Philosophy and Arguments
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Outline
1 – Arguments: valid vs sound
2. Conditionals
3. Common Forms of Bad Arguments
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Outline
1 – Arguments: valid vs sound
2. Conditionals
3. Common Forms of Bad Arguments
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Arguments
Argument: a sequence of sentences where one (the
conclusion) is meant to follow from or be
supported by the others (the premises).
Premise 1
Premise 2
Conclusion
P1 All men are mortal.
P2 Socrates is a man.
C. Socrates is mortal.
Arguments can be:
1. Valid / Invalid
2. Sound / Unsound
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Valid Arguments
Valid Arg.:
- The conclusion logically follows from the premises
- An argument where it is impossible for the premises to be
true and the conclusion false.
P1 All men are mortal.
P2 Socrates is a man.
CC Socrates is mortal.
P1 All cats are reptile.
P2 Bug Bunny is a cat.
CC Bugs Bunny is a reptile.
VALIDITY = LOGICAL FORM
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Valid Arguments
Attention!
- Just because an argument is valid, it does not mean that its
conclusion is true
- Just because an argument is invalid, it does not mean that
its conclusion is false.
P1 All cats are reptiles.
P2 Bugs Bunny is a cat.
CC Bugs Bunny is a reptile.
P1 If Bugs Bunny has big ears,
then he is a reptile
P2 Bugs Bunny is a reptile .
CC Bugs Bunny has big ears.
But if the premises are true and the argument is valid,
then the conclusion is always true
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Valid Arguments : Exercise
I Your high idle is caused either by a problem with the
transmission, or by too little oil, or both. You have too
little oil in your car. Therefore, your transmission is fine.
II If the moon is made of green cheese, then cows jump over
it. The moon is made of green cheese. Therefore, cows
jump over the moon.
III Either Colonel Mustard or Miss Scarlet is the culprit. Miss
Scarlet is not the culprit. Hence, Colonel Mustard is the
culprit.
IV All engineers enjoy ballet. Therefore, some males enjoy
ballet.
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Sound Arguments
Sound Argument = VALID + TRUE PREMISSES
Sound arguments always have true conclusions.
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Valid vs Sound
An argument which is valid but not sound:
P1. If the moon is made of green cheese, then
cows jump over it.
P2. The moon is made of green cheese.
CC Therefore, cows jump over the moon.
Sound Arg:
P1 Prof. Le Bihan’s baby is a girl or a boy.
P2 Prof. Le Bihan’s baby is not a boy.
CC. Prof. Le Bihan’s baby is a girl.
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Conclusion: Good and Bad Arguments
To Remember: distinction valid / sound arguments
Good arguments are SOUND, ie are valid and possess true
premises – They support the conclusion
Bad arguments are either:
- Invalid : the logical form is incorrect, or
- Unsound: the premises are false
 These are the two ways in which you can criticize an
argument from a philosopher !
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Arguments: Exercise!
I.
If Socrates is a man, then Socrates is mortal. Socrates is a
man. So, Socrates is mortal.
II. If Socrates is a horse, then Socrates is mortal. Socrates is
a horse. So, Socrates is mortal.
III. If Socrates is a horse, then Socrates has four legs.
Socrates is a horse. So, Socrates has four legs.
IV. If Socrates is a horse, then Socrates has four legs.
Socrates doesn’t have four legs. So, Socrates is not a
horse.
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Arguments: Exercise!
If Socrates is a man, then he’s a mammal. Socrates is not
a mammal. So Socrates is not a man.
II. If Socrates is a horse, then he’s warm-blooded. Socrates is
warm- blooded. So Socrates is a horse.
III. If Socrates was a philosopher then he wasn’t a historian.
Socrates wasn’t a historian. So, Socrates was a
philosopher.
I.
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Outline
1 – Arguments: valid vs sound
2. Conditionals
3. Common Forms of Bad Arguments
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Conditionals
Conditional :
IF P THEN Q
PQ
/
Necessary and Sufficient conditions:
IF P THEN Q
P Sufficient
Q Necessary
If you are pregnant then you put on weight
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Conditionals: Exercise!
– to be over 16 / to be legally driving
– to be human / to be an animal
– to be alive / to be sick
– to be alive / not to be dead
– to be rectangular / to be square
– to be possible / to be real
– to do your homework / to get a good grade
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Conditionals
Attention:
IF P THEN Q is NOT equivalent to IF Q then
P
If you are pregnant, you put on weight
Is NOT equivalent to:
If you put on weight then you are pregnant
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Contrapositions
Contraposition:
IF P THEN Q is equivalent to IF not Q then not
P
If you are pregnant, you put on weight
IS equivalent to:
If you DON’T put on weight then you are NOT pregnant
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Conclusion on Conditionals
To Remember:
1. What a conditional is
2. The distinction between necessary and sufficient
conditions
3. The notion of contraposition
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Conditionals: Exercise!
–You don’t drink? Oh, then you must be pregnant!
– You’re pregnant? Oh, poor girl, you’re stuck with carrot
juice then!
– No pregnant women drink alcohol
– You are drinking tonight? I see, you are not pregnant yet.
– Wait, you are not pregnant, right? So, you are drinking
tonight!
– If Justin is pregnant then he does not drink
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Outline
1 – Arguments: valid vs sound
2. Conditionals
3. Common Forms of Bad Arguments
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Using a conditional the wrong way
IF P THEN Q
If you are pregnant, then you gain weight
Affirming the
antecedent
P
you are pregnant,
Hence Q
then you gain weight
Affirming the
consequent
Q
you gain weight,
Hence P
then you are pregnant
Denying the
antecedent
Non Q
you are not pregnant,
Non P
then you don’t gain
weight
Denying the
consequent
Non P
you don’t gain weight,
Non Q
then you are not
pregnant
Two ways to use a conditional the wrong way:
Affirming the consequent/ Denying the antecedent
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Circular Arguments
Circular arguments assume what they want to
prove.
The police did not beat the suspect because beating
suspects in not something that police ever do.
We know that God exists, because it says so in the Bible.
And we can trust the Bible on this matter because it’s the
Word of God, and so it must be correct.
Darwin's account of evolution is just a theory. A theory is
an unproven hypothesis. So, there is no compelling
reason to believe Darwin's theory.
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Consequential Fallacy
Consequential fallacy: confuse the consequences
of holding a belief with evidence for that belief.
Darwin’s theory is false because if it were true, there
would be no morality.
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Equivocation
Equivocation: to use an ambiguous term in different
ways in an argument.
Nature is governed by fixed and unchangeable laws. But
every law is the work of some legislator. Therefore, there
is some legislator responsible for the governing of Nature.
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Appeal to Consensus
Appeal to Consensus: one appeals to consensus
to establish a claim.
Most people believe that McDonals is the best restaurant
in the world. McDonalds is the best restaurant in the
world.
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Slippery Slope
Slippery slope: incorrectly reasons that the
arbitrariness of marking a distinction along some
continuum shows that no distinction is possible.
There is no agreed upon number of hair that qualifies
someone as bald. Therefore, there is no difference
between being bald or hairy.
There is no agreed upon age that qualifies a fetus as a
person. To kill an innocent person is murder. Therefore, all
abortions are murders, independently of the age of the
fetus.
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Misleading Vividness
Misleading vividness: particularly vivid information
is weighted more than other information in coming to
a conclusion.
Elections in France 2007
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Genetic Fallacy
Genetic fallacy: taking the source of a claim as
evidence for or against the claim.
Tom Cruise said that there is no such thing as a chemical
imbalance of the body. Tom Cruise is crazy. Therefore,
there is such thing as a chemical imbalance of the body.
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Straw Man
Straw man: misrepesenting someone’s position,
arguing against it, and supposing that the actual
position is defeated.
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Straw Man
Nigel: I believe that some kinds of sexual lifestyles are
morally wrong.
Basil: So, you’re saying it’s OK for rednecks to beat up gay
people?
Nigel: No, I’m not saying that at all. All people in our society
should be protected from having unwanted violence
inflicted upon them. I’m just saying I think their chosen
lifestyles are immoral.
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Straw Man
Basil: What makes you think it’s OK for you to force your
morality on everyone else?
Nigel: I haven’t said anything about forcing my morality on
anybody. All I did was give my opinion about a certain
moral issue. I didn’t use any force or even the threat of
force to coerce others to agree with me.
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Straw Man
Basil: But you are saying that you don’t think gay people
should have the same rights as straight people, right?
Nigel: No. I think all people in a democratic society should
have the same rights. That means that people should have
the right to pursue lifestyles that others think are immoral.
I haven’t said anything about depriving people of their
rights or inflicting violence upon them. I’m only giving
my opinion about the morality of their behavior.
Bebee (2003) ``Good and Bad Arguments.’’
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Feelings
Feelings: a person argues for a position by
indicating that they feel a certain way.
Problem: No one cares how you feel.
More important problem: There is no warrant
the think that your feelings about something
are correlated to the truth or falsity of a
proposition.
Solution: Use good arguments!
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