The Categorical Syllogism (Exercises)
Answer Sheet


1.
All Canadians are people.
John is a person.
Ergo, John is Canadian.

Invalid.  Undistributed Middle Term. 

2.
Some Lifeissues.net readers are philosophers.
Sean is a philosopher.
Ergo, Sean is a Lifeissues.net reader.

Invalid.  Undistributed Middle Term. 

3.
No man is perfect
Some men are presidents.
Ergo, some presidents are not perfect.

Valid

4.
All matter obeys wave equations.
All waves obey wave equations.
Ergo, all matter is waves.

Invalid.  Undistributed Middle Term.

5.
All human action is conditioned by circumstances.
All human action involves morality.
Ergo, all that involves morality is conditioned by circumstances (moral relativism).

Invalid.  Any term which is distributed in the conclusion must also be distributed in the premises (“All that involves morality” is distributed in the conclusion, but not in the second premise).

6.
All that is good is pleasant.
All eating is pleasant.
Ergo, all eating is good.

Invalid.  Undistributed Middle Term. 

7.
All patriots are voters.
Some citizens are not voters.
Ergo, some citizens are not patriots.

Valid.  The logic is valid, even though the conclusion may be false.  For the first premise might be false.  In other words, one may have false premises and a false conclusion, while the logic remains valid.  It is also possible to have true premises and a true conclusion but false logic (the conclusion simply does not follow from the premises).  

8.
All potatoes have eyes.
Frank's head has eyes.
Ergo, Frank is a potato head.

Invalid.  Undistributed Middle Term.

9.
All A are B
Some C are not B.
Ergo, some C are not A.

Valid.

10.
All a priori categories are conditions for the possibility of knowing anything.
Some a posteriori imperatives of an a-cosmic ethics are not conditions for the possibility of knowing anything.
Ergo, some a posteriori imperatives of an a-cosmic ethics are not a priori categories.

Valid.  *This syllogism means absolutely nothing.  But in order to determine its validity, one need not know the meaning of the terms.

11.
No oak trees bear fruit.
No maple trees bear fruit.
Therefore, no oak trees are maples.

Invalid.  One cannot conclude anything from two negative premises.  The role of the Middle Term is to join the Major and Minor Terms.  The Middle Term cannot do this if both premises are negative.  

12.
All socialists favor higher taxes.   
Some Liberals favor higher taxes.   
Ergo, some Liberals are Socialists.

Invalid.  Undistributed Middle Term. 

13.
All educated people have worked hard.
Some students are not educated.
Ergo, some students have not worked hard.

Invalid.  The term “not worked hard” is distributed in the conclusion, but it is undistributed in the first premise.

14.
Mathematicians know what mathematics is.
No philosopher is a mathematician.
Ergo, no philosopher knows what mathematics is.

Invalid.  “Knows what mathematics is” is distributed in the conclusion, but is undistributed in the first premise.


15.
All scientific knowledge is a work of reason.
All scientific knowledge is true.
Ergo, all that is true is a work of reason.

Invalid. “All that is true” is distributed in the conclusion, but is undistributed in the second premise.

16.
All married people know about marriage problems.
No priests are married people.
Ergo, no priests know about marriage problems.

Invalid.  “Know about marriage problems” is distributed in the conclusion, but is undistributed in the first premise.

17.
All C are B
All T are B
Ergo, all T are C

Invalid.  Undistributed Middle Term. 


18.
All chickens are born from eggs.
All turkeys are born from eggs.
Ergo, all turkeys are chickens.

Invalid.  Undistributed Middle Term. 

19.
Nothing easy is worthwhile.
Nothing good is easy.
Ergo, nothing good is worthwhile.

Invalid.  No conclusion can be drawn from two negative premises.

20.
All contraceptives acts are for avoiding pregnancy.
All use of NFP is for avoiding pregnancy.
Ergo, All use of NFP is contraceptive.

Invalid.  Undistributed Middle Term. 

21.
All Germans despise Judaism.
All of the people reading this text are German.
Ergo, all of the people reading this text despise Judaism.

Valid.  The premises are false, and the conclusion is false, but the logic is valid.  No rules are broken.


22.
All parts of a living organism are inside the body.
The fetus is inside the (mother's) body.
Therefore, the fetus is a part of the living organism (mother's body)

Invalid.  Undistributed Middle Term.