Transcript Smith’s Invisible Hand

Validity, Soundness,
Strength, Cogency
Jason Chang
Critical Thinking
Lecture Outline
I.
Background
II.
Deductive argument terminology
III. Inductive argument terminology
Background
We have been focusing on
two types of arguments
• Deductive arguments
• Inductive arguments
Background
The labels “deductive” and
“inductive” refer to the type
of argument
• NOT whether the
argument has good
reasoning
• NOT whether the
argument has true
premises
Background
Deductive argument with bad
reasoning
Inductive argument with bad
reasoning
(P1) All U.S. presidents have been
men.
(P2) I am a man.
(P1) The murder victim owed John
money.
(P2) John was in town on the night
of the murder.
Therefore,
I was a U.S. president.
Therefore,
John probably committed the
murder.
Background
Deductive argument with false
premises
Inductive argument with false
premises
(P1) All men are cheaters.
(P2) Mary is a man.
(P1) It has snowed in San Jose for the
past 100 days.
Therefore,
Mary is a cheater.
Therefore,
It will probably snow tomorrow.
Background
We will now introduce labels
that refer to the quality of
the argument
Whether the argument
is “good” or “bad”
Labels for “good” and “bad”
deductive arguments
Deductive argument terminology
Definition
VALID
• A valid argument is a
deductive argument with
good reasoning
• The conclusion follows
necessarily from the
premises
Deductive argument terminology
Definition
INVALID
• An invalid argument is a
deductive argument with
bad reasoning
• The conclusion does not
follow necessarily from
the premises
Deductive argument terminology
(P1) All men are mortal.
(P2) Socrates is a man.
(P1) If the 49ers win, I will be happy.
(P2) If I am happy, I will dance.
Therefore,
Therefore,
Socrates is mortal.
If the 49ers win, I will dance.
Both are valid arguments – the conclusion follows
necessarily from the premises
Deductive argument terminology
(P1) All X are Y.
(P2) Z is an X.
(P1) If X, then Y.
(P2) If Y, then Z.
Therefore,
Therefore,
Z is a Y.
If X, then Z.
Are these valid arguments?
Deductive argument terminology
• Validity concerns
whether the argument
has good reasoning
• NOT whether the
premises are actually
true
Deductive argument terminology
It is possible to have
a valid argument
with false premises
(P1) If it rains, frogs will fall from the sky.
(P2) If frogs fall from the sky, the world
will end.
Therefore,
If it rains, the world will end. OH NO!
Deductive argument terminology
Possibilities for
valid arguments
TRUE
CONCLUSION
FALSE
CONCLUSION
TRUE PREMISES
FALSE PREMISES
(P1) All men are mortal.
(P2) Socrates is a man.
(P1) All wines are soft drinks.
(P2) Coke is a wine.
Therefore,
Therefore,
Socrates is mortal.
Coke is a soft drink.
?
(P1) If it rains, frogs will fall
from the sky.
(P2) If frogs fall from the
sky, the world will end.
Therefore,
If it rains, the world will end.
Deductive argument terminology
A valid argument is an
argument in which the
conclusion necessarily
follows from the premises
This means that there is
zero possibility that the
conclusion is false if all the
premises are true.
(If this was possible, the
conclusion would not
follow necessarily)
Deductive argument terminology
(P1) All students who ace
the exam will pass the
class.
(P2) You passed the class.
Therefore,
You must have aced the
exam.
Is it possible to envision a
scenario in which the
premises are true but
conclusion false?
If so, the conclusion does
not follow necessarily from
the premises.
The argument is INVALID.
Deductive argument terminology
Possible to envision true premises and false conclusion?
(P1) If you love him, you will stay with him.
(P2) You chose to stay with him.
Therefore,
You love him.
INVALID
Deductive argument terminology
Recap of major points
• A valid argument is a
deductive argument in
which the conclusion
follows necessarily from
the premises
• Validity does NOT concern
whether the premises are
actually true
• The conclusion of a valid
argument must be true if
the premises are true
Deductive argument terminology
Definition
SOUND
• A sound argument is a
valid argument with all
true premises
Deductive argument terminology
Definition
UNSOUND
• An unsound argument is a
deductive argument that:
(1) Is invalid, OR
(2) Has false premises, OR
(3) Both 1 and 2
Deductive argument terminology
(P1) If you are a student at this
school, you attend a school in
California.
(P2) You are a student at this
school.
Therefore,
You attend a school in California.
Conclusion follows
necessarily from premises
Premises are true
The argument is SOUND
Deductive argument terminology
VALID
SOUND
(P1)
(P2)
Therefore,
(C)
UNSOUND
(P1)
(P2)
Therefore,
(C)
INVALID
X
(P1)
(P2)
Therefore,
(C)
Labels for “good” and “bad”
inductive arguments
Inductive argument terminology
Definition
STRONG
• A strong argument is an
inductive argument with
good reasoning
• The conclusion follows
probably from the
premises
Inductive argument terminology
Definition
WEAK
• A weak argument is an
inductive argument with
bad reasoning
• The conclusion does not
follow probably from the
premises
Inductive argument terminology
(P1) In 98 of the 100 trials conducted, all rats who received
the drug Nitosol developed cancer.
Therefore,
The drug probably causes cancer in rats.
This is a strong argument – the conclusion follows
probably from the premises
Inductive argument terminology
(P1) In 8 of the 100 trials conducted, all rats who received
the drug Nitosol developed cancer.
Therefore,
The drug probably causes cancer in rats.
This is a weak argument – the conclusion does not
follow probably from the premises
Inductive argument terminology
Can a strong
argument have
false premises?
Inductive argument terminology
Yes!
Strength concerns
whether the
argument has good
reasoning – NOT
whether the premises
are actually true
(P1) In all 100 trials, the red pen has
floated to the ceiling when let go.
Therefore,
Next time I let go, the pen will probably
float to the ceiling.
Inductive argument terminology
Possibilities for
strong arguments
PROBABLY TRUE
CONCLUSION
PROBABLY FALSE
CONCLUSION
TRUE PREMISES
FALSE PREMISES
(P1) All dogs I have seen
cannot fly.
(P1) All women I have met
are over 5 feet tall.
Therefore,
Therefore,
The next woman I meet will
Probably all dogs can’t fly. be over 5 feet tall.
?
(P1) All U.S. presidents have
died in office
Therefore,
The next U.S. president will
die in office.
Inductive argument terminology
Just like for validity…
We can determine whether
an argument is strong by
envisioning the premises to
be true and then asking a
question about the
conclusion.
Inductive argument terminology
(P1) I met 3 Parisians
while visiting Paris.
(P2) All 3 were smokers.
Therefore,
All Parisians are smokers.
Is it possible to envision a
scenario in which the
premises are true but
conclusion probably false?
If so, the conclusion does
not follow probabilistically
from the premises.
The argument is WEAK.
Inductive argument terminology
(P1) In 8 of the 100 trials
conducted, all rats who
received the drug Nitosol
developed cancer.
(P1) In 50 of the 100 trials
conducted, all rats who
received the drug Nitosol
developed cancer.
(P1) In 98 of the 100 trials
conducted, all rats who
received the drug Nitosol
developed cancer.
Therefore,
Therefore,
Therefore,
The drug probably causes
cancer in rats.
The drug probably causes
cancer in rats.
The drug probably causes
cancer in rats.
Weak
Strong
Unlike validity, there are degrees of strength
Inductive argument terminology
Definition
COGENT
• A cogent argument is a
strong argument with all
true premises
• The conclusion follows
probably from the
premises
Inductive argument terminology
Definition
UNCOGENT
• An uncogent argument is an
inductive argument that:
(1) Is weak, OR
(2) Has false premises, OR
(3) Both 1 and 2
Deductive argument terminology
STRONG
COGENT
(P1)
(P2)
Therefore,
(C)
UNCOGENT
(P1)
(P2)
Therefore,
(C)
WEAK
X
(P1)
(P2)
Therefore,
(C)