PT 56, 2nd LG, "if and only if" rule - help Forum

[darkatillam2]

This is pissing me off.

I fail to see how this is a bi-conditional rule.


Rule:

Grace moves the sofa if, but only if, Heather moves the Recliner.

I understand that means if G=S then H must = R.

But how does that rule make if H=R, G must = S.

Why can't H=R but S be free to equal something else. I only see this as G can only = S if H=R.


Someone straighten me out please!

[kaiser]

Just break down the statements into 2 separate statements, and it will make sense:

Grace moves the sofa if, but only if, Heather moves the Recliner

--The first part of the sentence is the "if" part: Grace moves the sofa if Heather moves the recliner
You can easily flip this around, and rephrase it as "If Heather moves the recliner, then Grace moves the sofa"

So you get H Move R ---> G Move S

--The second part can be phrased as follows: Grace moves the sofa only if Heather moves the recliner
As you of course know, "only if" indicates a necessary condition. So Grace couldn't possibly move the sofa unless Heather moved the recliner

So you get G Move S ---> H Move R


Thats pretty much all there is to it. A biconditional is 2 statements stuffed into 1 sentence. Just break it down into its 2 parts.

[RaleighStClair]

You can also show the contrapositive:

~G moves S <---> ~H moves R

If either one doesn't move their respective piece of furniture, then the other does not either.

[darkatillam2]

How is that different from other games which say:


W is in the forest if G is in the forest.


That means G=W, but it would be a mistaken inference to assume W = G.

In the example Kaiser provided:

-The first part of the sentence is the "if" part: Grace moves the sofa if Heather moves the recliner
You can easily flip this around, and rephrase it as "If Heather moves the recliner, then Grace moves the sofa"

the language is set up in the same manner, yet W can be in the forest without G having to be.

[bgdddymtty]

How is that different from other games which say:


W is in the forest if G is in the forest.


That means G=W, but it would be a mistaken inference to assume W = G.

In the example Kaiser provided:

-The first part of the sentence is the "if" part: Grace moves the sofa if Heather moves the recliner
You can easily flip this around, and rephrase it as "If Heather moves the recliner, then Grace moves the sofa"

the language is set up in the same manner, yet W can be in the forest without G having to be.

Um, you quoted only one part of kaiser's post, the part that explained the "if" part of the statement, and then asked how the statement in question differs from another "if" statement that you came up with. Go read the part of the post that explains the "only if" portion of the statement.

[darkatillam2]

because I had already made the inference in the second part of his explanation.

I had the first part in quotes because in that part he makes the inference that I didn't think you could make, and used an example of why (regarding the

W is in the forest if G is in the forest.

) to show that in my response.


His explanation of the "only if" part of the statement I thought was given in my original G = S only when H = R

Am I missing something?

[suspicious android]

Yeah, something's not quite clicking. Kaiser's post laid it all out, but here's the cliff's notes version:

"if and/but only if" is always a biconditional indicator. Always.

"X if Y" and "X only if Y" mean different things, right? The first means "Y -->X" and the latter means "X -->Y". A sentence that says "X if, and only if, Y" means the same as both those sentences together, the conjunction "and" is just linking two relationships together.

[darkatillam2]

yea I'm a idiot. I realize what Kaiser was saying now. I need to read closer. Tip #1 to improving on the LSAT.....

[Errzii]

This is pissing me off.

Rule:

Grace moves the sofa if, but only if, Heather moves the Recliner.

I understand that means if G=S then H must = R.

But how does that rule make if H=R, G must = S.

Why can't H=R but S be free to equal something else. I only see this as G can only = S if H=R.


Someone straighten me out please!

From what I understand, "if and only if" implies that the condition is not only sufficient but it is also necessary. That is, it's occurrence both allows and guarantees an outcome. Someone correct me if I'm wrong.

[KevinP]

From what I understand, "if and only if" implies that the condition is not only sufficient but it is also necessary. That is, it's its occurrence is both allows required for and guarantees an outcome. Someone correct me if I'm wrong.

FTFY.

I understand what you were trying to say, I think maybe you just chose the wrong word for it.