Diagramming no + unless statements

[lucia]

Hello,

I've seen some contradictory explanations for this in different resources and around the web, so I am wondering if someone can provide some clarification!

Using the techniques in the Powerscore LR bible, "no apples are purple" would be
A ~P

And "all fruits are purple unless they are apples" would be
~FP A

So, if I have a statement that says something like "no fruits can be apples unless they are red" wouldn't it be:
~FA ~R ?


I know the sentences themselves don't make much sense but I'm focusing on the reasoning structure. I've seen the last statement diagrammed frequently as FA R, which is definitely not the same.

Can someone that understands this clarify? And potentially explain what leads some test prep companies to diagram the last sentence as FA R? Thank you very much!

[David Boyle]

Hello,

I've seen some contradictory explanations for this in different resources and around the web, so I am wondering if someone can provide some clarification!

Using the techniques in the Powerscore LR bible, "no apples are purple" would be
A ~P

And "all fruits are purple unless they are apples" would be
~FP A

So, if I have a statement that says something like "no fruits can be apples unless they are red" wouldn't it be:
~FA ~R ?


I know the sentences themselves don't make much sense but I'm focusing on the reasoning structure. I've seen the last statement diagrammed frequently as FA R, which is definitely not the same.

Can someone that understands this clarify? And potentially explain what leads some test prep companies to diagram the last sentence as FA R? Thank you very much!

Hello lucia,

I think that FA R may actually work. "No fruits can be apples unless they are red" commonsensically translates to, "Apples gotta be red", if you think about it. Or, even more succinctly, "Apples need redness". (Or the contrapositive, "If it ain't red, it ain't an apple.")
Your version above seems to say, "If it's not an apple, it's not red", which seems to be a mistaken negation. Apples may need to be red, but that does not preclude pomegranates being red, say.
"No fruits can be apples unless they are red" can be diagrammed: let's take what's after the "unless", which is "red". That's what comes after the arrow. Then negate what's before the arrow, and you get "Fruits can be apples". So, again, FA R actually seems to work here, though I see how the verbiage may have confused you some. It happens.


Hope this helps,
David

[lucia]

Hi David,

Thanks for your reply. I got to ~FA ~R by taking everything after unless to be the necessary and then negating the sufficient, which is what leads me to ~FA. I thought for No statements the No modifies the necessary, not the sufficient. Which is why I negated R. Why doesn't that apply in this case?

Thanks
Lucia

[Clay Cooper]

Hi Lucia,

Thanks for your follow up question.

That rule does not apply here because in the statement "No fruits are apples unless they are red," the negative term modifies the statement that "fruits are apples," rather than modifying whether the item being discussed is in fact red - this issue only arises in the second part of the statement.

To illustrate this idea, let's apply this statement to a particular (hypothetical) piece of fruit in my hand. Modifying the conditional rule to this particular instance, I can say that "This fruit is not an apple unless it is red." Since redness is modified by the unless, it is the necessary term. That leaves us with "this fruit is not an apple," which we can negate to "this fruit is an apple" to form the sufficient condition.

Thus we arrive at the correct form, FA -> R

Does that help?

[lucia]

Yes! That makes perfect sense. I understood why as soon as I got to your explanation for what 'no' modifies.

Just to reiterate, in a normal 'No' sentence, like 'No fruits are apples', the No modifies apples, but since that entire part is the sufficient in this case, the whole thing is negated, then negated again by the unless, so it just becomes "if fruits are apples, then they're red."

Thank you both very much!