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Some statements
smseraj3
Alum Member
Hey im still confused after reviewing the CC again
I know a some statement can be reversibly read but is there a way to negate it?
For example:
A some B --- C
If I negate C, what does that do to the some relationship?
Comments
Don't want to lead astray.
hey @smseraj3 would you mind clarifying the conditional statement in your question? Particularly the relationship between B and C.. is that supposed to read B-->C?
But yes, you can negate some-statements because they are ideas and we can negate all ideas (SS-->I-->N). When we negate an idea, we are just saying that there is a world/occurrence where that idea is not true. "Some people are assholes" negated is "hey you know what? No people are assholes".
@jkatz1488
Yeah. The condition can be:
Some cool people are smart, all smart people are rich
CP some S ----> R
not R
???
I know it would be "no cool people are smart", but what would the logical conclusion be drawn above?
Thanks
I completely messed up with my first comment, I will write another one. Sorry
Edited out.
In this case we are not even touching the some relationship.... let me try to explain why. @smseraj3 Here you have two separate ideas CPsomeS Some cool people are smart and S---->R All smart people are rich, or in other words we have a relationship between cool people and being rich for this is a valid argument form (AsomeB---->C=AsomeC) So, in other words, we have ourselves a conclusion: CPsomeR Some cool people are rich
Let's negate this...
If you remember from @JYPing's lesson, ALL negates to SOME NOT and SOME negates to NONE.... So, in this case, the only possible negation we can have is No cool people are rich. CP---->/R This is JY's explanation on the binary cut of ALL and SOME statements: https://7sage.com/lesson/advanced-negate-some-statements/
@smseraj3 I hope this helps, let me know if it doesn't and I'll try to explain better
And could a sage please confirm this, so I don't further confuse @smseraj3 .... @"Cant Get Right" maybe? I am most eager to know if the two relationships must be negated separately first and then to draw a conclusion instead of negating the resulting conclusion from the two original relationships and negating that. I don't think that should be the case but please correct me if I'm wrong. Thank you
@goingfor99th I think your are wrong. You are negating All Bs are Cs to No Bs are Cs and that is wrong. The way to negate this is to say that "It could be the case that a B is not a C" or in other words Bsome/C
@JYPing's explanation: https://7sage.com/lesson/how-to-negate-statements-in-english/
You're right.
Apologies.
It's an interesting example and I think it does well to show why the LSAT need not use more than just a few arguments because so much is possible by combining them or tossing in context via the messy English language.
Before I confuse anyone with my rambling, I believe @therealnas does a good job of explaining the principles in the cc. I definitely believe they are correct in the sense that in order to negate CPsomeR, you must show that CP-->/R.
However, what is /R? Is it "There are no rich people in the world" or is it "Jack is not rich". In the case of former, this does actually negate the some statement, but the latter does not lol. By saying "there are no rich people in the world", we must conclude that no CP are R since R doesn't exist. But if we are only saying "Jack is not rich", then as therealnas pointed out, it doesn't touch the some-statement. Just because jack isn't rich, doesn't mean that some CP aren't R. Is Jack cool? Maybe. Even if he is, we don't need all cool people to be rich, only some.
I see why you are confused @jkatz1488 In the statement CP---->/R you have created an entirely new world where it is the case that if you are a cool person, you are not rich. You do not get to conclude that there are NO rich people in the world; you can only conclude that you can be cool and not rich
@therealnas one of us is misunderstanding the other but I am not sure which.
I am not concluding /R. smeraj3 provided /R as a premise and I am musing about 2 different conclusions which are possible depending on the meaning of /R (which would be defined by a stimulus). That is the point of my comment. smeraj3 provided /R ambiguous (totally fine by the way). We don't know whether it means "there are no rich people in the world" or if it means "an individual is not rich". l believe you are assuming it means the latter or at least that is how it seems.
Well, I see more clearly now. Are you asking what the individual indicator /R means in the statement CP---->/R? I would be much more willing to say that it means "an individual is not rich" rather than "there are no rich people in the world." The reason why is because our stimulus is about some people being smart and some being rich... It is not giving us a conditional statement "Some cool people are smart; if there are smart people in the world then there are rich people in the world." See, in this case, the negation would be "it could be the case that there are cool people people in the world but some of them are not rich." in this case /R would mean "not rich"... Actually, never mind, I guess in both cases /R just means "not rich"... that's all you can say. I don't even think you can go as far as saying "an individual is not rich."... I think you can only say that "something is not rich"... It's just the adjective "NOT RICH" that's all
Later addition to this comment:
Here's where I tried to go with this: if we had the statement "Some cool people are smart; and if there are smart people in the world, this world has rich people"
CPsomeR (Sometimes, it is the case that if there are cool people, this world has rich people)
Same translation CPsome>R (or rather WorldHasRichPeople)
NOW, if you negate the statement you get "It could be the case that sometimes, if there are cool people, there are no rich people" ... well, now, in this case, the /R in (CP---->/R) would mean "no rich people," or "no rich people exist."
This is the most extensive explanation I can give, so I really hopes it explains your question @jkatz1488. Of course, I am still waiting for a sage or a mentor to confirm my points in this thread ...
@therealnas Well I hope this doesn't sound snarky but I am a mentor. I'm sure someone will jump in though since it seems like we are not connecting with each other lol.
I really appreciate the energy you're putting into this discussion. I've become a total nerd for this stuff and really enjoy these chats.But my initial question regarding the meaning of /R was rhetorical in order to show what is possible with two possible meanings. I agree with you that the most reasonable interpretation is "an individual is not rich" and based on that, your reasoning seems to make perfect sense to me. I think you applied the lessons really well.
However, /R taken to mean "there are no rich people" does in fact allow us to negate that some-statement. I only bring this up because exercises such as that where we tweak meanings and observe the results have been really helpful to me in cementing Lawgic. They have also been key in helping me to identify assumptions because when we get in the habit of playing with statements, we begin to see what they are actually saying and not saying more clearly.
Anyway. @smseraj3 I'm sorry we've gone down this rabbit hole. I'm not sure if we've been able to clearly answer your question so I want to address it again here.
AsomeB-->C
AsomeB negated = A-->/B
AsomeC negated = A-->/C
B-->C negated = Bsome/C
For each of the above ideas, we simply need to represent an exception in Lawgical form. When negating some-statements, we generally need to use a conditional statement with a universal indicator. That is because if we say some cats have tails, we can't negate it by saying some cats don't have tails because that is allowed by our original statement and therefore is not presenting an exception. No cats have tails, however allows us to blow up that original statement with the power of us universal indicator.
I really hope you've found some use in some of this. If you are still not clear, feel free to PM me.
@jkatz1488 I apologize, that is my fault for not noticing you are a mentor, but nonetheless I still don't agree with your english translation of /R. I do not agree that you can take it as meaning "there are no rich people." The reason being is your negation process:
Original statement:
"Some cool people are smart; all smart people are rich."
Therefore: "Some cool people are rich."
Negated:
"No cool people are rich."
In other words, the negation doesn't become "If you are cool, there are no rich people."
NO, not at all.... You cannot say that. There do still exist rich people; however, we now know for a fact that you cannot be cool and be rich at the same time.
As to the second part of your last comment, yes, I agree and do appreciate your clarification of general negation rules. But assigning the meaning of "there exist no rich people" to /R to me sounds utterly wrong. Again, my apologies for disrespecting your authority
I think @jkatz1488 is simply asking what @smseraj3 means by "not R" in the comment (which I quote below.)
Here I thought @smseraj3 was asking what valid conclusions can be drawn from:
CP some S --> P
/P
ーーーーーーーーー
but are you, @smseraj3 , asking what the negation of the statement "Some cool people are smart, all smart people are rich" would be?
I don't think that is what @jkatz1488 was trying to say.
The original statement made by @smseraj3 only said:
@jkatz1488 is saying that if "/R" meant "there are no rich people," it would actually deny the whole relationship because there would be no such thing as a "smart person."
Yes that is what I am saying. It is like a backdoor negation... cool stuff for LSAT nerds like us!
@therealnas Love the energy man and I have no authority for you to disrespect! But regardless, there's no disrespect here anyway. Just good discussion around Lawgic. @akistotle sees what I was saying by playing with the meaning of /R so now at least I know I am not losing my marbles.
I read OP's question to be less about negation and more about how taking the contrapositive affects a some statement in the chain.
You guys are doing a great job with this discussion. I think as far as negation, you're right on with it @therealnas .
So what do you guys make of the contrapositive issue? What does that do to the some statement at the front end? @jkatz1488 @akistotle
@"Cant Get Right"
/R-->/S (If a person isn't rich then that person isn't smart)
But from there we have no where to go, I believe. That person who isn't rich and therefore isn't smart may actually still be Cool, but we don't know because of the undefined nature of a some-statement.
Some cool people are smart allows for some /smart, dumb, genius, dead, vegetized etc people to be smart as well.
What about negating a "most" statement?
E.g.
"Most of the island's permanent residents oppose the passage of the law"
Would the negation be
"It could be the case that none oppose the law" (Which would also include the possibility that all support the passage of the law") My reasoning here comes from the fact that MOST is in fact a SOME statement, because some includes everything from 1 to 100.
I look at a statement plus its negation as encompassing 0 to 100. So most is from 51 to 100. Therefore not most is from 0-50.
@AllezAllez21 agree and like the way you put that. Thinking about it in those terms helps us to remain appropriate broad in our negations.
@jkatz1488 , that's exactly right about the contrapositive.
@AllezAllez21 , also good on negating most statements. "Not most" is zero to half, including half. I call "most" half plus one rather than 51 to account for something like 50.5. 50.5% of the vote in an election is a majority. I know you probably already know that distinction, but just wanted to throw that out there anyway.
@therealnas I'd negate "Most of the island's permanent residents oppose the passage of the law" as something like "No more than half of the island's permanent residents oppose the passage of the law." The problem with "It could be the case that none oppose the law" is that it doesn't make the clean binary cut. We must create a negation that, together with the term being negated, accounts for every possibility with no overlap.
So a very simple negation would be something like:
Planets + not planets. We can classify literally every object or abstraction in the universe using that distinction. There is no room for anything to fall outside of those terms, and there is no term that overlaps. It's a very simple but perfect classification.
Old Man Jenkins? not a planet
The Death Star? not a planet (or a moon)
puppies? not planets
Jupiter? planet
Yo mama? Ok that one could be debatable. jk, of course.
51 Pegasi b? planet.
Pluto? not a planet
So, that's the idea. Give me anything and I can classify it into one and only one group of planet or not planet. And every negation creates this type of perfect binary. So if it's the case that no one opposes the law, there are possibilities which fall outside of the dichotomy. What if Old Man Jenkins is like, "aw hell naw," (he's like that about everything) but everyone else is cool? Does this scenario fall under:
"Most of the island's permanent residents oppose the passage of the law"
Nope. It's just Old Man Jenkins, once again alone in his opposition.
or
"It could be the case that none oppose the law"
Well, we know that's not the case in this world. Once again, OMJ opposes.
So we can't classify this scenario under either. That means we have not created a perfect binary.
@"Cant Get Right" there's a reason you score 170 and you are a sage. That was a great explanation, and possibly better than JY's... i feel terrible saying this
But thank you!
I learned from the best!
@AllezAllez21 haha, I knew that'd ruffle some feathers!
https://img.buzzfeed.com/buzzfeed-static/static/2015-10/28/11/campaign_images/webdr10/the-sad-pluto-meme-is-making-the-internet-weep-2-17072-1446047759-0_dblbig.jpg
Would it not be easier to learn concepts regarding propositional relations? One must be careful because what I see is a mix of logics here.some people are confusing mathematical logic with classical logic. When you use the symbols it is absolutely not always equivalent to the classical formation. I can provide samples if needed. Let me explain WHY though.
The vocabulary terms change contexts is the simplest answer. For example Your so called contropositive has a different definition in Aristotelian logic. In Aristotelian logic you cannot contrapose a NO quantifier statement. Contropositive had a distinct meaning which is not what you guys use. In math they use contropositive to mean the exact same thing philosopher call TRANSPOSITION which is the more accurate name because you will never confuse the two context that way. Your contrpositve is simply symbol manipulation. I bring this up because logic is associated with philosophy, rhetoric / law, psychology, and mathematics which ALL have different purposes and differ in vocabulary and methods. Some of what works for the LSAT will not fly In a college class. I could say the vice Versa here.
The contradictory is how you negate any statement in mathematical logic. In Aristotelian logic it differs. Some plants are roses can be negated as some plants are non- roses. Before you says it is the same thing as a NOT think twice. Anyone familiar with the square of opposition would have to disagree and say a non is not the same as a NOT. The some s is p proposition is called an I proposition. The some s is not p is called an O proposition and they ARE NOT equivalent.
None of that is wrong @roychess , but like you say:
We're really only concerned with the LSAT here. Not with a college class. And as far as the LSAT goes, these distinctions don't matter. Sure, a lot of LSAT logic doesn't align with proper logic. For anyone trying to learn Logic, the LSAT is not necessarily a great tool.
So. damn. true.
Yeah, I tacked on an unnecessary philosophy minor hoping it would help immensely with law school / the LSAT. Honestly, aside from RC, I don't think most of the logic I learned in my college classes ended up being that helpful. Wish they had offered a 7Sage/LSAT minor instead....
Thank you for understanding my post. What I really wanted to make clear is that the subject you allegedly learn logic from does matter. The common deception is that most people think or believe logic is logic. That all logic is the same. We now see this is not the case. For the LSAT and Sage your logic is different but the original philosophical roots are still present. Rhetoric and law is the pattern of logic that is concerned with PERSUASION. Mathematical logic is the pattern of logic focused on Validity. Science reasoning mostly concerned are psychologist are focused on how humans do reason and how to be practical with it; that is how can we symbolize those practical arguments. Philosophy teaches deductive reasoning which all those other topics use partial knowledge of and they name it logic. The purpose of logic that I learned was defined as the act of correct reasoning which detects deception. Out of all the other subjects that teach their own logic none of those are designed to evaluate arguments for deception. That is deductive reasoning is not to simulate how people do in fact reason. Deductive reasoning is not about persuading an audience such as a jury.
Perhaps you can use detection techniques once in a blue moon but it is not your primary goal for using logic. Mathematical logic focuses on validity even when the premises make no sense: they make a context shift in the term validity. So in reality this will often fail because concepts were removed from mathematical logic.
These forms of logic come from one universal topic: deductive reasoning. That is if you study proper deductive reasoning you will be able to do or follow all the different purposes of logic easier. Nearly all topics use deductive reasoning. This does not make them all the same thing -- aka philosophy. For instance almost all science requires a lot of mathematics but getting a degree in physics does not mean you get a mathematics degree as a bonus. The mathematican will know more about math than the physicist no matter how good at math the physicist is; i.e., no matter how good at algebra, trigonometry and calculus he is.
Well the distinctions are absolutely important. Why would you say such a thing? I don't see a disclaimer to your students here that these techniques you teach are specialized to get students to reach a goal and that these teachings will not always serve you well outside of this subject.
I would think most people THINK of logic as a universal topic. That is most students come to sites and courses about logic or reasoning thinking they will learn something they can apply outside a class setting. The deception kicks in any place that teaches logic or reasoning (be it the place is a University, College, High school,Website, etc.) when there is no disclaimer stating that what we teach will not always work in every environment in reality.
No one advertises Material logic --aka specialized circumstance logic. The student will likely think "what do I need this for if it works only on SOME days of the week and only in special places?"
Deception is in play when one fails to mention RELEVANT information that could change the outcome.
This is the focus of how original logic was taught in the field of Philosophy. So the term LOGICis being brutalized because people are not clear there are different types, methods and PURPOSES of logic. The majority of students think logic is all the same. All mathematics teaches logic is mathematics which is not the case. The use of the term logic will become useless because different people teach logic one way WITHOUT disclosing there are indeed other ways as well depending on the focus. This deceives the student once he learns he has been duped: what he learned failed in reality and doesn't know why. The teacher forgot to mention this is not universal!
Notice I used the term deductive reasoning. This implies a universal topic and universal concepts at play.
Thank you, @roychess, for pointing out that there are in fact distinctions. I believe that 7Sage does acknowledge the distinctions, but as @"Cant Get Right" says, the distinctions are not important for solving questions on the LSAT. This is because we generally don't come across questions that make such distinctions on the LSAT. That is the general consensus.
But perhaps this may not be the case. If you think that "the distinctions are absolutely important," I would very much appreciate it if you could bring some examples of the actual LSAT questions that make such distinctions.
Yeah, and it's not that the distinctions are unimportant: It's that they're unimportant specifically to the tasks that we're all here for. I think it's pretty universally understood that this is an LSAT prep course. And I think through the curriculum, that context is pretty constantly referred to. If you sign up for the course and can see where our frame of reference is coming from, I think a lot of these issues will be addressed.