BrianLanier
Puritan Board Freshman
Test your reasoning skills (OP Updated With Answer)
Try this basic reasoning test.
Suppose there are four cards, each with a number on one side and a letter on the other, laid out next to each other on a table, like this: (|...| indicates the border of each card and has nothing to do with the content of each card.)
| I | | T | | 8 | | 5 |
Now consider the following rule:
(R) If there is a vowel on one side, there is an even number on the other.
-Objective:
Flipping over as few cards as possible, which cards would you have to turn over to see if the rule was true of these four cards?
-Justification:
Please provide your answer AND the *reason* why you came to the conclusion you did.
Now, no cheating (you can't do any research before you answer), just reason through the problem and respond. Reading the rest of this thread before answering counts as cheating.
(NOTE: If you already know the answer, don't post until the people who don't give it a try.)
And now the answer:
The Answer is the I and the 5. "To see why, just carefully think through the potential results of flipping each card over. You have to turn over the card with [ I ], because if there is an odd number on it, then the rule is disconfirmed, and you have to turn over the card with the [5] on it because if there is a vowel on the other side the rule will also be disconfirmed. Most people think you have to turn over the [8] as well, but to see why this isn't necessary, imagine that you turned over the card with [8] and there was a consonant on the other side. The rule would be neither confirmed nor disconfirmed. After all, the rule is, "If there is a vowel on one side there is an even number on the other." It says nothing about what must happen if there is an even number on one side. In other words, it does not say, "If there is an even number on one side, then ther is a vowel on the other." Some people (though considerably fewer) also think you need to turn over the [T], but since the rule doesn't tell you anything about what should happen happen if there is a consonant on one side, there could be an even number or an odd number on the other side of the [T] card, and it wouldn't either confirm or disconfirm the rule.
On average, 80-90% of people who take this kind of test don't come up with the right answer. Known as the Wason selection task after one of the psychologists who first performed it in 1966, the test was designed to assess ordinary people's logical abilities by measuring their understanding of 'if _____ then _____ sentences. One thing that many concluded from these results is that people frequently don't reason as logically as they should" [jump=1]1[/jump]
The test is just a simple conditional, p --> q (where '-->' is to be taken as the 'horseshoe'). The value of the cards were, I = p, T = ~p, 8 = q, and 5 = ~q. In classical logic, a conditional can only be false when the antecedent (p) is true and the consequent (q) is false (~q).
So all of you who got the right answer, good job (that includes those whose included the T card before I edited the OP, if they included 'T' for the right reason of course!).
If anyone would like to read more about conditionals (and the supposed problems that Paul and I were discussing, you may profit from the following two books:
(1) Fisher, Jennifer. On The Philosophy of Logic. Belmont, CA: Thomson-Wadsworth, 2008.
(2) Goble, Lou, ed. The Blackwell Guide to Philosophical Logic. Malden, MA: Blackwell, 2001. (Especially helpful is Dorothy Edgington's Chapter on Conditionals [Ch. 17].)
!hr!
[anchor=1]1[/anchor] Jennifer Fisher. On The Philosophy of Logic. Belmont, CA: Thomson-Wadsworth, 2008. 1-2, 190-191.
Try this basic reasoning test.
Suppose there are four cards, each with a number on one side and a letter on the other, laid out next to each other on a table, like this: (|...| indicates the border of each card and has nothing to do with the content of each card.)
| I | | T | | 8 | | 5 |
Now consider the following rule:
(R) If there is a vowel on one side, there is an even number on the other.
-Objective:
Flipping over as few cards as possible, which cards would you have to turn over to see if the rule was true of these four cards?
-Justification:
Please provide your answer AND the *reason* why you came to the conclusion you did.
Now, no cheating (you can't do any research before you answer), just reason through the problem and respond. Reading the rest of this thread before answering counts as cheating.
(NOTE: If you already know the answer, don't post until the people who don't give it a try.)
And now the answer:
The Answer is the I and the 5. "To see why, just carefully think through the potential results of flipping each card over. You have to turn over the card with [ I ], because if there is an odd number on it, then the rule is disconfirmed, and you have to turn over the card with the [5] on it because if there is a vowel on the other side the rule will also be disconfirmed. Most people think you have to turn over the [8] as well, but to see why this isn't necessary, imagine that you turned over the card with [8] and there was a consonant on the other side. The rule would be neither confirmed nor disconfirmed. After all, the rule is, "If there is a vowel on one side there is an even number on the other." It says nothing about what must happen if there is an even number on one side. In other words, it does not say, "If there is an even number on one side, then ther is a vowel on the other." Some people (though considerably fewer) also think you need to turn over the [T], but since the rule doesn't tell you anything about what should happen happen if there is a consonant on one side, there could be an even number or an odd number on the other side of the [T] card, and it wouldn't either confirm or disconfirm the rule.
On average, 80-90% of people who take this kind of test don't come up with the right answer. Known as the Wason selection task after one of the psychologists who first performed it in 1966, the test was designed to assess ordinary people's logical abilities by measuring their understanding of 'if _____ then _____ sentences. One thing that many concluded from these results is that people frequently don't reason as logically as they should" [jump=1]1[/jump]
The test is just a simple conditional, p --> q (where '-->' is to be taken as the 'horseshoe'). The value of the cards were, I = p, T = ~p, 8 = q, and 5 = ~q. In classical logic, a conditional can only be false when the antecedent (p) is true and the consequent (q) is false (~q).
So all of you who got the right answer, good job (that includes those whose included the T card before I edited the OP, if they included 'T' for the right reason of course!).
If anyone would like to read more about conditionals (and the supposed problems that Paul and I were discussing, you may profit from the following two books:
(1) Fisher, Jennifer. On The Philosophy of Logic. Belmont, CA: Thomson-Wadsworth, 2008.
(2) Goble, Lou, ed. The Blackwell Guide to Philosophical Logic. Malden, MA: Blackwell, 2001. (Especially helpful is Dorothy Edgington's Chapter on Conditionals [Ch. 17].)
!hr!
[anchor=1]1[/anchor] Jennifer Fisher. On The Philosophy of Logic. Belmont, CA: Thomson-Wadsworth, 2008. 1-2, 190-191.
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