# "Then and only then"

#### chris3737z

##### "Then and only then"
« on: August 27, 2007, 10:22:49 AM »
PS's Deconstructed book says that this should be diagrammed with a double arrow similar to "if and only If."  Why is this?  "Then" and "Only then" are both necessary indicators as opposed to "if" being a sufficient indicator and "only if" being a necesarry indicator.  This is illustrated in the June 2004 Test, Section 3, Question 17.  Thank You!

#### chris3737z

##### Re: "Then and only then"
« Reply #1 on: August 27, 2007, 10:56:34 AM »
Thank you!  I will have to accept that is the way to diagram it, but I do not understand the reasoning behind it.

It makes sense to me to use a double arrow for the other examples you gave because there are necessary and sufficient indicators introducing the term.  With "then and only then," though, you only have necessary indicators.

#### Lison

##### Re: "Then and only then"
« Reply #2 on: August 27, 2007, 11:12:48 AM »
It makes sense to me to use a double arrow for the other examples you gave because there are necessary and sufficient indicators introducing the term.  With "then and only then," though, you only have necessary indicators.

The two work pretty much the same way as if and only if.  If you're having trouble understanding why they would be diagrammed that way, it might be helpful to think about how you would rephrase the sentence without using "only then".

"If it rains, then I will get wet" is pretty standard.  Raining would be sufficient for you to get wet here.

"If it rains, only then will I get wet" is the same thing as saying "Only if it rains will I get wet".  Raining would be necessary for you to get wet here.

#### chris3737z

##### Re: "Then and only then"
« Reply #3 on: August 27, 2007, 11:29:10 AM »
Okay, I see: "then" and "only then" describe different terms thus making one term both sufficient and necessary for the other term.  Thank you!

#### OptiJamesJ

##### Re: "Then and only then"
« Reply #4 on: August 27, 2007, 07:50:45 PM »
Nice, thanks for the advice.  The A--B things get confusing sometimes.