My Favorite Russian Joke
• A Russian Woman borrows a teapot from
her neighbor. She returns it broken, and
the neighbor sues. In court, the woman
makes three statements in her defense:
My Favorite Russian Joke
1. I never borrowed the pot.
My Favorite Russian Joke
1. I never borrowed the pot.
2. When I borrowed the teapot, it was
already broken.
My Favorite Russian Joke
1. I never borrowed the pot.
2. When I borrowed the teapot, it was
already broken.
3. When I gave it back, it was undamaged.
• Nobody knows the future/God is
omniscient.
• Nobody knows the future/God is
omniscient.
• I can choose what to eat for breakfast
tomorrow/God knows what I will choose.
• Nobody knows the future/God is
omniscient.
• I can choose what to eat for breakfast
tomorrow/God knows what I will choose.
• Abortion is wrong because it is always
wrong to take a human life/Capital
punishment is a just punishment for
murder
• Abortion is wrong because it is always
wrong to take an innocent human
life/Capital punishment is a just
punishment for murder
• I am the same person that I was when I
was five years old/Everything changes
• I am the same person that I was when I
was five years old/Everything changes
• No animal has a soul/Humans are animals
Necessary and Sufficient
Conditions
• These terms refer to relations between
facts.
Necessary Conditions
• A condition q is necessary for p if it
is impossible for something to be p
without being q.
Necessary Conditions
Example:
Being an animal is a necessary
condition for being a mammal.
Necessary Conditions
Example:
Being an animal is a necessary
condition for being a mammal.
Being married is a necessary
condition for getting a divorce.
A Diagram of
Necessary Conditions
Everything inside the large circle is
an animal; nothing outside the
large circle is an animal.
Animals
Mammals
A Diagram of
Necessary Conditions
Everything inside the large circle is
an animal; nothing outside the
large circle is an animal.
Animals
Everything inside the small orange
circle is a mammal; nothing outside
the small circle is an animal.
Mammals
A Diagram of
Necessary Conditions
Everything inside the large circle is
an animal; nothing outside the
large circle is an animal.
Animals
Everything inside the small orange
circle is a mammal; nothing outside
the small circle is an animal.
Since the small circle is entirely
enclosed within the large one, you
can say that it has to be animal if it
is a mammal.
Mammals
A Diagram of
Necessary Conditions
Everything inside the large circle is
an animal; nothing outside the
large circle is an animal.
Animals
Everything inside the small orange
circle is a mammal; nothing outside
the small circle is an animal.
Since the small circle is entirely
enclosed within the large one, you
can say that it has to be animal if it
is a mammal.
Thus, being an animal is a
necessary condition for being a
mammal.
Mammals
Sufficient Conditions
• A condition p is sufficient for q if it
is impossible for something to be p
without being q.
Example of sufficient condition
• Being a mammal is a sufficient condition
for being an animal, because it is
impossible for something to be a mammal
and not be an animal.
Example of sufficient
condition
Put slightly different, if you know p
is a mammal, that’s enough to know
that p is an animal.
• .
Animals
Mammals
Example of sufficient
condition
Put slightly different, if you know p
is a mammal, that’s enough to know
that p is an animal.
• .
Animals
Mammals
Food 4 Thought
1. Being an animal is a _______ condition
for being a monkey.
Food 4 Thought
1. Being an animal is a necessary condition
for being a monkey.
Food 4 Thought
1. Being an animal is a necessary condition
for being a monkey.
2. Being a grandfather is a ________
condition for being a father.
Food 4 Thought
1. Being an animal is a necessary condition
for being a monkey.
2. Being a grandfather is a sufficient
condition for being a father.
Food 4 Thought
1. Being an animal is a necessary condition
for being a monkey.
2. Being a grandfather is a sufficient
condition for being a father.
Deductive Or Inductive?
• A completely drunk person is not
responsible for his actions. John behaves
as if he is completely drunk. Therefore:
John is not responsible for his actions.
Deductive Or Inductive?
1. A completely drunk person is not
responsible for his actions.
2. John behaves as if he is completely
drunk.
3. Therefore: John is not responsible for his
actions.
Deductive Or Inductive?
1. A completely drunk
• Inductive
person is not
responsible for his
actions.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
Deductive Or Inductive?
1. A completely drunk
• Inductive
person is not
• “as if” indicates
responsible for his
probability rather
actions.
than logical certainty.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
Deductive Or Inductive?
1. A completely drunk
person is not
responsible for his
actions.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
Deductive Or Inductive?
1. A completely drunk
• Deductive
person is not
responsible for his
actions.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
Deductive Or Inductive?
1. A completely drunk
• Deductive
person is not
responsible for his
• 1. All D = N
actions.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
Deductive Or Inductive?
1. A completely drunk
• Deductive
person is not
responsible for his
• 1. All D = N
actions.
• 2. J = D.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
Deductive Or Inductive?
1. A completely drunk
person is not
responsible for his
actions.
2. John behaves as if he
is completely drunk.
3. Therefore: John is
not responsible for
his actions.
• Deductive
• 1. All D = N
• 2. J = D.
• 3. Therefore: J = N.
Deductive or Inductive?
• Either human cloning is immoral, or it will
be a blessing for humanity. Human
cloning is certainly not a blessing for
humanity. So human cloning immoral.
Deductive Or Inductive?
1. Either human
cloning is immoral,
or it will be a
blessing for
humanity.
Deductive Or Inductive?
1. Either human
cloning is immoral,
or it will be a
blessing for
humanity.
2. Human cloning is
certainly not a
blessing for
humanity.
Deductive Or Inductive?
1. Either human
cloning is immoral,
or it will be a
blessing for
humanity.
2. Human cloning is
certainly not a
blessing for
humanity.
3. So human cloning
immoral.
Deductive Or Inductive?
1. Either human
cloning is immoral,
or it will be a
blessing for
humanity.
2. Human cloning is
certainly not a
blessing for
humanity.
3. So human cloning
immoral.
• Deductive
• 1. Either I or B
Deductive Or Inductive?
1. Either human
cloning is immoral,
or it will be a
blessing for
humanity.
2. Human cloning is
certainly not a
blessing for
humanity.
3. So human cloning
immoral.
• Deductive
• 1. Either I or B
• 2. Not B.
Deductive Or Inductive?
1. Either human
cloning is immoral,
or it will be a
blessing for
humanity.
2. Human cloning is
certainly not a
blessing for
humanity.
3. So human cloning
immoral.
• Deductive
• 1. Either I or B
• 2. Not B.
• 3. Therefore: I.
Valid or Not?
• If the premises of a deductive argument
are true, then the conclusive must be true.
Valid or Not?
1. No government has
the right to force
people to pay taxes.
2. Therefore: The U.S.
Government has no
right to force people
to pay taxes.
Valid or Not?
1. No government has
the right to force
people to pay taxes.
2. Therefore: The U.S.
Government has no
right to force people
to pay taxes.
• Valid
Valid or Not?
1. No government has
the right to force
people to pay taxes.
2. Therefore: The U.S.
Government has no
right to force people
to pay taxes.
• Valid
1. All G = ~R.
Valid or Not?
1. No government has
the right to force
people to pay taxes.
2. Therefore: The U.S.
Government has no
right to force people
to pay taxes.
• Valid
1. All G = ~R.
2. U = G.
Valid or Not?
1. No government has
the right to force
people to pay taxes.
2. Therefore: The U.S.
Government has no
right to force people
to pay taxes.
• Valid
1. All G = ~R.
2. U = G.
3. Therefore: U = ~R
Valid or Not?
1. All successful people
are happy.
Valid or Not?
1. All successful people
are happy.
2. Jill is happy.
Valid or Not?
1. All successful people
are happy.
2. Jill is Happy.
3. Therefore Jill is
successful.
Valid or Not?
1. All successful people
are happy.
2. Jill is Happy.
3. Therefore Jill is
successful.
1. All S = H.
Valid or Not?
1. All successful people
are happy.
2. Jill is Happy.
3. Therefore Jill is
successful.
1. All S = H.
2. All j = H.