Order of the terms in double arrow questions

[nmchelle9]

Hello,

When completing the double arrow diagramming drill on pg 208, I had some difficulty when checking my answers because of the order of the terms in double arrow questions. For example:

Question #4: "Taxes will be raised if and only if there is a government deficit."

My answer:

GD TR
TR GD

My reasoning behind the answer was:

TR if GD
GD TR

TR if only GD
TR GD

Therefore:
GD TR

The book's answer was:

TR GD
GD TR

I'm wondering if the order of the terms matter in double arrow questions? If it does, how do I make sure that I'm answering the question correctly?

[Dave Killoran]

Hi N,

Thanks for the question! On page 210 in the directions I tried to address this exact issue by stating: "Note: Because a conditional statement and its contrapositive are identical in meaning, the order in which the two arrow diagrams appear is not important." So, the good news is that your diagram is just fine, and it is functionally identical to the one in the book. Well done on your part!

Ok, to expand on your question, when looking at certain terms, some of them can be reversed, and some of them can not be reversed. For example, the following arrows are one-way:




Thus, when you have a statement such as A B, it only works in that one direction, and you can't "flip" the terms, meaning that B A would NOT be identical.

However, some arrows do reverse, including the following:





Thus, a statement such as A B is identical in meaning and use to B A.

There's more on the idea of Reversibility in the LRB on pages 408-409 (2017 edition).

Please let me know if that helps. Thanks!