CATEGORICAL LOGIC IN-CLASS EXERCISES
(1) Give the standard form notation of each of the four categorical forms A E I O.
A: All S is P
E: No S is P
I: Some S is P
O: Some S is not P
(2) Draw the Venn Diagram for the A E I and O categorical forms.
(3) Put the following propositions into standard categorical form:
a. Example: All jazz musicians play rock music
All jazz musicians are things that play rock music
b. No rock musicians play classical music No rock musicians are people that play classical music
c. Some rock musicians do not play jazz music Some rock musicians are not people that play jazz music
d. Beethoven was deaf All people that are Beethoven are people that are deaf (alternatively, All *Beethoven* are people that are deaf)
e. Mozart was not deaf No people that are Mozart are people that are deaf
f. A few philosophers have gone crazy Some philosophers are people that have gone crazy
g. Many philosophers do not go crazy Some philosophers are not people that have gone crazy
h. Some philosophy majors work at Walmart Some philosophy majors are people who work at Walmart
i. Some philosophy majors do not go to law school Some philosophy majors are not people who go to law school
j. Kant was the greatest philosopher of all time All people who are Kant are people who are the greatest philosopher of all time
k. People are deluded if they think that Kant was the greatest philosopher of all time All people who think Kant was the greatest philosopher of all time are people who are deluded
l. I have discovered the true meaning of life All people who are me are people who have discovered the true meaning of life
m. She screams whenever she looks in the mirror All people who are her are people who scream whenever she looks in the mirror
(4) Indicate the quality and quantity of the four forms.
A: All S is P (affirmative quality, universal quantity)
E: No S is P (negative quality, universal quantity)
I: Some S is P (affirmative quality, particular quantity)
O: Some S is not P (negative quality, particular quantity)
(5) Indicate the distribution of each term in the four categorical forms.
d u
A: All S is P
d d
E: No S is P
u u
I: Some S is P
u d
O: Some S is not P
(6) Give the Boolean notation of the A E I and O categorical forms.
A: SP = 0 (no members in the class of S and non-P)
E: SP = 0 (no members in the class of S and P)
I: SP ≠ 0 (at least one member in the class of S and P)
O: SP ≠ 0 (at least one member in the class of S and non-P)
(7) Use a Venn diagram to diagram the categorical proposition with the Boolian notation of SP=O
(8) Draw the square of opposition.
(9) Give the logical contradiction of the proposition All S is P Some S is not P
(10) Give the logical subcontrary of the proposition Some S is P Some S is not P
(11) Using S, P and M, give the syllogism with the mood and figure of AIE-4.
All P is M
Some M is S
No S is P
(12) Using S, P and M, give the syllogism with the mood and figure of OAO-3.
Some P is not M
All S is M
Some S is not P
(13) Using S, P and M, give the syllogism with the mood and figure of AEE-4.
All P is M
No M is S
No S is P
(14) Using S, P and M, give the syllogism with the mood and figure of AII-1.
All M is P
Some S is M
Some S is P
(15) Using S, P and M, give the syllogism with the mood and figure of AOO-2.
All P is M
Some S is not M
Some S is not P
(16) Use a Venn Diagram to test the validity of the following IAO-3 syllogism:
(1) Some M are P
(2) All M are S
(C) Some S are not P
(17) Use a Venn Diagram to test the validity of the following EIO-1 syllogism:
(1) No M are P
(2) Some S are M
(C) Some S are not P
(18) State in abbreviated form the rules of validity for categorical syllogisms.
1. One distributed middle term
2. Distributed term-distributed term
3. One affirmative premise
4. Negative-negative
5. Particular-particular
(19) Which rule or rules of validity are broken in the following syllogism: rules 2 and 4
(1) Some P are M
(2) All M are S
(C) Some S are not P
(20) Create a syllogism that violates as many rules as possible. rules 1, 2, 3, 4
Some M is not P
Some M is not S
Some S is P
(21) A enthymeme is a syllogism in which one of the three propositions is omitted. Put the following enthymeme into a standard syllogism and specify its mood and figure (for example, AEO-3, EAA-2): “All true art lovers are people who have a black velvet painting of Elvis, since all true art lovers are people who appreciate true Americana.”
AAA-1
(1) All people who appreciate true Americana are people who have a black velvet painting of Elvis [implied]
(2) All true art lovers are people who appreciate true Americana [stated]
(C) All true art lovers are people who have a black velvet painting of Elvis [stated]