#16 - Therapist: The ability to trust other people is

[goingslow]

Hi there! Can you take the "contrapositive" of (D) and say "at least some people who are not happy feel isolated"?

A more general question is, can you take the contrapositive of A B and say ~A ~B?

Thank you!

[Beth Hayden]

Hi Going,

You can't take contrapositives of "some" statements, only conditional statements. Answer choice (D) just doesn't tell us much because "at least some" could mean anything from 1% to 100%.

The reason we can take contrapositives of conditional statements is because once you see the sufficient condition, you know that the necessary condition is true also. That means that if the necessary condition is missing, the sufficient condition must also be missing (the contrapositive). The only reason we can make such a powerful inference is because the conditional statement is rock solid and true all the time. We just don't have that kind of certainty with a "some" statement.

The fact that at least some people who are not isolated are happy doesn't tell us anything about people who are not happy (or people who are not isolated for that matter). Answer choice (D) is a very weak statement, it just doesn't tell us enough to be able to make an inference like a contrapositive.

I hope that helps!
Beth

[ashpine17]

so my diagramming is correct but my main fundamental question is just how do we know which variables to connect? and why does it seem for these questions that there is only one way to connect?

/T--->MEC---->I

/I--->/MEC----->T

H---->T

since T is a common variable I leave that alone but my question is how do we know to connect H and /I versus H and MEC etc??

[ashpine17]

Oops, it's /T--->/MEC--->I so /I---->MEC---->Tand the correct connection is H--->/I which I do understand but why can't we connect the missing terms in some other way, like between MEC and H

[Jeff Wren]

Hi ashpine,

Before we look at the diagram for this argument, let's look at an example that may be easier to understand.

Imagine we had this argument:

Premise: If B, then C (diagrammed B -> C)
Premise: If C, then D (diagrammed C -> D)

Conclusion: If A, then D (diagrammed A -> D)

At this point, this is definitely a bad argument because the term "A" comes out of nowhere in the conclusion. In other words, it's completely new information.

In order to make this argument valid (i.e. Justify it), we need to add in a conditional statement that will let us go from A to D.

In this example, the correct answer could be:

if A, then B (diagrammed A -> B)

That would let us connect the conditional statements to form a chain, A -> B -> C -> D (which allows us to infer if A, then D).

However, it is also possible that the correct answer could "skip" B entirely and say "if A, then C."

This would also let us connect the conditional statements to form a chain, A -> C -> D (which also allows us to infer if A, then D).

Either one of these would be acceptable answers. However, the more "likely" answer to appear is "if A, then B" because this answer links all of the premises together, which the test makers generally prefer.

Now the reason that I used that example is that this argument follows the exact same form/pattern.

It is probably easier to see this pattern if you diagram the contrapositives of your diagrammed statements.

For example, using the Unless Equation, I would diagram the premises as:
1. MEC -> T
2. not FI -> MEC

Conc. H -> T

Hopefully, you see that this is exactly like the example above.

What I'd like to find is an answer that correctly links H to not FI (H -> not FI), then we could form a chain:

H -> not FI -> MEC -> T

Answer A (and only Answer A) does this.

Answer A would be diagrammed (FI -> not H) and the contrapositive (H -> not FI), which is what we need.

[thomas33]

Hi,

I thought I got this question right but got it wrong. After reading the other posts, I diagrammed the without statements using the "Unless Equation" where you negate the sufficient and the clause modified by "without" becomes the necessary condition. So my diagrams looked like this:

Conc: H--> ability to trust
Premises: FI---> Meaningful Emotional Connection --> Ability to Trust

Given these diagrams I identified the missing link between Happiness and Meaningful Emotional Connection and chose B. After translating in my head "if you feel isolated then you have a meaningful emotional connection.." that doesn't make sense but in the moment I suppose I was hyper focused on the diagram. Could someone please advise on how they knew to treat "without" similar to a "No" ?

[Jeff Wren]

Hi thomas,

You wrote "I diagrammed the without statements using the "Unless Equation" where you negate the sufficient and the clause modified by "without" becomes the necessary condition." This is the correct approach, as this is the correct way to diagram the word "without."

Unfortunately, it appears from your diagram that you did not negate the sufficient condition.

The relevant part of the stimulus is "without meaningful emotional connection to others we feel isolated."

Here "without" modifies "meaningful emotional connection to others" so that term becomes the necessary condition exactly as it is.

The remainder of the sentence "we feel isolated" is negated and becomes the sufficient. The negation of "we feel isolated" is "we do not feel isolated."

Perhaps what may have given you trouble is the fact that the remaining term "we feel isolated" appears after the necessary term? Of course, this does not matter to the logic. We could reorder the sentence to:

We feel isolated without meaningful emotional connection to others.

(This is identical in meaning to the sentence in the stimulus.)

So the sentence means, "if we do not feel isolated, then we have a meaningful emotional connection to others."

This could be diagrammed:

not FI -> MEC

With that conditional statement correctly diagrammed, please refer to my previous post explaining why Answer A is the contrapositive of what we need.