Flaw Question - Errors of Conditional Reasoning Forum

[nodummy]

Can anyone explain how to describe mistaken negation and mistaken reversal to me in laymans terms? I'm reading the flaw section of the LRB again and the conditional reasoning portion is giving me some trouble.

For isntance, what does "taking the non-existence of something as evidence that a necessary precondition for that thing also did not exist" mean in symbolic terms? How would I draw this out in conditional format?

Same goes for "mistakes being sufficient to justify punishment for being required to justify it."

Any help on understanding all aspects of conditional reasoning in LR would be great.

Thanks.

[dakatz]

Mistaken Negation:

If A then B
If -A then -B

To use a real world example, use the following. If I study for the test, then I will get an A+. A mistaken negation would be to say "if I do not study for the test, I will not get an A+". This statement is making a baseless assumption that studying is the only way to get an A+. How about I steal the answer key to the test? I could still get an A+, even without studying. So you can't just take a conditional and negate both factors. Studying is sufficient to get an A+, but it is not necessary.

Mistaken Reveral

If A than B
If B than A

Keep with the same example. If I study, then I will get an A+. The mistaken reversal just switches around the terms incorrectly. It would be, if I get an A+, then I must have studied. Again, studying is not necessary to get an A+. It is just a sufficient condition and could be one of a million ways to get an A+. This mistaken reversal would make it seem like studying is 100% necessary for an A+, but we know it isn't.


The only correct inference is the contrapositive:

If A then B
If -B then -A

So, one last time, use the same example. If I study, then I will get an A+. If I do not get an A+, we know for sure that I didn't study. Because if I had, I would surely have gotten an A+. This is a logical inference and can be very helpful for both logical reasoning and logic game questions. Hope this helps.

[Cambridge LSAT]

A mistaken negation occurs when both sides of a one-directional conditional statement are negated. See the following example:
Original Statement: if A, then B (A -> B)
Mistaken Negation: not A, then not B

To construct the contrapositive (the valid inference), we need to both reverse the order of the terms and negate both of them. Our valid inference would be if not B, then not A.

A mistaken reversal occurs when both sides of a one-directional conditional statement are reversed. From the example above, the mistaken negation would read, if B, then A. Again, we need to reverse the order and negate both terms to form the contrapositive.

"taking the non-existence of something as evidence that a necessary precondition for that thing also did not exist"
This is a mistaken negation. The necessary condition follows the arrow. Symbolically, the mistaken negation would look like this:
not A -> not B

"mistakes being sufficient to justify punishment for being required to justify it."
This is a mistaken reversal. For example, anyone who robs a bank should be punished. Symbolically, we have:
robs a bank -> should be punished
If an argument went on to state that only (necessary indicator) those who rob banks should be punished, we would have a mistaken reversal. Robbing a bank is sufficient to justify punishment, but it is not required, since there are many other offenses which also justify punishment.

[nodummy]

Thank you both. Some of these explanations and passages are so dense I cannot visualize what they're saying. But this helps.