Necessary and Sufficient

 

If A, then B

A – Sufficient

B – Necessary

 

Example

If I am eating, then I am awake

·      Knowing that I am eating is sufficient for knowing that I am awake

·      Being awake is necessary for eating

 

“The affluence of many of the September 11th hijackers cast doubt on the notion that poverty was a necessary, let alone sufficient, condition for suicidal terrorism.”

 

If sufficient: If poor, then a suicidal terrorist

If necessary: If a suicidal terrorist, then poor

 


Homework

 

P1) No one has been able to prove that children are not able to recall events prior to age 2.

C)   Therefore, children are able to recall events prior to age 2

 

P1) A is a middle child

P2) Middle children can’t make up their own minds

C)   Therefore, A’s homework is not worth the full 3 points.

 

P1) Only man is rational

P2) No woman is a man

C)   No woman is rational

 

P1) Michael Moore is a left-wing wacko

P2) Michael Moore gets rich peddling cynicism to naïve people

C)   Michael Moore’s claim that G.W. Bush is a deserter is false

 

P1) You have a chance to control our destiny

P2) Think about the countries in which people don’t have a choice about voting

C)   Register to vote and vote.


 

P1) Everyone supports John Kerry

C)   John Kerry should be the next president of the U.S.

 

P1) The track coach is lazy and overweight

P2) The track coach lives an unhealthy lifestyle

C)   The track coach cannot inform us of the positive benefits of exercise.

 

P1) We have no proof that there is life beyond our planet

C)   Therefore, there are no alien life forms on other planets

 

 


Begin Deductive Reasoning

 

 

Modus Ponens

If A, then B

A

Therefore, B

 

Modus Tollens

If A, then B

Not B

Therefore, not A

 

 

One Person’s Modus Ponens is Another Person’s Modus Tollens

 

P1)   If there is a God, then, given his benevolence, this is the best of all possible worlds

P2)   There is a benevolent God

C)     Therefore, this is the best of all possible worlds

 

P1)   If there is a God, then, given his benevolence, this is the best of all possible worlds

P2)   This is not the best of all possible world

C)     Therefore, there is no benevolent God