Classic Logic

Classic Logic

◦Ch. 5 of Introduction to Logic

◦Exercise 5.5, set A2

A. If we assume that the first proposition in each of the following sets is true, what can we affirm about the truth or falsehood of the remaining propositions in each set? B. If we assume that the first proposition in each set is false, what can we affirm?

2. a. No animals with horns are carnivores.

b. Some animals with horns are carnivores.

c. Some animals with horns are not carnivores.

d. All animals with horns are carnivores.

◦Exercise 5.6, proposition A2

A. State the converses of the following propositions, and indicate which of them are equivalent to the given propositions:

2. All graduates of West Point are commissioned officers in the U.S. Army.

◦Exercise 5.8, proposition 2

Express the following proposition as equality or inequality, representing each class by the first letter of the English term designating it, and symbolizing the proposition by means of a Venn diagram.

No peddlers are millionaires.

◦Exercise 6.1, syllogism 2

Rewrite each of the following syllogisms in standard form, and name its mood and figure. (Procedure: first, identify the conclusion; second, note its predicate term, which is the major term of the syllogism; third, identify the major premise, which is the premise containing the major term; fourth, verify that the other premise is the minor premise by checking to see that it contains the minor term, which is the subject term of the conclusion; fifth, rewrite the argument in standard form–major premise first, minor premise second, conclusion last; sixth, name the mood and figure of the syllogism.)

2. Some evergreens are objects of worship, because all fir trees are evergreens, and some objects of worship are fir trees.

◦Exercise 6.2, argument 3

Refute, by the method of constructing logical analogies, the following argument that is invalid:

No Republicans are Democrats, so some Democrats are wealthy stockbrokers, because some wealthy stockbrokers are not Republicans.

◦Exercise 6.3, syllogistic form A2

Write out the following syllogistic form, using S and P as the subject and predicate terms of the conclusion, and M as the middle term. (Refer to the chart of the four syllogistic figures, if necessary, on p. 235.) Then test the validity of the syllogistic form using a Venn diagram.



We are told that this syllogism is in the first figure, and therefore the middle term, M, is the subject term of the major premise and the predicate term of theminor premise. (See chart on p. 235.) The conclusion of the syllogism is an E proposition and therefore reads: No S is P. The first (major) premise (which contains the predicate term of the conclusion) is an A proposition, and therefore reads: All Mis P. The second (minor) premise (which contains the subject term of the conclusion) is an E proposition and therefore reads: No S is M. This syllogism therefore reads as follows: All M is P. No S is M. Therefore no S is P. Tested by means of a Venn diagram, as in Figure 6-10, this syllogism is shown to be invalid.


2. EIO-2.

◦Exercise 6.4, syllogism B3

B. Identify the rule that is broken by each invalid syllogism you can find in the following exercises, and name the fallacy that is committed:

3. No tragic actors are idiots.

Some comedians are not idiots.

Therefore some comedians are not tragic actors.

◦Exercise 7.2, syllogistic argument 2

Translate the syllogistic argument into standard form, and test its validity by using either Venn diagrams or the syllogistic rules set forth in chapter 6.

2. Some metals are rare and costly substances, but no welder’s materials are nonmetals; hence some welder’s materials are rare and costly substances.

◦Exercise 7.3, exercise 2

Translate the following into standard-form categorical proposition

2. Orchids are not fragrant.

Exercise 7.4, proposition 2 (in A).

A. Translate the following proposition into standard form, using parameters where necessary.

2. She never drives her car to work.