How to diagram a double negative

lsat_novice

I get confused when there's a double negative in a sentence. For example, "No duck doesn't like water."

Normally, I would diagram this:
/D --> W
Because I would negate the second term ("doesn't like water" becomes "does like water") and the sufficient condition would remain the same (no duck).

But when I think about it in English, I realize that the double negative cancels each other out so it's like saying, "All ducks like water" which would be diagrammed:
D --> W

Any suggestions on getting past this hiccup?
Thanks!

xenonhexafluoro

I diagram no statements as follows: "No duck likes water" as D -> /W because the statement paraphrases to "if you are a duck, then you do not like water". So if I had a double negative, I would diagram: "No duck does not like water" as D -> //W or D -> W

keets993

Hey there!

Essentially what you do is you pick one as your conditional indicator and negate the other item.

To take your example of, "No duck doesn't like water," let's first choose an indicator.

'No' is our conditional indicator which is group 4. With group 4 indicators we pick one item as the necessary condition and negate it.
Our two items are "ducks" and "don't like water".

Say you pick duck as sufficient and then "don't like water" as necessary. According to group 4 rules we would negate this and have it be "like water"

Ducks - > like water.

If something is a duck then it likes water. Now, what if we picked "doesn't like water" as our sufficient condition? Then our necessary would be "ducks". Again, we negate the necessary to "not ducks"

/doesn't like water -> /duck.

If something doesn't like water then it's not a duck.

You will notice that regardless of which we assign as sufficient /necessary, as long as we follow our rules, we get the same results.

/doesn't like water - > /duck

And

Duck - > likes water

Are contrapositives. They are logically the same. Hope that helps!

lsat_novice

Thank you!