Types of Arguments
Inductive Argument: An argument in
which the truth of the premises is
supposed to prove that the conclusion is
probably true.
Strong Inductive Argument: An
inductive argument in which the truth of
the premises really does prove that the
conclusion is probably true.
Weak Inductive Argument: An inductive
argument in which the truth of the
premises really does not prove that
the conclusion is probably true.
Cogent Argument: A strong inductive
argument in which all the premises
are actually true.
Uncogent Argument: A strong inductive
argument in which even one premise
is actually false.
Determining Whether an Inductive
Argument is Strong or Weak
1) Assume all the premises are true,
even if one or more is clearly false.
2. Using only the information in the
premises plus common knowledge
ask: What is the probability that the
conclusion is true?
Above 50%: Strong Argument
50% or Less: Weak Argument
Examples
Most recording artists have talent.
Britney Spears is a recording artist.
Therefore, Britney probably has talent.
This argument is strong.
Britney Spears is a recording artist.
Britney has blonde hair.
Therefore, most recording artists have
blonde hair.
This argument is weak.
Most boys like to play sports.
Britney Spears is a boy.
Therefore, Britney probably likes to play
sports.
This argument is strong but uncogent.
The first argument is cogent as well as
strong.
Deductive Argument: An argument in
which the truth of the premises is
supposed to necessitate the truth of
the the conclusion, i. e. if all the
premises are true, the conclusion has
to be true.
Valid Deductive Argument: A deductive
argument in which the truth of the
premises really does necessitate the
truth of the conclusion, i. e. it’s NOT
possible for all the premises to be true
and the conclusion still be false.
Invalid Deductive Argument: A deductive
argument in which the truth of the premises
really does not necessitate the truth of the
conclusion, i. e. it’s possible for all the
premises to be true and the conclusion still
be false.
Sound Argument: A valid deductive
argument in which all the premises are
actually true.
Unsound Argument: A valid deductive
argument in which even one premise is
actually false.
Determining Whether a Deductive
Argument is Valid or Invalid
1) Assume all the premises are true,
even if one or more is clearly false.
2) Using only the information in the
premises plus common knowledge
ask: Does the conclusion have to be
true?
Yes: Valid Argument
No: Invalid Argument
N.B.: An argument is invalid if it’s
possible for all the premises to be true
while the conclusion is false.
N.B.: Whether an argument is valid or
invalid depends solely on its form NOT
its content.
Examples
If Barack Obama is President of the USA,
then Michelle Obama is First Lady.
Barack is President of the USA.
Therefore, Michelle is First Lady.
This argument is valid.
Material Implication: The truth of the
antecedent (A) is sufficient by itself for
the truth of the consequent (B).
If A, then B.
A.
Therefore, B.
A’s being true makes B true. A is true.
So, B is also true.
If Abraham Lincoln died of cancer, then
Lincoln is dead today.
Lincoln is dead today.
Therefore, Abraham Lincoln died of
cancer.
(This argument is invalid.)
If A, then B.
B.
Therefore, A.
Counter-Example: A way to show that
an argument form is invalid. It’s an
argument in the which the all the
premises are clearly true and the
conclusion is clearly false.
If the moon is made of green cheese,
then astronauts can eat moon rocks.
The moon is made of green cheese.
Therefore, astronauts can eat moon
rocks.
If A, then B.
A.
Therefore, B.
This argument is valid but unsound.