Cannot Be True (Ch. 19, Problem #2)

[graymo]

Hi,

I'm having a bit of difficulty fully understanding Problem Set #2 on page 635 of the Logical Reasoning Bible.

2. Two things are true of all immoral actions. First, if they are performed in public, they offend public sensibilities. Second, they are accompanied by feelings of guilt.

I have no problem interpreting the Stimulus. I was able to identify that the two sufficient conditions addressed are not the same (as the Answer Key stresses), and diagrammed two conditional relationships:

Immoral Actions (public) Offend
Immoral Actions Guilt

Now using my knowledge from the Chapter, if a Cannot Be True question contains conditional reasoning, I should be searching for an answer that proves the sufficient condition can occur without the necessary condition occurring (because that would be false)****

Now I try to diagram each of the answer choices to find the (as mentioned above) false relationship:

(A) Some immoral actions that are not performed in public are not accompanied by feelings of guilt.

So my first reaction to this answer is huh, they're relating immoral actions not performed in public to guilt. I look at my two Stimulus diagrams and see that one contains one of the elements (immoral actions associated with public) and the other contains the other element (guilt). So this leaves me a bit confused in terms of coming up with a diagram to illustrate answer choice (A). But then I think, I guess "Immortal Actions" includes both in public and not in public? So does "immoral actions that are not performed in public" also equate to "immoral actions?" In other words, can I use simply the second diagram?

Immoral Actions (both in public and not in public) Guilt

If my logic so far is correct... then I can diagram the answer choice as:

Immoral actions (both in public and not in public) Guilt

Which is the incorrect relationship I was looking for. This answer proves the necessary condition is not in fact necessary, and is therefore incorrect -- which is the right answer, just unsure if my logic is correct.

Also, would you mind double-checking my logic in eliminating the rest of the answer choices?

(B) Immoral actions are wrong solely by virtue of being accompanied by feelings of guilt.

Assessing immoral actions as "wrong" seems out of left field (not talked about in the stimulus), so I eliminate this choice because of that.

(C) Some actions that offend public sensibilities if they are performed in public are not accompanied by feelings of guilt.

The stimulus addresses "immoral actions" and this answer choice addresses "some actions," so I don't even bother diagramming, and eliminate.

(D) Some actions that are accompanied by feelings of guilt are not immoral, even if they frequently offend public sensitivities.

Diagramming the first part of this answer choice (relationship between not immoral actions and guilt):

Guilt Immoral

But these "immoral actions" are not specified in the answer choice as having occurred in public, so how do I make a connection to whether or not they offend public sensitivities, if that condition is required for immoral actions performed in public? I don't really know where to go from here?

(E) Every action performed in public that is accompanied by feelings of guilt is immoral.

Guilt Immoral

This is a Mistaken Reversal... which we've learned is an invalid inference? The bible describes a Mistaken Reversal as might be true, but I don't understand why.

****So I guess another question I have is (relating to what I learned from the Chapter, and referred to at the beginning of this post), why is the only false answer the necessary condition not occurring, while the sufficient condition occurs? Why are Mistaken Negation and Mistaken Reversals not also false (as we know they are invalid inferences)?

Thank you! Hope I was fairly clear...

[Adam Tyson]

Let's first take a look at one thing you said, graymo:

I should be searching for an answer that proves the sufficient condition can occur without the necessary condition occurring

This isn't quite right. The task is not to find an answer that proves anything. The task is to find an answer that cannot occur, which is one that the stimulus proves to be false. The answer won't prove anything - the answer will make an impossible claim.

To go to a later question you asked, when faced with a conditional statement, the only thing that is impossible is that a sufficient condition occurs and a necessary condition fails to occur. That's why answer A is correct there, and your analysis of that answer is solid.

So why not a Mistaken Reversal or Mistaken Negation as a correct answer to a Cannot Be True question? Because although those mistakes are not provable, THEY ARE POSSIBLE! You cannot use a conditional statement to prove a MR or MN of that statement, but the MR or MN still might be true. Consider this example:

If I go out in the rain, I will get wet. Go Out in Rain Wet

Is it possible that I do not go out in the rain, and I do not get wet? Of course! I can stay inside and stay all warm and dry. Even though staying inside does nor PROVE I do not get wet (because I might take a shower, my roof might be leaking, I may take a dip in an indoor pool, etc), it is still possible that both of those things happen. The Mistaken Negation is therefore possible, and thus a wrong answer to a Cannot Be True question (which seeks the one IMPOSSIBLE answer.)

Is it possible that I get wet AND that I go out in the rain? Absolutely! My getting wet might not prove I went outside (see the above options for being wet indoors, and any others you might think of), it still could be true that I did both of those things. Again, that is not an impossible situation, just one that cannot be proven based on the original claim. Since it is possible, it is also a wrong answer to a Cannot Be True question.

Look for the answer that is impossible, which violates the conditional rule. The ONLY violation will be a sufficient condition occurring and a necessary condition not occurring.

[Hyunuk Park]

I need help with understanding answer choice E. The two statements derived were IP -> O and I -> G. Then "E" states IP -> G. How is this considered possible?

[Jeff Wren]

Hi Hyunuk,

First, let's just make sure that we're clear on the conditional statements in the stimulus.

1. IA + PP -> OPS

(meaning if immoral action and performed in public, then it offends public sensibilities)

2. IA -> AFG

(meaning if immoral action, then accompanied by feelings of guilt)

The only way to violate these conditional statements (and therefore be the correct answer to this Cannot Be True question) is to show the sufficient condition occurring without the necessary occurring.

One possibility would be to show an immoral action performed in public that did not offend public sensibilities.

Another possibility would be to show an immoral action that was not accompanied by feelings of guilt. (This is what happens in Answer A.)

Answer E would be diagrammed

PP + AFG -> IA

While this diagram mixes terms from both conditional statements in the stimulus, it does not violate either conditional statement, meaning that this can could be true according to the stimulus (since it doesn't directly contradict the stimulus).