A Study of Error: A Summary and Evaluation of Methods Used in Six Years of Study of the Scholastic Aptitude Test of the College Entrance Examination Board

By Carl C. Brigham | Go to book overview

CHAPTER V
Logical Inference
The logical inference test, the eighth test in Forms A and B given in 1926 and 1927, and the tenth (experimental) test in Form B11, was devised by Professor David C. Rogers of Smith College. All of the test items discussed in this chapter were prepared by Professor Rogers and his staff. The practice booklet sent to all candidates ten days before the test contained the sample items reproduced below.

DIRECTIONS. In each argument below, assume the premise or premises to be true and unquestioned, and judge the conclusion in relation to them.

If with the premises true the conclusion must necessarily be true, write in the margin the number 1 for Nec. T1.

If with the premises true the conclusion must necessarily be false, write in the margin the number 2 for Nec. F2.

If the truth of the premises would clearly indicate that the conclusion is probably true but not make it necessarily so, write in the margin the number 3 for Prob. T3.

If the truth of the premises would clearly indicate that the conclusion is probably false, but not make it necessarily so, write in the margin the number 4 for Prob. F4.

If the premises leave the conclusion undetermined, so that no necessity or clear probability of either its truth or falsity is indicated, write in the margin the number 5 for
Undet5.

SAMPLES: (a) Premise:--These shoes were made by Adam Brown, and all shoes made by Adam Brown are well-sewed.
Conclusion:--These shoes are well-sewed.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5. . . . . 1
(b) Premise:--All of the varnished canoes are in the boat- house.
Conclusion:--Some of the varnished canoes are not in the boat-house
Nec..T1 Nec. F2 Prob. T3 Prob. F4 Undet5. . . . . 2
(c) Premise:--Joseph has read a large number of books by Jint and has liked them all.
Conclusion:--Joseph will like this new book by Jint.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5. . . . . 3
(d) Premise:--In this country rain falls on the average about five days out of six during this season.
Conclusion:--It will not rain tomorrow.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5. . . . . 4
(e) Premise:--All of the houses on First Street were burned, but Mr. Smith's house was on Second Street.
Conclusion:--Mr. Smith's house was not burned.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5. . . . . 5
1. Premises:--I have read all of the magazines in this box.
2. Conclusion:--There are some magazines in this box which no one has read
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
3. Premises:--All of the short pencils are yours, and some of the short pencils are sharp.
4. Conclusion:--Some of the sharp pencils are yours.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
5. Premises:--The towns of Pitney, Paddet, Pidville, Penton, and Podridge are found, upon investigation, to have police systems better than the average.
6. Conclusion:--The town of Panvale, which also has a name beginning with P, will be found to have a police system better than the average.
Nec. T1 Nec. F2 Prob.T3 Prob. F4 Undet5 . . . . . . . . . .
7. Premises:--All of the waxed floors have been swept.
8. Conclusion:--None of the unswept floors are waxed.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
9. Premises:--This man looks exactly as I remember Thomas Brown to have looked, and his clothes look exactly like Thomas Brown's. Furthermore, I know of no reason to suspect he is not Thomas Brown.
10. Conclusion:--This man is Thomas Brown.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
11. Premises:--All of the boxes are full, but some of the boxes are not closed.
12. Conclusion:--Some of the closed boxes are not full.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
13. Premises:--None of the library cards have been sold.
14. Conclusion:--Some of the cards sold were library cards.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
15. Premises:--These are Macintosh apples, and all of the Macintosh apples have been sold.
16. Conclusion:--These apples have not been sold.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
17. Premises:--A, B, C, and D are the only persons that have left the car. B left before C or D, and A was the last to leave.
18. Conclusion:--B was the first to leave.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
19. Premises:--Every animal of this species that has ever been dissected had exactly thirty-five vertebrae.
20. Conclusion:--This animal of the same species has exactly thirty-five vertebrae.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5. . . . . . . . . .
21. Premises:--The sun shines on an average only one day in seven in this season of the year, but it has been sunny on five Saturdays in succession.
22. Conclusion:--It will be sunny next Saturday.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
23. Premises:--Thousands of samples of metal A, coming from many parts of the world, have been examined, and all so far have contained a small amount of metal B mixed with metal A.
24. Conclusion:--In many cases in which metal A is found in its natural state in the future it will not have metal B mixed with it.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
25. Premises:--The chances of throwing double sixes at dice are one in thirty-six. I have thrown a hundred times in succession without getting double sixes.
26. Conclusion:--I shall get double sixes in the next throw.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
27. Premises:--Simon's hand, of course, contains no card that has already been played. Two aces have already been played.
28. Conclusion:--Simon's hand contains all of the aces.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
29. Premises:--Among a tenth of the students in the class, chosen at random, all were able to answer the question.
30. Conclusion:--Most of the students in the class would be able to answer the question.
Nec. T 1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
31. Premises:--Only framed pictures have been accepted, and none of the new pictures are framed.
32. Conclusion:--None of the new pictures have been accepted.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .
33. Premises:--Any man who can turn sand into gold has the means to great wealth, and any man who can turn sand into gold is a magician.
34. Conclusion:--Some magicians have the means to great wealth.
Nec. T1 Nec. F2 Prob. T3 Prob. F4 Undet5 . . . . . . . . . .

-163-

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