# If, But Only If (LG question)

#### Harper

• 223
• works every time
##### If, But Only If (LG question)
« on: March 30, 2006, 10:52:52 AM »
Quick question - I was just doing a practice game from a recent LSAT, and one of the conditions for a grouping game was "X does such and such if, but only if, Y does also."  (Wording changed slightly to avoid the copyright violation wrath of the mods.)

My question is: Is X the sufficient condition and Y the necessary condition?  Or is this a case where it works both ways, as in: If X, Y; If Y, X.

I hope that makes some kind of sense.  Thanks!

#### squirt10

• 221
##### Re: If, But Only If (LG question)
« Reply #1 on: March 30, 2006, 11:44:52 AM »
If X does such and such, Y does such and such.
If Y does such and such, X doesn't necessarily do such and such, but may.

Edit:  This is WRONG

#### Bork

• 431
• Monkey Stealing My Stuff
##### Re: If, But Only If (LG question)
« Reply #2 on: March 30, 2006, 01:43:50 PM »
Agreed.

#### ivyhopeful

##### Re: If, But Only If (LG question)
« Reply #3 on: March 30, 2006, 02:13:51 PM »
Harper which prep test is that? I'd like to look it up because I'm curious myself.

I think it is X--->Y, and not the other way around. Because of the keyword BUT. In other words, if it said "If AND only if" it would be: X--->Y AND Y--->X.

#### bass

• 2849
• Retired
##### Re: If, But Only If (LG question)
« Reply #4 on: March 30, 2006, 02:45:52 PM »
He is referring to a recent december test...the one I took... Dec 04.

I am 100% certain (philosophy/logic dude here) that this is both X implies Y and Y implies X.  It is what is known as a "biconditional" or a "material equivalence."

Further, there is NO distinction between if BUT only if and if AND only if.

#### squirt10

• 221
##### Re: If, But Only If (LG question)
« Reply #5 on: March 30, 2006, 03:14:11 PM »
He is referring to a recent december test...the one I took... Dec 04.

I am 100% certain (philosophy/logic dude here) that this is both X implies Y and Y implies X.  It is what is known as a "biconditional" or a "material equivalence."

Further, there is NO distinction between if BUT only if and if AND only if.

"X does such and such if, but only if, Y does also."

Why does X do such and such every time Y does?

Billy walks the dog if, but only if, Sally does also ==> Sally walks the dog if, but only if, Billy walks the dog.

What?  How does that follow?  I think "if but only if" is a crappy way of wording conditions.

#### bass

• 2849
• Retired
##### Re: If, But Only If (LG question)
« Reply #6 on: March 30, 2006, 03:33:04 PM »
He is referring to a recent december test...the one I took... Dec 04.

I am 100% certain (philosophy/logic dude here) that this is both X implies Y and Y implies X.  It is what is known as a "biconditional" or a "material equivalence."

Further, there is NO distinction between if BUT only if and if AND only if.

"X does such and such if, but only if, Y does also."

Why does X do such and such every time Y does?

Billy walks the dog if, but only if, Sally does also ==> Sally walks the dog if, but only if, Billy walks the dog.

What?  How does that follow?  I think "if but only if" is a crappy way of wording conditions.

Think of two conditionals.  A if B.  A only if B.  First is B=>A, second is A=>B.  It goes both ways (and in the negative).  We call this material equivalence because, with respect to whatever property you are assigning, A and B must have the same truth value.

#### squirt10

• 221
##### Re: If, But Only If (LG question)
« Reply #7 on: March 30, 2006, 04:08:59 PM »
Think of two conditionals.  A if B.  A only if B.  First is B=>A, second is A=>B.  It goes both ways (and in the negative).

A only if B. is  A=>B.

I guess this is what I'm having trouble understanding.  It seems like this intrepretation of "only if" isn't founded on the popular interpretation of the words.  To me, "A if B" and "A only if B" seem like they should mean the same thing; LSAC shouldn't use specialized definitions of "only if..."

Anyway thanks for clearing this up for me, and I apologize for my misinformation above.

Here's a relevant wikipedia entry that implies this use of if and only if is specialized:
http://en.wikipedia.org/wiki/If_and_only_if

#### River

• 359
##### Re: If, But Only If (LG question)
« Reply #8 on: March 30, 2006, 06:08:40 PM »
X---only if Y=If X, Y.

Ex) I will go home only if my wife is home.
=If I go home, my wife will be home.

My wife's being present at home is necessary for me to go home.

No further discussion!

#### Harper

• 223
• works every time
##### Re: If, But Only If (LG question)
« Reply #9 on: March 31, 2006, 06:31:19 AM »
Thanks for the help - tricky one, isn't it?  The hallowed LG Bible mentions the "and only if" phenomenon, but the "but only if" really threw me off.

For those curious, yes, it is the December 2004 test, game #4.  And the exact wording of the condition is more like:

Nation X exports S if, but only if, Nation Y does also.