# Test your reasoning skills



## BrianLanier

*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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## Jim Johnston

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.


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## elnwood

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.


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## Devin

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.


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## BrianLanier

No one so far!


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## Mushroom

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.


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## Mushroom

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.


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## elnwood

BrianLanier said:


> 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.


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## Jim Johnston

I was wrong... :-( per usual

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


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## BrianLanier

elnwood said:


> BrianLanier said:
> 
> 
> 
> 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.
Click to expand...


Nope, not a trick question, and one is not the answer.


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## BrianLanier

Tom Bombadil said:


> 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!


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## BrianLanier

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


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## Devin

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...


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## Jim Johnston

BrianLanier said:


> 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


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## Jim Johnston

Devin said:


> 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!"


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## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> 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!
Click to expand...


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

(x) (Px --> Wx)


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## Vytautas

Is _ is the problem the letter I or the number 1?_


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## Vytautas

BrianLanier said:


> Nope, not a trick question, and one is not the answer.



Is choosing only card _ wrong or is it wrong that you only choose one card?_


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## BrianLanier

Tom Bombadil said:


> Devin said:
> 
> 
> 
> 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!"
Click to expand...


Hey you sound like Sudduth


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## BrianLanier

Vytautas said:


> Is _ is the problem the letter I or the number 1?_


_

Look carefully, it is '*I*'._


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## BrianLanier

Vytautas said:


> BrianLanier said:
> 
> 
> 
> Nope, not a trick question, and one is not the answer.
> 
> 
> 
> 
> Is choosing only card _ wrong or is it wrong that you only choose one card?_
Click to expand...

_

Now that's for you to figure out _


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## Vytautas

| 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.


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## Mushroom

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.


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## BrianLanier

Tom Bombadil said:


> BrianLanier said:
> 
> 
> 
> 
> 
> Tom Bombadil said:
> 
> 
> 
> 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!
> 
> Click to expand...
> 
> 
> Doesn't matter. "Paedobaptist" and "being wrong" is a tautology. What I said in my post was known a priori, then!
> 
> (x) (Px --> Wx)
Click to expand...


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)


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## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> 
> 
> Devin said:
> 
> 
> 
> 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!"
> 
> Click to expand...
> 
> 
> Hey you sound like Sudduth
Click to expand...



maybe I am


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## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> 
> 
> BrianLanier said:
> 
> 
> 
> Just don't let Gene Cook see this!
> 
> 
> 
> 
> Doesn't matter. "Paedobaptist" and "being wrong" is a tautology. What I said in my post was known a priori, then!
> 
> (x) (Px --> Wx)
> 
> 
> 
> Click to expand...
> 
> 
> 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)
Click to expand...


And since you are, you may be wrong too!


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## Mushroom

Brad said:


> 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.  Hmmm, think I'll go on to bed... _nevermind!_


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## Vytautas

Brad said:


> 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?


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## BrianLanier

Vytautas said:


> | 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.


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## BrianLanier

Brad said:


> Brad said:
> 
> 
> 
> 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.  Hmmm, think I'll go on to bed... _nevermind!_
Click to expand...


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


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## Answerman

You would have to flip the I the T and the 5:

You would have to flip the I to see if there is anything other than a even number.
You would have to flip the T to see if there is a vowel.
You would have to flip the 5 to see if there is a vowel.

I haven't read through all of the replies yet, but this is my guess.


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## Vytautas

T F
I V ~V
T E ~E
8 ~V+~E V+E
5 ~V+~E V+E

V = Vowel E= Even number 

Each card has an independent truth value of each other so that knowing the truth value under the assumption R is true will not give you the truth value to another card. Also the truth values have no point of intersection so that knowing one side of the card does not reveal the truth value of the other side.


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## BrianLanier

Answerman said:


> You would have to flip the I the T and the 5:
> 
> You would have to flip the I to see if there is anything other than a even number.
> You would have to flip the T to see if there is a vowel.
> You would have to flip the 5 to see if there is a vowel.
> 
> I haven't read through all of the replies yet, but this is my guess.



Almost! It is a good thing you had not read through all of the replies before answering, since that would have been cheating, vis-a-vis, the rule not to research first!!


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## Jim Johnston

How about this argument:

1. If it rains today, then it will not rain hard.
2. It did rain hard today.
3. Therefore, it did not rain today. (2,3, M.T.)


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## Mushroom

3 cards. No evidence that there is not a vowel under any of those that are not even numbers. What is under the 8 is immaterial since there is no requirement that anything else not have an even number on the reverse. My first answer was right, but for the wrong reason? I think Answerman got it right.

See? My pride wouldn't let me go to bed, and now I find I was wrong anyway. That which I will to do I do not.


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## BrianLanier

Vytautas said:


> T F
> I V ~V
> T E ~E
> 8 ~V+~E V+E
> 5 ~V+~E V+E
> 
> V = Vowel E= Even number
> 
> Each card has an independent truth value of each other so that knowing the truth value under the assumption R is true will not give you the truth value to another card. Also the truth values have no point of intersection so that knowing one side of the card does not reveal the truth value of the other side.



What logical connective are you trying to respresent with '+' in the above? (I am assuming it is a truth table, but I think the spacing was distorted when you posted it.)


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## BrianLanier

Brad said:


> 3 cards. No evidence that there is not a vowel under any of those that are not even numbers. What is under the 8 is immaterial since there is no requirement that anything else not have an even number on the reverse. My first answer was right, but for the wrong reason? I think Answerman got it right.
> 
> See? My pride wouldn't let me go to bed, and now I find I was wrong anyway. That which I will to do I do not.



I sent you a private message. You shouldn't be so quick to doubt yourself.


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## Mushroom

Oops! See what a mess pride can make? Let my fall be a lesson to you all. 

Thanks Brian. That was fun in spite of my portion of humble pie. I'm off to bed.


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## BrianLanier

Tom Bombadil said:


> How about this argument:
> 
> 1. If it rains today, then it will not rain hard.
> 2. It did rain hard today.
> 3. Therefore, it did not rain today. (2,3, M.T.)



Or how about this,

1) If I go to San Francisco this summer, I will see my brother. So if I go to San Francisco this summer, and my brother moves to New Mexico before I visit, I will see my brother.

p --> q
So, (p & r) --> q

and you got to love these,

1) I am tall.
2) I am not tall.
3) So, the moon is made of green cheese.

p
~p
So, q

(_ex contradictione quod libetum_)


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## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> How about this argument:
> 
> 1. If it rains today, then it will not rain hard.
> 2. It did rain hard today.
> 3. Therefore, it did not rain today. (2,3, M.T.)
> 
> 
> 
> 
> 
> 
> Or how about this,
> 
> 1) If I go to San Francisco this summer, I will see my brother. So if I go to San Francisco this summer, and my brother moves to New Mexico before I visit, I will see my brother.
> 
> p --> q
> So, (p & r) --> q
> 
> and you got to love these,
> 
> 1) I am tall.
> 2) I am not tall.
> 3) So, the moon is made of green cheese.
> 
> p
> ~p
> So, q
> 
> (_ex contradictione quod libetum_)
Click to expand...


But the problem is that we seem to be able to use (1) in my example all the time. We can imagine saying (1). Should we not make statements like (1) anymore?


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## Answerman

I would like to qualify my answer.

If 'I' is the Roman numeral one, you would still have to flip it to see if their is their is a vowel on the other side.

Am I right now?


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## Jim Johnston

'This sentence is false.'


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## Answerman

The barber of Seville shaves all of those and only those who do not shave themselves.

Does the barber of Seville shave himself?


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## BrianLanier

Answerman said:


> I would like to qualify my answer.
> 
> If 'I' is the Roman numeral one, you would still have to flip it to see if their is their is a vowel on the other side.
> 
> Am I right now?



No.


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## Barnpreacher

Answerman said:


> The barber of Seville shaves all of those and only those who do not shave themselves.
> 
> Does the barber of Seville shave himself?





Why am I seeing Alfalfa singing the barber of Seville in my head?


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## Barnpreacher

The more I sit and think about this I can also see him blowing out bubbles because he swallowed some soap before he sang. Am I crazy or does anyone else remember that episode?


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## Mushroom

OK, you've all heard this one, but I'll try it anyway.

There are two doors, one leads to heaven, the other to hell. In front of each door is one guard. You know that one guard always lies, and that one guard always tells the truth, but you don't know which guard is which, and you don't know which door is which. You are allowed one question only, and you can ask it of only one guard. What question might you ask that will tell you which door is the door to heaven?


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## Mushroom

> The more I sit and think about this I can also see him blowing out bubbles because he swallowed some soap before he sang. Am I crazy or does anyone else remember that episode?


Yes.


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## Answerman

Oh yes, I don't watch much TV anymore unless I want to quiz myself on propaganda techniques, but I do like to watch old classic movies and TV shows. I picked up a couple of sets of Little Rascals at Costco a few years ago, and I remember that part, good stuff!


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## Barnpreacher

Brad said:


> The more I sit and think about this I can also see him blowing out bubbles because he swallowed some soap before he sang. Am I crazy or does anyone else remember that episode?
> 
> 
> 
> Yes.
Click to expand...


That is a vague yes, brother.  Are you calling me crazy or do you remember Alfalfa singing this as well?


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## BrianLanier

Tom Bombadil said:


> BrianLanier said:
> 
> 
> 
> 
> 
> Tom Bombadil said:
> 
> 
> 
> How about this argument:
> 
> 1. If it rains today, then it will not rain hard.
> 2. It did rain hard today.
> 3. Therefore, it did not rain today. (2,3, M.T.)
> 
> 
> 
> 
> 
> 
> Or how about this,
> 
> 1) If I go to San Francisco this summer, I will see my brother. So if I go to San Francisco this summer, and my brother moves to New Mexico before I visit, I will see my brother.
> 
> p --> q
> So, (p & r) --> q
> 
> and you got to love these,
> 
> 1) I am tall.
> 2) I am not tall.
> 3) So, the moon is made of green cheese.
> 
> p
> ~p
> So, q
> 
> (_ex contradictione quod libetum_)
> 
> Click to expand...
> 
> 
> But the problem is that we seem to be able to use (1) in my example all the time. We can imagine saying (1). Should we not make statements like (1) anymore?
Click to expand...


I wonder if this has to do with the content (or semantics). Just like,

This sweater is green,
So, this sweater is not red,

seems to be an inference that we make all of time, but its form is not valid (p, so ~q). The form of the argument is invalid, but because of the content or semantics of the argument, it seems to be an inference we should be willing to accept.

Or, if not, then possibly one could say that the form of your argument is a 'default' form but doesn't perserve truth in *all* instances. But just because it is not truth-perserving in *all* cases, it does not follow that we should not make statements using its form anymore--for the same reason that just because sense experience isn't always reliable, it doesn't follow that we shouldn't generally rely on it.


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## Mushroom

> That is a vague yes, brother. Are you calling me crazy or do you remember Alfalfa singing this as well?


Only trying to be agreeable, brother (But on the serious side, yes, I do remember Alfalfa singing, with bubbles, but can't recall the song). 

Does anyone remember the episode where a wild man from Borneo kept saying, "Eat 'em up, eat 'em up" over and over?


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## Answerman

I do, I like when Spanky kept giving him food from the refrigerator, he had a bottomless stomach.


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## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> 
> 
> BrianLanier said:
> 
> 
> 
> Or how about this,
> 
> 1) If I go to San Francisco this summer, I will see my brother. So if I go to San Francisco this summer, and my brother moves to New Mexico before I visit, I will see my brother.
> 
> p --> q
> So, (p & r) --> q
> 
> and you got to love these,
> 
> 1) I am tall.
> 2) I am not tall.
> 3) So, the moon is made of green cheese.
> 
> p
> ~p
> So, q
> 
> (_ex contradictione quod libetum_)
> 
> 
> 
> 
> But the problem is that we seem to be able to use (1) in my example all the time. We can imagine saying (1). Should we not make statements like (1) anymore?
> 
> Click to expand...
> 
> 
> I wonder if this has to do with the content (or semantics). Just like,
> 
> This sweater is green,
> So, this sweater is not red,
> 
> seems to be an inference that we make all of time, but its form is not valid (p, so ~q). The form of the argument is invalid, but because of the content or semantics of the argument, it seems to be an inference we should be willing to accept.
> 
> Or, if not, then possibly one could say that the form of your argument is a 'default' form but doesn't perserve truth in *all* instances. But just because it is not truth-perserving in *all* cases, it does not follow that we should not make statements using its form anymore--for the same reason that just because sense experience isn't always reliable, it doesn't follow that we shouldn't generally rely on it.
Click to expand...


But my argument was valid, so your first response was disanalogous. Furthermore, I'd actually say that your first argument was an enthymeme. It's invalidity is due to missing premises.

Then, do we really want to deny the universality of M.T.?


----------



## Jim Johnston

Brad said:


> OK, you've all heard this one, but I'll try it anyway.
> 
> There are two doors, one leads to heaven, the other to hell. In front of each door is one guard. You know that one guard always lies, and that one guard always tells the truth, but you don't know which guard is which, and you don't know which door is which. You are allowed one question only, and you can ask it of only one guard. What question might you ask that will tell you which door is the door to heaven?



Ask one of them, "What will the other guard say if I asked him, 'Where does this door lead to.'" 

Then, do the opposite of what he says.


----------



## Barnpreacher

Answerman said:


> I do, I like when Spanky kept giving him food from the refrigerator, he had a bottomless stomach.



It was Uncle George from Borneo.  Classic episode.

I think it was Stymie that asked, "Do he eat people?"


----------



## Mushroom

> Ask one of them, "What will the other guard say if I asked him, 'Where does this door lead to.'"
> 
> Then, do the opposite of what he says.


Yep


> It was Uncle George from Borneo. Classic episode.
> 
> I think it was Stymie that asked, "Do he eat people?"


And yep. Lotta fun.


----------



## Wannabee

Good grief! I had to read almost this whole thread before it dawned on me. Hehe... ahem.


----------



## a mere housewife

I'm assuming that each card has a letter on one side and a number on the other.

I would think you'd have to flip over the one with the vowel, and the one with the 5. The one with the 8 is irrelevant: if it has a vowel on the other side, it fits the rule: if it doesn't have a vowel it doesn't disprove it: the rule is only applicable to cards that have vowels on one side and doesn't state that a card with a consonant has a corresponding odd number. Similarly the card with the T doesn't matter as it can't prove or disprove anything about cards with vowels. But if the card with the 5 turns out to have a vowel on the other side, it has disproved the rule. But no doubt this is like those peg games at Cracker Barrel, where you're only brilliant if you manage to wind up with one.


----------



## a mere housewife

PS. If I'm not supposed to assume that the cards having a letter/number rather than a number/number or letter/letter, I don't see how you can get away with anything less than turning over all four cards....? though I realize that by Cracker Barrel peg game standards that makes me something like a dim bulb.

-edit- I realized that my PS is wrong b/c I wouldn't have to turn over the eight. If it has a vowel well and good, but if not -even if it has another numeral- it doesn't disprove the rule as stated. Did you post the answer in the thread or do you U2U it or will it be a couple days (in which case I'm going to be thinking about this in my sleep) or what?


----------



## Civbert

BrianLanier said:


> Try this basic reasoning test.
> 
> Suppose there are four double-sided cards 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?



I guess someone already got it but I'll post before I look at all the answers.


You need to flip *two* cards.

(R) is "If V, then E".

You need to flip the | I | card.
Justification: to test (R).

You need to flip the |5| card. 
Justification: (R) implies "if not-E, then not-V" by _modus tollens_. 
Since 5 is an odd number (or not-E), then the flip side must be a consonant (or not-V). 

You do NOT need to flip | T |
Justification: (R) does _not _imply "if not-V, then not-E".

You do NOT need to flip | 8 | 
Justification: (R) does _not _imply "if E, then V".


*************************

*Correction:* I was assuming that on every card there is a letter on one side, and a number on the other. But since this is not the case, then you would need to also flip | T | since it is also "not-E" and the flip side must be "not-V" (a consonant or a number). 

So my answer then is *three *cards: | I | | 5 | | T |, since 'I' is a vowel, and '5' and 'T' are not even numbers. Since '8' is an even number, anything can be on the reverse side and not violate the rule.


----------



## Civbert

a mere housewife said:


> ...
> -edit- I realized that my PS is wrong b/c I wouldn't have to turn over the eight. If it has a vowel well and good, but if not -even if it has another numeral- it doesn't disprove the rule as stated. Did you post the answer in the thread or do you U2U it or will it be a couple days (in which case I'm going to be thinking about this in my sleep) or what?



I think you got it.


----------



## BrianLanier

I will post the answer tomorrow; I want to get more people a shot.


----------



## Civbert

BrianLanier said:


> I will post the answer tomorrow; I want to get more people a shot.



Brian, 

One thing that you did not mention in the problem was if each card will have a number on one side and a letter the other, or if a card may have a letter or number on both sides. I believe that would effect the answer. What say you?


----------



## BrianLanier

Civbert said:


> BrianLanier said:
> 
> 
> 
> I will post the answer tomorrow; I want to get more people a shot.
> 
> 
> 
> 
> Brian,
> 
> One thing that you did not mention in the problem was if each card will have a number on one side and a letter the other, or if a card may have a letter or number on both sides. I believe that would effect the answer. What say you?
Click to expand...


You are correct, I should have mentioned that! I will change the original post. (Although, most people probably assumed it anyway).


----------



## BrianLanier

Tom Bombadil said:


> BrianLanier said:
> 
> 
> 
> 
> 
> Tom Bombadil said:
> 
> 
> 
> But the problem is that we seem to be able to use (1) in my example all the time. We can imagine saying (1). Should we not make statements like (1) anymore?
> 
> 
> 
> 
> I wonder if this has to do with the content (or semantics). Just like,
> 
> This sweater is green,
> So, this sweater is not red,
> 
> seems to be an inference that we make all of time, but its form is not valid (p, so ~q). The form of the argument is invalid, but because of the content or semantics of the argument, it seems to be an inference we should be willing to accept.
> 
> Or, if not, then possibly one could say that the form of your argument is a 'default' form but doesn't perserve truth in *all* instances. But just because it is not truth-perserving in *all* cases, it does not follow that we should not make statements using its form anymore--for the same reason that just because sense experience isn't always reliable, it doesn't follow that we shouldn't generally rely on it.
> 
> Click to expand...
> 
> 
> But my argument was valid, so your first response was disanalogous. Furthermore, I'd actually say that your first argument was an enthymeme. It's invalidity is due to missing premises.
> 
> Then, do we really want to deny the universality of M.T.?
Click to expand...


The argument of the 'sweater' was not meant to be analogous or a counter-example to your valid argument. It was mearly intended to show the effect that 'content' and 'semantics' play in argument forms. (A counter-example to the sweater arugment would be: I have brown hair, so I don't wear glasses.) The form was invalid, but because of the semantics of the argument, it still has a true conclusion. I was just wondering whether or not that had something to do with your argument. (Not saying that it does, it was just a thought that popped into my head!) 

The 'sweater' argument is not an enthymeme, since adding more premises to the argument, while maintaining its *form*, would not then render it valid.

As far a M.T. goes, what would be wrong with denying its universality? If your example is a valid argument and is not truth perserving, then it seems to follow that M.T. is not *universally* truth-perserving. I think that this is because of the problems that have been noted with the conditional in general (since the first premise of M.T. is a conditional). These problems have been generally recognized within the literature (so far as I can tell). The same goes for L.E.M. (Hence the development of non-classical logics such as, fuzzy-logic, paraconsistent logics, multi-valued logics, modal logics, etc.) That is why I said that maybe it is best to maintain classical logic (since it seems to be the stongest) and think of these 'laws' as default functions, while noting the problems that we run into. I am by no means convinced that this *should* be the position to take, just that it seems to be a plausible one.


----------



## Croghanite

you may have to flip over all four cards to prove the rule is true.
I would start with the card that has a vowel on it. Then the card with the even number. If the rule proved to be true after flipping those cards in that order, then you must flip over the rest to make sure the rule is true with the four cards that are on the table.

The rule can be proved wrong with flipping as little as one card. You will have to flip them all to prove the rule is true.


----------



## Me Died Blue

I say two: the I and the 5.

The original statement (R1, "If there is a vowel on one side, there is an even number on the other") is equivalent to its contrapositive, which in this case is, "If there is not an even number on one side, there is not a vowel on the other." And since every number has to be either even or odd, every letter has to be a consonant or a vowel, that is equivalent to saying, "If there is an odd number on one side, there is a consonant on the other" (R2).

Of course one can prove the rule wrong in as little as one flip, depending on if it violates the rule or not. But if it is right, it would take exactly two flips to prove so:

|I|: To prove the rule (in the form of R1), one needs to ensure the other side is an even number.

|T|: Regardless of what it on the other side of this card, it can only violate the _converse_ or the _inverse_ (logically equivalent) of the original statement (R1/R2).

|8|: Same as T.

|5|: To prove the rule (in the form of R2), one needs to ensure the other side is a consonant.


----------



## Dan....

I would say three cards: "I" "T" and "5"

For the "I", there must be an even number on the opposite side.
For the "T" there must not be a vowel on the opposite side.
For the "5" there must not be a vowel on the opposite side.

Whatever is on the opposite side of the "8" is irrelevant because "if X then Y" does not prove "if Y then X."


----------



## Mushroom

This is new:


> each with a number on one side and a letter on the other



Since the original post has changed, I will return to my second(!) answer, 2 cards. Since it is now necessary that all the cards have one letter and one number, then it is unnecessay to flip the T. The rule does not specify that a consonant have either an even or odd number on the reverse, so the number on the other side is immaterial, and the same applies to the 8, since the rule does not stipulate a requirement for the reverse of an even number. Only the I and the 5 need to be flipped.

Prior to the change of the OP, I believe my third (!!) answer would have been correct, since it was possible that the T had a vowel on the reverse, which would have disproven the rule.

Of course, my first answer was wrong no matter what, so I don't win the door prize.


----------



## Croghanite

What if the other side of the T card was an even number? 



Brad said:


> This is new:
> 
> 
> 
> each with a number on one side and a letter on the other
> 
> 
> 
> 
> Since the original post has changed, I will return to my second(!) answer, 2 cards. Since it is now necessary that all the cards have one letter and one number, then it is unnecessay to flip the T. The rule does not specify that a consonant have either an even or odd number on the reverse, so the number on the other side is immaterial, and the same applies to the 8, since the rule does not stipulate a requirement for the reverse of an even number. Only the I and the 5 need to be flipped.
> 
> Prior to the change of the OP, I believe my third (!!) answer would have been correct, since it was possible that the T had a vowel on the reverse, which would have disproven the rule.
> 
> 
> 
> 
> 
> Of course, my first answer was wrong no matter what, so I don't win the door prize.
Click to expand...


----------



## Me Died Blue

LAYMAN JOE said:


> What if the other side of the T card was an even number?



That would not be a problem, for the rule only said, "If there is a vowel on one side, there is an even number on the other." That is not logically equivalent to saying, "If there is an even number on one side, there is a vowel on the other." It only means that all vowel-cards have to also have even numbers on them - but there also could be even numbers on other (non-vowel) cards as well. A good example one of my philosophy professors used to illustrate the difference is that it's a true statement (by definition) to say, "If someone is a bachelor, that person is a male." But we know that it's _not_ true to say, "If someone is a male, that person is a bachelor."


----------



## Cheshire Cat

I read the first post only, and here is my answer: 2 Cards. The first ‘I’ card, and the last ‘5’ card. 

‘I’ is the only vowel. T is not a vowel, so that card isn’t relevant. 

Now the rule is “if there is a vowel on one side, there is an even number on the other. It doesn’t say one way or the other whether or not a non-vowel could have an even number on its other side, so the 8 card doesn’t have to be flipped in order to verify the rule. The 5 card is the tricky one for me. I think the 5 card needs to be flipped in order to see if there is a vowel on the other side. Because if there is, then the rule would be falsified. 

Now its time to read the thread and see where I messed up haha.

edit: After reading the thread I'm still not sure if I'm right


----------



## Croghanite

your correct.
You would still need to flip the T card to see if a vowel is on the other side. 



Me Died Blue said:


> LAYMAN JOE said:
> 
> 
> 
> What if the other side of the T card was an even number?
> 
> 
> 
> 
> That would not be a problem, for the rule only said, "If there is a vowel on one side, there is an even number on the other." That is not logically equivalent to saying, "If there is an even number on one side, there is a vowel on the other." It only means that all vowel-cards have to also have even numbers on them - but there also could be even numbers on other (non-vowel) cards as well. A good example one of my philosophy professors used to illustrate the difference is that it's a true statement (by definition) to say, "If someone is a bachelor, that person is a male." But we know that it's _not_ true to say, "If someone is a male, that person is a bachelor."
Click to expand...


----------



## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> 
> 
> BrianLanier said:
> 
> 
> 
> I wonder if this has to do with the content (or semantics). Just like,
> 
> This sweater is green,
> So, this sweater is not red,
> 
> seems to be an inference that we make all of time, but its form is not valid (p, so ~q). The form of the argument is invalid, but because of the content or semantics of the argument, it seems to be an inference we should be willing to accept.
> 
> Or, if not, then possibly one could say that the form of your argument is a 'default' form but doesn't perserve truth in *all* instances. But just because it is not truth-perserving in *all* cases, it does not follow that we should not make statements using its form anymore--for the same reason that just because sense experience isn't always reliable, it doesn't follow that we shouldn't generally rely on it.
> 
> 
> 
> 
> But my argument was valid, so your first response was disanalogous. Furthermore, I'd actually say that your first argument was an enthymeme. It's invalidity is due to missing premises.
> 
> Then, do we really want to deny the universality of M.T.?
> 
> Click to expand...
> 
> 
> The argument of the 'sweater' was not meant to be analogous or a counter-example to your valid argument. It was mearly intended to show the effect that 'content' and 'semantics' play in argument forms. (A counter-example to the sweater arugment would be: I have brown hair, so I don't wear glasses.) The form was invalid, but because of the semantics of the argument, it still has a true conclusion. I was just wondering whether or not that had something to do with your argument. (Not saying that it does, it was just a thought that popped into my head!)
> 
> The 'sweater' argument is not an enthymeme, since adding more premises to the argument, while maintaining its *form*, would not then render it valid.
> 
> As far a M.T. goes, what would be wrong with denying its universality? If your example is a valid argument and is not truth perserving, then it seems to follow that M.T. is not *universally* truth-perserving. I think that this is because of the problems that have been noted with the conditional in general (since the first premise of M.T. is a conditional). These problems have been generally recognized within the literature (so far as I can tell). The same goes for L.E.M. (Hence the development of non-classical logics such as, fuzzy-logic, paraconsistent logics, multi-valued logics, modal logics, etc.) That is why I said that maybe it is best to maintain classical logic (since it seems to be the stongest) and think of these 'laws' as default functions, while noting the problems that we run into. I am by no means convinced that this *should* be the position to take, just that it seems to be a plausible one.
Click to expand...


The sweater argument could have been an enthymeme, I think. You just left out the first premise:

Unstated Premise. If my sweater is green, then it is not red.

1. My sweater is green.

2. Therefore, my sweater is not red.

Moving on....

The M.P. was a *valid* argument. It was not *sound.* P2 negated P1. So, we have no problems on that score which woulld make us challenege the universality (*other issues* with conditionals not withstanding). So, we're safe. 

As far as the challeneges to material implication (and other challenges to conditionals), I suggest these entries by Valicella:

Maverick Philosopher Clearing up Confusion about Material Implication

There's about 9 there.

It's at least the "other side" of the argument. 

As far as the rest, I'd begin by saying your comments may be similar to those who argue that "induction is a fallacy" by holding it to the standards of deductive logic. So, conditionals in porppositional logic must be used properly.


----------



## Me Died Blue

LAYMAN JOE said:


> your correct.
> You would still need to flip the T card to see if a vowel is on the other side.



With the _original_ wording of the question...


----------



## sotzo

I and 5.

"I" could have an odd # and negate the rule.
"T" doesn't matter because it wouldn't negate the rule whether an odd or even #.
"8" doesn't matter because it wouldn't negate the rule if it were a consonant.
"5" could have a vowel and negate the rule.

By the way, I think the Trinity Broadcasting Network website has a similar challenge on their boards...something to do with working out how many of their programs you have to watch before you turn into a Precious Moments character.


----------



## B.J.

I scrolled down as fast as I could so that I did not see any answers. My guess is that card |I| and |8| are the only ones that need to be verified because they are the only ones that have a vowel and even number. The other two cards are irrelavent given the rule. So go ahead nd tell me I am wrong. Whats the trick?


----------



## sotzo

BTW, did I miss the answer in the thread somewhere?

What is the official solution to this epistemic dilemma?


----------



## Croghanite

Me Died Blue said:


> LAYMAN JOE said:
> 
> 
> 
> your correct.
> You would still need to flip the T card to see if a vowel is on the other side.
> 
> 
> 
> 
> With the _original_ wording of the question...
Click to expand...




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



If you flip the T card and find a vowel, that would break the rule. You will have to flip all cards to prove the rule to be* true*. You may only need to flip as little as one card to prove the rule to be false.


----------



## Jaymin Allen

I'm going to say just 2 cards.

Step 1:
Flip over | I |, and check if there is an even number on the other side.

Step 2:
Flip over | 8 |, and check if there is a vowel on the other side.

The rules apply only to vowels and even numbers. Nothing was said about consonants and odd numbers. If I flip over | T |, the number can be odd or even. If I flip over | 5 |, the letter can be a vowel or a consonant. It doesn't matter.


----------



## swilson

I haven't read all the posts, because i dont have time....but here is my answer:

Zero

A rule is a rule whether followed or not...the rule is still true of the four cards even if it is not followed by the four cards....but, I am an absolutist.


----------



## Civbert

sotzo said:


> By the way, I think the Trinity Broadcasting Network website has a similar challenge on their boards...something to do with working out how many of their programs you have to watch before you turn into a Precious Moments character.


----------



## Mushroom

> If you flip the T card and find a vowel, that would break the rule.


Nay, friend, for this has been added:


> Suppose there are four cards, *each with a number on one side and a letter on the other*


Therefore the T must have a number on the other side, and whether an odd or even is immaterial to the rule.


----------



## Croghanite

Brad said:


> If you flip the T card and find a vowel, that would break the rule.
> 
> 
> 
> Nay, friend, for this has been added:
> 
> 
> 
> Suppose there are four cards, *each with a number on one side and a letter on the other*
> 
> Click to expand...
> 
> Therefore the T must have a number on the other side, and whether an odd or even is immaterial to the rule.
Click to expand...


How many times has the question changed ?!

The _new question_ answer is 2 cards. The I and the 5 card. The I card must have an even number and you must check to see if a vowel is on the other side of the 5 card.
Final answer, lock it in....... When will the official answer be given ?


----------



## Croghanite

What if the table the cards are on is made of glass ? you wouldn't have to flip any of the cards to see if the rule is true.


----------



## Jim Johnston

brian,

If we can deny the universality of M.T., why was my answer automatically wrong??


----------



## BrianLanier

Tom Bombadil said:


> brian,
> 
> If we can deny the universality of M.T., why was my answer automatically wrong??



Paul,

If we can deny the universality of our sense experience, then why is my seeing pink fairies right now automatically wrong.


----------



## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> brian,
> 
> If we can deny the universality of M.T., why was my answer automatically wrong??
> 
> 
> 
> 
> 
> 
> Paul,
> 
> If we can deny the universality of our sense experience, then why is my seeing pink fairies right now automatically wrong.
Click to expand...


Is that a fallacious shifting the burden of proof on your part? 

In any event, if you mean that you are being appeared to in a pink-fairy way, then it's not. 

If you mean that there are actual extra-mental objects that are pink and in ther fairy category, it's not *automatically* wrong either. Now perhaps *I* wouldn't be warranted in believing that said entities exist, but since I don't deny the possibilty that they exist, then I don't *automatically* conclude that you're wrong - if we grant the setting of the argument is that you're being honest about how you are being appeared to - in the sense of saying that you most certainly are not. Now, I may say that I *think* you are mistaken, and so for your claim to be analogius, you'd have to edit your answer on page one that "one *is not* the answer." In fact, if M.T. isn't a universally valid way of reasoning, then how don't see how you could say that my answer was wrong. At best you'd have to say something like, "I don't think it is correct, but it could be." (I'm just trying to save some face here, brother. if I can get you to say that my answer may also have been right, then I'll save the reputation of paedobaptists everywhere! )

Likewise, if what you said about M.T. above is correct, then I don't see how my answer was wrong; _given those assumtions_.


----------



## BrianLanier

I was obviously kidding in my last post.

I was just reading "Conditionals" by Dorothy Edgington in The Blackwell Guide to Philosophical Logic, and as usually, things are very much complicated. However, the extended discussion there still agrees with much of what Jennifer Fisher says in On the Philosophy of Logic that I was telling you about. The consensus still seems to remain, namely, that there does exist certain problem cases with the conditional, whether or not you take it as truth-functional (hook, or horseshoe), non-truth functional (arrow), or Probabilistically. I am so, so far from forming a confident belief in the matter.


----------



## Jim Johnston

I know you were, but I used it to springboard into a post. I also made some comments indicating the light-hearted nature I was responding in. Just so there's no misunderstanding, I'll add one of these  !

Btw, I ordered the Fisher book....


----------



## BrianLanier

Tom Bombadil said:


> I know you were, but I used it to springboard into a post. I also made some comments indicating the light-hearted nature I was responding in. Just so there's no misunderstanding, I'll add one of these  !
> 
> Btw, I ordered the Fisher book....



Ha...I was writing my last post before I saw yours! I know your posts were 'lightheartedness' instantiated! So no need for the , at least with me.


----------



## Jim Johnston

BrianLanier said:


> I know your posts were 'lightheartedness' instantiated!




do abstract universals have the property of being abstract? Is the property of being abstract instantiated in abstract entities?


----------



## BrianLanier

Tom Bombadil said:


> Now, I may say that I *think* you are mistaken, and so for your claim to be analogius, you'd have to edit your answer on page one that "one *is not* the answer." In fact, if M.T. isn't a universally valid way of reasoning, then how don't see how you could say that my answer was wrong. At best you'd have to say something like, "I don't think it is correct, but it could be."
> 
> Likewise, if what you said about M.T. above is correct, then I don't see how my answer was wrong; _given those assumtions_.



Not so!

We can empirically test our reasoning (sometimes) to see whether or not the rule that we take apriori to be truth-functional is in a certain instance. So in case of the test above, we can empirically test to see whether or not *this* use of the conditional is a truth-perserving instance (as a said before, *most* cases are). And as we can see, it is a truth-perserving instance, therefore I can have a lot more warrant for my belief that your answer was incorrect than just "I don't think it was incorrect".


----------



## Jim Johnston

Too fast!

Then why not test it on the | 8 | as well? Why assume affirming the consequent *necessarily* leads to a false conclusion?


----------



## BrianLanier

Tom Bombadil said:


> BrianLanier said:
> 
> 
> 
> I know your posts were 'lightheartedness' instantiated!
> 
> 
> 
> 
> 
> do abstract universals have the property of being abstract? Is the property of being abstract instantiated in abstract entities?
Click to expand...


If abstract universals have any property whatever, they must have the property of being identical to itself, namely of being 'abstract'.

I don't know what you mean by 'in' abstract entities. Do you mean 'in' as in 'in the description' of abstract entities? Or do you mean 'in' as in 'of' abstract entities? Wasn't the nature of your post an 'instance' of being 'lightheartedness'? If so, then wouldn't it be an instantiation of it?


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## Jim Johnston

BrianLanier said:


> Tom Bombadil said:
> 
> 
> 
> 
> 
> BrianLanier said:
> 
> 
> 
> I know your posts were 'lightheartedness' instantiated!
> 
> 
> 
> 
> 
> do abstract universals have the property of being abstract? Is the property of being abstract instantiated in abstract entities?
> 
> 
> 
> Click to expand...
> 
> 
> If abstract universals have any property whatever, they must have the property of being identical to itself, namely of being 'abstract'.
> 
> I don't know what you mean by 'in' abstract entities. Do you mean 'in' as in 'in the description' of abstract entities? Or do you mean 'in' as in 'of' abstract entities? Wasn't the nature of your post an 'instance' of being 'lightheartedness'? If so, then wouldn't it be an instantiation of it?
Click to expand...



it didn't have much to do with what you said, i was just spring boarding again and bringing up what some consider an interesting problem for realists....


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## BrianLanier

Tom Bombadil said:


> BrianLanier said:
> 
> 
> 
> 
> 
> Tom Bombadil said:
> 
> 
> 
> do abstract universals have the property of being abstract? Is the property of being abstract instantiated in abstract entities?
> 
> 
> 
> 
> 
> 
> If abstract universals have any property whatever, they must have the property of being identical to itself, namely of being 'abstract'.
> 
> I don't know what you mean by 'in' abstract entities. Do you mean 'in' as in 'in the description' of abstract entities? Or do you mean 'in' as in 'of' abstract entities? Wasn't the nature of your post an 'instance' of being 'lightheartedness'? If so, then wouldn't it be an instantiation of it?
> 
> Click to expand...
> 
> 
> 
> it didn't have much to do with what you said, i was just spring boarding again and bringing up what some consider an interesting problem for realists....
Click to expand...


I figured as much, since that is not something that I would expect you to argue for, at least not in the actual world (and given that you don't exist in any other world [given Actualism], I don't have much to worry about)!


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## Mushroom

Considering that both of you are merely figments of my (or your?) imagination, none of this actually (given Actualism) matters. This is an abstract universality that posesses the characteristic of being both abstract and universal both 'in' as 'in the description' of an abstract entity AND "in" as in 'in' an abstract entity.


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## Jim Johnston

Brad said:


> Considering that both of you are merely figments of my (or your?) imagination, none of this actually (given Actualism) matters. This is an abstract universality that posesses the characteristic of being both abstract and universal both 'in' as 'in the description' of an abstract entity AND "in" as in 'in' an abstract entity.



Especially since I'm a solipsist what you just said doesn't matter! Dang it! I said "you." It's so hard to be a solipsist these days, it was easier when no one was around.


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## BrianLanier

The answer has now been posted in the opening post. Thanks all for participating, and patiently waiting for the answer to be posted.


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## Cheshire Cat

booyaa! My logic class has finally payed off.


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## Cheshire Cat

Paul, you write "How about this argument:

1. If it rains today, then it will not rain hard.
2. It did rain hard today.
3. Therefore, it did not rain today. (2,3, M.T.)"

I didn't read the back and forth on this subject, partly because I am too lazy, but also because I don't have the time. Anyway, I don't really see what's wrong here. Of course the argument is valid, but it is not sound. Premise 2 necessitates the falsity of premise 1. If the argument is not sound, then what is the problem?


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## Brian Bosse

Hello Gentlemen,

Forgive me for jumping into a thread which I know not the context. 



> 1. If it rains today, then it will not rain hard.
> 2. It did rain hard today.
> 3. Therefore, it did not rain today. (2,3, M.T.)"
> 
> I didn't read the back and forth on this subject, partly because I am too lazy, but also because I don't have the time. Anyway, I don't really see what's wrong here. Of course the argument is valid, but it is not sound. Premise 2 necessitates the falsity of premise 1. If the argument is not sound, then what is the problem?



This argument is not valid. Premise 2 is not the antecedent of the conditional in premise 1. Here is what I think was meant...

*Premise 1:* A → B
*Premise 2:* A ∧ ¬B

From these two premises one can validly conclude to B. What is interesting is that one can validly conclude to anything. The reason for this is that the two premises are inconsistent. Premise 1 is logically equivalent to ¬(A ∧ ¬B), which is the contradiction of premise 2. From a contradiction everything (or anything) follows.

Brian


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## Cheshire Cat

Hmmm Brian I thought the form was...

premise 1: If p, then ~q
premise 2: ~~q (actually q, but its equivalent to ~~q)
C: Therefore ~p. 

Which would be a valid modus tollens. No?


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## Brian Bosse

Hello Caleb,

Yep, you are correct. My bad. I did not pay close enough attention. Let's make this precise.

Let 'P' stand for "it rains today". Let '¬Q' stand for "it will not rain hard today". Then our argument is like this...

*1.* P → ¬Q
*2.* Q (Notice: this says, "It will rain hard today.") 
*3.* ¬¬Q
*4.* ¬P

This is a valid argument. The conclusion states that "it is not the case that it rains today." Now, the trouble people are having here is that we understand Q → P to be the case. We have already proved ¬P (step 4). With the additional understanding that Q → P we can show ¬Q. In light of premise 2 (Q), this means the premises are inconsistent. Here is an interesting epistemological question, which premise do we give up?

*A.* Q → P
*B.* P → ¬Q
*C.* Q

They cannot all be held consistently. A seems to be definitionally true. However, A can be held consistently with both B and C. So, which one do we give up? How do we determine which premise to dismiss given contradictory premises? This question speaks to the heart of such issues as falsifiability. 

Brian


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