Parallel Principle Questions with Conditional Prohibitions

[CharlesPasselius]

I checked the LRB on this and I found something that I think applies, but I am not completely confident that I am rightly applying it. I think that I have realized something that will help me eliminate certain kinds of wrong answers more quickly, but I would like to explain my reasoning and see if I am right before I start using it as a machete. I will state it abstractly below.

Question stem: One should not do X, if A or if B.

Diagram of conditionals:

A
OR should not do X
B

Diagram of contrapositive:

/A
should do X AND
/B

My reasoning is that answer choices that say "I am allowed to do X, because I'm not violating condition A or B" are wrong, because they are committing a Mistaken Reversal based upon the contrapositive or a Mistaken Negation based upon the original conditional statement. Am I right in thinking this and can I use this fact to quickly and confidently eliminate such answers?

A second question related to this is: does this apply to any situation in which there is such a prohibition? Meaning, if I see "A or B can't do X/shouldn't do X," is it right to think that I can only determine what should not be done but that I cannot positively prove/justify what MAY be done in the particular situation? I am asking this question in a formal logic sense rather than in a common sense one.

Thanks in advance.

[Adam Tyson]

Don't confuse "should" with "may," Charles. While we don't see it tested very often, it is valid to say that when the Necessary Condition occurs, the Sufficient Condition "may" occur or "is allowed" to occur. The presence of the Necessary Condition doesn't prove that the Sufficient Condition WILL occur, but it does create a situation in which it might be possible.

A true Mistaken Reversal of your statement would be "I should not do X, therefore either A or B must have occurred." A Mistaken Negation of that statement would be "Neither A nor B has occurred, therefore I should not do X." Leave the "may" out of it when dealing with a statement about what should or should not occur.

[CharlesPasselius]

Thank you for taking the time to respond. However, I think that perhaps I did not write clearly. I will write a clearer hypothetical example that shows what I was actually asking.

Negative Principle (Prohibition) example:

One should not play a game, if it will hurt someone or if one believes that doing so would involve breaking the law.

• It will hurt someone
  
  OR one should not play the game
  
  One believes that doing so would involve breaking the law

So, what I was asking is, with this kind of principle set up in a parallel principle stem, would it be right to immediately eliminate any answer choice that says "(Conclusion indicator) he/I/whoever should play a game." My reasoning being that this kind of principle cannot justify any POSITIVE action being performed, it can only prohibit an action from being performed.

Because, even if we consider the contrapositive, justifying the action's permissibility on this basis would involve committing a Mistaken Reversal:

• It will not hurt someone
  One should play the game AND
  One believes that doing so would involve breaking the law

So, the answer choice would read, "Jack knows that it will not hurt anyone and he does not believe that doing so would involve breaking the law, so he should play the game." (or whatever possible permutations of this wording...)

My question was, when the question stimulus sets up this kind of prohibitive principle, am I right to immediately knock out (or hack down with my metaphorical machete) any answer choice that says "X should play the game" (or whatever the particular action is). I think this is right, but I wanted confirmation before I added it to my battle tactics.

[Dave Killoran]

So, what I was asking is, with this kind of principle set up in a parallel principle stem, would it be right to immediately eliminate any answer choice that says "(Conclusion indicator) he/I/whoever should play a game." My reasoning being that this kind of principle cannot justify any POSITIVE action being performed, it can only prohibit an action from being performed.

Hi Charles,

If I'm following you correctly, the answer is yes. The reason, at least how I'd put it, is that you can't make a Mistaken Reversal. Just because both necessary conditions occurred does not mean the sufficient will for sure happen. As Adam said, it may occur, but it does not have to.

You mentioned the LRB, and this concept is covered on pages 663-666 in the 2022 edition (specifically, it's under "What you cannot conclude, point #2").

Good eye on your part. Thanks!

[CharlesPasselius]

Thanks, Dave. That's helpful. I will check that part of the LRB again and study it more closely.