The way you listed all the "natural languages" in the exact same order as I learned my 2nd, 3rd, and 4th languages at 2:05 definitely caught my attention lol!
@LiviaLSAT for me at least it feels more natural to use the dots because it allows me to hold more information. like if you introduce many subsets together "like cats ->mammals dogs->mammals" etc it can quickly add up and become complicated.
The reason i have trouble with the store -> milk example is because there simple isn't enough information. I read this as relating to what one gets when at the store, in which case milk -> store would be correct because i could get orange juice at the store, not milk
@epayne17 the point of the -> element is to show the conditional relationship present in the argument, not to provide context. Reading the sentence/argument provides you with the context to which we figure out how to use the -> to show the conditional relationship.
In this context, the "If I go to the store [subset], then I will buy milk [superset]." Therefore, store -> milk; try not to rely on your intuition about what you might get at the store. Only what is presented in the argument.
@epayne17 Part of this is also picking out those indicator words.
He says: If I go to the store, then I will buy milk. "If" is a sufficient condition indicator. He's not saying he could buy milk - he will buy milk if the condition (going to the store) is met.
@Livandthecats lol going to the store does not require milk. I'd argue it makes far more logical sense to say that for the most part buying milk requires going to the store. You simply cannot make the claim that he will buy milk if he goes to the store. He could buy literally anything else at that store.... Picture the store and milk as the circles visualization JY gives for relationships. The milk circle should logically lie within the store's bigger circle. This makes the store the proper necessary condition, not milk.
@epayne17 Yes, buying milk typically involves going to a store. However, the argument that is being presented is in fact that if he goes to the store, he will buy milk.
In this case going to the store is your sufficient condition/subset because it follows the indicator "if". It doesn't matter that realistically there's not many other places to buy milk (unless you live near dairy farms), the argument is presented in such a way that store is the subset and milk is the superset.
If it was phrased as "If I bought milk, then I've gone to the store" then your argument makes sense. But the argument has not been presented that way.
WOW. So, I studied on my own for the first LSAT I did and always saw this notation but constantly messed it up because I didn't know that the arrow itself had this rule. This is such a big clarity moment.
@bcn but its not though. Buying milk would be the superset and going to the store would be the subset. The lesson on group 1 indicators explains this quite clearly: the "If" in I go to the store is a sufficient indicator, meaning going to the store is a sufficient indicator for triggering buying milk.
@TheBigFatPanda The way you just explained this, broke the barrier that I had in understanding this concept. Thank you. I was starting to get really frustrated.
What I cannot wrap my head around is putting the examples in reverse. Making the statements sufficient.
NYC -> USA
Being in NYC is sufficient for being in the USA. I can be in Florida (currently am) and also be in the USA.
How do I do the same for the milk/store example?
Store -> Milk
It is sufficient to go to the store in order to buy milk? But, every time I go to the store, I have to buy milk; I cannot go to the store to buy bread, without having to buy milk. If I buy milk at a farm, then the necessary statement would not work, am I right?
I guess I need help with deducing store -> milk to a sufficient statement. My brain cannot make sense of it.
@JRamirez If you go to the store, you will buy milk.
But that doesn't prevent you from buying milk elsewhere. Perhaps you can go to a farm and buy milk. Or maybe you can buy milk from Amazon.
Similarly, If you're in NYC, you're in the USA. But that doesn't prevent you from being somewhere else in the USA. You might be in Florida and in the USA. You might be in Alaska and in the USA.
@SWJ Just keep pushing through the lessons. Most days you will be thinking, why are they teach me this, why does it have to be this way, it makes no sense. It all starts coming together and starts making sense later on. I read comments in almost every lesson and that has been helping me. Asking questions and having them answered has also helped.
The best advice to give you to grasp the material is... DO NOT bring in your own assumptions or perceptions into the lessons or any questions.
Example:
If you are an astronaut then you are a cat
A -> C
Therefore, if you are not a cat, then you are not an astronaut
A -> C
/C -> /A
Not sure where you are on your lessons, and if my example makes no sense, that's ok— the important thing is that cats are astronauts! To us in our reality they are not astronauts but LSAT writers don't care about that, they care that you understand the structure of the stimulus (passages). You may see things more in depth of my example where they will include a human in the mix and you are thinking, wait, humans are astronauts not cats. The answer choices will try to hone in on your own assumptions of the real world and force you to answer the question wrong, because you didn't exclude your own perceptions and assumptions.
I went a little longer than I would have liked. Just trust the process, 7Sage knows what they are doing. I was a non-believer, but trust me, it all comes together.
This will probably be explained in a future lesson I imagine, but I'd like clarification on what happens when the necessary condition is true instead of the sufficient.
I'll use the milk/store example since I think that's the one most of us are confused about. I'll also write it out to specify the premises and conclusion:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I went to the store.
Conclusion: I bought milk.
And here the "Lawgic" version of Premise 1:
Store -> Milk
This might not make sense in our world, but in the world of this argument then if anyone ever goes to the store, they have to buy milk. I think this makes sense.
Now what if I change the argument to something like this:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I bought milk.
Conclusion: I went to the store.
I want to say that this does not make sense/is not valid, because Premise 1 is unchanged that means that the Lawgic is still "Store -> Milk," and not "Milk -> Store." In English, this would mean that I could have gotten milk from anywhere, not just the store.
@aidanro2003 You're totally right! The necessary condition being true means nothing for the sufficient condition. The only other true logical statement you could get out of this is if you didn't buy milk, you didn't go to the store as we know if you went to the store you must have bought milk.
He's already using A for P and B for Q, but does anyone know if this will follow a more formal/classical logic language or a sentential logic language? Or neither and I'm just going to get really confused?
Note for anyone confused by the store and milk example:
That example is not intended to map onto whatever real life understanding you have about stores and milk. When we get a statement saying "If I go to the store, then I will buy milk," we have to analyze the meaning of that specific statement. And that statement means that if I go to the store, I am guaranteed to buy milk.
You might be thinking, "But I don't have to buy milk when I go to the store..." That may be the case in real life. But the statement "If I go to the store, then I will buy milk" does assert that I have to buy milk when I go to the store.
And, "If I go to the store, then I will buy milk" does not assert that the store is the only place that I can buy milk. It's entirely possible that whenever I visit a local farm, I buy milk. Or that I often buy milk from my neighbor. But, according to the statement, if I go to the store, I am guaranteed to buy milk.
This is why the statement is diagrammed like this:
Store → Milk
If I go to the store, the arrow points to what is guaranteed to happen: I will buy milk.
Does this depend on the language being used in the statement? What if the statement was: If I go to the store, I MIGHT buy milk. Does this change the relationship of sufficiency and necessity?
Yes, because "might" now means buying milk is no longer necessary. "If A, then B might happen" is no longer a conditional relationship. We can't say that A is sufficient to guarantee anything. And we can't say that B is necessary in order for A. Because it's possible for A to happen without B.
Using your examples, the direction of the arrows would be reversed, though:
Milk --> Store
Cat --> Mammal
That's how we'd represent "You must go to the store in order to buy milk" and "You must be a mammal in order to be a cat."
In other words, if someone bought milk, that guarantees they went to the store.
If something is a cat, that guarantees it's a mammal.
If you represent the arrow the other way around: "Store --> Milk", that would assert that anyone who goes to the store buys milk.
Note that the example in the lesson was "If store, then milk." That is intended to say that anyone who goes to the store buys milk. The example in the lesson isn't intended to be a description of anything from real life.
So to be clear, if we have "If store, then milk", that means store is a sufficient condition and milk is a necessary condition.
If we have "If milk, then store", that means milk is a sufficient condition and store is a necessary condition.
It doesn't matter whether in real life going to the store is required to buy milk; we're simply analyzing the meaning of the given statements.
Hi Kevin, I still need some clarifications regarding this.
So, to better understand I took this example and compared it to the New York/ USA example.
If I go to New York then I'll be in the USA
New York -> USA
sufficiency -> Necessity
If I go to the store then I will buy milk
store -> milk
sufficiency -> necessity
So I get the sufficiency part but what I'm still not understanding is the necessity aspect.
We know that being in the USA is necessary to being in New York, after all New York is inside of the USA. But with the milk example this is tricky because it is the milk that's inside of the store, not the other way around.
You NEED to go to the USA in order to visit New York.
But you do NOT NEED to buy milk in order to visit the store, actually is the other way around, you NEED to be in the store to buy milk.
I get that you mentioned that we are not supposed to look at it from the real world view, but even if its guaranteed that you will get milk by going to the store, I am still failing to see how it is a necessity to buy milk in order to be in the store.
I'll appreciate if you could clarify that. Thanks.
I think one of the downsides to using examples like the "If New York --> USA" statement is that it draws upon your own real-life understanding of the relationship between being in New York and being in USA. That's why it's easy to understand "being in USA" as necessary to "being in NY."
With the statement "If I go to the store, I will buy milk," however, this statement doesn't make sense in real life. Obviously in real life it's possible for me to go to the store and not buy milk. But let's just accept the statement as true, regardless of whether it maps onto our understanding of real life stores and purchases of milk.
"If I go to the store, I will buy milk."
This means if I go to the store, it must be the case that I will buy milk. It's impossible for me to go to the store and not buy milk.
What if you learn the following fact about me: I went somewhere, and I did not buy milk.
If I didn't buy milk...then that proves I didn't go to the store. Because if I went to the store, I had to buy milk. So if I didn't buy milk, you can conclude that I didn't go to the store.
This is the sense in which "buying milk" is necessary for the condition "I go to the store." The necessity is a reference to the truth of the conditions -- in order for "I go to the store" to be true, it must also be true that I will buy milk.
We're not saying that for us to be physically in the store, there's something about the physical presence of being in the store that requires us to also buy milk. We're just saying that the "state of the world in which I buy milk" is necessary in order for "the state of the world in which I go to the store" to be true.
Does that make sense? Here's another example. This statement is easy to conceptualize in terms of what's necessary:
"In order to get into law school, I must take the LSAT."
It's easy to see that taking the LSAT is necessary because we conceptualize the LSAT as one of the things we have to do to get into law school -- there's a big list of requirements and the LSAT is one of them.
But what about this:
"In order for the sky to be red, my neighbor's dog must bark loudly."
Here, my neighbor's dog barking loudly is necessary in order for the sky to be red. You might think...how does that make sense? Why does the sky bring red require my neighbor's dog to bark? There's obviously no real relationship between the color of the sky and my neighbor's dog barking.
However, given what the statement says, we know that if the sky is red, it must be that my neighbor's dog has barked loudly. And if my neighbor's dog hasn't barked loudly, the sky can't be red. This is the sense in which my neighbor's dog barking is necessary. The "state of the world in which my neighbor's dog has barked loudly" is necessary in order for the "state of the world in which the sky is red" to be true. "Necessary" is simply desribing a relationship between the truth value of various states of the world. It's not a comment on any kind of physical requirement or some kind of causal connection between the sky being red and the dog barking.
Keep in mind, that "In order for the sky to be red, my neighbor's dog must bark loudly" is not true in real life. But what matters is the meaning of the statement. If you analyze the meaning of the statement, without caring about whether it's true in real life, then you will see that the words in the statement express the idea that "my neighbor's dog must bark loudly" is necessary for "sky to be red."
Interesting. I think I got it now. So I am imagining a world where if I got to the store then I absolutely have to buy milk, regardless of what else I get or don't get, milk is a requirement, otherwise I cannot step foot inside the store, which would then mean that no milk equals no store. You're right. I was trying my best to not use real world logic in the exercise but what kept tricking me was the fact that the milk is inside the store, however that doesn't matter because buying milk in that world can simply be a requirement to enter the store, sort of like when going to a bar, if I sit at the bar then I must order a drink" so even if the drink is inside the bar, if you don't order it you can't sit in. So I imagined a world where buying milk is required to enter the store, which would then make milk necessary. Thanks Kevin, I get it now. Thanks for providing such an in-depth clarification.
I think it's the other way around! The statement A --> B (if A then B) would be more accurately translated as B has to happen for A to happen. (B is the necessary condition that has to happen in order for A to be true.)
Exactly. The sentence structure is If A, then B. When diagramming it out,
It looks like B→A.
B is the sufficient condition; A is the necessary one. Example: If I go to the store, then I will buy milk.
If A, then B. Going to the store is necessary for buying the milk. The above would be diagrammed as Milk→Store. The lesson has it backwards, and it's confusing. Glad I'm not alone in that.
Yes, this is also my interpretation. A happening is sufficient to assume that B has happened already, because B is necessary for A to have happened. So if A happens, then B has also by definition happened
I really struggle like many in this comment list with the milk, store analogy. For me and most normal people I feel like you would identify the opposite. I would think the store would be the necessary condition because in my mind to buy milk you have to go to the store but you can go to the store without buying milk? I think im getting it more though that because the condition states if i will go to the store I will buy milk. So you know if she goes to the store she must buy milk but she can buy milk and not go to the store? someone please help me get this better
I had the same problem, and this is how I managed to work it out. Going to the store is sufficient to prove that you bought milk. If you go to the store, you're buying milk. Period. Just like being a cat means that you are a mammal.
Buying milk is necessary IF you go to the store. As in, buying milk is something that must necessarily take place if you go to the store. Much like being a mammal is necessary if you are a cat.
I totally understand where you got tripped up--she could hypothetically buy milk from somewhere else and not go to the store. But given the information in the sentence, that doesn't matter. If she goes to the store, that is sufficient to imply that she is buying milk. Buying milk is absolutely necessary if she goes to the store.
"So you know if she goes to the store she must buy milk but she can buy milk and not go to the store?"
You're right, she CAN buy milk and not go to the store. That's because buying milk is not sufficient for going to the store.
But if she goes to the store, she must buy milk. It is necessary. The information says if she goes to the store, she buys milk. Maybe she could also order milk online. But we know that if she does not buy milk, then she did not go to the store. That's why it's a necessary condition.
Honestly, I did not find any faults in this example. Look at it this way:
Even if someone gets milk from online, they would still have to utilize an online store. Shopping online is still going to the store in some way. Going to the store is sufficient for buying milk because you can get more than one thing besides milk from the store, or you may not even buy milk at all. However, in order to buy milk, you MUST go to the store, whether that'll be in person or online.
I was thinking the same thing. Because buying milk from this store is sufficient because I could also buy bread and fruits. But going to the store is necessary to buy milk.
Hi! I highly recommend looking up logic symbols and connectives. They are identical to the elements we are learning, but sometimes a little bit more simplified. Ex: Sufficient condition → Necessary condition (our lesson); X → Y = If X, then Y (logic symbols); Cat → Mammal = If Cat, then Mammal.
I think it is because you can go to the store and buy other things such as fruit, but going to the store you can still buy milk. Therefore, there is a great reason to assume (sufficient) reason to belive that if you go to the store you will buy milk.
The reasoning you gave explains why going to the store would be a necessary condition for buying the milk. I guess the store would be a superset and the milk would be a subset.
This is not "lawgic"; it's sentential logic. Sentential logic is very helpful in philosophy when discussing the bones of argumentation. There are plenty of resources that will teach you about it without coining it as something it's not.
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89 comments
Ballet --> Type of Dance
Basketball Player --> Person Who Can Dribble
so If I am... -> I must be ... ?
If I am a cat -> I must be a mammal
When he mentioned the abstract thought I immediately thought of an arrow like conditions. 🚶🏿♂️→buy milk 🏪
The way you listed all the "natural languages" in the exact same order as I learned my 2nd, 3rd, and 4th languages at 2:05 definitely caught my attention lol!
The arrow makes so much more sense to me, I am confused why circles and dots would ever be more beneficial
@LiviaLSAT for me at least it feels more natural to use the dots because it allows me to hold more information. like if you introduce many subsets together "like cats ->mammals dogs->mammals" etc it can quickly add up and become complicated.
The reason i have trouble with the store -> milk example is because there simple isn't enough information. I read this as relating to what one gets when at the store, in which case milk -> store would be correct because i could get orange juice at the store, not milk
@epayne17 the point of the -> element is to show the conditional relationship present in the argument, not to provide context. Reading the sentence/argument provides you with the context to which we figure out how to use the -> to show the conditional relationship.
In this context, the "If I go to the store [subset], then I will buy milk [superset]." Therefore, store -> milk; try not to rely on your intuition about what you might get at the store. Only what is presented in the argument.
@epayne17 Part of this is also picking out those indicator words.
He says: If I go to the store, then I will buy milk. "If" is a sufficient condition indicator. He's not saying he could buy milk - he will buy milk if the condition (going to the store) is met.
@Livandthecats lol going to the store does not require milk. I'd argue it makes far more logical sense to say that for the most part buying milk requires going to the store. You simply cannot make the claim that he will buy milk if he goes to the store. He could buy literally anything else at that store.... Picture the store and milk as the circles visualization JY gives for relationships. The milk circle should logically lie within the store's bigger circle. This makes the store the proper necessary condition, not milk.
@epayne17 Yes, buying milk typically involves going to a store. However, the argument that is being presented is in fact that if he goes to the store, he will buy milk.
In this case going to the store is your sufficient condition/subset because it follows the indicator "if". It doesn't matter that realistically there's not many other places to buy milk (unless you live near dairy farms), the argument is presented in such a way that store is the subset and milk is the superset.
If it was phrased as "If I bought milk, then I've gone to the store" then your argument makes sense. But the argument has not been presented that way.
in the "if i go to the store, i will buy milk", why is if i go to the store the sufficient? shouldn't that be necessary? please explain!!
@akhan1693 "if" is a sufficent condition indicator
WOW. So, I studied on my own for the first LSAT I did and always saw this notation but constantly messed it up because I didn't know that the arrow itself had this rule. This is such a big clarity moment.
CRAZY
I am excited to learn 'lawgic' as I think this will be really helpful for breaking down questions quickly! :)
Can we not put "going to the store" as a superset and "buying milk" as a subset? It is sufficient for you to go to the store to buy milk.
@ConqueringLSAT I think since they are actions and not characteristics, it may be harder to distinguish in a question
I think one way to understand the arrow, is that the arrow always points in the direction of certainty.
If I go to the store, I (must) buy milk).
Go to store -> buy milk.
Whereas you cannot say:
buy milk -> go to store. What if I got milk elsewhere?
@bcn but its not though. Buying milk would be the superset and going to the store would be the subset. The lesson on group 1 indicators explains this quite clearly: the "If" in I go to the store is a sufficient indicator, meaning going to the store is a sufficient indicator for triggering buying milk.
@TheBigFatPanda I see what you mean now.. this helps a lot; thanks for the clarification.
@TheBigFatPanda The way you just explained this, broke the barrier that I had in understanding this concept. Thank you. I was starting to get really frustrated.
What I cannot wrap my head around is putting the examples in reverse. Making the statements sufficient.
NYC -> USA
Being in NYC is sufficient for being in the USA. I can be in Florida (currently am) and also be in the USA.
How do I do the same for the milk/store example?
Store -> Milk
It is sufficient to go to the store in order to buy milk? But, every time I go to the store, I have to buy milk; I cannot go to the store to buy bread, without having to buy milk. If I buy milk at a farm, then the necessary statement would not work, am I right?
I guess I need help with deducing store -> milk to a sufficient statement. My brain cannot make sense of it.
@JRamirez If you go to the store, you will buy milk.
But that doesn't prevent you from buying milk elsewhere. Perhaps you can go to a farm and buy milk. Or maybe you can buy milk from Amazon.
Similarly, If you're in NYC, you're in the USA. But that doesn't prevent you from being somewhere else in the USA. You might be in Florida and in the USA. You might be in Alaska and in the USA.
@Kevin_Lin Thank you very much. I have finally grasped the material after several other lessons that expanded on this and other Lawgic lessons.
@JRamirez Any lessons in particular? I'm struggling with this one
@SWJ Just keep pushing through the lessons. Most days you will be thinking, why are they teach me this, why does it have to be this way, it makes no sense. It all starts coming together and starts making sense later on. I read comments in almost every lesson and that has been helping me. Asking questions and having them answered has also helped.
The best advice to give you to grasp the material is... DO NOT bring in your own assumptions or perceptions into the lessons or any questions.
Example:
If you are an astronaut then you are a cat
A -> C
Therefore, if you are not a cat, then you are not an astronaut
A -> C
/C -> /A
Not sure where you are on your lessons, and if my example makes no sense, that's ok— the important thing is that cats are astronauts! To us in our reality they are not astronauts but LSAT writers don't care about that, they care that you understand the structure of the stimulus (passages). You may see things more in depth of my example where they will include a human in the mix and you are thinking, wait, humans are astronauts not cats. The answer choices will try to hone in on your own assumptions of the real world and force you to answer the question wrong, because you didn't exclude your own perceptions and assumptions.
I went a little longer than I would have liked. Just trust the process, 7Sage knows what they are doing. I was a non-believer, but trust me, it all comes together.
This will probably be explained in a future lesson I imagine, but I'd like clarification on what happens when the necessary condition is true instead of the sufficient.
I'll use the milk/store example since I think that's the one most of us are confused about. I'll also write it out to specify the premises and conclusion:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I went to the store.
Conclusion: I bought milk.
And here the "Lawgic" version of Premise 1:
Store -> Milk
This might not make sense in our world, but in the world of this argument then if anyone ever goes to the store, they have to buy milk. I think this makes sense.
Now what if I change the argument to something like this:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I bought milk.
Conclusion: I went to the store.
I want to say that this does not make sense/is not valid, because Premise 1 is unchanged that means that the Lawgic is still "Store -> Milk," and not "Milk -> Store." In English, this would mean that I could have gotten milk from anywhere, not just the store.
@aidanro2003 You're totally right! The necessary condition being true means nothing for the sufficient condition. The only other true logical statement you could get out of this is if you didn't buy milk, you didn't go to the store as we know if you went to the store you must have bought milk.
He's already using A for P and B for Q, but does anyone know if this will follow a more formal/classical logic language or a sentential logic language? Or neither and I'm just going to get really confused?
Update.... You will be very confused if you keep trying to use any sort of logic symbols you previously learned.
Note for anyone confused by the store and milk example:
That example is not intended to map onto whatever real life understanding you have about stores and milk. When we get a statement saying "If I go to the store, then I will buy milk," we have to analyze the meaning of that specific statement. And that statement means that if I go to the store, I am guaranteed to buy milk.
You might be thinking, "But I don't have to buy milk when I go to the store..." That may be the case in real life. But the statement "If I go to the store, then I will buy milk" does assert that I have to buy milk when I go to the store.
And, "If I go to the store, then I will buy milk" does not assert that the store is the only place that I can buy milk. It's entirely possible that whenever I visit a local farm, I buy milk. Or that I often buy milk from my neighbor. But, according to the statement, if I go to the store, I am guaranteed to buy milk.
This is why the statement is diagrammed like this:
Store → Milk
If I go to the store, the arrow points to what is guaranteed to happen: I will buy milk.
Does this depend on the language being used in the statement? What if the statement was: If I go to the store, I MIGHT buy milk. Does this change the relationship of sufficiency and necessity?
Yes, because "might" now means buying milk is no longer necessary. "If A, then B might happen" is no longer a conditional relationship. We can't say that A is sufficient to guarantee anything. And we can't say that B is necessary in order for A. Because it's possible for A to happen without B.
This example doesn't make sense to me. This is what makes sense to me:
Store -> Milk
Mammal -> Cat
you have to go to the store to buy milk, but you dont have to buy milk if you go to the store.
just like how you have to be a mammal if you're a cat, but you dont have to be a cat if you are a mammal.
same! commenting to follow replies
Using your examples, the direction of the arrows would be reversed, though:
Milk --> Store
Cat --> Mammal
That's how we'd represent "You must go to the store in order to buy milk" and "You must be a mammal in order to be a cat."
In other words, if someone bought milk, that guarantees they went to the store.
If something is a cat, that guarantees it's a mammal.
If you represent the arrow the other way around: "Store --> Milk", that would assert that anyone who goes to the store buys milk.
Note that the example in the lesson was "If store, then milk." That is intended to say that anyone who goes to the store buys milk. The example in the lesson isn't intended to be a description of anything from real life.
So to be clear, if we have "If store, then milk", that means store is a sufficient condition and milk is a necessary condition.
If we have "If milk, then store", that means milk is a sufficient condition and store is a necessary condition.
It doesn't matter whether in real life going to the store is required to buy milk; we're simply analyzing the meaning of the given statements.
Hi Kevin, I still need some clarifications regarding this.
So, to better understand I took this example and compared it to the New York/ USA example.
If I go to New York then I'll be in the USA
New York -> USA
sufficiency -> Necessity
If I go to the store then I will buy milk
store -> milk
sufficiency -> necessity
So I get the sufficiency part but what I'm still not understanding is the necessity aspect.
We know that being in the USA is necessary to being in New York, after all New York is inside of the USA. But with the milk example this is tricky because it is the milk that's inside of the store, not the other way around.
You NEED to go to the USA in order to visit New York.
But you do NOT NEED to buy milk in order to visit the store, actually is the other way around, you NEED to be in the store to buy milk.
I get that you mentioned that we are not supposed to look at it from the real world view, but even if its guaranteed that you will get milk by going to the store, I am still failing to see how it is a necessity to buy milk in order to be in the store.
I'll appreciate if you could clarify that. Thanks.
I think one of the downsides to using examples like the "If New York --> USA" statement is that it draws upon your own real-life understanding of the relationship between being in New York and being in USA. That's why it's easy to understand "being in USA" as necessary to "being in NY."
With the statement "If I go to the store, I will buy milk," however, this statement doesn't make sense in real life. Obviously in real life it's possible for me to go to the store and not buy milk. But let's just accept the statement as true, regardless of whether it maps onto our understanding of real life stores and purchases of milk.
"If I go to the store, I will buy milk."
This means if I go to the store, it must be the case that I will buy milk. It's impossible for me to go to the store and not buy milk.
What if you learn the following fact about me: I went somewhere, and I did not buy milk.
If I didn't buy milk...then that proves I didn't go to the store. Because if I went to the store, I had to buy milk. So if I didn't buy milk, you can conclude that I didn't go to the store.
This is the sense in which "buying milk" is necessary for the condition "I go to the store." The necessity is a reference to the truth of the conditions -- in order for "I go to the store" to be true, it must also be true that I will buy milk.
We're not saying that for us to be physically in the store, there's something about the physical presence of being in the store that requires us to also buy milk. We're just saying that the "state of the world in which I buy milk" is necessary in order for "the state of the world in which I go to the store" to be true.
Does that make sense? Here's another example. This statement is easy to conceptualize in terms of what's necessary:
"In order to get into law school, I must take the LSAT."
It's easy to see that taking the LSAT is necessary because we conceptualize the LSAT as one of the things we have to do to get into law school -- there's a big list of requirements and the LSAT is one of them.
But what about this:
"In order for the sky to be red, my neighbor's dog must bark loudly."
Here, my neighbor's dog barking loudly is necessary in order for the sky to be red. You might think...how does that make sense? Why does the sky bring red require my neighbor's dog to bark? There's obviously no real relationship between the color of the sky and my neighbor's dog barking.
However, given what the statement says, we know that if the sky is red, it must be that my neighbor's dog has barked loudly. And if my neighbor's dog hasn't barked loudly, the sky can't be red. This is the sense in which my neighbor's dog barking is necessary. The "state of the world in which my neighbor's dog has barked loudly" is necessary in order for the "state of the world in which the sky is red" to be true. "Necessary" is simply desribing a relationship between the truth value of various states of the world. It's not a comment on any kind of physical requirement or some kind of causal connection between the sky being red and the dog barking.
Keep in mind, that "In order for the sky to be red, my neighbor's dog must bark loudly" is not true in real life. But what matters is the meaning of the statement. If you analyze the meaning of the statement, without caring about whether it's true in real life, then you will see that the words in the statement express the idea that "my neighbor's dog must bark loudly" is necessary for "sky to be red."
Interesting. I think I got it now. So I am imagining a world where if I got to the store then I absolutely have to buy milk, regardless of what else I get or don't get, milk is a requirement, otherwise I cannot step foot inside the store, which would then mean that no milk equals no store. You're right. I was trying my best to not use real world logic in the exercise but what kept tricking me was the fact that the milk is inside the store, however that doesn't matter because buying milk in that world can simply be a requirement to enter the store, sort of like when going to a bar, if I sit at the bar then I must order a drink" so even if the drink is inside the bar, if you don't order it you can't sit in. So I imagined a world where buying milk is required to enter the store, which would then make milk necessary. Thanks Kevin, I get it now. Thanks for providing such an in-depth clarification.
reading the comments below to look for some extra clarification but I see everyone seems lost as well.
Dear LittlePickleBigWorld,
I can explain how I understand the content. For me, this is how I am interpreting everything, given the Jedi example:
1. If one person is enough to assume (i.e sufficient enough) to be a jedi, then one is required to know how to use the force.
In the context of this example, the jedi is the subset & the force is the superset.
2 Luke, who is a member, is a Jedi.
That means that Luke has membership in the subset.
3 Therefore, Luke uses the force.
Because Luke has membership in the subset, it is required that he knows how to use the force.
If you get confused which goes at what side of the arrow, I remember it by "Start with Sufficient, Next is Necessary." S -> N
so if A then B.
A has to happen for B to happen
sufficient condition → necessary condition
Yes
I think it's the other way around! The statement A --> B (if A then B) would be more accurately translated as B has to happen for A to happen. (B is the necessary condition that has to happen in order for A to be true.)
Exactly. The sentence structure is If A, then B. When diagramming it out,
It looks like B→A.
B is the sufficient condition; A is the necessary one. Example: If I go to the store, then I will buy milk.
If A, then B. Going to the store is necessary for buying the milk. The above would be diagrammed as Milk→Store. The lesson has it backwards, and it's confusing. Glad I'm not alone in that.
Yes, this is also my interpretation. A happening is sufficient to assume that B has happened already, because B is necessary for A to have happened. So if A happens, then B has also by definition happened
Just to be clear, in your initial sentence "If A, then B", A is the sufficient condition and B is the necessary condition.
That would look like "A --> B".
So the statement "If I go to the store, then I will buy milk" would be diagrammed "Store --> Milk".
I really struggle like many in this comment list with the milk, store analogy. For me and most normal people I feel like you would identify the opposite. I would think the store would be the necessary condition because in my mind to buy milk you have to go to the store but you can go to the store without buying milk? I think im getting it more though that because the condition states if i will go to the store I will buy milk. So you know if she goes to the store she must buy milk but she can buy milk and not go to the store? someone please help me get this better
I had the same problem, and this is how I managed to work it out. Going to the store is sufficient to prove that you bought milk. If you go to the store, you're buying milk. Period. Just like being a cat means that you are a mammal.
Buying milk is necessary IF you go to the store. As in, buying milk is something that must necessarily take place if you go to the store. Much like being a mammal is necessary if you are a cat.
I totally understand where you got tripped up--she could hypothetically buy milk from somewhere else and not go to the store. But given the information in the sentence, that doesn't matter. If she goes to the store, that is sufficient to imply that she is buying milk. Buying milk is absolutely necessary if she goes to the store.
Does that make sense?
"So you know if she goes to the store she must buy milk but she can buy milk and not go to the store?"
You're right, she CAN buy milk and not go to the store. That's because buying milk is not sufficient for going to the store.
But if she goes to the store, she must buy milk. It is necessary. The information says if she goes to the store, she buys milk. Maybe she could also order milk online. But we know that if she does not buy milk, then she did not go to the store. That's why it's a necessary condition.
Hopefully that helps
Honestly, I did not find any faults in this example. Look at it this way:
Even if someone gets milk from online, they would still have to utilize an online store. Shopping online is still going to the store in some way. Going to the store is sufficient for buying milk because you can get more than one thing besides milk from the store, or you may not even buy milk at all. However, in order to buy milk, you MUST go to the store, whether that'll be in person or online.
"However, in order to buy milk, you MUST go to the store"
Right. So doesn't that mean that the necessity is the store? Not the milk?
You NEED the store, so by default the store should be the necessity.
On the other hand, buying milk is a sufficient reason to be in the store. Sufficient, but not a necessity.
So even with this example I think she can still go somewhere else to buy milk.
If I go to the store, then I buy milk
Store → Milk
Is different then
If I have milk, then I went to the store
Milk → Store
Store→milk
Means that every time they go to the store they MUST buy milk
They could milk a cow and not go to the store and still have milk
Milk→store
Means that every time you buy milk you MUST have been at the store
They have no other means of getting milk, but they could also go to the store without buying milk.
So if this argument was given it would be wrong:
*If I go to the store then I buy milk.
I bought milk
I went to the store*
because I could have bought milk elsewhere besides the store?
I was thinking the same thing. Because buying milk from this store is sufficient because I could also buy bread and fruits. But going to the store is necessary to buy milk.
I was thinking the same thing, I thought I was trippin
Hi! I highly recommend looking up logic symbols and connectives. They are identical to the elements we are learning, but sometimes a little bit more simplified. Ex: Sufficient condition → Necessary condition (our lesson); X → Y = If X, then Y (logic symbols); Cat → Mammal = If Cat, then Mammal.
"If you don't like it, sue me. But first, you have to take the LSAT and get into law school so pay attention." that was unannounced lol
LOL
Quick question in reference to the following:
store → milk
[sufficient condition] → [necessary condition]
So why would store be the sufficient thing in relation to milk and not the other way around?
I think it is because you can go to the store and buy other things such as fruit, but going to the store you can still buy milk. Therefore, there is a great reason to assume (sufficient) reason to belive that if you go to the store you will buy milk.
That is how I reasoned it anyway.
The reasoning you gave explains why going to the store would be a necessary condition for buying the milk. I guess the store would be a superset and the milk would be a subset.
This is not "lawgic"; it's sentential logic. Sentential logic is very helpful in philosophy when discussing the bones of argumentation. There are plenty of resources that will teach you about it without coining it as something it's not.