Test your reasoning skills

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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.
 
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I have not heard this, and I have not researched it. Here's my thoughts:

1 needs to be flipped. That is, | I |.

I reason thus: if there is a vowel, then there's an even number. This card has a vowel, therefore it should have an even number.

How about the others:

Take | T |. You never said anything about what a consonant had on the other side.

Take | 8 |. This would affirm the consequent. That is, because this card has an even number on one side, that doesn't mean that it has a vowel on the other. You never said there is a vowel on one side if and only if there is an even number on the other.

Take | 5 |. The converse of | T |. Your info doesn't tell us if odd numbers have vowels or consonants on the other side.

Anyway, that's my guess.
 
I'll bite. Maximum four, flipping one at a time. Fewer if the premise turns out to be false before flipping over all four.

|I| -- False if reverse is not an even number.
|T| -- False if reverse is vowel or even number.
|8|-- False if reverse is not a vowel.
|5| -- False if reverse is vowel or even number.
 
Don already got it methinks ;)

You'd have to flip all of them over. One of the consonants could have an even number on the other side, thus negating the rule (Even number -> Vowel, or vice versa)...or it could have a ketchup stain for all we know. ;)
 
3. The I to determine that there is an even number, the 8 to determine there is a vowel, the 5 to determine there is not a vowel. The T is immaterial since you did not say that a consonant would require anything.
 
Now in rethinking, I'd say two. The I to determine it's reverse was an even number, and the five to determine it's reverse was not a vowel. The other two are immaterial.
 
No one so far!

I'll assume that it's a trick question then. So here's my new guess:

One. There is a vowel on one side (I on the left), so all we need to do is flip over the 5 on the right side to see if there is an even number there.
 
Paul,

I was thinking after your phone cut out, regarding the phrase, "A fool and his money will soon part ways". Does the temporal aspect get formalized at all (soon)? It seems that it would not since it is not specific enough, or is there another reason?

(x)(y)(Fx&My)&Oxy-->Pxy
 
Actually...you first have to put forth a worldview in which your senses are trustworthy. If they are not or you can not, then you may be seeing an odd number when it's really even.

Anyways... ;)
 
Paul,

I was thinking after your phone cut out, regarding the phrase, "A fool and his money will soon part ways". Does the temporal aspect get formalized at all (soon)? It seems that it would not since it is not specific enough, or is there another reason?

(x)(y)(Fx&My)&Oxy-->Pxy


Correct, too general.

If it was at, say, 2:00 p.m., then we'd have a three place predicate

So, in the first formula (the one you posted) P = "soon parted with": "_______ soon parted with ______"

But, if we had a specific time, two pm, we'd have a three-place predicate:

"______ soon parted with _______, __________"

So, (x)(y)(Fx&My)&Oxy-->Pxy could have a "t" added to represent "two:" (x)(y)(Fx&My)&Oxy-->Pxyt
 
Actually...you first have to put forth a worldview in which your senses are trustworthy. If they are not or you can not, then you may be seeing an odd number when it's really even.

Anyways... ;)


Unless it's taken as a basic belief. Or, if we talk about the way we're appeared to, e.g., in an even-numbered way, etc., viz, immediate mental reports. But then we might actually have to do some real philosophical and apologetical argumentation with the unbeliever, and who wants to do that? ;) Might as well keep telling them, no matter what the subject is, that they can't account for logic and induction, etc.

"Hey, how do you reconclie the Geneologies?"

"Does it matter? To ask that question assumes that the words would have the same meaning as they did yesterday, viz, the problem of induction, so you had to assume my worldview in order to ask that question, therefore I don't have to reconcile any geneologies!"
 
Actually...you first have to put forth a worldview in which your senses are trustworthy. If they are not or you can not, then you may be seeing an odd number when it's really even.

Anyways... ;)


Unless it's taken as a basic belief. Or, if we talk about the way we're appeared to, e.g., in an even-numbered way, etc., viz, immediate mental reports. But then we might actually have to do some real philosophical and apologetical argumentation with the unbeliever, and who wants to do that? ;) Might as well keep telling them, no matter what the subject is, that they can't account for logic and induction, etc.

"Hey, how do you reconclie the Geneologies?"

"Does it matter? To ask that question assumes that the words would have the same meaning as they did yesterday, viz, the problem of induction, so you had to assume my worldview in order to ask that question, therefore I don't have to reconcile any geneologies!"

Hey you sound like Sudduth :)
 
| I | | T | | 8 | | 5 |

R1) If there is a vowel on one side, there is an even number on the other.

R2) There is not an even number on the one side, then there is not a vowel on the other side.

R3) There is a letter or odd number on one side, then there is a consonant or number on the other side.

R1 , R2 and R3 are equivalent.

Rule R is only false when the antecedent is true and the consequence is false.

You must flip all four cards, since it is always possible that the card is a letter or odd number on one side and vowel on the other side. And that the card is a vowel on one side and not an even number on the other. You can only be sure if you look on the other side.
 
Still say 2 cards. Is that incorrect? The I to determine the reverse an even number, the 5 to determine the reverse is not a vowel. The T is immaterial since no requirement is given as to the reverse of a consonant, and the 8 is immaterial for the same reason.
 
I was wrong... :-( per usual

I know what it is now, though! Sloppy thinking gets you every time....

Just don't let Gene Cook see this! :lol:

Doesn't matter. "Paedobaptist" and "being wrong" is a tautology. What I said in my post was known a priori, then!

(x) (Px --> Wx)

:p

But since you're a paedobaptist, you must be wrong that "'Paedobaptist' and 'being wrong' is a tautology". So, (assuming classical logic and not paraconsistent logics!)

~(x) (Px --> Wx)
 
Actually...you first have to put forth a worldview in which your senses are trustworthy. If they are not or you can not, then you may be seeing an odd number when it's really even.

Anyways... ;)


Unless it's taken as a basic belief. Or, if we talk about the way we're appeared to, e.g., in an even-numbered way, etc., viz, immediate mental reports. But then we might actually have to do some real philosophical and apologetical argumentation with the unbeliever, and who wants to do that? ;) Might as well keep telling them, no matter what the subject is, that they can't account for logic and induction, etc.

"Hey, how do you reconclie the Geneologies?"

"Does it matter? To ask that question assumes that the words would have the same meaning as they did yesterday, viz, the problem of induction, so you had to assume my worldview in order to ask that question, therefore I don't have to reconcile any geneologies!"

Hey you sound like Sudduth :)


maybe I am:eek:
 
Just don't let Gene Cook see this! :lol:

Doesn't matter. "Paedobaptist" and "being wrong" is a tautology. What I said in my post was known a priori, then!

(x) (Px --> Wx)

:p

But since you're a paedobaptist, you must be wrong that "'Paedobaptist' and 'being wrong' is a tautology". So, (assuming classical logic and not paraconsistent logics!)

~(x) (Px --> Wx)

And since you are, you may be wrong too!
 
Still say 2 cards. Is that incorrect? The I to determine the reverse an even number, the 5 to determine the reverse is not a vowel. The T is immaterial since no requirement is given as to the reverse of a consonant, and the 8 is immaterial for the same reason.

Disheartening to be ignored. While I appreciate the old boy ribbing, its getting late, and my silly pride wants to know if I got it right or not. :think: Hmmm, think I'll go on to bed... nevermind!
 
Still say 2 cards. Is that incorrect? The I to determine the reverse an even number, the 5 to determine the reverse is not a vowel. The T is immaterial since no requirement is given as to the reverse of a consonant, and the 8 is immaterial for the same reason.

Given that you know "I" and "5", it cannot be determined if R is true or false. The card T can agree or disagree with R. If the back of T is R, then for the card [T], R is true. If the back of T is E then R is false. This is shown from R3.

R3) There is a letter or odd number on one side, then there is a consonant or number on the other side.

Do you disagree that R3 is equivalent to R?
 
| I | | T | | 8 | | 5 |

R1) If there is a vowel on one side, there is an even number on the other.

R2) There is not an even number on the one side, then there is not a vowel on the other side.

R3) There is a letter or odd number on one side, then there is a consonant or number on the other side.

R1 , R2 and R3 are equivalent.

Rule R is only false when the antecedent is true and the consequence is false.

You must flip all four cards, since it is always possible that the card is a letter or odd number on one side and vowel on the other side. And that the card is a vowel on one side and not an even number on the other. You can only be sure if you look on the other side.

Partially right. R3 is haning you up. It is not equivalent ot R1 or R2. R3 = (L V O) --> (C V N) is not equivalent to R1 = (V --> E) or R2 = (~E --> ~V), at least not that I can see.
 
Still say 2 cards. Is that incorrect? The I to determine the reverse an even number, the 5 to determine the reverse is not a vowel. The T is immaterial since no requirement is given as to the reverse of a consonant, and the 8 is immaterial for the same reason.

Disheartening to be ignored. While I appreciate the old boy ribbing, its getting late, and my silly pride wants to know if I got it right or not. :think: Hmmm, think I'll go on to bed... nevermind!

Sorry, I wanted to give more people a shot. I'll let you know soon!
 
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