Mistaken reversal and Negation

[hyk1310]

Aren't mistaken reversal and mistaken negation the same thing? They seem to be contrapositives of each other.

This is why I am puzzled with question 7 from PT 16. I'm not really trying to ask the answer to a specific question here, but I'm curious about why the explanation on the board says that AC) B,D are mistaken negations so they're wrong, and that AC) C is correct because it's a mistaken reversal.

More so, another question I have is, can you make the following statement into an understandable conditional statement?

"The public did not have access to the bay, and it got polluted." To me, if you represent this as: No access --> Polluted, it doesn't seem to be the right representation because the two events could have occured coincidentally, and not as a matter of any causal or conditional relationship.

Please enlighten me on this topic. Thank you!

[ohthatpatrick]

You're correct (in my mind): illegal reversals and negations are the same thing, since they are just two different ways of expressing the same, bad conditional inference.

The only time it would ever matter whether you got a negation or a reversal would be on Matching questions, because if the test feels like getting THAT granular, there is a different FEEL to a reversal than a negation.

I usually treat them interchangeably, but the question you're pointing out (and one I've seen on a more recent test) actually DO test that distinction.

The idea is that the question stem asks us to BEST match the original argument, so the order of ideas presented and the truth-value of the ideas presented (going from A -> B to B -> A doesn't involve flipping truth values ... going from A -> B to ~A -> ~B does) are possible distinctions they can make.

Agreed, for Q7 that the original statement is not conditional, nor is the the original fact in correct answer (C). They are both just historical facts.

That's all the more reason why we would want to replicate the idea of a "negation" rather than a reversal.

If I say "As the ambulance went by, Sam cried", there is no conditional certainty. If I reason "Thus, whenever there is no ambulance anymore, Sam will not be crying" then I've constructed a conditional using counterfactuals.