Problems and Examples

The following examples serve to show the possible combinations of truth values in valid categorical syllogisms.

	Case 1	Case 2	Case 3	Case 4
Premisses	T	F	T	F
Conclusion	T	T	logically impossible	F
			to be false

Examples:

Case 1A

(T) All cattle are mammals.

(T) All Angus are cattle.

(T) All Angus are mammals.

Case 2A

(F) All plants are animals.

(F) All deer are plants.

(T) All deer are animals.

Case 3A

An example is logically impossible to construct. (If a valid argument could have true premisses and a false conclusion, then deductive arguments could not be used to anything.)

Case 4A

(F) No pens are markers.

(F) All pencils are pens.

(F) No pencils are markers.

The following examples serve to show the possible combinations of truth values in invalid categorical syllogisms. Note that every combination of truth values is possible in invalid arguments. Also, note that Case 1B is invalid even though all statements happen to be true.

	Case 1	Case 2	Case 3	Case 4
premisses	T	F	T	F
conclusion	T	T	F	F

Examples:

Case 1B

(T) Some states are tyrannies.

(T) All dictatorship are tyrannies.

(T) Some dictatorships are states.

Case 2B

(F) No sparrows are birds.

(F) No flying creatures are birds.

(T) Some flying creatures are sparrows.

Case 3B

(T) All acids are chemicals.

(T) Some carbon compounds are not acids.

(F) Some carbon compounds are not chemicals.

Case 4B

(F) All essays are books.

(F) No tomes are books.

(F) All tomes are essays.

All of the following statements are true. Study each carefully. Refer to the cases mentioned in order to see how each statement is true.

1. A sound deductive argument is a deductive argument which is valid and whose premiss or premisses are true. (Cf., Case 1A above.)
2. It is possible for a deductive argument to be both valid and unsound. (Cf., Cases 2A and 3A above.)
3. If a deductive argument is sound, it cannot be invalid. (Cf., Cases 1A and 3A above.)
4. If the premisses of a deductive argument are true, then the argument can be valid or invalid. (Cf., Cases 1A, 1B, and 3B above.)
5. If the conclusion of a deductive argument is true, then the premisses can be true or false. (Cf., Cases 1A, 2A, 1B, and 2B above.)
6. If a deductive argument is sound, then its conclusion must be true. (Cf., Cases 1A and 3A above.)
7. If the premisses of a deductive argument are true, then the conclusion can be true or false. (Cf., Cases 2A, 4A, 2B, and 4B above.)
8. If a deductive argument has a false premiss, then the argument must be unsound. (Cf., Cases 2A, 4A, 2B, and 4B above.)
9. If a deductive argument is valid, then its conclusion can be true or it can be false. (Cf., Cases 1A, 2A, and 4A above.)
10. if every proposition in a deductive argument is true, then the argument can be either sound or unsound. (Cf., Cases 1A, and 1B above.)

See

http://philosophy.lander.edu/logic/tvs_quiz.html

for more examples of true-false questions on the topic of ``Truth, Validity, and Soundness.'' Also, see

http://philosophy.lander.edu/logic/tvs.html

for lecture notes on this topic.