PT18.S2.Q23 - teachers are effective only when

The 180 Bro_OVO

https://7sage.com/lsat_explanations/lsat-18-section-2-question-23/
Here is my conditional reasoning:

teachers are effective ------> when they help students become independent learners

teachers have power to make decisions in their own classrooms ------> enable their own students to make their own decisions

become independent learners -------> students' capability to make their own decisions

teachers are to be effective --------> have power to make decisions in their own classrooms


Apparently my conditional reasoning in line two is incorrect??

But I don't understand why it would be.
"Yet not until teachers have the power to make decisions in their own classrooms can they enable their students to make their own decisions."

This looks like: Not until TD can they enable SID

"until" is group 3, negate sufficient

So negate "not TD" which would make it just TD and keep it in the sufficient spot which would turn to TD --> SID.

But this screws up the chain.
Can someone explain?

c.janson35

Think of it this way: "not until you pass the bar can you be a practicing lawyer." What does this sentence mean? If you pass the bar you must be a practicing lawyer? No, not at all, because you can pass the bar and never choose to practice law. But what it does mean is that if you are a practicing lawyer, then you must have passed the bar. Why? Because you cannot be a practicing lawyer until you've passed the bar. This last sentence is the same as the first.

So, one more time: not until X can Y occur. So that means that if Y occurred, X must have also occurred (because Y cannot occur without it, hence the not until). And it also means that if C doesn't occur, then Y cannot occur either! Because not until imbues X with necessity for Y.

This can be applied to the question at hand:

Not until TPIC can they ESMD. So, if /TPIC then /ESMD, or ESMD-->TPIC.

Hope this helps!

The 180 Bro_OVO

Ahh! It does!


So I guess it's a mistake to just look for indicator words. Should first look at their context in relation to the sentence. As sometimes they are not activated. Yes?

dcdcdcdcdc

You can also translate correctly by applying the "until" group three negation and then seeing the NOT as applying to the whole conditional statement (which I believe is the grammatically correct way to read it) and then do the logical negation of the all statement.

Not(Until TP can ES)

NOT(/TP -> ES) [it is not the case that...]

/TP some /ES (recall that some can include all, so we can plug this back in as /TP --> /ES

and the contrapositive: ES-->TP, enabling students requires teacher power.

quinnxzhang

@dcdcdcdcdc said:
Not(Until TP can ES)

NOT(/TP -> ES) [it is not the case that...]

/TP some /ES (recall that some can include all, so we can plug this back in as /TP --> /ES

You make a jump from 'Not(Until TP can ES)' to 'NOT(/TP -> ES)', but these are not logically equivalent. Even more, "/TP some /ES (recall that some can include all, so we can plug this back in as /TP --> /ES" is certainly not a kosher move. "Some not-A's are not-B's" does NOT imply that "All not-A's are not-B's". This is a textbook fallacy.

@"The 180 Bro_OVO", I think this is another case where fishing for keywords and mechanically applying rules hurts students. You have to really understand what the sentence is saying.

In this particular instance, it looks like you straight up dropped the "can" in your translation, which you shouldn't do. Think about what it means to say "only if A happens can B happen" (this is LSAT-equivalent to "not until A happens can B happen"). This means that A is necessary for B, but your original translation is that B is necessary for A.

Slightly more formally, "can" takes the widest scope, so if there is a wide-scope negation, it applies to the "can" first. This is why "not until A happens can B happen" is equivalent to "until A happens B cannot happen".

nye8870

@quinnxzhang said:
This is not correct.

I agree... To negate the conditional is to say that the stated relationship does not exist. Applying the 'until' rule negate sufficient better clarifies the relationship (not deny it altogether).

The 180 Bro_OVO

Great stuff everyone!

Thank you!

dcdcdcdcdc

@quinnxzhang said:
You make a jump from 'Not(Until TP can ES)' to 'NOT(/TP -> ES)

How so? I applied UNTIL as negate sufficient to the stuff inside the parenthesis. TP until ES does translate to /TP --> ES...

I agree, you have to be cognizant of using all when you have a some statement. However, the other alternative was to just realize that the "NOT" at the beginning of the whole statement actually belongs with the "can" of the second element and then just treat this as a group 3 and group 4 sentence, but a lot of people were having issues getting to that stage.

quinnxzhang

@dcdcdcdcdc said:

How so? I applied UNTIL as negate sufficient to the stuff inside the parenthesis. TP until ES does translate to /TP --> ES...

'NOT(/TP -> ES)' is, by your admission, equivalent to 'some(/TP & /ES)'. But this is not what the sentence is saying, nor is this presumably what you're trying to say by 'Not(Until TP can ES)'. The sentence is not saying that *some* teachers who do not have the power to make their own decisions have students who are unable make their own decisions. The sentence is saying this for *all* teachers. In general, we can't just drop the "can", as you and @"The 180 Bro_OVO" did.

dcdcdcdcdc

@quinnxzhang: Thanks for your input. I concede your points about some and all statements above as well as the ability of the NOT() to negate the entire conditional of unless.

I went back and looked over the question carefully and it is clear that negating the all statement would lead to /TP <--Some--> /ES

In this case I got lucky and the elements were in the right order to just pop an all arrow in between /TP and /ESMOD. However, some statements can be switched, so we could have ended up with /ES <--Some--> /TP if we translated the until statement in the other way and then attempted to apply the negation to the resulting conditional. Clearly, that the elements in some can be switched around means you cannot just stick the all arrow in there.

I see now that "all IMPLIES most IMPLIES some" shows that we could substitute out the all arrow for a most, some and even an AND, but we could not then return to an all arrow. The switching out an all arrow for a most, some or and is helpful in some problems, but I have now learned through experience that it cannot be then returned to an all statement.

For what it is worth, I also attempted to apply some of JY's techniques for handling conditionals that show up in the comments of the embedded conditional lessons, thinking the negation of the all statement that he performs there, which does not use "some" but rather "or" would shed some light.
[the below is an incorrectly worked example for others to see the error]

1: NOT(TP until ES) - not statement encompassing conditional statement of until
2: NOT(/TP --> ES) - applied the group 3 indicator
3: NOT(TP or ES) - switched out the all arrow for and or; or statement is equivalent to /TP->ES
4: /TP and /ES - applied not as demorgens law.

This dead ends because, like some, the elements are interchangeable, so we can't determine the relationship between the two elements in terms of a necessary/sufficient condition.

My view now is that "not until" is operating as a sort of double negative, which others noted above. If we read the sentence leaving out the double negated terms, it becomes TP can ES, with the can suggesting chronology, that one happens before the other and hence is required. Very interesting to grasp the concept of something that has to happen first as being in the required spot for a sufficient condition, but it does make sense the more you think about it.