I have commented in the past about what I call the "some people say" principle. I have just finished checking every "main conclusion" question in Preptests 62-71, and have found that the "some people say" formula appears in 14 out of 27 MC questions. In every single one of these instances, the "main conclusion" can be easily and accurately determined by taking the "some people say" text and negating it. (In many cases, the stimulus does this for you--the next sentence after a "some people say" formula is often something like, "But these critics are wrong," or "This suggestion is unreliable, because..."
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Just went over this and got to try out the "A/B" and "/[AB]" explanations. It went great. SO much for making up two new symbols to replace the "double not arrow." Let's go with Quinn's approach!
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So... I'm still thinking through what you said, Quinn. I hadn't thought of writing down the original statement in the "A or B" form. THAT would be fast, easy, and powerful. Likewise, I should read a "A->/B" rule and write down "/A or /B," which is probably better expressed as "NOT (A AND B)" (which I would write as an AB block with a slash through it.
So... thinking this out... I read "/A->B," and I write down "A/B." I read "A->/B," and I write down "NOT [AB]." Right?
Quinn, I agree with your logic but not your advice. I can figure out "/A->B" on the fly by saying, "So... if A is IN, B can go anywhere, so they can both be in." But... it takes a moment to work that out, and it would take ME a moment to work out the same result using your method. PowerScore uses the "double-not arrow" to save that moment, and I think there is some merit to that. It's just that I haven't figured out a way to reliably USE the double-not arrow for its intended purpose because I'm always second-guessing myself (is that both in or both out? Did I write that down properly?).
Bottom line: there's a trade-off between fast and simple. People who use flashcards are trying to get their speed up by exchanging a thought process for instant recognition. I PREFER working out the logic in my head, but I only have 35 minutes on a logic game section, and a fast, reliable mnemonic may have its advantages.
Having said all that... I love your explanation of the "NOT A or B" mode, and I'm going to try it out with some guinea pigs. If I can explain that effectively, I'll gladly use it instead of a new mnemonic. If I can't, though, I think I'll stick with my "erupting volcano" and "leaky faucet" pictures.
I just posted a new idea that is especially intended to help in/out games. Look for my "better than a double not" post.
The "/A->B" rule is so important for grouping games that PowerScore uses a special symbol ("A(-|-)B", or "the double-not arrow") to note it. As a person who understands how important this is for grouping games, I think the "double-not arrow" is brilliant. As a person who has tried to explain it to others, it is both frustrating and confusing. The "double not arrow" is ONLY used when the sufficient term is negative and the necessary term is positive--or is it the opposite? It makes a huge difference, but I find it almost impossible to keep it straight in my head, much less explain it to someone else. For that reason, I think JY is wise to avoid using it here at 7Sage.
But what if it were not confusing? I have come up with TWO arrows that practically write themselves and make grouping games much easier. All you have to do is look at the way we write out "/A->B" and "A->/B."
Note how the slash comes first in the "/A->B" situation, but comes second in the "A->/B" case. Let's turn those slashes into pictures. If we put the forward slash first, we can make a "/\" picture. If we put it second, we get a "\/" picture.
/A->B turns into A(-/\-)B
A->/B turns into A(-\/-)B
Pictures are helpful if they mean something, so let's call the "/\" picture an "erupting volcano." The "erupting volcano arrow" means that something is erupting, so that something must be in your slot. The "\/" looks like a "leaky funnel," which means something is leaking, which means something must be OUT.
If you can remember that "slash comes first" means "/\," and "/\" means "erupting volcano," and "erupting volcano" means something must be in, you can turn a "/A->B" rule into a full slot within seconds. And if you can remember what a "leaky funnel" does, you'll fill an out slot just as fast.
And there's no reason to ever get them mixed up!
Good example, @. Interesting example, too, since I had gone over it and used it to support the "some people say" principle (which I have discussed elsewhere) without noticing that it broke the "should" principle.
"Normative" is a better term than "moral" for this purpose. It expresses what I wanted to say much better than "moral" does, which has a lot of unnecessary connotations.
In light of the general feedback and specific counterexamples, I'm deleting the "should" principle.
PrepTest 63, Section I, Question 8 has an extreme case of "some people say." I won't quote the actual text, since it is copyrighted, but the logic of it is identical to this:
Student complaint: Professor Smith was wrong to say that "climate science deniers" falsely claim that the earth has not gotten hotter over the last eighteen years. He claimed that surface temperature measurements show a steady increase in temperature over time. But satellite measurements, which are not subject to local "hot spots" and other instrumentation problems, do not show an increase in temperature.
Question stem: what is the main point?
(A) The increase in surface temperature measurements does not support the professor's rejection of the "climate science deniers" claim.
This question pushes the "some people say" principle to its limits... but it also shows the value of the principle. This is a case of "some people say that some (other) people say." Despite the exponential complexity of the case, the right answer happens to be exactly what the "some people say" principle would indicate--the correct answer is, in effect, "What some people say that some (other) people say is wrong."
I'm sorry, @, I miscommunicated. What I TRIED to say (as clearly as possible) was that "IF the word should appears in a stimulus, THEN it appears in the conclusion." In a moral argument, "should" often appears as a premise... but I have yet to find a moral argument that uses "should" in a premise but avoids the word in the conclusion.
As @'t_get_right noted earlier, these empirical observations are NOT logical rules. The fact that the LSAT writers tend to do the same things over and over is NOT proof that they will always do the same in the future.
That said... I'd like somebody to do a little more digging and come up with an actual counterexample. There are a lot of published tests out there...
You guys are truly terrific. Thank you for your honest feedback, and the broader perspective on the LSAT that informs it.
That said... Quinnxzhang, what do you perceive to be the conclusion in PT9.S2.Q20? I think it is "A university should not be entitled to patent the inventions of its faculty members." Do you disagree with that? If so, what do you perceive as the conclusion, and why?
DEEPLY grateful for the all the constructive criticism and counterexamples, folks. I have edited the title of this post (it's a "principle," not a "rule" now).
"Finding the conclusion" is as easy as riding a bicycle... and as hard, for struggling students.
I have noticed that the word "should" is as helpful as "thus" or "therefore" when it comes to finding a conclusion. Unlike the typical conclusion keywords, "should" appears in conclusions because conclusions tend to be recommendations, predictions, and judgments. (See Kaplan's list of six conclusion types for more on this.) "Should" can be used for all three of those sentence forms.
Sometimes "should" appears in a premise as well as the conclusion. This routinely happens in moral arguments (we should obey the law, the law says drive 55, therefore we should drive 55). While it is possible to use "should" in a premise but not in the conclusion, I have yet to find example of that happening in a published LSAT question.
As usual, I'm looking for criticism (constructive or otherwise) and counterexamples. This may not be a big deal for you folks who have been riding your bicycle for years, but it's a small step forward for the folks who are still on training wheels.
Can't_Get_Right, I am simultaneously humbled and flattered by your comment. I couldn't agree more that we need to distinguish between the "laws of logic," which are necessarily and always valid, and empirical observations about LSAT stimuli. No matter how often the "some people say" phenomenon occurs, it always theoretically possible for it NOT to occur, and we need to remember that in the same way that we remember that "A->/B" means A is out, or B is out, or BOTH are out.
I also agree that the word "rule" is too strong for this observation. A "rule" should always apply, without the possibility of an exception. It's more of a "rule of thumb" than a rule, but that's too cumbersome for my purposes.
But leaving aside those weaknesses in my initial presentation, I am flattered humbled by your "great and advanced realization" wording... but I don't disagree. If a "some people say" statement is, in fact, the "antithesis" (as it is in every instance I have observed so far), then it is (a) unusually easy to identify and (b) unusually instructive. The instant you see a "some people say" formulation, you can look for its negation. It you find that in the stimulus, then you have an "antithesis," and (in an unflawed argument) you have a pretty good idea of what evidence you will need to prove the antithesis wrong.
This gets us to another point I haven't seen addressed very often--there are surprisingly few argument structures that are used in "typical" LSAT questions. If the "antithesis" affirms something, then the conclusion will deny it. The most common argument type that produces a simple negative is a modus tolens. If the "anthithesis" states a conditional ("All dogs are mammals," or "if it rains, it pours") then the ONLY argument type that negates that is "A and /B." This means that not only can you spot a "some people say" statement quickly, but you can prephrase the entire argument as soon as you do.
MrSamlam, your point SHOULD be accurate... but in practice, I have found few, if any, actual LSAT stimuli where the conclusion does NOT deny the "antithesis" statement. It makes a certain amount of sense that they wouldn't--LSAT stimuli are a tightly constrained medium, and the LSAT writers don't just throw in random text. The closest I have seen to something that ISN'T a negation of the conclusion is the example Runiggyron found, where the antithesis is "musicians are being robbed" and the conclusion was, "the music-sharing services are not to blame," which may or may not be a denial of the "robbed" claim.
I love the bicycle analogy. I'm going to use it from now on. Do I owe you royalties?
Three cheers for being brave enough to challenge the contrapositives! I hope I can demonstrate why they work to your satisfaction. If I can't, I'm pretty sure someone else will be able to do so.
Let's turn an abstract "A->B" statement into something concrete. I like geographical examples. Your specific case is "~C->~B," so let's say, "If you are not in Canada, then you are not in British Columbia." (You can see why I like geography--it's clear, and you can generally find something that starts with the proper letters!)
Assuming you agree with me that "if you're not in Canada, you're not in British Columbia," how do you feel about the contrapositive? "If you ARE in British Columbia, then you ARE in Canada." Does that sound like a far-fetched assumption, or does it seem inarguably true?
Elegant and essential distinction, Runniggyrun.
I have been studying logical reasoning stimuli that include a sentence about what someone OTHER than the author says, usually near the start of the paragraph. I call these the "some people say" statements. They are different from "expert testimony," which supports the conclusion. These "some people say" statements do NOT support the conclusion. In fact, after looking at them carefully, it looks like almost every conclusion in a "some people say" stimulus is a simple negation of the "some people say" statement.
I like the term "antithesis" for these statements, since the "thesis" of the stimulus is the conclusion and the "some people say" text is the logical opposite of that.
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I would love to know if anybody can find any counterexamples to this "some people say" rule. If not, then it would provide a simple and teachable logical reasoning shortcut. Just "find the anthithesis" near the top of the stimulus, negate it, and find the evidence to support that negation. It's easy to find if you know what you're looking for.
I have been analyzing all the June 2007 (public domain) questions one by one, and find that they all neatly fit into very neat symbolic argument patterns--except for Section II Question 24. I would appreciate any comments on this particular question, especially if someone can help me write up a symbolic logic representation of it.
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https://classic.7sage.com/lsat_explanations/lsat-june-2007-section-2-question-24
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Your argument assumes that "1+1=3" is false without stating that it is false. If you spelled it out fully instead of making that assumption, the atomic proposition would appear twice.
It is certainly possible to make assumptions that are never spelled out in an argument. MOST LSAT questions either don't make such assumptions or else make the assumptions a part of the answer, but that is not always necessarily so as a matter of logic.
In trying to figure out the key parts of a stimulus, I want to be able to assure myself that there's something really there which one really can find if one really looks hard enough. (Really.) If I can count on there ALWAYS being two instances of every "key term" (in the stimulus+answer), then it's worth pushing them to keep hunting until they find it. If it could even theoretically be possible that a well-formed, complete, and non-trivial argument does not have at least two "key terms," both of which appear at least twice, then I don't want to go looking for them.
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I hate this kind of question. Normally, I read the stimulus very carefully because I find it easier to find the flaw than to match it with the answer. That's especially true here--it is a classic example of an incorrect negation but that's not what the answer says. The credited answer is that the author "overlooks" a negation of the conclusion. That's certainly true, but you could say that about ANY argument.
I guess the take-away is, "If one of the answers is a negation of the conclusion, it might be just what you're looking for!" Somehow I don't see that being all that helpful all that often.
Thanks, Quinn. I took academic logic a long time ago... very likely before you were born, which means you're much more likely to be correct than I am, working from memory.
Insofar as the large majority of LR stimuli involve conditional or categorical reasoning, I'm happy to use the term "atomic proposition" if you think it would be clearer than "term." (I certainly don't find the term "term" to be unambiguously clear.)
So, partly echoing you and partly repeating myself from above, there are completely trivial arguments that only use one atomic proposition, but I haven't seen this in any actual LSAT stimuli. Until we discover one, I'm sticking with the observation that a VERY large majority of LR questions have at least two atomic propositions.
Moving on to the more controversial claim--I can't think of a way to write a conditional or categorical argument in which an atomic proposition only appears once. Can you?
I chose the term "term" after looking around hard for another word to express the concept. If you know a better word for the symbols we use in conditional statements, please let me know. I know that logicians routinely refer to the "terms" of a categorical statement as "terms," which is why I used the word in this context.
A->B
A
Therefore B
It seems to me that it is impossible to form a complete logical argument in which the key terms do not appear at least twice, and it also seems that every logical argument but one necessarily uses at least two terms. (The only logical argument that only uses one term is the "double negative," which states: "A," therefore "~(~A)," and I have never seen this in an LSAT stimulus.)
As far as I can tell, a complete LSAT question (by which I mean the stimulus plus the correct answer) must necessarily include at least two terms, and each of these terms must appear at least twice.
I may be failing to consider certain unusual question types that don't actually consist of logical arguments as such. If so, that might be the exception that proves the rule.
If anybody can provide an example of an argument (other than the "double negative" above) that has less than two terms, or refers to a key term only once, please let me know.
Is it Beta? I just heard about it on June 1 (launch day) and am experimenting with it. Didn't have to make any non-disclosure agreements that I recall.
What are some ways you can prepare yourself for the "shock and awe" of the actual test? A lot of people do great on practice tests, routinely scoring about where they want to be... and then get into the testing center and forget everything they ever learned. What are some ways we can get ready for the pressure, hormones, and emotions of test day?
For example:
Would it help to time each questions with a stop watch?
Would it help to set some artificial consequences for failure (like, "Get 8 out 10 questions right in 10 minutes or else you have to clean the refrigerator")?
Would it help to have somebody else hover over you and time you?
I agree with your hunch, here. Not all strengthen questions involve a necessary assumption, but I think that every "eliminate the weakness" variant does.
Nice insights!
This is a "must be true" question, so you're going to have to PROVE the answer is true using ONLY the premises in the stimulus. If we find the right answer, it MUST BE TRUE, which means it CAN'T BE FALSE. So let's see how that works for answer choice D:
D) In many municipalities there is, or eventually will be, a shortage of rental units.
Let's make answer choice D false and see whether there's anything in the stimulus that gets in the way. Let's do this is study buddy form.
Antonia: I think the answer is D, there will be a shortage of rental units in many cities.
Trevor: A shortage of rental units? Huh uh! There won't be any shortage.
Antonia: It says here rent-control ordinances have negative effects, and one of them is a shortage of rental units.
Trevor: Yeah, UNLESS they are strictly temporary. Maybe they're all strictly temporary!
Antonia: Except it says down here that in many municipalities, tenants get political power. They're not going to give up their low-cost rent!
Trevor: Huh. Well, okay, so, but that doesn't mean there will be shortages.
Antonia: Yes it does -- that's what the first sentence says!
Trevor. Oh. Well, that doesn't mean D has to be right.
Antonia: Yes it does! If it CAN'T be false, it MUST BE TRUE!
Why is there no such thing on YouTube? Generations of future lawyers will thank whoever comes up with one of these...
Actually, I don't know why you edited it, but I see I better err on the super safe side. I value the input I get here tremendously, and I am NOT trying to exploit this side to boost my own business. This community is one of the finest places on the Internet for testing out ideas and seeing what is the BEST way to learn the LSAT, and I am eager to promote 7Sage.