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CPHL 214

6. Categorical Logic

Exercise 1)

(a) Translate the following sentences into categorical form and state which of the four forms— A, E, I, O—you have used.

(b) If you think that any sentence is ambiguous as to which of the categorical forms it exemplifies, say so and explain why.

Note: The point here is not to consider whether the statements made are true or false, acceptable or unacceptable, but merely to write them in categorical form as A, E, I, or O.

 

1. Every dog has his day.

 

 

2. No man can serve two masters.

 

 

3. Fools rush in where angels fear to tread.

 

 

4. A rolling stone gathers no moss.

 

 

5. At least one new drug proved to be harmful to the patients.

 

 

6. Nothing succeeds like success.

 

 

7. Finders keepers, losers weepers. (Hint: Use two statements.)

 

 

8. Some consumers are not concerned to save money.

 

 

9. Good fences make good neighbours.

 

 

10. Experience is the mother of wisdom.

 

 

11. Early to bed and early to rise, makes a man healthy, wealthy, and wise.

 

 

 

 

Exercise 2

For each of the following arguments, (a) put the premises and the conclusion into categorical form. Check to see whether the argument is a syllogism. (Remember, in a syllogism, there are two premises and one conclusion. All are in categorical form, and there are exactly three categories in the statements; each category term appears twice.)

 

1. The common cold has economic costs. Any illness that has economic costs should be taken seriously. Therefore the common cold should be taken seriously.

 

 

 

2. Some businesses succeed by cutting labor costs. Any business that cuts labor costs is exploiting its workers. Therefore, some businesses exploit their workers.

 

 

3. All foods that can be kept on the shelf for several weeks without rotting are foods containing additives. Some foods that contain additives are hazardous to the health of allergy sufferers. Therefore, some foods that can be kept on the shelf for several weeks are hazardous to allergy sufferers.

 

 

4. No fishermen are loggers and some loggers are not hunters; therefore some fishermen are hunters.

 

 

5. Some lions are mammals because all animals that give birth to their young alive are mammals, and all lions give birth to their young alive.

 

 

6. All zoos are places in which animals may be bred, and no places in which animals may be bred should keep animals in cramped conditions. Thus, no zoo should keep animals in cramped conditions.

 

 

7. No shoes without traction are safe for mountain climbing. All shoes safe for mountain climbing are sturdily built. Therefore some shoes without traction are not sturdily built.

 

 

8. Only those who are fast cyclists can manage the trip from Calgary to Banff. Pedro is a fast cyclist. Therefore, Pedro can manage the trip from Calgary to Banff.

 

 

9. All appeals to supernatural causes are ultimately based on ignorance. All arguments based on ignorance are fallacious. Therefore, all appeals to supernatural causes are fallacious.

 

 

10. Only candidates under the age of 30 are eligible for the internship program. Malema is not under 30. Therefore Malema is not eligible for the internship program.