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Philosophy 103: Introduction to Logic
Logic Assessment Pretest Question 7

7. What statement logically follows from the following statement?  Not all eyes that see well are healthy eyes.  a. If your eyes are healthy, then you see well.  b. If you see well, then your eyes are healthy.  c. Some healthy eyes see well, and some don't.  d. If your eyes are unhealthy, then you won't see well.  e. Make sure you maintain good eye health. Purpose for the Question:  One objective of logic is to grasp the features of traditional logic and to obtain facility in symbolic manipulations. Statements beginning with the phrase "Not all" or "None but" are called "exclusive statement" and imply not only "Some are" but "Some are not." Thus, the statement, "Not all eyes that see well are healthy eyes" is a compound statement.		Phil 103 02 Archie
		Engl 373 04 Dumont-Poston
		Engl 101 22 Westcott

Answer Choices: 

a. This answer means "All eyes that are healthy are eyes that see well," and this answer is consistent with converse by limitation "Some eyes that see well are healthy eyes.  This latter statement is consistent with the statement in the question "Not all eyes that see well are healthy eyes."  12% of logic students are then partially correct.  Answer a is implied;  however, answer a is only part of the meaning of the original statement.

b. This answer implies "All eyes that see well are healthy eyes," and this implication contradicts the original statement.

c. The original statement implies "Some eyes that see well are healthy eyes," and "Some eyes that see well are not healthy eyes,"  but this answer is the converse of each of the two statements given in answer c. "Some healthy eyes are not eyes that see well" is not implied by the original statement.

d.  By contraposition, answer d is equivalent to "If your eyes see well, then your eyes are healthy"--the original statement denies this state of affairs.

e. This answer, an imperative, is not relevant to the question asked.  

Evaluation:   The answers to this question are fairly consistent across the disciplines. This type of question quite probably will show a substantial difference in assessment outcomes between logic and other courses when logic students begin to be aware of the logical operations of exclusive statements, contraposition, and modus tollens..

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