promiscuous behavior maximizes the reproductive success of males.
61
1. P.
2. If P, then Q.
3. Q.
4. If Q, then R.
5. R.
“Natural selection has selected men to be promiscuous.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
4. If promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs, then promiscuous behavior maximizes the reproductive success of males.
5. Promiscuous behavior maximizes the reproductive success of males.
62
1. P
2. If P, then Q.
3. Q.
4. If Q, then R.
5. R.
“Natural selection has selected men to be promiscuous.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
4. If promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs, then promiscuous behavior maximizes the reproductive success of males.
5. Promiscuous behavior maximizes the reproductive success of males.
6. If promiscuous behavior maximizes the reproductive success of males, then natural selection has selected men to be
63
1. P
2. If P, then Q.
3. Q.
4. If Q, then R.
5. R.
6. If R, then S.
“Natural selection has selected men to be promiscuous.”
1. Men can reproduce successfully with minimal energy costs.
2. If men can reproduce successfully with minimal energy costs, then promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
3. Promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs.
4. If promiscuous behavior is a trait or behavior that allows for successful reproduction with minimal energy costs, then promiscuous behavior maximizes the reproductive success of males.
5. Promiscuous behavior maximizes the reproductive success of males.
6. If promiscuous behavior maximizes the reproductive success of males, then natural selection has selected men to be promiscuous.
7. Natural selection has selected men to be promiscuous.
64
1. P
2. If P, then Q.
3. Q.
4. If Q, then R.
5. R.
6. If R, then S.
7. S.
“Natural selection has selected men to be promiscuous.”
Argument Reconstruction:
Men can reproduce successfully with minimal energy. Natural selection chooses for traits and behaviors that maximize an organism’s reproductive success. Promiscuous behavior maximizes the reproductive success of males. Therefore, natural selection has selected men to be promiscuous.
65
End.
