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1 Like
could we ignore indicators in sentences with both group 3 and group 4 translations?
dcdcdcdcdc
Alum Member
In looking through the combination of conditional logic lessons on 7Sage and in The LSAT Trainer, I think I may have hit on a much more simple way to translate sentences that contain both a group 3 and group 4 indicator.
The 7Sage group 3 indicators require negating an idea and making it sufficient. However, these indicators actually identify the necessary condition in the statement.
The group 4 indicators require negating an idea and making it necessary. However, these indicators identify the sufficient condition.
As a result, the suggested translation rule in lawgic that we pick one indicator to set the rule and then treat the other as a negation is actually somewhat of an extra step.
For example: No A, unless B. Typically we would choose "No" as the rule to apply (negate necessary) and then treat "unless" as a negation. So we would get A and /B and would instinctively apply the group 4 rule to the already negated element because that is easier to write out, thus giving us A-->B.
Likewise, choosing to apply the group 3 indicator rule (negate sufficient) and treat the other indicator as negation we get: /A and B and instinctively would apply the negate sufficient condition to the already negated element because that is easier to write out, thus given us A-->B.
We can reach the same result by just ignoring the indicator rules and instead understanding them as identifying either the sufficient or necessary condition, as applicable. In other words, when translating a statement with both group 3 and group 4 indicators treat the group 3 indicator as group 2 and the group 4 indicator as group 1.
Examples:
No dog (D) is without an owner (O).
D --> O
---
None of the participants were certified in special education (C) except for the director (D). (treating except as group 3 here)
C --> D
---
You should never go outside (G) unless you bring your umbrella (U).
G- -> U
----
Until the fire department gives the all clear (C), we cannot return to our offices (R).
R-->C
The 7Sage group 3 indicators require negating an idea and making it sufficient. However, these indicators actually identify the necessary condition in the statement.
The group 4 indicators require negating an idea and making it necessary. However, these indicators identify the sufficient condition.
As a result, the suggested translation rule in lawgic that we pick one indicator to set the rule and then treat the other as a negation is actually somewhat of an extra step.
For example: No A, unless B. Typically we would choose "No" as the rule to apply (negate necessary) and then treat "unless" as a negation. So we would get A and /B and would instinctively apply the group 4 rule to the already negated element because that is easier to write out, thus giving us A-->B.
Likewise, choosing to apply the group 3 indicator rule (negate sufficient) and treat the other indicator as negation we get: /A and B and instinctively would apply the negate sufficient condition to the already negated element because that is easier to write out, thus given us A-->B.
We can reach the same result by just ignoring the indicator rules and instead understanding them as identifying either the sufficient or necessary condition, as applicable. In other words, when translating a statement with both group 3 and group 4 indicators treat the group 3 indicator as group 2 and the group 4 indicator as group 1.
Examples:
No dog (D) is without an owner (O).
D --> O
---
None of the participants were certified in special education (C) except for the director (D). (treating except as group 3 here)
C --> D
---
You should never go outside (G) unless you bring your umbrella (U).
G- -> U
----
Until the fire department gives the all clear (C), we cannot return to our offices (R).
R-->C
Comments
Group 4 X Group 3 Y
I would assert that there is a difference between knowing the word and being able to apply the rule it is associated with. The group 3 and 4 rules are the least intuitive of the bunch, especially when combined and with the addition of more complicated ideas. My suggestion was a way to simplify the process. The reason that I might not opt to do it "properly" is in the following paragraph.
@"Cant Get Right" I would also restate my claim that the above does remove a step from the process. The 7sage method says to 1) treat one indicator as negation and then 2) apply the other indicator rule.
https://7sage.com/lesson/group-3-group-4
As I laid out above, the negation that is applied in step one is undone by the application of step 2. The suggestion I offered does not require that double negation. I think that is especially useful when you are dealing with complicated ideas under time pressure.
Take the example from the 7sage lesson. Never go to Hawaii unless you want to have a good time. I see group 4 followed by group 3 and immediately pick out the two ideas, block out the indicators and draw an arrow between them to create the conditional statement. Done. No need to choose a rule and choose a concept to negate.
First, I think it's questionable whether having to memorize an additional rule for one specific corner case constitutes a simplification, especially when you still have to memorize the original rules anyway for all the circumstances that don't involve exactly one g3 and one g4 indicator. It seems to me like a strictly additional thing, not a replacement.
Second, when you have to 'instinctively' do anything, that destroys the value of the mechanic in the first place. If peoples' instincts were that good, then they wouldn't have trouble with conditionals in the first place. The entire point is to have rules that you can always rely on when you're not sure. And if you just memorize that g3=g2 and g4=g1, then you're back to my first point - strictly additional.
Third, the fact that you turn a g3 into a g2 and g4 into g1, while it may yield the correct final result, doesn't capture what I consider to be the more important piece of this whole exercise - what the words actually mean and how they actually function. I think it's actively harmful to your ability to parse a sentence if you rely on 'tricks' like this. We learn conditionals because that's how the English language works; it's not just an arbitrary exercise in drawing funny arrows. "Without" is a group 3 word because it literally means "if not", and "only if" is a group 2 word because it literally takes the place of "then" in an if-then construction. When you equate them, you lose the meaning of both words and reduce the whole thing into some arbitrary thing. Put another way, it seems to me like you're looking at formal logic purely as a thing to do because reasons, so even if this one particular thing works, it doesn't illuminate the bigger picture. I wrote "Why Formal Logic" specifically to address this point.
As I see it, at the point that you're able to (1) identify exactly one each of g3 and g4 indicators in a sentence, (2) remember that this rule exists and is different from the 'standard' rules, (3) remember that g3=g2 and g4=g1 if you chop the negations, and (4) put it all together, you'd probably also have been able to just do it in the 'proper' way and not bother at all. To the extent that your intuition fails to do it the right way but can do it the 'trick' way, it just means that your intuition isn't up to par and you need to work on it, not ditch it entirely for quick fixes. It's a false economy, because if you learn the fundamentals you get an intuition for everything that uses those words, while if you learn this one trick you might be faster in this one specific situation, but you're still slower all of the other times that you aren't faced with this specific situation, and it also legitimizes the idea that "it's just unintuitive" instead of actually working on your intuition. Learning a bunch of 'tricks' like this is how people stack up a bunch of 'knowledge' and still get absolutely murdered by the test.
For the record, you're right that this mechanic should theoretically always work - g3 negates sufficient and leaves a negated element in the necessary, g4 negates necessary while leaving a negated element in the sufficient, and contraposing in either scenario takes care of both negations and swaps sufficient/necessary (hence g3->g2 and g4->g1). It'll also work with a singular g3/g4 indicator and a negated other element as well, for the same reason (the fact that the heuristic misses this case is a good example of missing the forest for the trees). It's good that you figured this out instinctively and you should keep thinking like this, but I'd highly encourage you to not set up shortcuts like this unless you can prove to yourself that it'll always work (indicating your true understanding of the concepts in question). And even then, I'd be hesitant, because if you can actually do that then you don't really need the shortcut anymore...
A few things I want to clarify from my original post.
First of all, I am grateful for all the work that 7Sage has put into this curriculum and I could not even be in this discussion without it. I wrote the title of the post in the hopes of drawing attention to its content so that others might suss out what I thought I had learned. I want to be clear that I did not intend to recommend it as a replacement for the lawgic lesson. (I've since edited the title of the post to hedge my position a bit).
Secondly, your cautions about relying on a trick are well-heeded. I might be taking an unusual approach, but my attempt to streamline this process was actually born of an attempt to understand the underlying fundamentals better. I have a strong interest in language, grammar and logic and so the group 3 and group 4 words hold a special place in my thought process because it often seems that people understand the meaning in simple conversation, yet their use in complicated texts is hard to parse. I will keep in mind your warning not to rely upon a shortcut as a means to avoid building up my intuition. Furthermore, this discussion and my original exploration have aided my own understanding of the group 3 and group 4 words, as Jonathon said, as not simply identifying conditions, but rather illustrating a logical relationship. For example, the concepts of words such as "unless" and "until" now have a stronger intuitive pull on my senses.
Two minor additions related to the specifics of posts by JY and Jonathon:
J.Y. - In your video you state that I may have missed the issue of applying the suggested technique left-to-right. The problem would be incorrectly reading sentences where the group 3 indicator appears before the group 4 indicator. My final example in the original post addresses this and is an example of being aware of such an issue.
Jonathon - I particularly appreciate your final paragraph as that is very helpful in understanding how these indicators function in a sentence. My focus on the combination of group 3 and group 4 indicators in one sentence was because the construction, in particular where the group 4 indicators lead, seems to be a very common use case. I am certain that LSAT writers intentionally switch this order around as a result. For myself I didn't so much as view the idea of g3=g2 and g4=g1 (only in cases where g3 and g4 occur together) as an additional burden, but rather as an overarching concept that brought more clarity why those indicators were used together and what relationships it was illustrating. I see now that the mechanical presentation of that idea did not translate that well.
I came here because I was working on PT 23 S3 Q25. I had stumbled across a case of 'except' being used as a group 3 indicator and wanted to determine if it could be added to that group as a rule (now I believe it can). The search engine found @dcdcdcdcdc's second example and brought me to this page.
Thank you. Not only have you answered my question, but also introduced me to extrapolations on-top of the curriculum that will bring me closer to mastery.
And J.Y.'s humanizing moment makes my goal seem all the more attainable.
Good Thread: 10/10