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

[Glenn Nall]

I'm cutting myself off now. have phun...

[Paul Hailes]

I think the answer is E and 7.

E to check that there is an even number on the other side ( if an odd number is seen we have proven the statement false immediately, but not yet proven only even numbers will appear) and 7 because if a vowel appears on the other side we have again disproven the statement .

Turning over K proves nothing. There is no reason to assume it cannot have an even number on its reverse side. And 4 is not an option because, as mentioned by Mark above, there is no reason to suppose a card with an even number has to have a vowel on its reverse.

[Terry Martin]

I am making an assumption that the cards have a letter on one side and a number on the reverse. This may not be true as it is not stipulated in the original premise.

Going on that assumption, you would have to turn over all cards except the K.

The E to prove there is an even number on the reverse, the 4 to prove there is a vowel on the reverse, and the 7 to prove there is a consonant on the reverse.

Of course, my original assumption may be in error.

[Robert Prudhomme]

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:

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)?

Discuss it among yourselves...

All four cards have to be turned over. The "K" could have an even number on the other side, and the "7" could have a vowel on the other side. To only turn over the "E" and the "4" would be to make an assumption about the other two cards.

Edit:

I changed my answer from four cards to two, the "E" and the "4", after looking more closely at the conditions. Our statement is only establishing a relationship between vowels and even numbers, and says nothing about consonants and odd numbers. In other words, consonants and odd numbers can have anything they want on the reverse side, and it will not affect the stated condition.

Edit:

On the other hand, if the "K" had an even number on the reverse, or the "7" had a vowel on the reverse, that would tend to invalidate the statement. I think I will go with four again.

Edited August 11, 2015 by Robert Prudhomme

[Mark Knight]

Robert, the word "only" is not found in the statement we are dealing with.

The statement does not say that ONLY vowels will have even numbers on the reverse. The statement does not say that even numbers will ONLY have vowels on the reverse.

Those are ASSUMPTIONS that are not based upon our statement. They MAY or MAY NOT be true.

So turning over ANY card beyond the E would only tend to prove or disprove those ASSUMPTIONS, and not necessarily affect the statement we were given.

Now...have I said anything that is incorrect?

[Robert Prudhomme]

Robert, the word "only" is not found in the statement we are dealing with.

The statement does not say that ONLY vowels will have even numbers on the reverse. The statement does not say that even numbers will ONLY have vowels on the reverse.

Those are ASSUMPTIONS that are not based upon our statement. They MAY or MAY NOT be true.

So turning over ANY card beyond the E would only tend to prove or disprove those ASSUMPTIONS, and not necessarily affect the statement we were given.

Now...have I said anything that is incorrect?

However, saying that "if a card has a vowel on one side, then it has an even number on the other side" is the same as saying "if a card has an even number on one side, then it has a vowel on the other side". This establishes a rule for vowels and even numbers.

Finding an even number opposite of the "K" or a vowel opposite of the "7" will make the rule about vowels and even numbers untrue.

[Mark Knight]

However, saying that "if a card has a vowel on one side, then it has an even number on the other side" is the same as saying "if a card has an even number on one side, then it has a vowel on the other side". This establishes a rule for vowels and even numbers.

Finding an even number opposite of the "K" or a vowel opposite of the "7" will make the rule about vowels and even numbers untrue.

Nope.

You are making assumptions.

Remember the examples? Let's say we are given the statement, "If it is raining, then I will get wet." It does NOT necessarily follow that " If I am wet, then it is raining." Just because ONE statement is true, it does NOT mean that the converse must also be true.

And nowhere in the original statement does it say that even numbers are ONLY found on the reverse of cards with vowels. For all we know, even numbers might also be on the reverse of some cards with consonants. The "rule," as given to us, ONLY applied to vowels having even numbers on the reverse side.

ANYTHING else we conclude is NOT supported by the original statement we are given.

ANYTHING else we conclude is merely an assumption.

[Glenn Nall]

I am making an assumption that the cards have a letter on one side and a number on the reverse. This may not be true as it is not stipulated in the original premise.

Going on that assumption, you would have to turn over all cards except the K.

The E to prove there is an even number on the reverse, the 4 to prove there is a vowel on the reverse, and the 7 to prove there is a consonant on the reverse.

Of course, my original assumption may be in error.

yes, don't make assumptions - a good rule in any investigation, i'd assume ( ), is to not jump to any conclusions, no matter how small. yours will take you down the wrong road.

[Glenn Nall]

However, saying that "if a card has a vowel on one side, then it has an even number on the other side" is the same as saying "if a card has an even number on one side, then it has a vowel on the other side". This establishes a rule for vowels and even numbers.

Finding an even number opposite of the "K" or a vowel opposite of the "7" will make the rule about vowels and even numbers untrue.

Nope.

You are making assumptions.

Remember the examples? Let's say we are given the statement, "If it is raining, then I will get wet." It does NOT necessarily follow that " If I am wet, then it is raining." Just because ONE statement is true, it does NOT mean that the converse must also be true.

And nowhere in the original statement does it say that even numbers are ONLY found on the reverse of cards with vowels. For all we know, even numbers might also be on the reverse of some cards with consonants. The "rule," as given to us, ONLY applied to vowels having even numbers on the reverse side.

ANYTHING else we conclude is NOT supported by the original statement we are given.

ANYTHING else we conclude is merely an assumption.

Just because ONE statement is true, it does NOT mean that the converse must also be true.

when put like that, we all say, "well, of COURSE!," but it's our tendency to do just this that makes this test tricky.

i read Robert's input - it's amazing, we are all a bunch of higher than average, (some MUCH higher than average), intelligent people - and yet, the mistake that is being made is the simplest little thing...!

From Wikipedia:

"The _______ selection task (or four-card problem) is a logic puzzle devised by ______ _______ in 1966. It is one of the most famous tasks in the study of deductive reasoning. An example of the puzzle is:

You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?

A response that identifies a card that need not be inverted, or that fails to identify a card that needs to be inverted, is incorrect. The original task dealt with numbers (even, odd) and letters (vowels, consonants). <<< ...that's this one...

The importance of the experiment is not in justifying one answer of the ambiguous problem, but in demonstrating the inconsistency of applying the logical rules by the people when the problem is set in two different contexts but with very similar connection between the facts."

Edited August 11, 2015 by Glenn Nall

[Mark Knight]

To apply this to JUST the situation on the 6th floor of the TSBD...

Just because three empty shells from a 6.5 mm Carcano were found on the floor near the window, that is not necessarily PROOF that the shells were fired that day, or in that location.

Now...have I stated anything that is incorrect up to this point?

[Glenn Nall]

To apply this to JUST the situation on the 6th floor of the TSBD...

Just because three empty shells from a 6.5 mm Carcano were found on the floor near the window, that is not necessarily PROOF that the shells were fired that day, or in that location.

Now...have I stated anything that is incorrect up to this point?

THAT's where i'm trying to get this to go - it's the whole purpose of this exercise, to exercise our decision-making in WHAT is a given and what is NOT...

the sounding out of the parameters, of our reasoning, of what exactly is postulated and what is not... these are all helpful in understanding a piece of evidence.

the question that is asked is what the existence of empty bullet shells on the floor alone expressly means, and NO MORE. what expressly can be derived from the existence of these shells and the existence of the rifle that IS registered to LHO (expressly, meaning EXACTLY and ONLY...?). adding suppositions only corrupts the evidence, and takes you to the incorrect answer, as is exemplified with this test.

[Glenn Nall]

one thing i've tried to do is write a replica of this test using variables available from the JFK files. it's not easy.

"You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?"

this is just a variant of the numbers and letters. it does state here, in fact, that each card will be one side alpha and the other numeric, as I think Robert decided, but i don't see as how that makes a difference in arriving at the solution (which has already been found in this thread, by the way).

to JFK:

A set of givens (what we know):

LHO was seen on 6 of TSBD

a rifle registered to LHO was found on 6 the day the pres was shot.

bullets SHELLS matching the RIFLE were found on the floor of 6.

LHO left TSBD soon after the shooting

i tried to arrange these or something like these into a similar if then statement so as to THEN seek a LOGICAL conclusion of some kind or another.

for instance:

IF LHO was seen on 6 and the RIFLE was found on 6, THEN ... see, it's hard to establish a truth, since we are in fact working with a real case and real facts...

how about:

IF the SHELLS found on 6 match the RIFLE found on 6, THEN it is established that the SHELLS were FIRED in that RIFLE (now, technically one does not prove the next, so this works just like the RULE IF a VOWEL, then an EVEN number. it's given to us, so we can go with the SHELLS WERE FIRED from the RIFLE).

and the puzzle:

WHAT has to be shown to prove that LHO did or did NOT fire that RIFLE on that day...?

i don't think that works too well as a replica of this puzzle, but it's good exercise thinking of these facets in these terms...

[Glenn Nall]

To apply this to JUST the situation on the 6th floor of the TSBD...

Just because three empty shells from a 6.5 mm Carcano were found on the floor near the window, that is not necessarily PROOF that the shells were fired that day, or in that location.

Now...have I stated anything that is incorrect up to this point?

hell, Mark, i didn't mean to contradict you - i agree with this premise - it's NOT proven, as far as i know, by anyone.

only for the sake of trying to replicate this test did i use that scenario...

maybe you can write a better one that will be a good example of how reason is used in this thing...?

[Chris Davidson]

Glenn,

I tend to think in terms of the Zfilm.

If the anomalies in the extant Zfilm can be reproduced with modern day technology, then is it indicative of what was applied to the original film?

chris

Edited August 11, 2015 by Chris Davidson

[Mark Knight]

I'm not arguing against your scenario.

My comment was posted before yours, not after.