Jump to content
The Education Forum

Conditional Reasoning, Skills in Deduction & Forming Proper Conclusions in this JFK Thing of Ours


Glenn Nall
 Share

Recommended Posts

I don't mean to annoy anyone - i do feel that this is an appropriate (and fun) topic in each of us understanding more what's involved in the conclusion forming process which can either lead to errors in deduction or to progress in our pursuit of accuracy and truth in the solution.

one of the real reasons i'm into this thing so much is my passion for 'problem solving,' and i'm sure that's the case for many of ya'll. so these kinds of things are fun, and good for our brains (which we need to solve this thing!)

i'm just pasting in this little bit of text and this quick test i found (that I failed) without the answer. if any of you have seen it already, which is very likely, please don't publish the answer, or cheat. ;)

so, check it out:

If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
Conditional traps
A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.
You can affirm or deny either the antecedent or consequent, which may lead to error.
Denying the consequent
Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.
Denying the antecedent
Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.
Affirming the consequent
This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.
The card trap
A classic trap was created some years ago;
Four cards are laid out as below:
EK47.jpg
The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'
The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?
OR (these are the same challenges, just worded a little differently):
Which card(s) must you turn over in order to test the truth of the proposition that if a card shows a vowel on one face, then its opposite face is an EVEN number?
Discuss it among yourselves... :)
Edited by Glenn Nall
Link to comment
Share on other sites

  • Replies 129
  • Created
  • Last Reply

Top Posters In This Topic

moved to Quote -

Edited by Glenn Nall
Link to comment
Share on other sites

I don't mean to annoy anyone - i do feel that this is an appropriate (and fun) topic in each of us understanding more what's involved in the conclusion forming process which can either lead to errors in deduction or to progress in our pursuit of accuracy and truth in the solution.

one of the real reasons i'm into this thing so much is my passion for 'problem solving,' and i'm sure that's the case for many of ya'll. so these kinds of things are fun, and good for our brains (which we need to solve this thing!)

i'm just pasting in this little bit of text and this quick test i found (that I failed) without the answer. if any of you have seen it already, which is very likely, please don't publish the answer, or cheat. ;)

so, check it out:

If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
Conditional traps
A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.
You can affirm or deny either the antecedent or consequent, which may lead to error.
Denying the consequent
Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.
Denying the antecedent
Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.
Affirming the consequent
This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.
The card trap
A classic trap was created some years ago;
Four cards are laid out as below:
EK47.jpg
Given the condition: 'If a card has a vowel on one side, then it has an even number on the other side.'
The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

SO - do these statements follow?

- E HAS an EVEN NUMBER on the flip side

- K CAN HAVE an EVEN NUMBER on the flip side

- 4 ...?

- 7 ...?

As has been established, turning E, a vowel, over proves an EVEN number is on the other side.

What does turning K establish...?

What does turning 4 establish...?

What does turning 7 establish...?

here's another way of looking at it: Each card has FOUR possibilities - a Vowel, a Consonant, an Even # or an Odd #.

given ONLY that Vowel = Even, then what do we KNOW about the others?

Consonant CAN = Even, Odd or Vowel

Even CAN = Odd, Even, Consonant or Vowel

Odd CAN = ...

which one CANNOT = something...?

Edited by Glenn Nall
Link to comment
Share on other sites

"The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side."

Glenn,

Your post reminds me of the importance of accepted definition. With DVP, as you're aware, I've asked for his definition of "evidence" so that he and I may have a rational discussion of "evidence" that implicates Oswald.

This post of yours lays out this predicate: "If a card has a vowel on one side...."

The problem here is, how do you define "vowel"?

E is clearly a vowel; K is clearly not. The numerals 4 and 7, being numbers, have no vowel or consonant. But if by "4" you mean the word "four", then taking the word we've got two vowels. Same for "7".

So what's your definition of vowel?

It appears to me you're arguing as I do with DVP on the one hand, but weasling as I think DVP does on definitions on the other.

Link to comment
Share on other sites

this is a reasoning test designed by a psychologist in the 70's in order to exemplify the trap that people can get themselves into so easily. the test is a bit tricky, but it IS based on the standard definitions that most people are familiar with.

the 5, not 7, vowels, and the numbers are numbers - the problem is presented at face value, and nothing extra should be read into it. It's simply a problem based on eliminating impossibilities and using reason to arrive at an answer.

i'm a little disappointed that you feel i've ever given a reason to suspect i weasle or waffle on anything, that my definition of anything is other than what (most of) the rest of you seem to take as a given. where in these instructions does it even suggest a whole word is in play?

(these are not my instructions. as i think i stated at the beginning, i've just pasted this in from its original webpage. I chose not to disclose the author so that no one would be tempted to just google the answer.)

i posted this to provide a way of thinking about how we arrive at conclusions, and how we can make mistakes arriving at conclusions. if you think my aim is to be sneaky, i'd be honored if you could show me something i've done to suggest that this is my motive in here.

i was trying to offer something constructive, relative and fun. i was not trying to start yet one more argument.

P.S. How do YOU define "vowel", Jon? I truly didn't realize there were alternate definitions.

Edited by Glenn Nall
Link to comment
Share on other sites

this is what follows the description of the problem:

"More than half of people questioned said * * * * * * [wrong answer].
[...]
Only 4% said * * * * * * [the correct answer]. [...] "
it said more, but i've hidden the giveaways. Most people missed this. 4% got it right.
Edited by Glenn Nall
Link to comment
Share on other sites

I don't mean to annoy anyone - i do feel that this is an appropriate (and fun) topic in each of us understanding more what's involved in the conclusion forming process which can either lead to errors in deduction or to progress in our pursuit of accuracy and truth in the solution.

one of the real reasons i'm into this thing so much is my passion for 'problem solving,' and i'm sure that's the case for many of ya'll. so these kinds of things are fun, and good for our brains (which we need to solve this thing!)

i'm just pasting in this little bit of text and this quick test i found (that I failed) without the answer. if any of you have seen it already, which is very likely, please don't publish the answer, or cheat. ;)

so, check it out:

If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
Conditional traps
A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.
You can affirm or deny either the antecedent or consequent, which may lead to error.
Denying the consequent
Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.
Denying the antecedent
Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.
Affirming the consequent
This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.
The card trap
A classic trap was created some years ago;
Four cards are laid out as below:
EK47.jpg
Given the condition: 'If a card has a vowel on one side, then it has an even number on the other side.'
The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

so, do these follow?

- E HAS an EVEN NUMBER on the flip side

- K CAN HAVE an EVEN NUMBER on the flip side

- 4 ...?

- 7 ...?

Turning E proves an EVEN number. Turning K proves...

Only 1 of those cards can be used to prove your statement. Turn over the E and if it has an even number, then it's proved. turning over the other 3 prove nothing. You can't assume anything about any of the cards, you can only use what you see. you only see one vowel, that's the only card you can consider a vowel. You can't hunt for a hidden definition to make a vowel. Correct answer is 1.

Note: I answered this before I saw your answer.

Edited by Kenneth Drew
Link to comment
Share on other sites

I don't mean to annoy anyone - i do feel that this is an appropriate (and fun) topic in each of us understanding more what's involved in the conclusion forming process which can either lead to errors in deduction or to progress in our pursuit of accuracy and truth in the solution.

one of the real reasons i'm into this thing so much is my passion for 'problem solving,' and i'm sure that's the case for many of ya'll. so these kinds of things are fun, and good for our brains (which we need to solve this thing!)

i'm just pasting in this little bit of text and this quick test i found (that I failed) without the answer. if any of you have seen it already, which is very likely, please don't publish the answer, or cheat. ;)

so, check it out:

If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
Conditional traps
A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.
You can affirm or deny either the antecedent or consequent, which may lead to error.
Denying the consequent
Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.
Denying the antecedent
Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.
Affirming the consequent
This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.
The card trap
A classic trap was created some years ago;
Four cards are laid out as below:
EK47.jpg
Given the condition: 'If a card has a vowel on one side, then it has an even number on the other side.'
The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

so, do these follow?

- E HAS an EVEN NUMBER on the flip side

- K CAN HAVE an EVEN NUMBER on the flip side

- 4 ...?

- 7 ...?

Turning E proves an EVEN number. Turning K proves...

Only 1 of those cards can be used to prove your statement. Turn over the E and if it has an even number, then it's proved. turning over the other 3 prove nothing. You can't assume anything about any of the cards, you can only use what you see. you only see one vowel, that's the only card you can consider a vowel. You can't hunt for a hidden definition to make a vowel. Correct answer is 1.

Note: I answered this before I saw your answer.

MY Bad, if it appears that i wrote the answer. those were prompts to encourage participation. I corrected the wording.

[edited] - I hid my response cause i want to see, if any, what kind of discussion this could prompt. The discussion would be more interesting than the solution. big time.

Edited by Glenn Nall
Link to comment
Share on other sites

I don't mean to annoy anyone - i do feel that this is an appropriate (and fun) topic in each of us understanding more what's involved in the conclusion forming process which can either lead to errors in deduction or to progress in our pursuit of accuracy and truth in the solution.

one of the real reasons i'm into this thing so much is my passion for 'problem solving,' and i'm sure that's the case for many of ya'll. so these kinds of things are fun, and good for our brains (which we need to solve this thing!)

i'm just pasting in this little bit of text and this quick test i found (that I failed) without the answer. if any of you have seen it already, which is very likely, please don't publish the answer, or cheat. ;)

so, check it out:

If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
Conditional traps
A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.
You can affirm or deny either the antecedent or consequent, which may lead to error.
Denying the consequent
Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.
Denying the antecedent
Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.
Affirming the consequent
This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.
The card trap
A classic trap was created some years ago;
Four cards are laid out as below:
EK47.jpg
Given the condition: 'If a card has a vowel on one side, then it has an even number on the other side.'
The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

so, do these follow?

- E HAS an EVEN NUMBER on the flip side

- K CAN HAVE an EVEN NUMBER on the flip side

- 4 ...?

- 7 ...?

Turning E proves an EVEN number. Turning K proves...

Only 1 of those cards can be used to prove your statement. Turn over the E and if it has an even number, then it's proved. turning over the other 3 prove nothing. You can't assume anything about any of the cards, you can only use what you see. you only see one vowel, that's the only card you can consider a vowel. You can't hunt for a hidden definition to make a vowel. Correct answer is 1.

Note: I answered this before I saw your answer.

incorrect answer.

MY Bad, if it appears that i left an answer. those were prompts to encourage participation. I'll correct the wording.

it can't be incorrect. turning one card tells you something, turning all or one of the other three tell you nothing. That's the only possibilities. There is only one of the 4 cards that have a vowel on the side you can see.

Your clues..... K can have an even number on the back side means nothing as the K is not a vowel

the 4 card or 7 card are not vowels, so it doesn't matter what is on the other side.

Remember that no other assumptions bear on this test. Only 4 cards are involved, no more. only one of those have a vowel so that is the only card that can be considered.

Link to comment
Share on other sites

not exactly correct. depending on what is revealed on the other side, turning certain other(s) can tell you something. this is the problem, in fact - finding what you can learn from turning a card (asking the right question).

and not reading the question correctly is probably the single biggest mistake made, i'm seeing.

Edited by Glenn Nall
Link to comment
Share on other sites

the key is understanding EXACTLY what this means:

If a card has a vowel on one side, then it has an even number on the other side.

a lot like understanding exactly and ONLY what three empty shells on the floor means...

unless someone has a direct question, I'll stay out of this for now. if someone hits the right answer, or doesn't, i'll leave it to discussion.

i like seeing how people think - this doesn't mean that one way of thinking is right and another wrong - one way may lead to the correct conclusion more easily than another - and one way may lead AWAY from the correct answer, (which is not a 'right' way of thinking if fact is what's sought, i guess).

John Dolva's explanation is what's so neat about this...

Edited by Glenn Nall
Link to comment
Share on other sites

e is a card, k is a card etc. k and seven are not cards covered by the condition. only e and 4 are. if turning e over shows a even number it's true for e which is a card. ditto 4.

answer 2.

Link to comment
Share on other sites

e is a card, k is a card etc. k and seven are not cards covered by the condition. only e and 4 are. if turning e over shows a even number it's true for e which is a card. ditto 4.

answer 2.

The reason I would not agree that the answer is two is because of how the question is asked.

If a card has a vowel on one side, then it has an even number on the other side. The first qualifier is "if a card has a vowel on one side, then"

So looking at those 4 cards, the 'only thing' you can look for is, "if it has a vowel on one side'. If it does, then you can look at the other side. If you don't see a vowel on one side, 'then' you don't get to look at the other side. There is an "if" "then" If you can't find the 'first' if, then you don't get to look for the 'then'.

It is not worded as " you may also look to see if there is a vowel on the back side of an even number. " You have to satisfy the "if" before you can go further.

Link to comment
Share on other sites

hmmm... ahh but which is one side and which is the other?

Link to comment
Share on other sites

reading these tells me where mistakes are made in the thinking process. so fascinating. i've never looked at one of these from this end.

when a proper explanation is made here, you'll be able to go through this and see what constitutes simple logic - getting from one point to another accurately - and how mistakes are easily made without even being noticed...

(note i did not say "when a correct answer is reached...")

Edited by Glenn Nall
Link to comment
Share on other sites

Please sign in to comment

You will be able to leave a comment after signing in



Sign In Now
 Share

×
×
  • Create New...