"Only" Conditionals Forum

[aquyenl]

For some reason I struggle badly with certain types of only conditionals. I usually diagram these conditionals mechanically with whatever follows "only" as the necessary condition. Obviously, as I've churned through several PTs this does not always work.

How do you diagram these only conditionals and is there a better way to figure out how to diagram these?

"The only students with special education needs are students with learning disabilities."

"Only those who understand the architecture of personal computers appreciate the advances in technology made in the last decade."

"Only those who appreciate advances in technology are computer scientists."

"Only those students who are genuinely curious about a topic can successfully learn about that topic."

Any insight would be great!

[TatteredDignity]

I find it helpful to substitute "only" for "if not then not". As you said, this sets up a necessary condition. Unlike what you said, this will always work. However, if you use the substitution I suggested, your conditional statement will look like what we typically think of as the contrapositive. Using one of your examples from above, "If you are not a student with special learning needs then you are not a student with a learning disability." From there, it's pretty easy to make the "contrapositive"- if you are a student with a learning disability, you are a student with special needs.

[tamlyric]

I find it helpful to substitute "only" for "if not then not". As you said, this sets up a necessary condition. Unlike what you said, this will always work. However, if you use the substitution I suggested, your conditional statement will look like what we typically think of as the contrapositive. Using one of your examples from above, "If you are not a student with special learning needs then you are not a student with a learning disability." From there, it's pretty easy to make the "contrapositive"- if you are a student with a learning disability, you are a student with special needs.

This.

"Only As are Bs" = "If not A, then not B" or "If B, then A"

[Richie Tenenbaum]

I find it helpful to substitute "only" for "if not then not". As you said, this sets up a necessary condition. Unlike what you said, this will always work. However, if you use the substitution I suggested, your conditional statement will look like what we typically think of as the contrapositive. Using one of your examples from above, "If you are not a student with special learning needs then you are not a student with a learning disability." From there, it's pretty easy to make the "contrapositive"- if you are a student with a learning disability, you are a student with special needs.

This is wrong. The statement, "The only students with special education needs are students with learning disabilities" only tells us that that all students who have special education needs must also have a learning disability. It does not tell us that everyone with a learning disability must also have special education needs.

Maybe one of the current LSAT teachers on here can point out why the shortcut doesn't work on the first statement. (It works fine on the other statements.) What I find helpful for myself is to imagine the statement as a venn diagram, with one set completely encompassed by the other set. The smaller set will be your necessary sufficient clause and the larger set will be your sufficient necessary clause.

Is there particular LSAT questions where a statement like the first popped up? I don't remember the LR formal logic questions being tricky in this way, but I could have forgotten.

Edit: stupid mistake fixed.

[bp shinners]

Because the first statement is "the only" and the others are all "only". As one of the nastiest LR questions ever taught us (I forget what test it was on), those two are worlds apart (the two answer choices only differed in the word 'the' before 'only').

You need to treat them differently. You can use the 'if not then not' trick for 'only' (which, as a further shortcut, tells us that 'only' introduces the necessary condition). It's the opposite for 'the only' (which, again, shortcutting, introduces the sufficient condition). Adding the article 'the' shifts which part of the sentence 'only' is referring to (and the referent of 'only' is the necessary condition).

Bonus examples?
1) The only thing we have to fear is fear itself.
If we fear it, then it is fear itself.

2) Only the good die young.
If you died young, then we know you were good.

[TatteredDignity]

I find it helpful to substitute "only" for "if not then not". As you said, this sets up a necessary condition. Unlike what you said, this will always work. However, if you use the substitution I suggested, your conditional statement will look like what we typically think of as the contrapositive. Using one of your examples from above, "If you are not a student with special learning needs then you are not a student with a learning disability." From there, it's pretty easy to make the "contrapositive"- if you are a student with a learning disability, you are a student with special needs.

This is wrong. The statement, "The only students with special education needs are students with learning disabilities" only tells us that that all students who have special education needs must also have a learning disability. It does not tell us that everyone with a learning disability must also have special education needs.

Maybe one of the current LSAT teachers on here can point out why the shortcut doesn't work on the first statement. (It works fine on the other statements.) What I find helpful for myself is to imagine the statement as a venn diagram, with one set completely encompassed by the other set. The smaller set will be your necessary clause and the larger set will be your sufficient clause.

Is there particular LSAT questions where a statement like the first popped up? I don't remember the LR formal logic questions being tricky in this way, but I could have forgotten.

Be careful about calling someone out for being wrong with something as straightforward and objective as formal logic.

1. There is no logical difference between the statement I selected and any of the others. I'm not sure why you think there is. If you agree with the method I outlined in general, you shouldn't have a problem with that example.

2. Yes, the conditional statement to be made absolutely is "if you have a learning disability, you are a special needs student." It's simply the contrapositive of "if you are not a special needs student, you do not have a learning disability."

3. Venn Diagrams? No. Just no.

[Richie Tenenbaum]

Because the first statement is "the only" and the others are all "only". As one of the nastiest LR questions ever taught us (I forget what test it was on), those two are worlds apart (the two answer choices only differed in the word 'the' before 'only').

You need to treat them differently. You can use the 'if not then not' trick for 'only' (which, as a further shortcut, tells us that 'only' introduces the necessary condition). It's the opposite for 'the only' (which, again, shortcutting, introduces the sufficient condition). Adding the article 'the' shifts which part of the sentence 'only' is referring to (and the referent of 'only' is the necessary condition).

Bonus examples?
1) The only thing we have to fear is fear itself.
If we fear it, then it is fear itself.

2) Only the good die young.
If you died young, then we know you were good.

Wow, I think I remember that question. I think I actually had to draw out 2 Venn diagrams b/c I was initially confused. Never had to do that before (and it's probably a waste of time for an average FL question).

Great explanation.

[zanda]

When I was taking the LSAT I didn't worry about memorizing formulas, but just considered what the sentence meant. Doing that, there were no nasty questions since "new" wording was no harder than frequently repeated wording.

[Richie Tenenbaum]

I find it helpful to substitute "only" for "if not then not". As you said, this sets up a necessary condition. Unlike what you said, this will always work. However, if you use the substitution I suggested, your conditional statement will look like what we typically think of as the contrapositive. Using one of your examples from above, "If you are not a student with special learning needs then you are not a student with a learning disability." From there, it's pretty easy to make the "contrapositive"- if you are a student with a learning disability, you are a student with special needs.

This is wrong. The statement, "The only students with special education needs are students with learning disabilities" only tells us that that all students who have special education needs must also have a learning disability. It does not tell us that everyone with a learning disability must also have special education needs.

Maybe one of the current LSAT teachers on here can point out why the shortcut doesn't work on the first statement. (It works fine on the other statements.) What I find helpful for myself is to imagine the statement as a venn diagram, with one set completely encompassed by the other set. The smaller set will be your necessary clause and the larger set will be your sufficient clause.

Is there particular LSAT questions where a statement like the first popped up? I don't remember the LR formal logic questions being tricky in this way, but I could have forgotten.

Be careful about calling someone out for being wrong with something as straightforward and objective as formal logic.

1. There is no logical difference between the statement I selected and any of the others. I'm not sure why you think there is. If you agree with the method I outlined in general, you shouldn't have a problem with that example.

2. Yes, the conditional statement to be made absolutely is "if you have a learning disability, you are a special needs student." It's simply the contrapositive of "if you are not a special needs student, you do not have a learning disability."

3. Venn Diagrams? No. Just no.

1. Read the post by bp shinners
2. Take a formal logic class or anything that touches on set theory to see how Venn diagrams relate. (Please note that I'm not advocating the use of Venn diagrams when doing FL on LR questions. There usually is zero need to do so. It can just help clarify things on tricky FL statements like the 1st statement in the OP.)

[rubydandun]

A bit off topic and not trying to hijack the thread but, WTF does If and Only If mean in Logic Games?

E.g., A can go if and only if B goes. Does this mean that either A&B will both be selected, or neither will be selected?

[bp shinners]

A bit off topic and not trying to hijack the thread but, WTF does If and Only If mean in Logic Games?

E.g., A can go if and only if B goes. Does this mean that either A&B will both be selected, or neither will be selected?

Bingo.

'If' introduces a sufficient condition; 'only if' a necessary condition. Since both A&B are sufficient AND necessary, either one gives you the other, and missing either one throws out the other.

[Richie Tenenbaum]

A bit off topic and not trying to hijack the thread but, WTF does If and Only If mean in Logic Games?

E.g., A can go if and only if B goes. Does this mean that either A&B will both be selected, or neither will be selected?

Yep.

It's two conditional statements packed into one sentence.
1. A if B (which means B-->A)
2. A only if B (which mean A-->B)

Thus, if one is chosen then the other must be chosen as well, and if one is not chosen, then the other cannot be chosen.

edit: blarg, got beaten to it.

[jortiz682]

I'd brush up on this before the exam. LSAC has been throwing in randomly hard formal logic Q's in the 20-25 range lately. To fuck with kids, I think. Sorta how the Heat are gonna fuck with the Mavericks starting Tuesday at 9PM EDT, if you aren't too busy to watch the crowning of the King.

[aquyenl]

Is there particular LSAT questions where a statement like the first popped up? I don't remember the LR formal logic questions being tricky in this way, but I could have forgotten.

Edit: stupid mistake fixed.

all of these sentences are from actual lsat lr questions

[aquyenl]

Because the first statement is "the only" and the others are all "only". As one of the nastiest LR questions ever taught us (I forget what test it was on), those two are worlds apart (the two answer choices only differed in the word 'the' before 'only').

You need to treat them differently. You can use the 'if not then not' trick for 'only' (which, as a further shortcut, tells us that 'only' introduces the necessary condition). It's the opposite for 'the only' (which, again, shortcutting, introduces the sufficient condition). Adding the article 'the' shifts which part of the sentence 'only' is referring to (and the referent of 'only' is the necessary condition).

Bonus examples?
1) The only thing we have to fear is fear itself.
If we fear it, then it is fear itself.

2) Only the good die young.
If you died young, then we know you were good.

ah thanks so much this was great. let me see if i'm doing this correctly...

The only people who water ski are those who can swim.
If you water ski, you can swim.

Only those who water ski are those who can swim.
If you can swim, you can water ski.

I also stumbled this sentence on PT 54:
The only food in Diane's apartment is in her refrigerator.

so...
If food is in diane's apt, then it is in her refrigerator?